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Poor maths skills are associated with negative outcomes throughout life, such as lower academic qualifications, decreased professional success and socio-economic results. Mathematical skills emerge continuously throughout childhood and those that children acquire in pre-school are crucial for activities that support analytical thinking, problem-solving and reasoning and argumentation skills. Many of these activities are related to motor skills, since certain cognitive and motor areas of the brain are activated simultaneously when solving maths problems. Of all motor skills, visuomotor integration skills have been documented as those that are most consistently positively and significantly associated with maths performance in pre-school children. These skills are influenced by visual perception (spatial and attention skills), fine motor coordination and gross motor skills. Early intervention can improve visuomotor integration skills in pre-school children. Of all skills that make up visuomotor integration, spatial skills, in addition to being the first skills to influence numerical knowledge and the recognition of geometric shapes, are also those skills that form part of the majority of programs and activities to be worked on with pre-school children for the development of mathematical concepts. However, most intervention programs or activities to develop spatial skills are carried out in the classroom, usually through activities involving handling small objects. In this sense and given the significant association between visuomotor integration skills and gross motor skills, the main objective of this study was to list a set of activities to develop spatial skills, with a strong involvement of gross motor skills, in a classroom, playground or home context.
数学技能差与一生中的负面结果有关，例如较低的学术资格、降低专业成功和社会经济成果。数学技能在整个童年时期不断出现，孩子们在学前班获得的数学技能对于支持分析思维、解决问题以及推理和论证技能的活动至关重要。其中许多活动与运动技能有关，因为在解决数学问题时，大脑的某些认知和运动区域会同时被激活。在所有运动技能中，视觉运动整合技能已被证明与学龄前儿童的数学表现最一致且最显著相关。这些技能受视觉感知（空间和注意力技能）、精细运动协调和粗大运动技能的影响。早期干预可以提高学龄前儿童的视觉运动整合技能。在构成视觉运动整合的所有技能中，空间技能除了是影响数字知识和几何形状识别的第一技能外，还是构成大多数与学龄前儿童一起为发展数学概念而进行的程序和活动的一部分的技能。然而，大多数培养空间技能的干预计划或活动都是在课堂上进行的，通常是通过涉及处理小物体的活动。从这个意义上说，鉴于视觉运动整合技能和粗大运动技能之间的显着关联，本研究的主要目标是列出一组在课堂、操场或家庭环境中发展空间技能的活动，这些活动强烈参与粗大运动技能。

1 Introduction 1 引言

Mathematics is a way of thinking about the world and organizing experiences, involving reasoning and problem solving (Spodek, 2002). Poor maths skills are associated with negative outcomes throughout life, such as lower academic qualifications (Duncan et al., 2007; Chernyak et al., 2016), decreased professional success (Parsons and Bynner, 2005) and socio-economic outcomes (Ritchie and Bates, 2013). The development of these skills occurs in a hierarchical way (Von Aster and Shalev, 2007), already present in babies through discrimination of the numerosity of two sets (Hyde, 2011; Starr et al., 2013) and sense of measure (greater than and more than…) (Geist, 2009). In this sense, maths is learnt before school through numbers and quantities (McWayne et al., 2004; Geist, 2009). However, mathematical skills emerge continuously throughout childhood (Geist, 2009) and those that children acquire in pre-school are crucial for activities that support analytical thinking, problem solving and reasoning and argumentation skills (Clements et al., 2004). In this sense, it is essential in pre-school education to give continuity to this learning, which requires experiences related to their interests in everyday life, when they play and explore their daily lives (Silva et al., 2016), since at this stage of education children enjoy activities that develop their mathematical skills (Ginsburg et al., 2006).
数学是一种思考世界和组织经验的方式，涉及推理和解决问题（Spodek，2002）。糟糕的数学技能与一生中的负面结果有关，例如较低的学术资格（Duncan et al.， 2007;Chernyak et al.， 2016），职业成功率下降（Parsons and Bynner， 2005）和社会经济成果（Ritchie and Bates， 2013）。这些技能的发展以分层的方式发生（Von Aster 和 Shalev，2007 年），通过区分两组的数量性已经存在于婴儿中（Hyde，2011 年;Starr等人，2013 年）和度量感（大于和大于......（Geist，2009 年）。从这个意义上说，数学是在上学前通过数字和数量学习的（McWayne et al.， 2004;Geist，2009 年）。然而，数学技能在整个童年时期不断出现（Geist，2009 年），儿童在学前班获得的数学技能对于支持分析思维、解决问题以及推理和论证技能的活动至关重要（Clements et al.，2004）。从这个意义上说，在学前教育中，保持这种学习的连续性是必不可少的，这需要与他们在日常生活中的兴趣相关的经验，当他们玩耍和探索自己的日常生活时（Silva et al.， 2016），因为在这个教育阶段，孩子们喜欢发展他们数学技能的活动（Ginsburg et al.， 2006）。

Many of these activities are related to those that require bodily movement, and according to the theory of “Embodied Cognition,” cognition emerges from the individual’s “coupling” (embodied relationship) with the physical and social context, as a result of sensorimotor activity (Smith, 2005; Wilson and Foglia, 2011; Soylu and Newman, 2016). According to this theory, mathematical skills are interconnected with motor skills, since representations of distance, quantities and numbering are based on bodily experiences (Link et al., 2013; Fisher et al., 2018) and certain cognitive and motor areas of the brain are activated simultaneously when solving mathematical problems (Fischer and Brugger, 2011). Also, the idea of “learning to learn” suggests that early learning is centered around the motor system and as the child adapts to changes, cognitive and motor skills develop simultaneously (Adolph, 2005). Today, there is neurophysiological and neuroimaging evidence that the prefrontal cortex, cerebellum and connecting structures are coactivated in certain cognitive and motor tasks, suggesting an interrelationship between motor and cognitive development (Diamond, 2000; Abe and Hanakawa, 2009). In this sense, motor skills influence academic performance in the early years (Alvarez-Bueno et al., 2017;; Macdonald et al., 2018; De Waal, 2019; Duncan et al., 2019; Malambo et al., 2022), being described as one of the criteria for school readiness (Department for Education, 2020; Jones et al., 2021).
其中许多活动与需要身体运动的活动有关，根据“具身认知”理论，作为感觉运动活动的结果，认知来自个人与身体和社会环境的“耦合”（具身关系）（Smith，2005;Wilson 和 Foglia，2011 年;Soylu 和 Newman，2016 年）。根据这一理论，数学技能与运动技能相互关联，因为距离、数量和编号的表示是基于身体体验的（Link et al.， 2013;Fisher et al.， 2018）和大脑的某些认知和运动区域在解决数学问题时同时被激活（Fischer 和 Brugger，2011）。此外，“学会学习”的想法表明，早期学习以运动系统为中心，随着孩子适应变化，认知和运动技能会同时发展（Adolph，2005）。今天，有神经生理学和神经影像学证据表明，前额叶皮层、小脑和连接结构在某些认知和运动任务中被共同激活，这表明运动和认知发展之间存在相互关系（Diamond，2000 年;Abe 和 Hanakawa，2009 年）。从这个意义上说，运动技能会影响早期的学习成绩（Alvarez-Bueno et al.， 2017;;Macdonald et al.， 2018;De Waal， 2019;Duncan等人，2019 年;Malambo et al.， 2022），被描述为入学准备的标准之一（Department for Education， 2020;Jones et al.， 2021）。

1.1 Maths curriculum guidelines for pre-school
1.1 学前班数学课程指南

Since the development of mathematical notions begins at a very early age (McWayne et al., 2004; Geist, 2009; Hyde, 2011; Starr et al., 2013), it is essential to continue this learning in pre-school (Silva et al., 2016), as the knowledge acquired in the early years will positively influence later learning (Clements et al., 2004).
由于数学概念的发展始于很小的时候（McWayne et al.， 2004;Geist， 2009;Hyde，2011 年;Starr et al.， 2013），在学前教育中继续这种学习是必不可少的（Silva et al.， 2016），因为早期获得的知识将对以后的学习产生积极影响（Clements et al.， 2004）。

Learning maths at these ages should be centered on activities that are meaningful to the child and that are associated with other content areas (Silva et al., 2016). Thus, according to the “Curriculum Guidelines for Pre-School” (Silva et al., 2016), in order to develop the various mathematical notions, the educator must take into account: (1) General processes; (2) Mathematical components.
这些年龄段的数学学习应该以对孩子有意义且与其他内容领域相关的活动为中心（Silva et al.， 2016）。因此，根据“学前教育课程指南”（Silva et al.， 2016），为了发展各种数学概念，教育者必须考虑：（1） 一般过程;（2） 数学分量。

The general processes are a set of processes that are transversal to the approach to mathematics, namely classification, sorting, reasoning and problem solving, and the mathematical components concern numbers and operations, organization and data processing, geometry and measurement, and interest and curiosity in mathematics (Figure 1).
一般过程是一组与数学方法横向的过程，即分类、排序、推理和解决问题，数学组成部分涉及数字和运算、组织和数据处理、几何和测量，以及对数学的兴趣和好奇心（图 1）。

Figure 1 图 1

Figure 1. Mathematical notions to be developed according to the curriculum guidelines for pre-school (Silva et al., 2016).
图 1.根据学前教育课程指南开发数学概念（Silva et al.，2016）。

1.1.1 General processes 1.1.1 一般流程

Classification implies that the child is able to distinguish, organize and establish relationships between objects by equality or difference.
分类意味着孩子能够通过相等或差异来区分、组织和建立对象之间的关系。

Sorting implies that the child is able to order objects by quantity, height, size, thickness, speed and duration.
排序意味着孩子能够按数量、高度、大小、厚度、速度和持续时间对对象进行排序。

Mathematical reasoning involves using objects where children are encouraged to explain and justify solutions. Recognizing, understanding, and creating sequences of patterns are important elements in the development of mathematical reasoning.
数学推理涉及使用鼓励孩子们解释和证明解决方案的物体。识别、理解和创建模式序列是数学推理发展中的重要元素。

Problem solving is the process of appropriating and integrating mathematical learning. The problems proposed to the child must have meaning for them (everyday activities) and the educator must use games and play for this purpose.
解决问题是挪用和整合数学学习的过程。向孩子提出的问题必须对他们有意义（日常活动），并且教育者必须为此目的使用游戏和游戏。

Regarding the mathematical components, four approaches are proposed: numbers and operations, data organization and processing, geometry and measurement, and interest and curiosity in mathematics.
关于数学成分，提出了四种方法：数字和运算、数据组织和处理、几何和测量以及对数学的兴趣和好奇心。

1.1.2 Maths components 1.1.2 数学组件

1.1.2.1 Numbers and operations
1.1.2.1 数字和运算

Numbers are abstractions that apply to a wide range of real and imaginary situations. They do not exist in isolation but make up a system of relationships and operations by which they can be compared, added, subtracted, multiplied and divided. It is these relationships that apply to a wide variety of problems (National Research Council, 2009). The development of number sense is progressive, as counting involves knowing the number sequence and matching term to term (Wynn, 1992; Sarnecka and Carey, 2008). Also, the ordering of numerals and the ability to compare magnitudes is related to the construction of a mental number line, where children become aware of the relationship between numbers (5 is more than 4; 6 is more than 5) (Silva et al., 2016).
数字是适用于各种真实和虚构情况的抽象概念。它们不是孤立存在的，而是构成了一个关系和操作系统，通过该系统可以比较、添加、减少、乘以和划分它们。正是这些关系适用于各种各样的问题（国家研究委员会，2009 年）。数感的发展是渐进的，因为计数涉及了解数字序列和将术语与术语匹配（Wynn，1992 年;Sarnecka 和 Carey，2008 年）。此外，数字的顺序和比较大小的能力与心理数字线的构建有关，儿童在其中意识到数字之间的关系（5 大于 4;6 大于 5）（Silva et al.， 2016）。

Operations refer to basic arithmetic skills such as adding and subtracting and are used to relate quantities. Children are only prepared to develop these skills when they understand the concepts of cardinality and counting. These skills prepare children to develop more complex arithmetic skills such as multiplication and division (Barth et al., 2008; Canobi and Bethune, 2008).
运算是指基本的算术技能，例如加法和减法，用于关联数量。只有当孩子们理解了基数和计数的概念时，他们才能准备好发展这些技能。这些技能为儿童发展更复杂的算术技能做好准备，例如乘法和除法（Barth et al.， 2008;Canobi 和 Bethune，2008 年）。

1.1.3 Organization and data processing
1.1.3 组织和数据处理

The collection, organization and data processing is based on classification, counting and comparison. Statistics, as the quantitative analysis of data, is a very important area of maths that provides multiple opportunities for numerical development. In kindergarten life, there are many opportunities to collect, organize and interpret quantitative data from everyday situations and from carrying out experiments and projects (Silva et al., 2016).
收集、组织和数据处理基于分类、计数和比较。统计学作为数据的定量分析，是数学中非常重要的一个领域，为数值发展提供了多种机会。在幼儿园生活中，有很多机会从日常情况以及进行实验和项目中收集、组织和解释定量数据（Silva et al.， 2016）。

1.1.4 Geometria e medida 1.1.4 几何和测量

Geometry and measurement provide systems for describing, representing, and understanding the world. Geometry is the study of shapes and spaces (two-dimensional—2-D and three-dimensional—3-D). Measurement has to do with how to determine the size of object shapes (National Research Council, 2009). In everyday life, these skills are present in countless situations and can be mobilized so that the child realizes how useful they are in everyday life (Silva et al., 2016).
几何和测量提供了用于描述、表示和理解世界的系统。几何学是对形状和空间（二维 - 二维和三维 - 三维）的研究。测量与如何确定物体形状的大小有关（国家研究委员会，2009 年）。在日常生活中，这些技能存在于无数情况下，并且可以被调动起来，以便孩子意识到它们在日常生活中是多么有用（Silva et al.， 2016）。

1.1.5 Geometry 1.1.5 几何体

Strongly associated with spatial development (orientation and spatial visualization) (Gelman and Williams, 1997) and analysis and operations with shapes (Anderson, 2000).
与空间开发（方向和空间可视化）（Gelman 和 Williams，1997 年）以及形状的分析和操作（Anderson，2000 年）密切相关。

Spatial development includes two main skills, spatial orientation, and spatial visualization of images. Spatial orientation involves knowing where you are and how to get around in the world (Gelman and Williams, 1997). Children learn words like “next to” and “between.” Later, they learn words referring to frames of reference, such as “in front of,” “behind.” The words “left” and “right” are learnt much later, and are a source of confusion for several years (Gopnik and Meltzoff, 1986). In these early years, children can also learn to analyze a route through a space (Wang and Spelke, 2002). A visualização espacial de imagens é compreender e executar movimentos imaginados de objetos 2-D e 3-D. Para o efeito, é necessário ser capaz de criar uma imagem mental e manipulá-la através de uma estreita relação entre estas duas capacidades cognitivas. A visualização espacial de imagens tem sido positivamente associada à construção e composição de formas (Sarama et al., 1996).
空间发展包括两个主要技能，空间定位和图像的空间可视化。空间定位包括知道你在哪里以及如何在世界上四处走动（Gelman 和 Williams，1997）。孩子们学习 “next to” 和 “between” 等词。后来，他们学习了指代参考系的单词，例如“在前面”、“后面”。“左”和“右”这两个词的学习时间很晚，并且是几年来混淆的根源（Gopnik 和 Meltzoff，1986）。在这些早期，孩子们还可以学习分析穿过空间的路线（Wang 和 Spelke，2002 年）。A visualização espacial de imagens é compreender e executar movimentos imaginados de objetos 2-D e 3-D. Para o efeito， é necessário ser capaz de criar uma imagem mental e manipulá-la através de uma estreita relação entre estas duas capacidades cognitivas.A visualização espacial de imagens tem sido positivamente associada à construção e composição de formas （Sarama et al.， 1996）.

