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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).