What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education

  title={What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education},
  author={Elida V. Laski and Jamilah R. Jor’dan and Carolyn Jean Daoust and Angela K. Murray},
  journal={SAGE Open},
Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels… 

Figures and Tables from this paper

Math achievement outcomes associated with Montessori education

ABSTRACT The math curriculum of the Montessori system of education for children ages 3–12 is distinctive, incorporating multiple manipulatives and educational practices which have theoretical and

Promoting Conceptual Foundations of Manipulatives for Elementary Mathematics Instruction

The purpose of this study was to determine the effects of instructional strategies on teacher self- efficacy beliefs about teaching mathematics. The findings revealed that respondents’ perceived

Effects of Instructional Guidance and Sequencing of Manipulatives and Written Symbols on Second Graders’ Numeration Knowledge

Two factors hypothesized to impact second-graders’ learning of place value and regrouping with manipulatives are examined: the sequencing of concrete and abstract representations of the standard addition algorithm and the level of instructional guidance on the structural relations between the representations.

Probabilities and Preschoolers: Do Tangible Versus Virtual Manipulatives, Sample Space, and Repetition Matter?

Probabilities tend to become an integral part of early childhood mathematics curricula. Research has shown that at the age of 4, children indicate basics of probabilistic reasoning and can engage

How Much Guidance Do Students Need? An Intervention Study on Kindergarten Mathematics with Manipulatives

  • E. HoranM. Carr
  • Education
    International Journal of Educational Psychology
  • 2018
Research has shown that the efficacy of learning with manipulatives (e.g., fingers, blocks, or coins) is affected by multiple variables, including the amount of guidance teachers provide during

From Concrete Manipulatives to Digital Manipulatives : A Paradigm Shift in Mathematics Education

The use of manipulatives has a long tradition in the teaching of Mathematics. Manipulatives have evolved over the years with the rapid advancements in the field of technology. The paper discusses the

Development of mathematics manipulative for slow learner and dyscalculia student in elementary school by using Montessori’s characteristic

Mathematics has an abstract object of study. That’s why many students have difficulty understanding Mathematics, especially for slow learners or dyscalculia. This research was conducted based on the


This study investigates three particular aspects hypothesized to affect the transition between a third grade Montessori mathematics class and a fourth grade non-Montessori mathematics class. These

Effect of Cognitively Guided Instruction on Primary School Teachers’ Teaching Skills in Mathematics: Mombasa County, Kenya

The study investigated the effect of Cognitively Guided Instruction on the teaching skillsemployed by primary school teachers to conductmathematics lessons.The Cognitively Guided Instruction (CGI)

Manipulatives and Multiplicative Thinking

This small study sought to determine students’ knowledge of multiplication and division and whether they are able to use sets of bundling sticks to demonstrate their knowledge. Manipulatives are



Effects of Manipulative Materials in Mathematics Instruction

Using meta-analysis, the results of 60 studies were combined to determine the effectiveness of mathematics instruction with manipulative materials. Students ranged in age from kindergarteners to

Are We Having Fun Yet? How Teachers Use Manipulatives to Teach Mathematics

Teachers often comment that using manipulatives to teach mathematics is ‘fun!’ Embedded in the word ‘fun’ are important notions about how and why teachers use manipulatives in the teaching of

Teacher Learning and Mathematics Manipulatives: A Collective Case Study About Teacher Use of Manipulatives in Elementary and Middle School Mathematics Lessons

This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional

Rethinking the use of concrete materials in learning: Perspectives from development and education

Abstract— The idea that concrete materials benefit children’s learning has a long history in developmental psychology and education, dating back to M. Montessori (1917), J. Piaget (1970), and J. S.

A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives

The use of manipulatives to teach mathematics is often prescribed as an efficacious teaching strategy. To examine the empirical evidence regarding the use of manipulatives during mathematics

Concreteness Fading in Mathematics and Science Instruction: a Systematic Review

A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the

When Theories Don't Add Up: Disentangling he Manipulatives Debate

The use of manipulatives in the classroom has been advocated for decades. However, the theoretical and empirical support for this practice is mixed. Some researchers suggest that manipulatives

Magical Hopes: Manipulatives and the Reform of Math Education.

T HIS ARTICLE begins wi th a s tory f rom my o w n teaching of third-grade mathematics. ' It centers on an unusual idea about odd and even numbers that one of my students proposed. 2 The crux of the

Elementary School Teachers' Manipulative Use.

Using data from 503 inservice elementary teachers, this study investigated the relationship between teachers' background characteristics, teachers' beliefs about manipulatives, and the frequency with

Young children's representations and strategies for addition.

A study of the representations and strategies for addition used by a sample of 55 children in years 1, 2 and 3 in three schools in Brisbane suggests that some of the difficulties occur because teachers introduce procedures that are recommended in curriculum documents without being aware of the cognitive load that they impose.