Analysis and operations with shapes is the basic way in which children learn the names of objects (Jones and Smith, 2002) and the ability to recognize and combine shapes (Anderson, 2000).
分析和操作形状是儿童学习对象名称 （Jones and Smith， 2002） 以及识别和组合形状的能力 （Anderson， 2000） 的基本方式。

In this sense, it is through spatial development, as well as the relationship and manipulation of objects, that children can learn what is “far” and “near,” “inside,” “outside” and “between,” “open” and “closed,” “above” and “below,” which also allows them to recognize and represent different geometric shapes that they will gradually learn to differentiate, name and characterize (Silva et al., 2016).
从这个意义上说，正是通过空间发展，以及物体的关系和操纵，孩子们可以学习什么是“远”和“近”、“内部”、“外部”和“之间”、“开放”和“封闭”、“上方”和“下方”，这也使他们能够识别和表示不同的几何形状，他们将逐渐学会区分、命名和表征（Silva 等人， 2016 年）。

1.1.6 Measurement 1.1.6 测量

Measuring is a process that involves children starting to identify the measurable attributes of objects (length, weight, capacity, volume, time, temperature, etc.) from their everyday experiences (Silva et al., 2016). Initially, this process is based on directly comparing and ordering objects (longer, shorter, of equal length, heavier, lighter, etc.), gradually making it more difficult by using non-standardized units of measurement (cup, foot or shoe, etc.). These experiences enable children to gradually understand the usefulness of measuring instruments and standardized measures, as these are also part of their daily lives (Silva et al., 2016).
测量是一个过程，让孩子们开始从他们的日常经验中识别物体的可测量属性（长度、重量、容量、体积、时间、温度等）（Silva et al.， 2016）。最初，这个过程是基于直接比较和排序对象（更长、更短、等长、更重、更轻等），逐渐通过使用非标准化的测量单位（杯、脚或鞋等）使其变得更加困难。这些经历使孩子们逐渐了解测量仪器和标准化测量的有用性，因为这些也是他们日常生活的一部分（Silva et al.， 2016）。

One way of more formally assessing children’s understanding of measurement is through comparison tasks (Mullet and Paques, 1991).
更正式地评估儿童对测量的理解的一种方法是通过比较任务（Mullet 和 Paques，1991）。

1.1.7 Interest and curiosity in maths
1.1.7 对数学的兴趣和好奇心

Maths is present in the majority of children’s everyday activities (National Research Council, 2009). In this sense, the teacher has a fundamental role to play in developing their interest and curiosity by drawing the child’s attention to the presence of maths in the world around them (Silva et al., 2016). In this sense, the aim is to stimulate children’s natural curiosity by providing them with favorable mathematical experiences so that mathematics becomes an engaging and permanently interesting challenge (Geist, 2009).
数学存在于儿童的大多数日常活动中（国家研究委员会，2009 年）。从这个意义上说，教师通过吸引孩子的注意力关注他们周围世界中数学的存在，在培养他们的兴趣和好奇心方面发挥着重要作用（Silva et al.， 2016）。从这个意义上说，其目的是通过为孩子们提供有利的数学体验来激发他们天生的好奇心，使数学成为一个引人入胜且永远有趣的挑战（Geist，2009 年）。

1.2 Motor skills 1.2 运动技能

Traditionally, motor skills are divided into two categories, gross motor skills (GMS) and fine motor skills (FMS) (Grissmer et al., 2010; Oberer et al., 2017; Goodway et al., 2019). As for GMS, they basically use movements produced by large muscle groups. They include locomotor skills, which involve moving the body in space (walking, running, jumping and sliding), postural or balance skills, which refer to the ability to maintain a controlled position or posture during a task (dynamic balance—maintaining position in activities that require movement; or static balance—maintaining position in stationary tasks) and manipulative skills, used to control objects in actions with the hands or feet (grasping, tapping, absorbing, lifting, etc.)., which can be propulsive (sending objects) or receptive (receiving objects) (Lopes et al., 2013; Magistro et al., 2015; Kokstejn et al., 2017; Haywood and Getchell, 2019). FMS are defined as movements produced by small muscle groups. One type of FMS is fine motor coordination (FMC) or visuomotor coordination, which refers to movements involving hand-eye coordination, manual dexterity, motor sequencing and speed and precision, and can also be referred to as non-graphomotor skills (Davis and Matthews, 2010; Suggate et al., 2018). Another type of FMS is visual and motor integration, called visuomotor integration (VMI) or visuospatial integration, which refers to the organization of small muscle movements of the hand and fingers through the processing of visual and spatial stimuli, based more on synchronized hand-eye movements (Carlson et al., 2013; Goodway et al., 2019) and are typically tasks involving writing, drawing, copying shapes, letters or other stimuli (Beery and Buktenica, 1997; Oberer et al., 2017), which can be referred to as graphomotor skills (Davis and Matthews, 2010).
传统上，运动技能分为两类，粗大运动技能 （GMS） 和精细运动技能 （FMS）（Grissmer 等人，2010 年;Oberer等人，2017 年;Goodway等人，2019 年）。至于 GMS，它们基本上使用大肌肉群产生的动作。它们包括运动技能，涉及在空间中移动身体（行走、跑步、跳跃和滑动），姿势或平衡技能，指的是在任务中保持受控位置或姿势的能力（动态平衡——在需要移动的活动中保持位置;或静态平衡——在静止任务中保持位置）和操纵技能，用于用手或脚控制物体的动作（抓握、 敲击、吸收、提升等）.，可以是推进性的（发送对象）或接受性的（接收对象）（Lopes 等人，2013 年;Magistro et al.， 2015;Kokstejn等人，2017 年;Haywood 和 Getchell，2019 年）。FMS 被定义为由小肌肉群产生的运动。FMS 的一种类型是精细运动协调 （FMC） 或视觉运动协调，指的是涉及手眼协调、手部灵巧性、运动顺序以及速度和精度的运动，也可以称为非图形运动技能（Davis 和 Matthews，2010 年;Suggate等人，2018 年）。另一种类型的 FMS 是视觉和运动整合，称为视觉运动整合 （VMI） 或视觉空间整合，它是指通过处理视觉和空间刺激来组织手和手指的小肌肉运动，更多地基于同步的手眼运动（Carlson 等人，2013 年;Goodway 等人。，2019 年），通常是涉及书写、绘画、复制形状、字母或其他刺激的任务（Beery 和 Buktenica，1997 年;Oberer et al.， 2017），可以称为图形运动技能（Davis 和 Matthews，2010）。

Among these skills, recent systematic review studies concluded that it was mainly the FMS that justified mathematical academic performance in preschool children (van der Fels et al., 2015;Macdonald et al., 2018; Flores et al., 2023a; Figure 2).
在这些技能中，最近的系统评价研究得出结论，主要是 FMS 证明了学龄前儿童的数学学习成绩是合理的（van der Fels et al.， 2015;Macdonald et al.， 2018;Flores 等人，2023a;图 2）。

Figure 2 图 2

Figure 2. Summary of fine motor skills categories (adapted from Flores et al., 2023a).
图 2.精细运动技能类别总结（改编自 Flores 等人，2023a）。

Although a relationship between VMI and FMC has been demonstrated (Sortor and Kulp, 2003; Beery and Beery, 2006; Carlson et al., 2013; Byers et al., 2016), where children with better FMC may be better at manipulating objects, which allows them to direct additional attention resources to new learning, namely VMI (Kim et al., 2018), FMC has not been found to be a consistent predictor of later academic performance (Kim et al., 2018). In this sense, among the FMS, VMI skills have been documented as those that are most consistently positively and significantly associated with maths performance (Macdonald et al., 2018; Flores et al., 2023a).
尽管已经证明了 VMI 和 FMC 之间的关系（Sortor 和 Kulp，2003 年;Beery 和 Beery，2006 年;Carlson et al.， 2013;Byers et al.， 2016），其中 FMC 较好的孩子可能更擅长操纵物体，这使他们能够将额外的注意力资源引导到新的学习中，即 VMI（Kim et al.， 2018），尚未发现 FMC 是以后学习成绩的一致预测指标（Kim et al.， 2018）。从这个意义上说，在 FMS 中，VMI 技能已被记录为与数学成绩最一致且最显著相关的技能（Macdonald 等人，2018 年;Flores et al.， 2023a）。

1.3 Development of the VMI and its connection to maths
1.3 VMI 的发展及其与数学的联系

The development of VMI skills is very sensitive and dynamic with rapid growth between the ages of 4 and 7 (Decker et al., 2011), peaking between the ages of 4 and 5 (Fang et al., 2017), but continuing until at least the age of 12 (Decker et al., 2011). In this sense, considering the age of rapid growth of the VMI and the age of preschool attendance, it is important that this skill is well worked on at this academic stage.
VMI 技能的发展非常敏感和动态，在 4 到 7 岁之间快速增长（Decker et al.， 2011），在 4 到 5 岁之间达到顶峰（Fang et al.， 2017），但至少持续到 12 岁（Decker et al.， 2011）。从这个意义上说，考虑到 VMI 快速增长的年龄和学龄前教育的年龄，在这个学术阶段很好地锻炼这项技能非常重要。

The literature has been consistent in describing that VMI skills are a multidimensional construct and its main components are visual perception and FMC skills (Osborn et al., 1984; Korkman et al., 1998; Tseng and Chow, 2000; Beery and Beery, 2006, 2010; Newcombe and Frick, 2010; Carlson et al., 2013; Dinehart and Manfra, 2013; Memisevic and Hadzic, 2013; Wang et al., 2013; Verdine et al., 2014; Goodway et al., 2019). VMI is defined as a person’s ability to visually perceive and understand the spatial relationships between objects and to manipulate, construct or reproduce models using the FMC (Korkman et al., 1998; Beery and Beery, 2010; Carlson et al., 2013; Verdine et al., 2014). However, success in tasks that require VMI skills not only requires children to coordinate their visual, spatial and motor skills (Verdine et al., 2014), but also attention control (Korkman et al., 1998; Beery and Beery, 2004; Becker et al., 2014). In this sense, VMI requires the integration of visual and spatial skills and executive attention, as well as FMC (Beery and Beery, 2004; Figure 3).
文献一致地描述 VMI 技能是一种多维结构，其主要组成部分是视觉感知和 FMC 技能（Osborn et al.， 1984;Korkman et al.， 1998;Tseng 和 Chow，2000 年;Beery 和 Beery，2006 年、2010 年;Newcombe 和 Frick，2010 年;Carlson et al.， 2013;Dinehart 和 Manfra，2013 年;Memisevic 和 Hadzic，2013 年;Wang et al.， 2013;Verdine et al.， 2014;Goodway等人，2019 年）。VMI 被定义为一个人在视觉上感知和理解物体之间的空间关系以及使用 FMC 操纵、构建或复制模型的能力（Korkman 等人，1998 年;Beery 和 Beery，2010 年;Carlson et al.， 2013;Verdine et al.， 2014）。然而，在需要 VMI 技能的任务中取得成功不仅需要儿童协调他们的视觉、空间和运动技能（Verdine 等人，2014 年），还需要注意力控制（Korkman 等人，1998 年;Beery 和 Beery，2004 年;Becker et al.， 2014）。从这个意义上说，VMI 需要整合视觉和空间技能以及执行注意力，以及 FMC（Beery 和 Beery，2004 年;图 3）。

Figure 3 图 3

Figure 3. Components of VMI.
图 3.VMI 的组件。

Vision is the system best equipped to structure space, since it structures, organizes and interprets all the spatial dimensions, and only then can motor actions come into play. It is between the ages of 3 and 7 that children should master all the notions of orientation: up, down, in front, behind, inside/outside, big, small, high, low, here, there, near, far, etc. In this sense, if children have spatial difficulties, they may have problems with localization, orientation, conservation of distance, surface area, volume and speed, which are the basis for the formulation of many mathematical concepts (Fonseca, 2010).
视觉是构建空间的最佳系统，因为它构建、组织和解释所有空间维度，只有这样，运动动作才能发挥作用。在 3 到 7 岁之间，孩子们应该掌握所有的方向概念：上、下、前、后、内/外、大、小、高、低、这里、那里、近、远等。从这个意义上说，如果儿童有空间困难，他们可能在定位、定向、距离守恒、表面积、体积和速度方面存在问题，这些都是许多数学概念形成的基础（Fonseca，2010）。

It has been documented that tasks requiring VMI skills, i.e., the integration of motor and visual processes, are highly related to the development of mathematical skills (Zebian, 2005; Puranik and Lonigan, 2012; Becker et al., 2014). This skill allows children to represent quantities, reproduce and perform transformations of shapes (Cameron et al., 2019). These activities are strongly associated with the development of quantitative tasks, numerical representations and mathematical performance (Verdine et al., 2017).
据记载，需要 VMI 技能的任务，即运动和视觉过程的整合，与数学技能的发展高度相关（Zebian，2005 年;Puranik 和 Lonigan，2012 年;Becker et al.， 2014）。这项技能允许儿童表示数量、复制和执行形状的转换（Cameron et al.， 2019）。这些活动与定量任务、数字表示和数学表现的开发密切相关（Verdine et al.， 2017）。

The literature has been consistent in supporting that in preschoolers executive function and VMI contribute unique and shared variance to mathematics performance (Cameron et al., 2012; Becker et al., 2014; Cragg and Gilmore, 2014; Verdine et al., 2014), revealing bidirectional influences between mathematics, executive function and VMI (Brock et al., 2018a). Executive function refers to higher-order cognitive skills used in information processing and problem solving (Blair, 2010; Beck et al., 2011) and its components include inhibition, cognitive flexibility, working memory, planning and updating (Blair and Razza, 2007; Herbers et al., 2011).
文献一致支持在学龄前儿童中，执行机能和 VMI 对数学成绩有独特和共享的方差（Cameron 等人，2012 年;Becker等人，2014 年;Cragg 和 Gilmore，2014 年;Verdine et al.， 2014），揭示了数学、执行功能和 VMI 之间的双向影响（Brock et al.， 2018a）。执行功能是指用于信息处理和解决问题的高阶认知技能（Blair， 2010;Beck et al.， 2011）其组成部分包括抑制、认知灵活性、工作记忆、计划和更新（Blair 和 Razza，2007 年;Herbers et al.， 2011）。

In early childhood, executive function and VMI co-develop (Cameron et al., 2016). Although these skills are considered separate processes, any task that requires visual perception (spatial and attention skills) to solve problems will require executive function (Korkman et al., 1998). However, it has been suggested that VMI is related to mathematical performance even after executive function has been controlled, specifically in geometry (spatial reasoning) (Duran et al., 2018). Verdine et al. (2014) concluded that even when the effects of other variables are removed, such as vocabulary and executive function, spatial abilities are a unique predictor of overall math performance, explaining 27.1% of its variability. In this sense, VMI skills can independently contribute to math performance (Verdine et al., 2014; Duran et al., 2018).
在儿童早期，执行功能和 VMI 共同发展 （Cameron et al.， 2016）。尽管这些技能被认为是独立的过程，但任何需要视觉感知（空间和注意力技能）来解决问题的任务都需要执行功能（Korkman et al.， 1998）。然而，有人认为，即使在执行功能得到控制之后，VMI 也与数学性能相关，特别是在几何学（空间推理）中（Duran et al.， 2018）。Verdine 等人（2014 年）得出结论，即使去除其他变量（如词汇和执行功能）的影响，空间能力也是整体数学表现的独特预测指标，解释了其 27.1% 的可变性。从这个意义上说，VMI 技能可以独立地促进数学成绩（Verdine et al.， 2014;Duran等人，2018 年）。

Also, in a recent study by Flores et al. (2023b), the authors concluded that VMI directly, positively and significantly influenced maths performance in preschool children with typical development and that GMS could indirectly contribute to maths performance, justified by the positive and direct associations with VMI skills. In this sense, the results of this study suggest the inclusion of GMS in structured programs to develop VMI and thus contribute to mathematical performance (Flores et al., 2023b).
此外，在 Flores 等人 （2023b） 最近的一项研究中，作者得出结论，VMI 直接、积极和显着地影响了具有典型发育的学龄前儿童的数学成绩，并且 GMS 可以间接促进数学成绩，这与 VMI 技能的积极和直接关联是合理的。从这个意义上说，本研究的结果表明，将 GMS 纳入结构化程序以开发 VMI，从而有助于数学性能（Flores 等人，2023b）。

Although deficits in any of these processes affect the results of VMI (Daly et al., 2003; Carlson et al., 2013; Van Wyk et al., 2020), all these skills are malleable and can be trained (Diamond and Lee, 2011; Uttal et al., 2013).
尽管这些过程中任何一个的缺陷都会影响 VMI 的结果（Daly 等人，2003 年;Carlson et al.， 2013;Van Wyk et al.， 2020），所有这些技能都是可塑的，可以训练的（Diamond 和 Lee，2011 年;Uttal et al.， 2013）。

VMI skills are used in most everyday tasks with an emphasis on early maths learning (Mix and Cheng, 2012; Verdine et al., 2014; Zhang and Lin, 2015; Mix et al., 2016). It has been shown that basic maths skills are directly dependent on VMI (Cameron et al., 2012; Becker et al., 2014; Carlson et al., 2014; Grissmer et al., 2014; Verdine et al., 2014), which is justified by the fact that classroom tasks often require this type of skill (Dehaene and Cohen, 2007). In addition to VMI skills influencing maths skills in preschool, they are a significant predictor of maths when children enter school (Gunderson et al., 2012; Rittle-Johnson et al., 2019). Furthermore, research in cognitive neuroscience points to a neural basis that links VMI skills with maths (Hubbard et al., 2005; St Clair-Thompson and Gathercole, 2006; Dehaene, 2011), namely in numerical operations skills (Dehaene et al., 2004; Hubbard et al., 2009) and damage to the parietal cortex often results in deficiencies in spatial and numerical skills (Bueti and Walsh, 2009).
VMI 技能用于大多数日常任务，重点是早期数学学习（Mix 和 Cheng，2012 年;Verdine et al.， 2014;Zhang 和 Lin，2015 年;Mix et al.， 2016）。已经表明，基本的数学技能直接取决于 VMI（Cameron 等人，2012 年;Becker等人，2014 年;Carlson et al.， 2014;Grissmer et al.， 2014;Verdine et al.， 2014），这可以通过课堂任务通常需要这种类型的技能这一事实来证明（Dehaene 和 Cohen，2007）。除了 VMI 技能影响学前班的数学技能外，它们还是儿童入学时数学的重要预测指标（Gunderson 等人，2012 年;Rittle-Johnson et al.， 2019）。此外，认知神经科学的研究指出了将 VMI 技能与数学联系起来的神经基础（Hubbard 等人，2005 年;St Clair-Thompson 和 Gathercole，2006 年;Dehaene，2011 年），即数值运算技能（Dehaene 等人，2004 年;Hubbard et al.， 2009）顶叶皮层的损伤通常会导致空间和数字技能的缺陷（Bueti 和 Walsh，2009 年）。

In a recent systematic review carried out by Flores et al. (2023a), the authors found that all the mathematical skills proposed by National Research Council (2009) for preschool were associated with VMI skills: numeracy (Verdine et al., 2014; Osorio-Valencia et al., 2017; Duran et al., 2018; Kim et al., 2018; Nesbitt et al., 2019; Escolano-Pérez et al., 2020; Khng and Ng, 2021), addition and subtraction (Becker et al., 2014; Brock et al., 2018a; Duran et al., 2018; Cameron et al., 2019; Nesbitt et al., 2019; Khng and Ng, 2021), measurement (Dinehart and Manfra, 2013; Manfra et al., 2017; Duran et al., 2018; Kim et al., 2018; Nesbitt et al., 2019; Greenburg et al., 2020) and geometry (Manfra et al., 2017; Duran et al., 2018; Kim et al., 2018; Greenburg et al., 2020).
在 Flores 等人（2023a）最近进行的一项系统评价中，作者发现国家研究委员会（2009 年）为学龄前儿童提出的所有数学技能都与 VMI 技能有关：算术（Verdine 等人，2014 年;Osorio-Valencia 等人，2017 年;Duran等人，2018 年;Kim et al.， 2018;Nesbitt等人，2019 年;Escolano-Pérez等人，2020 年;Khng 和 Ng，2021 年）、加法和减法（Becker et al.， 2014;Brock等人，2018a;Duran等人，2018 年;Cameron等人，2019 年;Nesbitt等人，2019 年;Khng 和 Ng，2021 年）、测量（Dinehart 和 Manfra，2013 年;Manfra等人，2017 年;Duran等人，2018 年;Kim et al.， 2018;Nesbitt等人，2019 年;Greenburg等人，2020 年）和几何学（Manfra et al.， 2017;Duran等人，2018 年;Kim et al.， 2018;Greenburg et al.， 2020）。

Since the development of VMI skills seems to be positively influenced by the visual perception skills (spatial and attention skills) of FMC and GMS, it was necessary to understand the relationship between these components of VMI and maths skills.
由于 VMI 技能的发展似乎受到 FMC 和 GMS 的视觉感知技能（空间和注意力技能）的积极影响，因此有必要了解 VMI 的这些组成部分与数学技能之间的关系。

1.3.1 Spatial skills and its connection to maths
1.3.1 空间技能及其与数学的联系

Spatial ability is a generic term for a multitude of related abilities that include the mental manipulation of information about objects in the environment and spaces we inhabit (Uttal et al., 2013). A recent meta-analysis sought to define spatial abilities and concluded that there were four distinct types of spatial abilities based on the intersection of two dimensions. One is related to information, which can be intrinsic and extrinsic, and the other is related to tasks, which can be static and dynamic (Uttal et al., 2013). Intrinsic information concerns the properties of an object (constitution/shape) and extrinsic information concerns the location of the object (left/right/front/back/near/far, etc.). In terms of tasks, static tasks do not change the object’s properties (shape or position), while dynamic tasks change the object’s properties. Spatial skills develop very early in children through everyday activities, such as observing and exploring their surroundings (Barros and Palhares, 2001; Uttal et al., 2013). With regard to tasks, in static tasks the object’s properties (shape or position) do not change, while in dynamic tasks the object’s properties change. Spatial skills are developed very early in children through everyday activities such as observing and exploring their surroundings (Barros and Palhares, 2001; Uttal et al., 2013). These activities allow children to explore space and become aware of their relationship and position with objects (near/far/outside/inside/open/closed/top/bottom), as well as progressively recognizing their geometric shapes (Silva et al., 2016). There is a growing realization that spatial abilities are an important aspect of intellectual capacity and that they are separable from general intelligence (Hegarty and Waller, 2004), and although they are always present in children’s daily lives, they have been largely ignored in formal educational environments (Clements and Sarama, 2011). However, some efforts have already been made to include this approach in school environments (Moss et al., 2015; Silva et al., 2016).
空间能力是多种相关能力的通用术语，包括对我们居住的环境和空间中的物体信息的心理操纵（Uttal et al.， 2013）。最近的一项荟萃分析试图定义空间能力，并得出结论，基于两个维度的交集，有四种不同类型的空间能力。一个与信息有关，可以是内在的和外在的，另一个与任务有关，可以是静态的和动态的（Uttal et al.， 2013）。内在信息涉及对象的属性（构成/形状），外在信息涉及对象的位置（左/右/前/后/近/远等）。在任务方面，静态任务不会更改对象的属性 （形状或位置），而动态任务会更改对象的属性。空间技能在儿童早期通过日常活动发展起来，例如观察和探索周围的环境（Barros 和 Palhares，2001 年;Uttal et al.， 2013）。对于任务，在静态任务中，对象的属性 （形状或位置） 不会更改，而在动态任务中，对象的属性会更改。空间技能在儿童的早期就通过日常活动发展起来，例如观察和探索周围的环境（Barros 和 Palhares，2001 年;Uttal et al.， 2013）。这些活动让孩子们探索空间，意识到他们与物体的关系和位置（近/远/外/内/开/闭/上/下），并逐渐识别它们的几何形状（Silva et al.， 2016）。 人们越来越意识到空间能力是智力能力的一个重要方面，它们与一般智力是分开的（Hegarty 和 Waller，2004），尽管它们总是存在于儿童的日常生活中，但它们在正规教育环境中基本上被忽视了（Clements 和 Sarama，2011）。然而，已经做出了一些努力，将这种方法纳入学校环境（Moss et al.， 2015;Silva等人，2016 年）。

Literature has shown a strong association between these spatial and mathematical skills (Ansari et al., 2003; Gunderson et al., 2012; Mix and Cheng, 2012). A factor analysis found that these skills are significant predictors of maths skills in preschool, third and sixth grades (Mix et al., 2016). In children aged between 4.5 and 7.5 years, positive and significant relationships have been identified in tasks that required children to remember and reproduce a series of spatial locations with number naming and number magnitude processing (LeFevre et al., 2010), as well as problem solving (Cheng and Mix, 2014; Zhang and Lin, 2015; Skagerlund and Träff, 2016). Children who develop better spatial representations acquire additional mathematical skills earlier (Bachot et al., 2005; Bailey et al., 2014). In a study carried out by Hawes et al. (2017), which aimed to investigate the extent to which spatial learning supports children’s numerical development, the results showed that only those in the intervention group made significant gains in mathematical numerical comparison skills. These skills are strongly related to simultaneous and subsequent mathematical performance (De Smedt et al., 2013; Nosworthy et al., 2013).
文献表明这些空间技能和数学技能之间存在很强的关联（Ansari et al.， 2003;Gunderson等人，2012 年;Mix 和 Cheng，2012 年）。因子分析发现，这些技能是学前班、三年级和六年级数学技能的重要预测因子（Mix et al.，2016）。在 4.5 至 7.5 岁的儿童中，在需要儿童通过数字命名和数字幅度处理（LeFevre 等人，2010 年）以及解决问题（Cheng 和 Mix，2014 年;Zhang 和 Lin，2015 年;Skagerlund 和 Träff，2016 年）。发展出更好的空间表征的孩子会更早地获得额外的数学技能（Bachot et al.， 2005;Bailey et al.， 2014）。在 Hawes 等人（2017 年）进行的一项研究中，旨在调查空间学习在多大程度上支持儿童的数值发展，结果表明，只有干预组的人在数学数值比较技能方面取得了显着进步。这些技能与同步和随后的数学表现密切相关（De Smedt et al.， 2013;Nosworthy et al.， 2013）。

There is evidence that early spatial skills longitudinally predicted early numerical knowledge skills (such as plus, minus, equals and second) and that spatial skills assessed at 3 years and later at 4 years, even after controlling for executive functioning and vocabulary skills, predicted approximately 15% of the variability in early number knowledge (Verdine et al., 2014), thus early interventions aimed at improving spatial skills are justified (De Smedt et al., 2013; Grissmer et al., 2013).
有证据表明，早期空间技能纵向预测了早期数字知识技能（如加、减、等于和第二），并且在 3 岁和后来的 4 岁时评估的空间技能，即使在控制了执行功能和词汇技能之后，也预测了早期数字知识中大约 15% 的变异性（Verdine 等人，2014 年）， 因此，旨在提高空间技能的早期干预是合理的（De Smedt et al.， 2013;Grissmer et al.， 2013）。

Mathematical concepts are also based on mental representations of objects that are developed by the child’s interaction with physical objects through play and games (Ginsburg, 1977; Clements and Sarama, 2011) where children are able to represent and interpret numerical information spatially (Gunderson et al., 2012) and use strategies to solve problems (Mata et al., 2011). Recently, it has been suggested that infants’ spatial processing acts as a later precursor to maths at the age of 4 (Lauer and Lourenco, 2016). In addition, spatial memory in young children has been associated with their mathematical performance (Holmes et al., 2008; LeFevre et al., 2010; Meyer et al., 2010; Hornung et al., 2011; Passolunghi and Mammarella, 2012; Szucs et al., 2013). Given the importance of spatial memory, it has been recommended that it should be given the same importance and the same amount of instructional time as numeracy from pre-school to 8th grade (National Council of Teachers of Mathematics, 2006). However, geometry and spatial thinking are often minimized in pre-school education (Clements and Sarama, 2011). This can be explained by the fact that preschool teachers receive little professional training in geometry and spatial thinking (Ginsburg et al., 2006), compared to other maths topics (Lee, 2010). During preschool education, it is essential that children are able to use symmetry, create mental images of geometric shapes, recognize and represent shapes from different perspectives and assemble and disassemble two- and three-dimensional shapes (Frick et al., 2014; Hawes et al., 2015). In this sense, there is an urgent need for more training for preschool teachers on the importance and teaching of spatial skills in pre-school education. It has been shown that children show high levels of motivation during activities involving spatial skills (Naqvi et al., 2013; Taylor and Hutton, 2013).
数学概念也基于对物体的心理表征，这些表征是通过儿童通过游戏和游戏与物理物体的互动而发展起来的（Ginsburg， 1977;Clements 和 Sarama，2011 年）孩子们能够在空间上表示和解释数字信息 （Gunderson et al.， 2012） 并使用策略来解决问题 （Mata et al.， 2011）。最近，有人提出婴儿的空间处理是 4 岁时数学的后期先驱（Lauer 和 Lourenco，2016 年）。此外，幼儿的空间记忆与他们的数学成绩有关（Holmes et al.， 2008;LeFevre 等人，2010 年;Meyer等人，2010 年;Hornung等人，2011 年;Passolunghi 和 Mammarella，2012 年;Szucs等人，2013 年）。鉴于空间记忆的重要性，建议从学前班到 8 年级，应赋予它与算术同等的重要性和相同的教学时间（全国数学教师委员会，2006 年）。然而，在学前教育中，几何和空间思维往往被最小化（Clements 和 Sarama，2011 年）。这可以通过以下事实来解释：与其他数学主题相比，学前教师很少接受几何和空间思维方面的专业培训（Ginsburg et al.， 2006）（2010）。在学前教育中，儿童必须能够使用对称性，创建几何形状的心理图像，从不同的角度识别和表示形状，以及组装和拆卸二维和三维形状（Frick et al.， 2014;Hawes等人，2015 年）。 从这个意义上说，迫切需要对学前教师进行更多培训，让他们了解学前教育中空间技能的重要性和教学。研究表明，儿童在涉及空间技能的活动中表现出高水平的积极性（Naqvi et al.， 2013;Taylor 和 Hutton，2013 年）。

1.3.2 Executive attention skills and its connections to maths
1.3.2 执行注意力技能及其与数学的联系

Regarding attention, theoretical and empirical evidence, supported by the results of neuroimaging studies, indicates that the processes of attention and VMI are related (Diamond, 2000; Floyer-Lea and Matthews, 2004), since tasks that require VMI also require attentional control (Beery and Beery, 2004; Becker et al., 2014). In the light of the embodied cognition theory, attention control and VMI co-develop as children interact with the environment (Campos et al., 2000). Also, automaticity theory argues that cognitive resources become available as someone is able to automatize or perform a task without using all their attention, which in turn makes it easier to simultaneously perform a second task that requires attention (Floyer-Lea and Matthews, 2004). In this sense, children who automate a task that requires VMI do not need to pay as much attention to the execution of visual and motor movements, so they can have additional cognitive resources available for other tasks (Floyer-Lea and Matthews, 2004). In this sense, executive attention is related to the development of a variety of early mathematical skills in the face of the influence exerted by VMI (LeFevre et al., 2013).
关于注意力，由神经影像学研究结果支持的理论和实证证据表明，注意力和 VMI 的过程是相关的（Diamond，2000 年;Floyer-Lea 和 Matthews，2004 年），因为需要 VMI 的任务也需要注意力控制（Beery 和 Beery，2004 年;Becker et al.， 2014）。根据具身认知理论，注意力控制和 VMI 随着儿童与环境的互动而共同发展（Campos et al.， 2000）。此外，自动性理论认为，当某人能够在不使用所有注意力的情况下自动化或执行一项任务时，认知资源就会变得可用，这反过来又使得同时执行需要注意的第二项任务变得更加容易（Floyer-Lea 和 Matthews，2004 年）。从这个意义上说，自动化需要 VMI 的任务的儿童不需要那么多关注视觉和运动运动的执行，因此他们可以有额外的认知资源可用于其他任务（Floyer-Lea 和 Matthews，2004）。从这个意义上说，执行注意力与面对 VMI 施加的影响时各种早期数学技能的发展有关（LeFevre et al.， 2013）。

1.3.3 FMC skills and its connection to maths
1.3.3 FMC 技能及其与数学的联系

FMC refers to muscular coordination that produces minute and precise movements (Kimmel and Ratliff-Schaub, 2011) without strongly needing visual and spatial information (Korkman et al., 1998; Carlson et al., 2013). Although FMC does not depend on visual and spatial information, these motor skills can be relevant for many tasks in the early years of schooling (Marr et al., 2003). Since VMI involves the mental representation of an image that is replicated by controlling the minute movement of the fingers (Carlson et al., 2013), FMC plays a very important role in school success (Roebers et al., 2014; Kim et al., 2015; Fischer et al., 2020), since children with better FMC may be better at manipulating objects, such as pencils or notebooks, which allows them to direct additional attention resources to learning instead of focusing them on movements associated with FMC (Kim et al., 2018). In this sense, a child with good FMC, when performing an academic task, can impose a lower cognitive load compared to a child who still shows difficulties in FMC (Floyer-Lea and Matthews, 2004; Luo et al., 2007; Cameron et al., 2015). Therefore, FMC is considered a precursor to VMI (Kim et al., 2016) and the correlations are positive and significant (Carlson et al., 2013).
FMC 是指产生微小而精确的运动的肌肉协调（Kimmel 和 Ratliff-Schaub，2011 年），而无需强烈需要视觉和空间信息（Korkman 等人，1998 年;Carlson et al.， 2013）。尽管 FMC 不依赖于视觉和空间信息，但这些运动技能可能与学校教育早期的许多任务相关（Marr et al.， 2003）。由于 VMI 涉及通过控制手指的微小运动来复制图像的心理表征（Carlson et al.， 2013），因此 FMC 在学校成功中起着非常重要的作用（Roebers et al.， 2014;Kim et al.， 2015;Fischer et al.， 2020），因为 FMC 较好的孩子可能更擅长操作物体，例如铅笔或笔记本，这使他们能够将额外的注意力资源用于学习，而不是将注意力集中在与 FMC 相关的运动上（Kim et al.， 2018）。从这个意义上说，与仍然在 FMC 中表现出困难的孩子相比，具有良好 FMC 的孩子在执行学术任务时可以施加较低的认知负荷（Floyer-Lea 和 Matthews，2004 年;Luo et al.， 2007;Cameron et al.， 2015）。因此，FMC 被认为是 VMI 的前体 （Kim et al.， 2016），并且相关性是正且显著的 （Carlson et al.， 2013）。

In a recent systematic review, one of the aims of which was to identify the specific motor skills that were positively associated with mathematics in pre-school children, the authors concluded that VMI was, among all the motor skills, the one that stood out the most (Flores et al., 2023a). However, the authors also identified positive and significant relationships between FMC and mathematical skills. A cross-sectional study involving 4- and 5-year-old preschool children concluded that performance on FMC significantly predicts fractional reasoning tasks (R2 = 0.258; p = 0.003) (Clark et al., 2021). Other cross-sectional studies found that FMC was related to finger-based numerical representations (Suggate et al., 2017; Fischer et al., 2020) and counting (Manfra et al., 2017; Fischer et al., 2018). Fingers have long been used to help with counting and calculation and their use in early counting is almost universal (Butterworth, 1999; Crollen and Noël, 2015). Using the finger not only helps children learn to count, but can also help them understand the meaning of numbers (Fischer, 2008; Fischer et al., 2018). Recent studies have found that only CMF (agility and dexterity) predicted initial calculation skills in the early years (Suggate et al., 2017; Fischer et al., 2018). However, as the child’s age progresses, finger dexterity no longer correlated significantly with ordinal and cardinal representations, and it is possible that the child’s spatial abilities play a more important role in counting (Fisher et al., 2020). Therefore, given the importance of manual dexterity in counting in the early preschool years, the use of the finger should be encouraged to develop numerical skills and simultaneously train these skills (Fisher et al., 2020). Longitudinal studies have also positively associated FMC with later mathematical performance (Dinehart and Manfra, 2013; Osorio-Valencia et al., 2017; Kim et al., 2018; Greenburg et al., 2020). In this sense, given the relationship between FMC and VMI and mathematical skills, these types of motor skills should be developed through intervention programs.
在最近的一项系统评价中，其目的之一是确定与学龄前儿童数学呈正相关的特定运动技能，作者得出结论，在所有运动技能中，VMI 是最突出的（Flores 等人，2023a）。然而，作者还确定了 FMC 与数学技能之间的正向和显著关系。一项涉及 4 岁和 5 岁学龄前儿童的横断面研究得出结论，FMC 的表现显着预测分数推理任务 （R2 = 0.258;p = 0.003）（Clark等人，2021 年）。其他横断面研究发现 FMC 与基于手指的数字表示有关（Suggate et al.， 2017;Fischer等人，2020 年）和计数（Manfra et al.， 2017;Fischer等人，2018 年）。长期以来，手指一直被用来帮助计数和计算，它们在早期计数中的使用几乎是普遍的（Butterworth，1999 年;Crollen 和 Noël，2015 年）。使用手指不仅可以帮助孩子学习数数，还可以帮助他们理解数字的含义（Fischer，2008 年;Fischer等人，2018 年）。最近的研究发现，只有 CMF（敏捷性和灵巧性）可以预测早期的初始计算技能（Suggate 等人，2017 年;Fischer等人，2018 年）。然而，随着孩子年龄的增长，手指的灵巧性不再与序数和基数表示显着相关，孩子的空间能力可能在计数中发挥更重要的作用（Fisher et al.， 2020）。 因此，鉴于学龄前早期手工灵巧性在计数中的重要性，应鼓励使用手指来发展数字技能并同时训练这些技能（Fisher et al.， 2020）。纵向研究也使 FMC 与后来的数学表现呈正相关（Dinehart 和 Manfra，2013 年;Osorio-Valencia 等人，2017 年;Kim et al.， 2018;Greenburg et al.， 2020）。从这个意义上说，鉴于 FMC 和 VMI 与数学技能之间的关系，这些类型的运动技能应该通过干预计划来发展。

1.3.4 GMS and its connections to maths
1.3.4 GMS 及其与数学的联系

GMS refers to movements produced by large muscle groups (Haywood and Getchell, 2019) and there is neural evidence to support that the development of these motor skills stimulates the development of the central nervous system, contributing to the development of VMI (Mujkic and Papric, 2013; Wang et al., 2015; Fang et al., 2017; Zhang et al., 2019). It has also been argued that in the same motor action it is complex to clearly differentiate the independent involvement of each of the motor skills (GMS and FMS), since they coexist and are fundamental for the efficient performance of the task (Payne and Isaacs, 2012; Flatters et al., 2014). This can be justified by the fact that higher-order neuromotor processes seem to be involved simultaneously in GMS and FMS, since these processes do not occur independently (Roebers and Kauer, 2009; Oberer et al., 2017). Thus, children with difficulties in GMS are more likely to show problems in VMI skills (Wassenberg et al., 2005; Oberer et al., 2017).
GMS 是指由大肌肉群产生的运动（Haywood 和 Getchell，2019 年），并且有神经证据支持这些运动技能的发展会刺激中枢神经系统的发展，从而促进 VMI 的发展（Mujkic 和 Papric，2013 年;Wang et al.， 2015;Fang et al.， 2017;Zhang et al.， 2019）。还有人认为，在同一个运动动作中，明确区分每种运动技能（GMS 和 FMS）的独立参与是很复杂的，因为它们共存并且是有效执行任务的基础（Payne 和 Isaacs，2012 年;Flatters et al.， 2014）。这可以通过以下事实来证明：高阶神经运动过程似乎同时参与 GMS 和 FMS，因为这些过程不是独立发生的（Roebers 和 Kauer，2009 年;Oberer等人，2017 年）。因此，在 GMS 中有困难的儿童更有可能表现出 VMI 技能问题（Wassenberg 等人，2005 年;Oberer等人，2017 年）。

Although some authors suggest significant associations between GMS and maths mastery (Son and Meisels, 2006; Pagani et al., 2010; De Waal, 2019), the literature is inconsistent and insufficient to report the relationships between specific components of GMS and maths performance in preschool (Macdonald et al., 2018; Escolano-Pérez et al., 2020; Macdonald et al., 2020; Flores et al., 2023a). Despite the inconsistency of the results, these skills should be part of the work of early childhood teachers, since this educational period should contribute to the integral development of children (Escolano-Pérez et al., 2020). In any case, this inclusion is justified by the fact that studies have concluded that GMS promote the development of social skills, physical well-being (Cameron et al., 2016; Goodway et al., 2019; Haywood and Getchell, 2019) and perceived athletic competence in childhood (Piek et al., 2006). In addition, preschool children involved in a structured, cognitively challenging GMS program could contribute to the improvement of mathematical skills through the direct effect exerted on the improvement of FMS (Hudson et al., 2021). Flores et al. (2023b), in a study carried out with pre-school children (between 3 and 6 years old), concluded that GMS could indirectly contribute to mathematical performance, justified by the significant, positive and direct associations with VMI skills. In this sense, the results of this study suggest the inclusion of GMS in structured programs to develop VMI and thus contribute to mathematical performance (Flores et al., 2023b).
尽管一些作者认为 GMS 与数学掌握之间存在显着关联（Son 和 Meisels，2006 年;Pagani et al.， 2010;De Waal，2019 年），文献不一致且不足以报告 GMS 的特定组成部分与学前数学表现之间的关系（Macdonald 等人，2018 年;Escolano-Pérez等人，2020 年;Macdonald 等人，2020 年;Flores et al.， 2023a）。尽管结果不一致，但这些技能应该是幼儿教师工作的一部分，因为这个教育时期应该有助于儿童的全面发展（Escolano-Pérez et al.，2020）。无论如何，这种纳入是合理的，因为研究得出的结论是 GMS 促进了社交技能、身体健康的发展（Cameron 等人，2016 年;Goodway等人，2019 年;Haywood 和 Getchell，2019 年）以及童年时期的感知运动能力（Piek et al.， 2006）。此外，参与结构化、认知具有挑战性的 GMS 计划的学龄前儿童可以通过对 FMS 改善的直接影响为数学技能的提高做出贡献（Hudson 等人，2021 年）。Flores 等人 （2023b） 在对学龄前儿童（3 至 6 岁）进行的一项研究中得出结论，GMS 可以间接促进数学成绩，这与 VMI 技能有显著、积极和直接的关联。从这个意义上说，本研究的结果表明，将 GMS 纳入结构化程序以开发 VMI，从而有助于数学性能（Flores 等人，2023b）。

As the literature shows, in order to promote the development of VMI skills, it will be necessary to include work on the visual perception skills (spatial and attention skills) of FMC and GMS in intervention programs.
正如文献所示，为了促进 VMI 技能的发展，有必要将 FMC 和 GMS 的视觉感知技能（空间和注意力技能）的工作纳入干预计划。

2 Intervention programs to develop VMI
2 开发 VMI 的干预计划

As already mentioned, all the processes that can directly influence VMI, namely visual perception (spatial skills and attention skills), FMC and GMS, are malleable and trainable (Diamond and Lee, 2011; Uttal et al., 2013). Early intervention improves VMI skills in preschool and early school-age children (Parush and Hahn-Markowitz, 1997; Dankert et al., 2003). There is evidence from the fields of physiotherapy and occupational therapy to indicate that early deficits in fine motor skills can be improved or corrected through interventions (Bayona et al., 2006; Ratzon et al., 2007). Most studies have proven the effectiveness of long interventions, at least 7 months, to improve VMI skills (Parush and Hahn-Markowitz, 1997; Case-Smith, 2002), however, a 3-month period of just 12 therapeutic sessions is of great importance for improving VMI (Ratzon et al., 2009).
如前所述，所有可以直接影响 VMI 的过程，即视觉感知（空间技能和注意力技能）、FMC 和 GMS，都是可塑和可训练的（Diamond 和 Lee，2011 年;Uttal et al.， 2013）。早期干预提高了学龄前和学龄前儿童的 VMI 技能（Parush 和 Hahn-Markowitz，1997 年;Dankert et al.， 2003）。来自物理治疗和职业治疗领域的证据表明，精细运动技能的早期缺陷可以通过干预来改善或纠正（Bayona 等人，2006 年;Ratzon et al.， 2007）。大多数研究已经证明了长期干预（至少 7 个月）对提高 VMI 技能的有效性（Parush 和 Hahn-Markowitz，1997 年;Case-Smith，2002 年），然而，仅 3 个月的 12 次治疗对于改善 VMI 非常重要（Ratzon 等人，2009 年）。

In this sense, given the implications of VMI for mathematical skills, it is essential to include programs in the preschool curriculum that aim to explicitly train VMI skills (Uttal and Cohen, 2012; Newcombe et al., 2013; Brock et al., 2018b).
从这个意义上说，鉴于 VMI 对数学技能的影响，必须在学前课程中包括旨在明确训练 VMI 技能的计划（Uttal 和 Cohen，2012 年;Newcombe等人，2013 年;Brock等人，2018b）。

The literature has highlighted some programs to improve mathematical skills with the inclusion of activities that promote the development of VMI. Table 1 shows some of these programs, the objectives to be worked on related to VMI skills, the associated activities, the context in which the program is developed, and the main motor skills involved.
文献强调了一些提高数学技能的计划，其中包括促进 VMI 发展的活动。表 1 显示了其中一些计划、与 VMI 技能相关的要实现的目标、相关活动、计划开发的环境以及涉及的主要运动技能。

Table 1 表 1

Table 1. Programs to develop VMI.
表 1.开发 VMI 的计划。

Looking at Table 1, all the programs aim to develop VMI by working on spatial skills using manipulative objects to reproduce/construct geometric shapes (Hohmann and Weikart, 2002; Klein and Starkey, 2002; Casey, 2004; Sarama and Clements, 2004; Casey et al., 2008), patterns (Groth-Marnat and Teal, 2000; Hohmann and Weikart, 2002; Klein and Starkey, 2002; Moss et al., 2016; Brock et al., 2018b), positions and orientations in space (Hohmann and Weikart, 2002; Greenes et al., 2004; Moss et al., 2016; Brock et al., 2018b). Some of the activities that prevail in these programs are: matching games; manipulating and building with Legos and blocks (horizontally and vertically); constructing puzzles; going through and tracing labyrinths; making threads with various sequences (different patterns - size, colors, shapes, etc.); copying sequences of shapes and figures; making graphs; manipulating different objects to reproduce shapes and patterns; identifying positions in space.
从表 1 来看，所有程序都旨在通过使用操纵对象来复制/构建几何形状的空间技能来开发 VMI（Hohmann 和 Weikart，2002 年;Klein 和 Starkey，2002 年;Casey， 2004;Sarama 和 Clements，2004 年;Casey et al.， 2008）、模式（Groth-Marnat 和 Teal， 2000;Hohmann 和 Weikart，2002 年;Klein 和 Starkey，2002 年;Moss等人，2016 年;Brock等人，2018b）、空间中的位置和方向（Hohmann 和 Weikart，2002 年;Greenes 等人，2004 年;Moss等人，2016 年;Brock等人，2018b）。这些计划中盛行的一些活动是：配对游戏;用乐高积木和积木（水平和垂直）操纵和建造;构建拼图;穿过并追踪迷宫;制作具有各种序列的线程（不同的图案 - 大小、颜色、形状等）;复制形状和图形序列;制作图表;操纵不同的对象以再现形状和图案;识别空间中的位置。

A common element of all these intervention programs/activities to develop VMI is that they are applied in a classroom context without heavy reliance on GMS. In this sense, the aim of this article is to present and justify a set of activities to develop spatial skills with a significant involvement of GMS, to be applied in a classroom, playground or family (home) context.
所有这些开发 VMI 的干预计划/活动的一个共同要素是它们应用于课堂环境，而不需要严重依赖 GMS。从这个意义上说，本文的目的是提出并证明一系列活动，以发展空间技能，并有 GMS 的大量参与，以应用于教室、操场或家庭（家庭）环境。

3 Activities to develop spatial skills with a strong contribution from GMS
3 大泥湄公河次区域 （GMS） 做出巨大贡献的培养空间技能的活动

Spatial skills can be developed through specific physical activity programs for pre-school children (Hraste et al., 2018). For example, in Sweden, maths teaching in preschool is supported by physical activity and music (National Research Council, 2009). Elofsson et al. (2018) showed that children with and without motor skills problems benefited in mathematical learning when they were placed in an environment characterized by physical activity and music. These results are consistent with previous research (Donelly and Lambourne, 2011; Rasberry et al., 2011).
空间技能可以通过针对学龄前儿童的特定体育活动计划来发展（Hraste et al.， 2018）。例如，在瑞典，学前班的数学教学由体育活动和音乐支持（国家研究委员会，2009 年）。Elofsson 等人（2018 年）表明，当有和没有运动技能问题的儿童被放置在以体育活动和音乐为特征的环境中时，他们都会受益于数学学习。这些结果与以前的研究一致（Donelly 和 Lambourne，2011 年;Rasberry et al.， 2011）。

Structured physical activity programs for preschool children should focus on playful activities in the form of games (Geist, 2009; Yu et al., 2018; Zosh et al., 2018). These types of activities do not guarantee mathematical development, but they offer great opportunities for discovering mathematical concepts (Geist, 2009). Simple motor actions, exploring and mastering certain materials (balls, ropes, hoops, balloons, rackets, etc.), allow children to explore the relationship between their bodies and objects moving in space (Silva et al., 2016). There is evidence that using words such as inside, outside, below, above, near, far, etc. helps children to solve spatial problems and consequently improve their skills in this area (Pruden et al., 2011). However, some specific motor skills of locomotion or object manipulation are not acquired innately as children grow (Clark, 2005), they must be learned and practiced (Pic et al., 2018, 2020) through structured programs during early childhood (Logan et al., 2012; Robinson et al., 2015; Coutinho et al., 2016; Dapp et al., 2021), suggesting that early intervention could reduce or prevent potential mathematical difficulties (Duncan et al., 2007).
学龄前儿童的结构化体育活动计划应侧重于游戏形式的游戏活动（Geist，2009 年;Yu等人，2018 年;Zosh et al.， 2018）。这些类型的活动并不能保证数学发展，但它们为发现数学概念提供了很好的机会（Geist，2009 年）。简单的运动动作，探索和掌握某些材料（球、绳索、铁环、气球、球拍等），让孩子们探索他们的身体与空间中移动的物体之间的关系（Silva et al.， 2016）。有证据表明，使用诸如 inside， outside， below， above， near， far 等词可以帮助儿童解决空间问题，从而提高他们在这方面的技能（Pruden et al.， 2011）。然而，一些特定的运动技能，如运动或物体操作并不是随着儿童的成长而天生获得的（Clark，2005），它们必须通过幼儿期的结构化计划来学习和练习（Pic et al.， 2018， 2020）（Logan et al.， 2012;Robinson等人，2015 年;Coutinho et al.， 2016;Dapp et al.， 2021），这表明早期干预可以减少或防止潜在的数学困难（Duncan et al.， 2007）。

In this sense, there are manuals and books that promote mathematical performance through the exploration of motor skills. An extraordinary example is the book “Mathekings” (Hoenisch and Niggemeyer, 2007). According to the authors, children explore the world and discover mathematics through their senses. This book, designed for children aged between 4 and 8, allows them to work with and develop mathematical concepts such as quantities, sorting and matching, patterns and symmetry, numbers, geometry, space and time, weighing, measuring and comparing, graphs, matching and function, and even statistics, through the handling of everyday materials and body movements, whether in the classroom, on the playground or at home. Another example is the book Preschool Math (Williams et al., 2005). This book encourages educators to listen to and observe young children in order to better understand how they think about their world. The book uses these stimuli to develop useful and appropriate mathematical experiences in which children use their senses and bodies to explore ideas, record and talk about concepts and learn how mathematics is felt, tasted and seen. The proposed activities allow children to evaluate, explore, experiment, solve problems, make assumptions and form hypotheses, while using interesting materials and environments in a mathematical way. To enrich and diversify activities for children, the book “Why Play Matters: 101 Activities for Developmental Play to Support Young Children” (Essame, 2023), is full of play-based activities to support the development of children between the ages of 0 and 8. Based on the holistic and inclusive model of Developmental Play, which includes sensory play, creative-exploratory play, meaning-making play and higher play, the activities focus on supporting aspects of social, emotional, physical and cognitive development. Since play is fundamental to a child’s holistic development, this book is essential reading for early childhood professionals, elementary school teachers, occupational therapists and parents.
从这个意义上说，有一些手册和书籍通过探索运动技能来促进数学表现。一个非凡的例子是《Mathekings》一书（Hoenisch 和 Niggemeyer，2007 年）。据作者介绍，孩子们通过他们的感官探索世界并发现数学。这本书专为 4 至 8 岁的儿童设计，允许他们通过处理日常材料和身体动作，无论是在课堂上，还是在课堂上，都可以使用和发展数学概念，例如数量、排序和匹配、图案和对称性、数字、几何、空间和时间、称重、测量和比较、图形、匹配和函数，甚至统计数据。 在操场上或家里。另一个例子是《学前数学》一书（Williams et al.， 2005）。这本书鼓励教育工作者倾听和观察幼儿，以便更好地了解他们如何看待自己的世界。这本书利用这些刺激来发展有用和适当的数学经验，让孩子们用他们的感官和身体来探索想法，记录和谈论概念，并学习如何感受、品尝和看到数学。拟议的活动允许孩子们评估、探索、实验、解决问题、做出假设和形成假设，同时以数学方式使用有趣的材料和环境。为了丰富和多样化儿童活动，《为什么游戏很重要：支持幼儿的 101 项发展性游戏活动》（Essame，2023 年）一书中充满了以游戏为基础的活动，以支持 0 至 8 岁儿童的发展。 这些活动基于发展游戏的整体和包容性模式，包括感官游戏、创造性探索游戏、意义创造游戏和高级游戏，侧重于支持社交、情感、身体和认知发展的各个方面。由于游戏是儿童全面发展的基础，因此本书是幼儿专业人士、小学教师、职业治疗师和家长的必读之作。

Spatial reasoning is an integral part of everyday life, and having good spatial skills strongly predicts children’s future performance in various subjects. In this sense, the books “Exploring the 3-D World: Developing Spatial and Math Skills for Young Children” (Hansel, 2021) and “Blocks and Beyond: Strengthening Early Math and Science Skills through Spatial Learning” are resources that promote the teaching of spatial skills in early childhood that contain research-based ideas and practical activities for early childhood educators to promote spatial development in children throughout the school day.
空间推理是日常生活中不可或缺的一部分，拥有良好的空间技能可以强烈预测孩子未来在各种学科中的表现。从这个意义上说，《探索 3-D 世界：为幼儿培养空间和数学技能》（Hansel，2021 年）和《Blocks and Beyond：通过空间学习加强早期数学和科学技能》等书是促进幼儿空间技能教学的资源，其中包含基于研究的思想和实践活动，供幼儿教育工作者在整个上学日促进儿童的空间发展。

In this sense, considering the direct influence of GMS on VMI skills (Flores et al., 2023b) and that numerous programs to develop VMI skills include working on spatial skills through the manipulation of objects in a classroom context, the aim of this study was to present a set of activities to develop spatial skills, using playful activities with a strong involvement of GMS, which could be carried out in a classroom context, at the playground or at home.
从这个意义上说，考虑到 GMS 对 VMI 技能的直接影响（Flores et al.， 2023b）以及许多培养 VMI 技能的计划包括通过在课堂环境中操纵物体来培养空间技能，本研究的目的是提出一系列发展空间技能的活动，使用有 GMS 深度参与的有趣活动， 这可以在课堂环境中、操场上或家中进行。

The activities presented in the next section of this manuscript were taken and adapted from the book “Exercitar para Aprender” (Flores and Magalhães, 2019).
本手稿下一节中介绍的活动取自《Exercitar para Aprender》一书（Flores 和 Magalhães，2019 年）。

3.1 Ativities 3.1 行动

All the proposed activities should be carried out in a playful way in the context of a game. The purpose of the activity should be well explained and practiced before the games begin. For each activity, it should be said: “let us see who does it well,” or “who is faster,” or “who hits the most,” etc. The teacher should correct whenever the child’s performance requires it (Weisberg and Zosh, 2018; Yu et al., 2018; Zosh et al., 2018). The proposed activities can be worked on in the classroom, playground or at home (Table 2).
所有提议的活动都应该在游戏的背景下以有趣的方式进行。在游戏开始之前，应该很好地解释和练习活动的目的。对于每项活动，应该说：“让我们看看谁做得好”，或者“谁更快”，或者“谁打得最多”，等等。只要孩子的表现需要，老师就应该纠正（Weisberg 和 Zosh，2018 年;Yu等人，2018 年;Zosh et al.， 2018）。拟议的活动可以在教室、操场或家中进行（表 2）。

Table 2 表 2

Table 2. Activities to develop spatial skills with a strong contribution from GMS.
表 2.在 GMS 的大力支持下开展培养空间技能的活动。

4 Discussion 4 讨论

Given the importance of mathematics in future academic and professional outcomes (Parsons and Bynner, 2005; Duncan et al., 2007) there has been increasing attention to mathematical learning and development in preschool education (Cross et al., 2009; Elofsson et al., 2016). In this sense, it is important to give children the same opportunities to support early mathematical development through interventions (Jordan et al., 2012).
鉴于数学在未来学术和专业成果中的重要性（Parsons 和 Bynner，2005 年;Duncan et al.， 2007）学前教育中的数学学习和发展越来越受到关注（Cross et al.，2009;Elofsson等人，2016 年）。从这个意义上说，重要的是要给孩子同样的机会，通过干预来支持早期数学发展（Jordan et al.，2012）。

VMI skills have been documented as those that are most consistently positively and significantly associated with math performance in preschool children (Cameron et al., 2012; Carlson et al., 2014; Grissmer et al., 2014; Verdine et al., 2014; Flores et al., 2023a). These skills are influenced by visual perception (spatial and attention skills) (Ansari et al., 2003; Gunderson et al., 2012; Mix and Cheng, 2012; Mix et al., 2016), the FMC (Dinehart and Manfra, 2013; Manfra et al., 2017; Osorio-Valencia et al., 2017; Suggate et al., 2017; Fischer et al., 2018, 2020; Kim et al., 2018; Greenburg et al., 2020) and GMS skills (Son and Meisels, 2006; Pagani et al., 2010; De Waal, 2019). Of all the processes that influence VMI, spatial skills are worked on in most of the activities proposed to preschool children for the development of mathematical concepts. Although there are several educational programs aimed at developing arithmetic skills in preschoolers (Elofsson et al., 2018), these programs include working on spatial skills using board games (Elofsson et al., 2016). In this sense, most of these activities are carried out in the classroom context only through the handling of small objects, without strong dependence on GMS (Elofsson et al., 2018).
VMI 技能已被证明与学龄前儿童的数学成绩最一致且最显著相关（Cameron 等人，2012 年;Carlson et al.， 2014;Grissmer et al.， 2014;Verdine et al.， 2014;Flores et al.， 2023a）。这些技能受视觉感知（空间和注意力技能）的影响（Ansari et al.， 2003;Gunderson等人，2012 年;Mix 和 Cheng，2012 年;Mix等人，2016 年）、FMC（Dinehart 和 Manfra，2013 年;Manfra等人，2017 年;Osorio-Valencia 等人，2017 年;Suggate et al.， 2017;Fischer 等人，2018 年、2020 年;Kim et al.， 2018;Greenburg等人，2020 年）和 GMS 技能（Son 和 Meisels，2006 年;Pagani et al.， 2010;De Waal，2019 年）。在影响 VMI 的所有过程中，为学龄前儿童提出的大多数活动都涉及空间技能，以发展数学概念。尽管有几个教育计划旨在培养学龄前儿童的算术技能（Elofsson et al.， 2018），但这些计划包括使用棋盘游戏来培养空间技能（Elofsson et al.， 2016）。从这个意义上说，这些活动中的大多数都是在课堂环境中仅通过处理小物体进行的，而没有对 GMS 的强烈依赖（Elofsson et al.， 2018）。

Given the significant association between GMS and VMI, the aim of this study was to propose a set of activities to develop spatial skills, with a strong participation of GMS in the classroom, playground or at home.
鉴于 GMS 和 VMI 之间的显著关联，本研究的目的是提出一系列活动来发展空间技能，GMS 在课堂、操场或家中都有很大的参与。

The inclusion of GMS is not only due to the fact that these skills contribute directly to the development of VMI skills, but is also justified by the fact that the main objective of this educational period is to contribute to the child’s overall development (Goodway et al., 2019; Haywood and Getchell, 2019). However, the reality is that the work on motor skills in preschool has not been highly valued, a fact that seems to be due to the common misconception that children develop their motor skills naturally (Escolano-Pérez et al., 2020). The truth is that the development of motor skills is related to practicing them (Logan et al., 2012; Pic et al., 2020). However, learning focuses primarily on academic content, limiting preschool children’s opportunities to develop motor skills in these educational environments (Cameron et al., 2016; Macdonald et al., 2020).
纳入 GMS 不仅是因为这些技能直接促进了 VMI 技能的发展，而且还因为这个教育时期的主要目标是促进儿童的全面发展（Goodway 等人，2019 年;Haywood 和 Getchell，2019 年）。然而，现实情况是，学前班运动技能的工作并未得到高度重视，这一事实似乎是由于普遍的误解，即儿童会自然发展他们的运动技能（Escolano-Pérez et al.， 2020）。事实是，运动技能的发展与练习它们有关（Logan et al.， 2012;Pic et al.， 2020）。然而，学习主要集中在学术内容上，限制了学龄前儿童在这些教育环境中发展运动技能的机会（Cameron et al.， 2016;Macdonald et al.， 2020）。

A meta-analysis of 50 studies showed that 25 of the studies reported a positive correlation between physical activity and math learning (Rasberry et al., 2011). Donelly and Lambourne (2011) revealed that students who integrated physical activity into their learning activities performed significantly better than the control group in mathematics. Studies have also shown that there is a correlation between children’s motor skills and mathematical performance (Lopes et al., 2013; Elofsson et al., 2018) and that children’s motor skills explained almost 16% of the variation in mathematical measures (Elofsson et al., 2018). Thus, a learning environment characterized by the inclusion of physical activity seems to have a positive effect on students’ general and specific learning of mathematics.
对 50 项研究的荟萃分析表明，其中 25 项研究报告了体育活动与数学学习之间存在正相关关系（Rasberry 等人，2011 年）。Donelly 和 Lambourne （2011） 揭示了将体育活动融入学习活动的学生在数学方面的表现明显优于对照组。研究还表明，儿童的运动技能和数学表现之间存在相关性（Lopes et al.， 2013;Elofsson等人，2018 年）儿童的运动技能解释了数学测量中近 16% 的差异（Elofsson et al.， 2018）。因此，以体育活动为特征的学习环境似乎对学生的一般和特定数学学习有积极影响。

Structured physical activity should be a routine part of the preschool curriculum (Escolano-Pérez et al., 2020). These activities should be taught primarily in a playful way, as this is the most natural way for children to learn and develop (Yu et al., 2018; Zosh et al., 2018).
结构化的体育活动应该是学前课程的常规部分（Escolano-Pérez et al.， 2020）。这些活动应该主要以游戏的方式教授，因为这是儿童学习和发展最自然的方式（Yu et al.， 2018;Zosh et al.， 2018）。

Educators often lament the lack of resources and materials available to implement practices that improve preschoolers’ motor skills (Robinson et al., 2012). In this sense, this article seeks to respond to the current need to present a set of practical motor activities that make it possible to work on spatial skills, with a strong participation of GMS and thus develop VMI skills and consequently mathematical skills.
教育工作者经常感叹缺乏可用的资源和材料来实施提高学龄前儿童运动技能的做法（Robinson 等人，2012 年）。从这个意义上说，本文旨在回应当前提出一系列实用运动活动的需求，这些活动可以在 GMS 的大力参与下锻炼空间技能，从而发展 VMI 技能，从而发展数学技能。

It will therefore be necessary for educators to increase play opportunities through physical activity programs to develop spatial skills, with a strong participation of the GMS, to ensure the development of VMI skills and thus contribute to the development of mathematical skills.
因此，教育工作者有必要通过体育活动计划来增加游戏机会，以发展空间技能，并在 GMS 的大力参与下，以确保 VMI 技能的发展，从而促进数学技能的发展。

5 Conclusion 5 总结

Since motor skills are not acquired innately, they must be learnt and practiced. In this study, the proposal to include gross motor skills in activities to develop visuomotor integration skills, namely spatial skills, will not only contribute to mathematical learning, but also the possibility of developing other coordinative and conditional physical skills, and contribute to the child’s health. In this sense, it is up to the teacher, depending on the material and spatial conditions, to select a set of activities, adjusted to the characteristics and abilities of the children, to develop visuomotor integration skills, through spatial skills, with a large involvement of gross motor skills.
由于运动技能不是天生获得的，因此必须学习和练习。在这项研究中，建议将粗大运动技能纳入发展视觉运动整合技能（即空间技能）的活动中，不仅有助于数学学习，还有助于发展其他协调和有条件的身体技能，并有助于孩子的健康。从这个意义上说，由教师根据材料和空间条件选择一组活动，根据孩子的特点和能力进行调整，通过空间技能发展视觉运动整合技能，并大量参与粗大运动技能。

Author contributions 作者贡献

PFl: Writing – original draft, Conceptualization. EC: Writing – review & editing, Supervision. MM-C: Writing – review & editing, Supervision. PFo: Writing – review & editing, Supervision.
PFl： 写作 – 原稿，概念化。EC：写作 - 审查和编辑，监督。MM-C：写作 - 审查和编辑，监督。PFo： 写作 - 审查和编辑，监督。

Funding 资金

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.
作者声明，未收到对本文的研究、作者身份和/或出版的财务支持。

Conflict of interest 利益冲突

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
作者声明，该研究是在没有任何可能被解释为潜在利益冲突的商业或财务关系的情况下进行的。

Publisher’s note 出版商注

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
本文中表达的所有声明仅代表作者的观点，并不一定代表其附属组织或出版商、编辑和审稿人的观点。本文中可能评估的任何商品或制造商可能提出的声明均不受出版商的保证或认可。

References 引用

Abe, M., and Hanakawa, T. (2009). Functional coupling underlying motor and cognitive functions of the dorsal premotor cortex. Behav. Brain Res. 198, 13–23. doi: 10.1016/j.bbr.2008.10.046
Abe， M. 和 Hanakawa， T. （2009）。背侧前运动皮层运动和认知功能背后的功能耦合。行为。大脑研究。198, 13–23.doi： 10.1016/j.bbr.2008.10.046

PubMed Abstract | Crossref Full Text | Google Scholar
PubMed 摘要 |Crossref 全文 |谷歌学术

Adolph, K. E. (2005). “Learning to learn in the development of action” in Action as an organizer of learning and development: Minnesota symposia on child psychology. eds. J. J. Rieser, J. J. Lockman, and C. A. Nelson (Mahwah, NJ: Erlbaum), 91–122.
阿道夫，KE（2005 年）。“在行动的发展中学习”，作为学习与发展的组织者行动：明尼苏达州儿童心理学研讨会。编辑 J. J. Rieser、J. J. Lockman 和 C. A. Nelson（新泽西州马瓦：Erlbaum），91-122。

Google Scholar 谷歌学术

Alvarez-Bueno, C., Pesce, C., Cavero-Redondo, I., Sánchez-López, M., Garrido Miguel, M., and Martínez-Vizcaíno, V. (2017). Academic achievement and physical activity: a meta-analysis. Pediatrics 140:e20171498. doi: 10.1542/peds.2017-1498
阿尔瓦雷斯-布埃诺，C.，佩谢，C.，卡维罗-雷东多，I.，桑切斯-洛佩斯，M.，加里多·米格尔，M.和马丁内斯-比斯卡伊诺，V.（2017 年）。学业成绩和身体活动：荟萃分析。儿科 140：e20171498。doi： 10.1542/peds.2017-1498

Crossref Full Text | Google Scholar
Crossref 全文 |谷歌学术

Anderson, J. R. (2000). Cognitive psychology and its implications. 5th Edn. New York: W.H. Freeman.
安德森，JR（2000 年）。认知心理学及其影响。第 5 版。纽约：W.H. Freeman。

Google Scholar 谷歌学术

Ansari, D., Donlan, C., Thomas, M. S. C., Ewing, S. A., Peen, T., and Karmiloff-Smith, A. (2003). What makes counting count? Verbal and visuo-spatial contributions to typical and atypical number development. J. Exp. Child Psychol. 85, 50–62. doi: 10.1016/S0022-0965(03)00026-2
安萨里，D.，唐兰，C.，托马斯，MSC，尤因，SA，皮恩，T.和卡米洛夫-史密斯，A.（2003 年）。什么让计数有意义？语言和视觉空间对典型和非典型数字发展的贡献。J. Exp. 儿童心理学。85, 50–62.doi： 10.1016/S0022-0965（03）00026-2

PubMed Abstract | Crossref Full Text | Google Scholar

Bachot, J., Gevers, W., Fias, W., and Roeyers, H. (2005). Number sense in children with visuospatial disabilities: orientation of the mental number line. Psychol. Sci. 47, 172–183,

Google Scholar

Bailey, D. H., Siegler, R. S., and Geary, D. C. (2014). Early predictors of middle school fraction knowledge. Dev. Sci. 17, 775–785. doi: 10.1111/desc.12155

PubMed Abstract | Crossref Full Text | Google Scholar

Barros, M., and Palhares, P. (2001). Emergência da matemática no jardim-de-infância. Porto: Porto Editora.

Google Scholar

Barth, H., Beckmann, L., and Spelke, E. S. (2008). Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction. Dev. Psychol. 44, 1466–1477. doi: 10.1037/a0013046

PubMed Abstract | Crossref Full Text | Google Scholar

Bayona, C. L., McDougall, J., Tucker, M. A., Nichols, M., and Mandich, A. (2006). School-based occupational therapy for children with fine motor difficulties: evaluating functional outcomes and fidelity of services. Phys. Occup. Ther. Pediatr. 26, 89–110. doi: 10.1300/J006v26n03_07

PubMed Abstract | Crossref Full Text | Google Scholar

Beck, D. M., Schaefer, C., Pang, K., and Carlson, S. M. (2011). Executive function in preschool children: test–retest reliability. J. Cogn. Dev. 12, 169–193. doi: 10.1080/15248372.2011.563485

PubMed Abstract | Crossref Full Text | Google Scholar

Becker, D. R., Miao, A., Duncan, R., and McClelland, M. M. (2014). Behavioral self-regulation and executive function both predict visuomotor skills and early academic achievement. Early Child. Res. Q. 29, 411–424. doi: 10.1016/j.ecresq.2014.04.014

Crossref Full Text | Google Scholar

Beery, K. E., and Beery, N. A. (2004). The Beery-Buktenica developmental test of visual-motor integration (Manual). Bloomington, MN: Pearson Assessments.

Google Scholar

Beery, K. E., and Beery, N. A. (2006). The Beery-Buktenica developmental test of visual-motor integration with supplemental developmental tests of visual perception and motor coordination: administration, scoring and teaching manual. 5th Edn: Pearson.

Google Scholar

Beery, K. E., and Beery, N. A. (2010). The Beery-Buktenica developmental test of visual-motor integration (Beery VMI): administration, scoring, and teaching manual. 6th Edn: Pearson.

Google Scholar

Beery, K. E., and Buktenica, N. A. (1997). The Beery-Buktenica developmental test of visual-motor integration: administration, scoring and teaching manual. 4th Edn. Parsippany, NJ: Modern Curriculum.

Google Scholar

Blair, C. (2010). Stress and the development of self-regulation in context. Child Dev. Perspect. 4, 181–188. doi: 10.1111/j.1750-8606.2010.00145.x

PubMed Abstract | Crossref Full Text | Google Scholar

Blair, C., and Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Dev. 78, 647–663. doi: 10.1111/j.1467-8624.2007.01019.x

PubMed Abstract | Crossref Full Text | Google Scholar

Brock, L. L., Kim, H., and Grissmer, D. W. (2018a). Longitudinal associations among executive function, visuomotor integration, and achievement in a high-risk sample. Mind Brain Educ. 12, 23–27. doi: 10.1111/mbe.12164

Crossref Full Text | Google Scholar

Brock, L. L., Murrah, W. M., Cottone, E. A., Mashburn, A. J., and Grissmer, D. W. (2018b). An after-school intervention targeting executive function and visuospatial skills also improves classroom behavior. Int. J. Behav. Dev. 42, 474–484. doi: 10.1177/0165025417738057

Crossref Full Text | Google Scholar

Bueti, D., and Walsh, V. (2009). The parietal cortex and representation of time, space, number and other magnitudes. Philos. Trans. R. Soc. Biol. Sci. 364, 1831–1840. doi: 10.1098/rstb.2009.0028

PubMed Abstract | Crossref Full Text | Google Scholar

Butterworth, B. (1999). A head for figures. Science 284, 928–929. doi: 10.1126/science.284.5416.928

Crossref Full Text | Google Scholar

Byers, A. I., Cameron, C. E., Michelle, K., LoCasale-Crouch, J., and Grissmer, D. W. (2016). What preschool classroom experiences ate associated with whether children improve in visuomotor integration? Early Educ. Dev. 27, 976–1003. doi: 10.1080/10409289.2016.1175243

Crossref Full Text | Google Scholar

Cameron, C. E., Brock, L., Hatfield, B., Cottone, E., Rubinstein, E., LoCasale-Crouch, J., et al. (2015). Visuomotor integration and inhibitory control compensate for each other in school readiness. Dev. Psychol. 51, 1529–1543. doi: 10.1037/a0039740

PubMed Abstract | Crossref Full Text | Google Scholar

Cameron, C. E., Brock, L. L., Murrah, W. M., Bell, L. H., Worzalla, S. L., Grissmer, D., et al. (2012). Fine motor skills and executive function both contribute to kindergarten achievement. Child Dev. 83, 1229–1244. doi: 10.1111/j.1467-8624.2012.01768.x

PubMed Abstract | Crossref Full Text | Google Scholar

Cameron, C. E., Cottone, E. A., Murrah, W. M., and Grissmer, D. W. (2016). How are motor skills linked to children’s school performance and academic achievement? Child Dev. Perspect. 10, 93–98. doi: 10.1111/cdep.12168

Crossref Full Text | Google Scholar

Cameron, C. E., Kim, H., Ducan, R., Becker, D., and McClelland, M. (2019). Bidirectional and co-developing association of cognitive, mathematics, and literacy skills during kindergarten. J. Appl. Dev. Psychol. 62, 135–144. doi: 10.1016/j.appdev.2019.02.004

Crossref Full Text | Google Scholar

Campos, J. J., Anderson, D. I., Barbu-Roth, M. A., Hubbard, E. M., Hertenstein, M. J., and Witherington, D. (2000). Travel broadens the mind. Infancy 1, 149–219. doi: 10.1207/S15327078IN0102_1

Crossref Full Text | Google Scholar

Canobi, K. H., and Bethune, N. E. (2008). Number words in young children’s conceptual and procedural knowledge of addition, subtraction, and inversion. Cognition 108, 675–686. doi: 10.1016/j.cognition.2008.05.011

PubMed Abstract | Crossref Full Text | Google Scholar

Carlson, A. G., Rowe, E. W., and Curby, T. W. (2013). Disentangling fine motor skills’ relation to academic achievement: the differential impact of visual-spatial integration and visual motor coordination. J. Genet. Psychol. 174, 514–533. doi: 10.1080/00221325.2012.717122

Crossref Full Text | Google Scholar

Case-Smith, J. (2002). Effectiveness of school-based occupational therapy intervention on handwriting. Am. J. Occup. Ther. 56, 17–25. doi: 10.5014/ajot.56.1.17

PubMed Abstract | Crossref Full Text | Google Scholar

Casey, B. M. (2004). “Mathematics problem-solving adventures: A language-arts-based supplementary series for early childhood that focuses on spatial sense” in Engaging young children in mathematics: Standards for early childhood mathematics education. eds. D. H. Clements, J. Sarama, and A.-M. DiBiase (Mahwah, NJ: Lawrence Erlbaum Associates, Publishers), 377–389.

Google Scholar

Casey, B. M., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., and Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cogn. Instr. 26, 269–309. doi: 10.1080/07370000802177177

Crossref Full Text | Google Scholar

Cheng, Y. L., and Mix, K. S. (2014). Spatial training improves children’s mathematics ability. J. Cogn. Dev. 15, 2–11. doi: 10.1080/15248372.2012.725186

Crossref Full Text | Google Scholar

Chernyak, N., Sandham, B., Harris, P. L., and Cordes, S. (2016). Numerical cognition explains age-related changes in third-party fairness. Dev. Psychol. 52, 1555–1562. doi: 10.1037/dev0000196

Crossref Full Text | Google Scholar

Clark, J. E. (2005). From the beginning: a developmental perspective on movement and mobility. Quest 57, 37–45. doi: 10.1080/00336297.2005.10491841

Crossref Full Text | Google Scholar

Clark, L., Shelley-Tremblay, J., and Cwikla, J. (2021). Shared developmental trajectories for fractional reasoning and fine motor ability in 4 and 5 year olds. Behav. Sci. 11:26. doi: 10.3390/bs11020026

PubMed Abstract | Crossref Full Text | Google Scholar

Clements, D. H., and Sarama, J. (2011). Early childhood teacher education: the case of geometry. J. Math. Teach. Educ. 14, 133–148. doi: 10.1007/s10857-011-9173-0

Crossref Full Text | Google Scholar

Clements, D. H., Sarama, J., and DiBiase, A. M. (2004). Engaging young children in mathematics: Standards for early childhood mathematics. Mahwah, NJ: Lawrence Erlbaum.

Google Scholar

Coutinho, P., Mesquita, I., Davids, K., Fonseca, A. M., and Côté, J. (2016). How structured and unstructured sport activities aid the development of expertise in volleyball players. Psychol. Sport Exerc. 25, 51–59. doi: 10.1016/j.psychsport.2016.04.004

Crossref Full Text | Google Scholar

Cragg, L., and Gilmore, C. (2014). Skills underlying mathematics: the role of executive function in the development of mathematics proficiency. Trends Neurosci. Educ. 3, 63–68. doi: 10.1016/j.tine.2013.12.001

Crossref Full Text | Google Scholar

Crollen, V., and Noël, M. P. (2015). The role of fingers in the development of counting and arithmetic skills. Acta Psychol. 156, 37–44. doi: 10.1016/j.actpsy.2015.01.007

PubMed Abstract | Crossref Full Text | Google Scholar

Cross, C. T., Woods, T. A., and Schweingruber, H. (2009). Mathematics learning in early childhood: paths toward excellence and equity. Washington, DC: National Academies Press.

Google Scholar

Daly, C. J., Kelley, G. T., and Krauss, A. (2003). Relationship between visual-motor integration and handwriting skills of children in kindergarten: a modified replication study. Am. J. Occup. Ther. 57, 459–462. doi: 10.5014/ajot.57.4.459

PubMed Abstract | Crossref Full Text | Google Scholar

Dankert, H. L., Davies, P. L., and Gavin, W. J. (2003). Occupational therapy effects on visual-motor skills in preschool children. Am. J. Occup. Ther. 57, 542–549. doi: 10.5014/ajot.57.5.542

PubMed Abstract | Crossref Full Text | Google Scholar

Dapp, L. C., Gashaj, V., and Roebers, C. M. (2021). Physical activity and motor skills in children: a differentiated approach. Psychol. Sport Exerc. 54:101916. doi: 10.1016/j.psychsport.2021.101916

Crossref Full Text | Google Scholar

Davis, J. L., and Matthews, R. N. (2010). Review of NEPSY-second edition (NEPSY-II). J. Psychoeduc. Assess. 28, 175–182. doi: 10.1177/0734282909346716

Crossref Full Text | Google Scholar

De Smedt, B., Noël, M. P., Gilmore, C., and Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends Neurosci. Educ. 2, 48–55. doi: 10.1016/j.tine.2013.06.001

Crossref Full Text | Google Scholar

De Waal, E. (2019). Fundamental movement skills and academic performance of 5- to 6-year-old preschoolers. Early Childhood Educ. J. 47, 455–464. doi: 10.1007/s10643-019-00936-6

Crossref Full Text | Google Scholar

Decker, S. L., England, J. A., Carboni, J. A., and Brooks, J. H. (2011). Cognitive and developmental influences in visual-motor integration skills in young children. Psychol. Assess. 23, 1010–1016. doi: 10.1037/a0024079

PubMed Abstract | Crossref Full Text | Google Scholar

Dehaene, S. (2011). The number sense: how the mind creates mathematics (rev upd p. 352). New York: Oxfrod Univeristy Press.

Google Scholar

Dehaene, S., and Cohen, L. (2007). Cultural recycling of cortical maps. Neuron 56, 384–398. doi: 10.1016/j.neuron.2007.10.004

PubMed Abstract | Crossref Full Text | Google Scholar

Dehaene, S., Molko, N., Cohen, L., and Wilson, A. J. (2004). Arithmetic and the brain. Curr. Opin. Neurobiol. 14, 218–224. doi: 10.1016/j.conb.2004.03.008

Crossref Full Text | Google Scholar

Department for Education (2020). Early years foundation stage profile: 2020 handbook. Department for Education: London.

Google Scholar

Diamond, A. (2000). Close interrelation of motor development and cognitive development and of the cerebellum and prefrontal cortex. Child Dev. 71, 44–56. doi: 10.1111/1467-8624.00117

PubMed Abstract | Crossref Full Text | Google Scholar

Diamond, A., and Lee, K. (2011). Interventions shown to aid executive function development in children 4-12 years old. Science 333, 959–964,

Google Scholar

Dinehart, L., and Manfra, L. (2013). Associations between low-income children's fine motor skills in preschool and academic performance in second grade. Early Educ. Dev. 24, 138–161. doi: 10.1080/10409289.2011.636729

Crossref Full Text | Google Scholar

Donelly, J. E., and Lambourne, K. (2011). Classroom-based physical activity, cognition, and academic achievement. Prev. Med. 52, S36–S42. doi: 10.1016/j.ypmed.2011.01.021

Crossref Full Text | Google Scholar

Duncan, G. J., Claessens, A., Magnuson, K., Klebanov, P., Pagani, L. S., Feinstein, L., et al. (2007). School readiness sand later achievement. Dev. Psychol. 43, 1428–1446. doi: 10.1037/0012-1649.43.6.1428

Crossref Full Text | Google Scholar

Duncan, M., Cunningham, A., and Eyre, E. (2019). A combined movement and story-telling intervention enhances motor competence and language ability in pre-schoolers to a greater extent than movement or story-telling alone. Eur. Phys. Educ. Rev. 25, 221–235. doi: 10.1177/1356336X17715772

Crossref Full Text | Google Scholar

Duran, C. A. K., Byers, A., Cameron, C. E., and Grissmer, D. (2018). Unique and compensatory associations of executive functioning and Visuomotor integration with mathematics performance in early elementary school. Early Child. Res. Q. 42, 21–30. doi: 10.1016/j.ecresq.2017.08.005

Crossref Full Text | Google Scholar

Elofsson, J., Bohm, A. E., Jeppsson, C., and Samuelsson, J. (2018). Physical activity and music to support pre-school children’s mathematics learning. Education 46, 483–493. doi: 10.1080/03004279.2016.1273250

Crossref Full Text | Google Scholar

Elofsson, J., Gustafsson, S., Samuelsson, J., and Träff, U. (2016). Playing number board games supports 5-year-old Children’s early mathematical development. J. Math. Behav. 43, 134–147. doi: 10.1016/j.jmathb.2016.07.003

Crossref Full Text | Google Scholar

Escolano-Pérez, E., Herrero-Nivela, M. L., and Losada, J. L. (2020). Association between preschoolers’ specific fine (but not gross) motor skills and later academic competencies: educational implications. Front. Psychol. 11:1044. doi: 10.3389/fpsyg.2020.01044

PubMed Abstract | Crossref Full Text | Google Scholar

Essame, C. (2023). Why play matters: 101 activities for developmental play to support young children : Routledge.

Google Scholar

Fang, Y., Wang, J., Zhang, Y., and Qin, J. (2017). The relationship of motor coordination, visual perception, and executive function to the development of 4-6-year-old Chinese preschoolers’ visual motor integration skills. Biomed. Res. Int. 2017, 42–54. doi: 10.1155/2017/6264254

PubMed Abstract | Crossref Full Text | Google Scholar

Fischer, M. H. (2008). Finger counting habits modulate spatial numerical associations. Cortex 44, 386–392. doi: 10.1016/j.cortex.2007.08.004

PubMed Abstract | Crossref Full Text | Google Scholar

Fischer, M. H., and Brugger, P. (2011). When digits help digits: spatial-numerical associations point to finger counting as prime example of embodied cognition. Front. Psychol. 2:260. doi: 10.3389/fpsyg.2011.00260

PubMed Abstract | Crossref Full Text | Google Scholar

Fischer, U., Suggate, S. P., Schmirl, J., and Stoeger, H. (2018). Counting on fine motor skills: links between preschool finger dexterity and numerical skills. Dev. Sci. 21:e12623. doi: 10.1111/desc.12623

PubMed Abstract | Crossref Full Text | Google Scholar

Fischer, U., Suggate, S. P., and Stoeger, H. (2020). The implicit contribution of fine motor skills to mathematical insight in early childhood. Front. Psychol. 11:1143. doi: 10.3389/fpsyg.2020.01143

PubMed Abstract | Crossref Full Text | Google Scholar

Flatters, I., Mushtaq, F., Hill, L. J. B., Rossiter, A., Jarrett-Peet, K., Culmer, P., et al. (2014). Children’s head movements and postural stability as a function of task. Exp. Brain Res. 232, 1953–1970. doi: 10.1007/s00221-014-3886-0

PubMed Abstract | Crossref Full Text | Google Scholar

Flores, P., Coelho, E., Mourão-Carvalhal, M. I., and Forte, P. (2023a). Association between motor and math skills in preschool children with typical development: systematic review. Front. Psychol. 14:1105391. doi: 10.3389/fpsyg.2023.1105391

PubMed Abstract | Crossref Full Text | Google Scholar

Flores, P., Coelho, E., Mourão-Carvalhal, M. I., and Forte, P. (2023b). Relationships between math skills, motor skills, physical activity, and obesity in typically developing preschool children. Behav. Sci. :1000:13. doi: 10.3390/bs13121000

Crossref Full Text | Google Scholar

Flores, P., and Magalhães, M. (2019). Exercitar para Aprender. Lisboa: Chiado Editora.

Google Scholar

Floyer-Lea, A., and Matthews, P. M. (2004). Changing brain networks for visuomotorcontrol with increased movement automaticity. J. Neurophysiol. 92, 2405–2412. doi: 10.1152/jn.01092.2003

PubMed Abstract | Crossref Full Text | Google Scholar

Fonseca, V. (2010). Manual de Observação Psicomotora: Significação Psiconeurológica dos seus Factores. 3rd Edn. Lisboa: Âncora Editora.

Google Scholar

Frick, A., Möhring, W., and Newcombe, N. S. (2014). Development of mental transformation abilities. Trends Cogn. Sci. 18, 536–542. doi: 10.1016/j.tics.2014.05.011

Crossref Full Text | Google Scholar

Geist, E. (2009). Children are born mathematicans - supporting mathematical development, birth to age 8. Columbus: Pearson.

Google Scholar

Gelman, R., and Williams, E. M. (1997). “Enabling constraints for cognitive development and learning: domain specificity and epigenesis” in Cognition, perception, and language, volume 2: handbook of child psychology. eds. D. Kuhn and R. Siegler. 5th ed (New York: Wiley), 575–630.

Google Scholar

Ginsburg, H. P. (1977). Children’s arithmetic: the learning processitle. Oxford: D. Van Nostrand.

Google Scholar

Ginsburg, H. P., Kaplan, R. G., Cannon, J., Cordero, M. I., Eisenband, J. G., Galanter, M., et al. (2006). “Helping early childhood educators to teach mathematics” in Critical issues in early childhood professional development. eds. M. Zaslow and I. Martinez-Beck (Paul H. Brookes: Baltimore, MD), 171–202.

Google Scholar

Goodway, J., Ozmun, J., and Gallahue, D. (2019). Understanding motor development: infants, children, adolescents, adults. 8th Edn. Burlington, MA: Jones & Bartlett Learning.

Google Scholar

Gopnik, A., and Meltzoff, A. N. (1986). “Words, plans, things, and locations: interactions between semantic and cognitive development in the one-word stage” in The development of word meaning. eds. A. I. I. KuczajS and M. D. Barrett (Berlin: Springer-Verlag), 199–223.

Google Scholar

Greenburg, J. E., Carlson, A. G., Kim, H., Curby, T. W., and Winsler, A. (2020). Early visual-spatial integration skills predict elementary school achievement among low-income, ethnically diverse children. Early Educ. Dev. 31, 304–322. doi: 10.1080/10409289.2019.1636353

Crossref Full Text | Google Scholar

Greenes, C., Ginsburg, H. P., and Balfanz, R. (2004). Big math for little kids. Early Child. Res. Q. 19, 159–166. doi: 10.1016/j.ecresq.2004.01.010

Crossref Full Text | Google Scholar

Grissmer, D., Grimm, K. J., Aiyer, S. M., Murrah, W. M., and Steele, J. S. (2010). Fine motor skills and early comprehension of the world: two new school readiness indicators. Dev. Psychol. 46, 1008–1017. doi: 10.1037/a0020104

PubMed Abstract | Crossref Full Text | Google Scholar

Grissmer, D. W., Mashburn, A. J., Cottone, E., Chen, W. B., Brock, L. L., Murrah, W. M., et al. (2013). Play-based afterschool curriculum improves measures of executive function, visuospatial and math skills and classroom behavior for high risk K-1 children. Seattle, WA: Presented at the Society for Research in Child Development.

Google Scholar

Groth-Marnat, G., and Teal, M. (2000). Block design as a measure of everyday spatial ability: a study of ecological validity. Percept. Mot. Skills 90, 522–526. doi: 10.2466/pms.2000.90.2.522

PubMed Abstract | Crossref Full Text | Google Scholar

Gunderson, E. A., Ramirez, G., Beilock, S. L., and Levine, S. C. (2012). The relation between spatial skill and early number knowledge: the role of the linear number line. Dev. Psychol. 48, 1229–1241. doi: 10.1037/a0027433

PubMed Abstract | Crossref Full Text | Google Scholar

Hansel, R. R. (2021). Exploring the 3-D world: developing spatial and math skills for young children : Redleaf Press.

Google Scholar

Hawes, Z., LeFevre, J. A., Xu, C., and Bruce, C. D. (2015). Mental rotation with tangible three-dimensional objects: a new measure sensitive to developmental differences in 4-to 8-year-old children. Mind Brain Educ. 9, 10–18. doi: 10.1111/mbe.12051

Crossref Full Text | Google Scholar

Hawes, Z., Moss, J., Caswell, B., Naqvi, S., and MacKinnon, S. (2017). Enhancing children's spatial and numerical skills through a dynamic spatial approach to early geometry instruction: effects of a 32-week intervention. Cogn. Instr. 35, 236–264. doi: 10.1080/07370008.2017.1323902

Crossref Full Text | Google Scholar

Haywood, K. M., and Getchell, N. (2019). Life span motor development. 7th Edn. Champaign, IL: Human Kinetics.

Google Scholar

Hegarty, M., and Waller, D. (2004). A dissociation between mental rotation and perspective-taking. Intelligence 32, 175–191. doi: 10.1016/j.intell.2003.12.001

Crossref Full Text | Google Scholar

Herbers, J. E., Cutuli, J. J., Lafavor, T. L., Vrieze, D., Leibel, C., Obradović, J., et al. (2011). Direct and indirect effects of parenting on the academic functioning of young homeless children. Early Educ. Dev. 22, 77–104. doi: 10.1080/10409280903507261

Crossref Full Text | Google Scholar

Hoenisch, N., and Niggemeyer, E. (2007). Mathe-kings: Junge kinder fassen Mathematik an : Verlag Das Netz.

Google Scholar

Hohmann, M., and Weikart, D. P. (2002). Educating young children: Active learning practices for preschool and child care. 2nd Edn. Ypsilanti, MI: High/Scope Press.

Google Scholar

Holmes, J., Adams, J. W., and Hamilton, C. J. (2008). The relationship between visuospatial sketchpad capacity and children’s mathematical skills. Eur. J. Cogn. Psychol. 20, 272–289. doi: 10.1080/09541440701612702

Crossref Full Text | Google Scholar

Hornung, C., Brunner, M., Reuter, R. A. P., and Martin, R. (2011). Children’s working memory: its structure and relationship to fluid intelligence. Intelligence 39, 210–221. doi: 10.1016/j.intell.2011.03.002

Crossref Full Text | Google Scholar

Hraste, M., De Giorgio, A., Jelaska, P. M., Padulo, J., and Granić, I. (2018). When mathematics meets physical activity in the school-aged child: the effect of an integrated motor and cognitive approach to learning geometry. PLoS One 13:e0196024. doi: 10.1371/journal.pone.0196024

PubMed Abstract | Crossref Full Text | Google Scholar

Hubbard, E. M., Piazza, M., Pinel, P., and Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nat. Rev. Neurosci. 6, 435–448. doi: 10.1038/nrn1684

Crossref Full Text | Google Scholar

Hubbard, E. M., Piazza, M., Pinel, P., and Dehaene, S. (2009). “Numerical and spatial intuitions: a role for posterior parietal cortex?” in Cognitive biology: evolutionary and developmental perspectives on mind, brain and behavior. eds. L. Tommasi, L. Nadel, and M. A. Peterson (Cambridge, MA: MIT Press), 221–246.

Google Scholar

Hudson, K. N., Ballou, H. M., and Willoughby, M. T. (2021). Short report: Improving motor competence skills in early childhood has corollary benefits for executive function and numeracy skills. Developmental Science 2021:e13071. doi: 10.1111/desc.13071

Crossref Full Text | Google Scholar

Hyde, D. C. (2011). Two systems of non-symbolic numerical cognition. Front. Hum. Neurosci. 5:150. doi: 10.3389/fnhum.2011.00150

PubMed Abstract | Crossref Full Text | Google Scholar

Jones, D., Innerd, A., Giles, E. L., and Azevedo, L. B. (2021). The association between physical activity, motor skills and school readiness in 4–5-year-old children in the northeast of England. Int. J. Environ. Res. Public Health 18:11931. doi: 10.3390/ijerph182211931

PubMed Abstract | Crossref Full Text | Google Scholar

Jones, S. S., and Smith, L. B. (2002). How children know the relevant properties for generalizing object names. Dev. Sci. 5, 219–232. doi: 10.1111/1467-7687.00224

Crossref Full Text | Google Scholar

Jordan, N. C., Glutting, J., Dyson, N., Hassinger-Das, B., and Irwin, C. (2012). Building kindergartners’ number sense: a randomized controlled study. J. Educ. Psychol. 104, 647–660. doi: 10.1037/a0029018

PubMed Abstract | Crossref Full Text | Google Scholar

Khng, K. H., and Ng, E. L. (2021). Fine motor and executive functioning skills predict maths and spelling skills at the start of kindergarten: a compensatory account. Infan. Aprend. 44, 675–718. doi: 10.1080/02103702.2021.1897232

Crossref Full Text | Google Scholar

Kim, H., Byers, A. I., Cameron, C. E., Brock, L. L., Cottone, E. A., and Grissmer, D. W. (2016). Unique contributions of attentional control and visuomotor integration on concurrent teacher-reported classroom functioning in early elementary students. Early Child. Res. Q. 36, 379–390. doi: 10.1016/j.ecresq.2016.01.018

Crossref Full Text | Google Scholar

Kim, H., Duran, C. A. K., Cameron, C. E., and Grissmer, D. (2018). Developmental relations among motor and cognitive processes and mathematics skills. Child Dev. 89, 476–494. doi: 10.1111/cdev.12752

PubMed Abstract | Crossref Full Text | Google Scholar

Kim, H., Murrah, W. M., Cameron, C. E., Brock, L. L., Cottone, E. A., and Grissmer, D. (2015). Psychometric properties of the teacher-reported motor skills rating scale. J. Psychoeduc. Assess. 33, 640–651. doi: 10.1177/0734282914551536

Crossref Full Text | Google Scholar

Kimmel, S. R., and Ratliff-Schaub, K. (2011). “Growth and development” in Textbook of family medicine. ed. R. E. Rakel . 8th ed (Philadelphia, PA: Saunders Elsevier), 421–441.

Google Scholar

Klein, A., and Starkey, P. (2002). Pre-K mathematics curriculum. Glenview, IL: Scott Foresman.

Google Scholar

Kokstejn, J., Musálek, M., and Tufano, J. J. (2017). Are sex differences in fundamental motor skills uniform throughout the entire preschool period? PLoS One 12:e0176556. doi: 10.1371/journal.pone.0176556

PubMed Abstract | Crossref Full Text | Google Scholar

Korkman, M., Kirk, U., and Kemp, S. (1998). NEPSY: a developmental neuropsychological assessment : Psychological Corp.

Google Scholar

Lauer, J. E., and Lourenco, S. F. (2016). Spatial processing in infancy predicts both spatial and mathematical aptitude in childhood. Psychol. Sci. 27, 1291–1298. doi: 10.1177/0956797616655977

PubMed Abstract | Crossref Full Text | Google Scholar

Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. Int. J. Early Child. 42, 27–41. doi: 10.1007/s13158-010-0003-9

Crossref Full Text | Google Scholar

Lefevre, J. A., Berrigan, L., Vendetti, C., Kamawar, D., Bisanz, J., Skwarchuk, S. L., et al. (2013). The role of executive attention in the acquisition of mathematical skills for children in grades 2 through 4. J. Exp. Child Psychol. 114, 243–261. doi: 10.1016/j.jecp.2012.10.005

PubMed Abstract | Crossref Full Text | Google Scholar

LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., et al. (2010). Pathways to mathematics: longitudinal predictors of performance. Child Dev. 81, 1753–1767. doi: 10.1111/j.1467-8624.2010.01508.x

PubMed Abstract | Crossref Full Text | Google Scholar

Link, T., Moeller, K., Huber, S., Fischer, U., and Nuerk, H. (2013). Walk the numberline an embodied training of numerical concepts. Trends Neurosci. Educ. 2, 74–84. doi: 10.1016/j.tine.2013.06.005

Crossref Full Text | Google Scholar

Logan, S. W., Robinson, L. E., Wilson, A. E., and Lucas, W. A. (2012). Getting the fundamentals of movement: a meta-analysis of the effectiveness of motor skill interventions in children. Child Care Health Dev. 38, 305–315. doi: 10.1111/j.1365-2214.2011.01307.x

PubMed Abstract | Crossref Full Text | Google Scholar

Lopes, L., Santos, R., Pereira, B., and Lopes, V. P. (2013). Associations between gross motor coordination and academic achievement in elementary school children. Hum. Mov. Sci. 32, 9–20. doi: 10.1016/j.humov.2012.05.005

PubMed Abstract | Crossref Full Text | Google Scholar

Luo, Z., Jose, P., Huntsinger, C., and Pigott, T. (2007). Fine motor skills and mathematics achievement in east Asian American and European American kindergartners and first graders. Br. J. Dev. Psychol. 25, 595–614. doi: 10.1348/026151007X185329

Crossref Full Text | Google Scholar

Macdonald, K., Milne, N., Orr, R., and Pope, R. (2018). Relationships between motor proficiency and academic performance in mathematics and reading in school-aged children and adolescents: a systematic review. Int. J. Environ. Res. Public Health 15, 1–28. doi: 10.3390/ijerph15081603

Crossref Full Text | Google Scholar

Macdonald, K., Milne, N., Orr, R., and Pope, R. (2020). Associations between motor proficiency and academic performance in mathematics and reading in year 1 school children: a cross-sectional study. BMC Pediatr. 20:69. doi: 10.1186/s12887-020-1967-8

PubMed Abstract | Crossref Full Text | Google Scholar

Magistro, D., Bardaglio, G., and Rabaglietti, E. (2015). Gross motor skills and academic achievement in typically developing children: the mediating effect of ADHD related behaviours. Cogn. Brain Behav. 19, 149–163,

Google Scholar

Malambo, C., Nová, A., Clark, C., and Musálek, M. (2022). Associations between fundamental movement skills, physical fitness, motor competency, physical activity, and executive functions in pre-school age children: a systematic review. Children 9:1059. doi: 10.3390/children9071059

PubMed Abstract | Crossref Full Text | Google Scholar

Manfra, L., Squires, C., Dinehart, L., Bleiker, C., Hartman, S., and Winsler, A. (2017). Preschool writing and premathematics predict grade 3 achievement for low-income, ethnically diverse children. J. Educ. Res. 110, 528–537. doi: 10.1080/00220671.2016.1145095

Crossref Full Text | Google Scholar

Marr, D., Cermak, S., Cohn, E. S., and Henderson, A. (2003). Fine motor activities in head start and kindergarten classrooms. Am. J. Occup. Ther. 57, 550–557. doi: 10.5014/ajot.57.5.550

PubMed Abstract | Crossref Full Text | Google Scholar

Mata, R., von Helversen, B., and Rieskamp, J. (2011). When easy comes hard: the development of adaptive strategy selection. Child Dev. 82, 687–700. doi: 10.1111/j.1467-8624.2010.01535.x

PubMed Abstract | Crossref Full Text | Google Scholar

McWayne, C. M., Fantuzzo, J. W., and McDermott, P. A. (2004). Preschool competency in context: an investigation of the unique contribution of child competencies to early academic success. Dev. Psychol. 40, 633–645. doi: 10.1037/0012-1649.40.4.633

PubMed Abstract | Crossref Full Text | Google Scholar

Memisevic, H., and Hadzic, S. (2013). Development of fine motor coordination and visual-motor integration in preschool children. J. Spec. Educ. Rehabil. 14, 45–53. doi: 10.2478/v10215-011-0032-4

Crossref Full Text | Google Scholar

Meyer, M. L., Salimpoor, V. N., Wu, S. S., Geary, D. C., and Menon, V. (2010). Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders. Learn. Individ. Differ. 20, 101–109. doi: 10.1016/j.lindif.2009.08.004

PubMed Abstract | Crossref Full Text | Google Scholar

Mix, K. S., and Cheng, Y. L. (2012). The relation between space and math: developmental and educational implications. Adv. Child Dev. Behav. 42, 197–243. doi: 10.1016/B978-0-12-394388-0.00006-X

Crossref Full Text | Google Scholar

Mix, K. S., Levine, S., Cheng, Y.-L., Young, C., Hambrick, D., Ping, R., et al. (2016). Separate but correlated: the latent structure of space and mathematics across development. J. Exp. Psychol. Gen. 145, 1206–1227. doi: 10.1037/xge0000182

PubMed Abstract | Crossref Full Text | Google Scholar

Moss, J., Bruce, C. D., Caswell, B., Flynn, T., and Hawes, Z. (2016). Taking shape: activities to develop geometric and spatial thinking: grades K-2. Toronto, ON: Pearson Canada.

Google Scholar

Moss, J., Hawes, Z., Naqvi, S., and Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study. ZDM Math. Educ. 47, 377–390. doi: 10.1007/s11858-015-0679-2

Crossref Full Text | Google Scholar

Mujkic, A., and Papric, Z. (2013). The influence of the exercises of gross and fine motor skills on visuo-motor coordination of the cerebral palsy children. Hum. J. Interdiscip. Stud. 3, 19–22. doi: 10.21554/hrr.091301

Crossref Full Text | Google Scholar

Mullet, E., and Paques, P. (1991). The height + width = area of a rectangle rule in five-year olds: effects of stimulus distribution and graduation of the response scale. J. Exp. Child Psychol. 52, 336–343. doi: 10.1016/0022-0965(91)90067-3

PubMed Abstract | Crossref Full Text | Google Scholar

Naqvi, S., Hawes, Z., Chang, D., and Moss, J. (2013). “Exploring pentominoes in 7 diverse pre-k/K classrooms” in Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. eds. M. Martinez and A. Castro Superfine (Chicago, IL: University of Illinois at Chicago).

Google Scholar

National Council of Teachers of Mathematics (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: a quest for coherence. Reston, VA: National Council of Teachers of Mathematics.

Google Scholar

National Research Council (2009). Mathematics learning in early childhood: paths toward excellence and equity. Washington, DC: The National Academies Press.

Google Scholar

Nesbitt, K. T., Fuhs, M. W., and Farran, D. C. (2019). Stability and instability in the co-development of mathematics, executive function skills, and visual-motor integration from prekindergarten to first grade. Early Child. Res. Q. 46, 262–274. doi: 10.1016/j.ecresq.2018.02.003

Crossref Full Text | Google Scholar

Newcombe, N. S., and Frick, A. (2010). Early education for spatial intelligence: why,what, and how. Mind Brain Educ. 4, 102–111. doi: 10.1111/j.1751-228X.2010.01089.x

Crossref Full Text | Google Scholar

Newcombe, N. S., Uttal, D. H., and Sauter, M. (2013). “Spatial development” in Oxford handbook of developmental psychology. ed. P. D. Zelazo (Oxford University Press). 564–590.

Google Scholar

Nosworthy, N., Bugden, S., Archibald, L., Evans, B., and Ansari, D. (2013). A two-minute paper-and-pencil test of symbolic and nonsymbolic numerical magnitude processing explains variability in primary school children’s arithmetic competence. PLoS One 8:e67918. doi: 10.1371/journal.pone.0067918

PubMed Abstract | Crossref Full Text | Google Scholar

Oberer, N., Gashaj, V., and Roebers, C. M. (2017). Motor skills in kindergarten: internal structure, cognitive correlates and relationships to background variables. Hum. Mov. Sci. 52, 170–180. doi: 10.1016/j.humov.2017.02.002

PubMed Abstract | Crossref Full Text | Google Scholar

Osborn, A., Butler, N., and Morris, A. (1984). The social life of Britain’s five year olds: a report of the child health and education study. London: Routledge and Kegan Paul.

Google Scholar

Osorio-Valencia, E., Torres-Sánchez, L., López-Carrillo, L., Rothenberg, S. J., and Schnaas, L. (2017). Early motor development and cognitive abilities among Mexican preschoolers. Child Neuropsychol. 24, 1015–1025. doi: 10.1080/09297049.2017.1354979

PubMed Abstract | Crossref Full Text | Google Scholar

Pagani, L., Fitzpatrick, C., Archambault, I., and Janosz, M. (2010). School readiness and later achievement: a French Canadian replication and extension. Dev. Psychol. 46, 984–994. doi: 10.1037/a0018881

Crossref Full Text | Google Scholar

Parsons, S., and Bynner, J. (2005). Does numeracy matter more? London: National Research and Development Centre for Adult Literacy and Numeracy.

Google Scholar

Parush, S., and Hahn-Markowitz, J. (1997). A comparison of two settings for group treatment in promoting perceptual-motor function of learning disabled children. Phys. Occup. Ther. Pediatr. 17, 45–57. doi: 10.1080/J006v17n01_03

Crossref Full Text | Google Scholar

Passolunghi, M. C., and Mammarella, I. C. (2012). Selective spatial working memory impairment in a group of children with mathematics learning disabilities and poor problem-solving skills. J. Learn. Disabil. 45, 341–350. doi: 10.1177/0022219411400746

PubMed Abstract | Crossref Full Text | Google Scholar

Payne, V. G., and Isaacs, L. D. (2012). Human motor development. Mc Graw Hill-Connect Learn Succeed, McGraw-Hill Education.

Google Scholar

Pic, M., Navarro-Adelantado, V., and Jonsson, G. K. (2018). Detection of ludic patterns in two triadic motor games and differences in decision complexity. Front. Psychol. 8:2259. doi: 10.3389/fpsyg.2017.02259

PubMed Abstract | Crossref Full Text | Google Scholar

Pic, M., Navarro-Adelantado, V., and Jonsson, G. K. (2020). Gender differences in strategic behavior in a triadic persecution motor game identified through an observational methodology. Front. Psychol. 11:109. doi: 10.3389/fpsyg.2020.00109

PubMed Abstract | Crossref Full Text | Google Scholar

Piek, J. P., Baynam, G. B., and Barrett, N. C. (2006). The relationship between fine and gross motor ability, self-perceptions and self-worth in children and adolescents. Hum. Mov. Sci. 25, 65–75. doi: 10.1016/j.humov.2005.10.011

Crossref Full Text | Google Scholar

Pruden, S. M., Levine, S. C., and Huttenlocher, J. (2011). Children's spatial thinking: does talk about the spatial world matter? Dev. Sci. 14, 1417–1430. doi: 10.1111/j.1467-7687.2011.01088.x

PubMed Abstract | Crossref Full Text | Google Scholar

Puranik, C. S., and Lonigan, C. J. (2012). Name-writing proficiency, not length of name, is associated with preschool children's emergent literacy skills. Early Child. Res. Q., 27, 284–294. doi: 10.1016/j.ecresq.2011.09.003

Crossref Full Text | Google Scholar

Rasberry, N. C., Lee, S. M., Robin, L., Laris, B. A., Russell, L. A., Coyle, K. K., et al. (2011). The association between school-based physical activity, including physical education, and academic performance: a systematic review of the literature. Prev. Med. 52, S10–S20. doi: 10.1016/j.ypmed.2011.01.027

PubMed Abstract | Crossref Full Text | Google Scholar

Ratzon, N. Z., Efraim, D., and Bart, O. (2007). A short-term graphomotor program for improving writing readiness skills of first-grade students. Am. J. Occup. Ther. 61, 399–405. doi: 10.5014/ajot.61.4.399

PubMed Abstract | Crossref Full Text | Google Scholar

Ratzon, N. Z., Lahav, O., Cohen-Hamsi, S., Metzger, Y., Efraim, D., and Bart, O. (2009). Comparing different short-term service delivery methods of visual-motor treatment for first grade students in mainstream schools. Res. Dev. Disabil. 30, 1168–1176. doi: 10.1016/j.ridd.2009.03.008

PubMed Abstract | Crossref Full Text | Google Scholar

Ritchie, S. J., and Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychol. Sci. 24, 1301–1308. doi: 10.1177/0956797612466268

PubMed Abstract | Crossref Full Text | Google Scholar

Rittle-Johnson, B., Zippert, E. L., and Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Child Res. Q. 46, 166–178. doi: 10.1016/j.ecresq.2018.03.006

Crossref Full Text | Google Scholar

Robinson, L. E., Stodden, D. F., Barnett, L. M., Lopes, V. P., Logan, S. W., Rodrigues, L. P., et al. (2015). Motor competence and its effect on positive developmental trajectories of health. Sports Med. 45, 1273–1284. doi: 10.1007/s40279-015-0351-6

PubMed Abstract | Crossref Full Text | Google Scholar

Robinson, L. E., Webster, E. K., Logan, S., Lucas, W. A., and Barber, L. T. (2012). Exploring preschoolers’ engagement and perceived physical competence in an autonomy-based object control skill intervention: a preliminary study. Eur. Phys. Educ. Rev. 19, 302–314. doi: 10.1177/1356336x13495627

Crossref Full Text | Google Scholar

Roebers, C. M., and Kauer, M. (2009). Motor and cognitive control in a normative sample of 7-year-olds. Dev. Sci. 12, 175–181. doi: 10.1111/j.1467-7687.2008.00755.x

PubMed Abstract | Crossref Full Text | Google Scholar

Roebers, C. M., Röthlisberger, M., Neuenschwander, R., Cimeli, P., Michel, E., and Jäger, K. (2014). The relation between cognitive and motor performance and their relevance for children's transition to school: a latent variable approach. Hum. Mov. Sci. 33, 284–297. doi: 10.1016/j.humov.2013.08.011

PubMed Abstract | Crossref Full Text | Google Scholar

Sarama, J., and Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Child. Res. Q. 19, 181–189. doi: 10.1016/j.ecresq.2004.01.014

Crossref Full Text | Google Scholar

Sarama, J., Clements, D. H., and Vukelic, E. B. (1996). The role of a computer manipulative in fostering specific psychological/mathematical processes. in Proceedings of the 18th Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education (2)eds. E. Jakubowski, D. Watkins, and H. Biske, Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education, 567–572.

Google Scholar

Sarnecka, B. W., and Carey, S. (2008). How counting represents number: what children must learn and when they learn it. Cognition 108, 662–674. doi: 10.1016/j.cognition.2008.05.007

Crossref Full Text | Google Scholar

Silva, I., Marques, L., Mata, L., and Rosa, M. (2016). Orientações curriculares para a educação pré-escolar. Lisboa: Ministério da Educação.

Google Scholar

Skagerlund, K., and Träff, U. (2016). Processing of space, time, and number contributes to mathematical abilities above and beyond domain-general cognitive abilities. J. Exp. Child Psychol. 143, 85–101. doi: 10.1016/j.jecp.2015.10.016

PubMed Abstract | Crossref Full Text | Google Scholar

Smith, L. (2005). Cognition as a dynamic system: principles from embodiment. Dev. Rev. 25, 278–298. doi: 10.1016/j.dr.2005.11.001

Crossref Full Text | Google Scholar

Son, S. H., and Meisels, S. J. (2006). The relationship of young children’s motor skills to later reading and math achievement. Merrill Palmer Q. 52, 755–778. doi: 10.1353/mpq.2006.0033

Crossref Full Text | Google Scholar

Sortor, J. M., and Kulp, M. T. (2003). Are the results of the beery-buktenica developmental test of visual-motor integration and its subtests related to achievement test scores? Optom. Vis. Sci. 80, 758–763. doi: 10.1097/00006324-200311000-00013

PubMed Abstract | Crossref Full Text | Google Scholar

Soylu, F., and Newman, S. D. (2016). Anatomically ordered tapping interferes more with one-digit addition than two-digit addition: a dual-task fMRI study. Cogn. Process. 17, 67–77. doi: 10.1007/s10339-015-0737-2

PubMed Abstract | Crossref Full Text | Google Scholar

Spodek, B. (2002). Manual de Investigação em Educação de Infância. Lisboa: Fundação Calouste Gulbenkian.

Google Scholar

St Clair-Thompson, H. L., and Gathercole, S. E. (2006). Executive functions and achievements in school: shifting, updating, inhibition, and working memory. Q. J. Exp. Psychol. 59, 745–759. doi: 10.1080/17470210500162854

PubMed Abstract | Crossref Full Text | Google Scholar

Starr, A., Libertus, M. E., and Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proc. Natl. Acad. Sci. USA 110, 18116–18120. doi: 10.1073/pnas.1302751110

PubMed Abstract | Crossref Full Text | Google Scholar

Suggate, S., Pufke, E., and Stoeger, H. (2018). Do fine motor skills contribute to early reading development? J. Res. Read. 41, 1–19. doi: 10.1111/1467-9817.12081

Crossref Full Text | Google Scholar

Suggate, S., Stoeger, H., and Fischer, U. (2017). Finger-based numerical skills link fine motor skills to numerical development in preschoolers. Percept. Mot. Skills 124, 1085–1106. doi: 10.1177/0031512517727405

PubMed Abstract | Crossref Full Text | Google Scholar

Szucs, D., Devine, A., Soltesz, F., Nobes, A., and Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex 49, 2674–2688. doi: 10.1016/j.cortex.2013.06.007

PubMed Abstract | Crossref Full Text | Google Scholar

Taylor, H. A., and Hutton, A. (2013). Think3d!: training spatial thinking fundamental to STEM education. Cogn. Instr. 31, 434–455. doi: 10.1080/07370008.2013.828727

Crossref Full Text | Google Scholar

Tseng, M., and Chow, S. (2000). Perceptual motor function of school-aged children with slow handwriting speed. Am. J. Occup. Ther. 54, 83–88. doi: 10.5014/ajot.54.1.83

PubMed Abstract | Crossref Full Text | Google Scholar

Uttal, D. H., and Cohen, C. A. (2012). Spatial thinking and STEM education: when, why and how. Psychol. Learn. Motiv. 57, 147–181. doi: 10.1016/B978-0-12-394293-7.00004-2

Crossref Full Text | Google Scholar

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., et al. (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychol. Bull. 139, 352–402. doi: 10.1037/a0028446

PubMed Abstract | Crossref Full Text | Google Scholar

van der Fels, I. M., Te Wierike, S. C., Hartman, E., Elferink-Gemser, M. T., Smith, J., and Visscher, C. (2015). The relationship between motor skills and cognitive skills in 4-16 year old typically developing children: a systematic review. J. Sci. Med. Sport 18, 697–703. doi: 10.1016/j.jsams.2014.09.007

PubMed Abstract | Crossref Full Text | Google Scholar

Van Wyk, Y., Pienaar, A. E., and Coetzee, D. (2020). Relationship between academic achievement, visual-motor integration, gender and socio-economic status: north-west child health integrated with learning and development study. S. Afr. J. Childh. Educ. 10, 1–11. doi: 10.4102/sajce.v10i1.646

Crossref Full Text | Google Scholar

Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., and Newcombe, N. S. (2017). I. Spatial skills, their development, and their links to mathematics. Monogr. Soc. Res. Child Dev. 82, 7–30. doi: 10.1111/mono.12280

Crossref Full Text | Google Scholar

Verdine, B. N., Irwin, C. M., Golinkoff, R. M., and Hirsh-Pasek, K. (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. J. Exp. Child Psychol. 126, 37–51. doi: 10.1016/j.jecp.2014.02.012

PubMed Abstract | Crossref Full Text | Google Scholar

Von Aster, M. G., and Shalev, R. S. (2007). Number development and developmental dyscalculia. Dev. Med. Child Neurol. 49, 868–873. doi: 10.1111/j.1469-8749.2007.00868.x

Crossref Full Text | Google Scholar

Wang, X. Q., Chen, H. X., Ma, H. J., Guo, X. R., and Cui, X. H. (2015). Investigation on gross motor development of preschool children and analysis of influencing factors. Chin. J. Child Health Care 23, 188–191,

Google Scholar

Wang, R. F., and Spelke, E. S. (2002). Human spatial representation: insights from animals. Trends Cogn. Sci. 6, 376–382. doi: 10.1016/S1364-6613(02)01961-7

Crossref Full Text | Google Scholar

Wang, Y. L., Zhang, C. W., and Yan, L. (2013). Visual brain : People’s Military Medical Press.

Google Scholar

Wassenberg, R., Kessels, A. G. H., Kalff, A. C., Hurks, P. P. M., Jolles, J., Feron, F. J. M., et al. (2005). Relation between cognitive and motor performance in 5- to 6-year-old children- results from a large-scale cross-sectional study. Child Dev. 76, 1092–1103.

Google Scholar

Weisberg, D. S., and Zosh, J. M. (2018). “How guided play promotes early childhood learning” in Encyclopedia on Early Childhood Development. eds. R. E. Tremblay, M. Boivin, and R. Peters (Montreal: Centre of Excellence for Early Childhood Development and Strategic Knowledge Cluster on Early Child Development), 1–4.

Google Scholar

Williams, R., Cunningham, E., and Lubawy, J. (2005). Preschool math : Gryphon House Inc.

Google Scholar

Wilson, R. A., and Foglia, L. (2011). “Embodied cognition” in The Stanford encyclopedia of philosophy. ed. E. N. Zalta . (Fall 2011 Edition). Available at: http://plato.stanford.edu/archives/fall2011/entries/embodied-cognition

Google Scholar

Wynn, K. (1992). Children’s acquisition of the number words and the counting system. Cogn. Dev. 24, 220–251. doi: 10.1016/0010-0285(92)90008-P

Crossref Full Text | Google Scholar

Yu, Y., Shafto, P., Bonawitz, E., Yang, S. C. H., Golinkoff, R. M., Corriveau, K. H., et al. (2018). The theoretical and methodological opportunities afforded by guided play with young children. Front. Psychol. 9:1152. doi: 10.3389/fpsyg.2018.01152

PubMed Abstract | Crossref Full Text | Google Scholar

Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: the SNARC effect and the REVERSE SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. J. Cogn. Cult. 5, 165–190. doi: 10.1163/1568537054068660

Crossref Full Text | Google Scholar

Zhang, Y., Cai, G. L., Zhao, C. Q., Wang, C. X., and Wang, D. D. (2019). Research progress of children’s motor development from the perspective of human motor development. Sichuan Sports Sci. 38, 37–39. doi: 10.13932/j.cnki.sctykx.2019.02.09

Crossref Full Text | Google Scholar

Zhang, X., and Lin, D. (2015). Pathways to arithmetic: the role of visual–spatial and language skills in written arithmetic, arithmetic word problems, and nonsymbolic arithmetic. Contemp. Educ. Psychol. 41, 188–197. doi: 10.1016/j.cedpsych.2015.01.005

Crossref Full Text | Google Scholar

Zosh, J. M., Hirsh-Pasek, K., Hopkins, E. J., Jensen, H., Liu, C., Neale, D., et al. (2018). Accessing the inaccessible: redefining play as a spectrum. Front. Psychol. 9:1124. doi: 10.3389/fpsyg.2018.01124

PubMed Abstract | Crossref Full Text | Google Scholar