# There’s no magic in Maths MANIPULATIVES…

There’s no magic in that plastic! (Although, truth be told, we don’t do plastic around here.)

As is common in mathematics education, the research suggests that manipulatives and representations are just **TOOLS**. It’s actually **HOW** they are used that is important. Maths manipulatives need to be used **PURPOSEFULLY** and **APPROPRIATELY **in order to have an impact.

It's only when learners use the manipulatives themselves to support their own SENSE MAKING that they will begin to see their power as TOOLS rather than just relying on them as crutches… I’ve written a blog on this already **THINKING BOARDS - REPRESENTING MATHEMATICAL THINKING**

For children to use concrete representations effectively without increased demands on their processing capacity, they must know the materials well enough to use them automatically (Boulton-Lewis, 1998)

Moyer (2001) draws attention to the need for familiarity of the learner with the resource that is being used as a tool so as to reduce the cognitive demand of its use.

**What to do? **

**Let learners of ALL ages have a chance to play freely with a range of MANIPLUATIVES for a while before setting a mathematical task** (Black, 2019). Otherwise getting them to address the agenda (say, counting) can be at best inefficient, and at worst, a serious struggle! (Sarama and Clements, 2016).

Although children can and do learn pre-mathematical foundations through their self-directed play, especially with structured manipulatives, such as pattern blocks or building blocks (Seo and Ginsburg 2004). However, these experiences are rarely mathematical without grown-up guidance (Sarama and Clements 2016).

Some research indicates the more manipulatives, the better (Moscardini, 2009; Carpenter 1999). However, there are opposing practices and evidence…

**These few manipulatives should be used for multiple tasks, so children do not view them as objects to play with but tools for thinking (Sowell 1989).**

**Do not neglect fingers as manipulatives, as they play a fundamental role (Crollen and Noël 2015).**

For this we need to introduce RICH MATHEMATICAL TASKS which encourage children to use the manipulatives to investigate and understand the mathematical structures and processes and can support their mathematical truths and arguments.

We want to discourage learners using them in a rote manner, without a sense of the ways in which the apparatus can reflect the mathematical structures. The learner needs opportunities to make sense of both the manipulative used and their relation to the mathematical idea which they are being used for.

Our **Number TOOLKITS** contain RICH TASKS that encourage learners to use TOOLS to demonstrate results and prove their mathematical truth in some sense (as this helps to develop mathematical thinking and support conceptual understanding).

You can download my favourite 3 TOOLS HERE for FREE... **These few manipulatives can be used for multiple tasks I share on social media.**

It should be noted that some teachers tend to use different manipulatives to increase “motivation” and “make math more fun” (Moyer 2000; Uttal 1997). By using manipulatives for ‘fun math,’ teachers artificially set up a classroom situation in which materials may not be used effectively. If “teachers act as if student interest will be generated only by diversions outside of mathematics” (Stigler and Hiebert, 1999).

**FINAL WORDS...**

Manipulatives are meaningful for learning only with respect to learners activities and thinking:

To further inform your thinking here are some useful links to literature that support the research and the pedagogy:

Ball, D. L. (1992). Magical hopes: Manipulatives and the reform of math education.

Baroody, A. J. (1989). Manipulatives don’t come with guarantees. Arithmetic Teacher, 37(2), 4–5.

Black, Jenni: 2019 Manipulatives in the Classroom. NRICH

Boulton-Lewis: 1998, ‘Children’s strategy use and interpretations of mathematical repres- entations’, Journal of Mathematical Behavior 17(2), 219–237.

Burns, M. (1996). How to make the most of math manipulatives. Instructor

Carbonneau, K. J., & Marley, S. C. (2015). Instructional guidance and realism of manipulatives influence preschool children’s mathematics learning. The Journal of Experimental Education.

Clements, D. H. (1999). ‘Concrete’ manipulatives, concrete ideas. Contemporary Issues in Early Childhood.

Clements, D. H., & McMillen, S. (1996). Rethinking “concrete” manipulatives. Teaching Children Mathematics.

Meira, L.: 1998, ‘Making sense of instructional devices: The emergence of transparency in mathematical activity’, Journal for Research in Mathematics Education.

Sarama, J., & Clements, D. H. (2016). Physical and Virtual Manipulatives: What Is “Concrete”?

Seo, K.-H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education

Sowell, E.J.: 1989, ‘Effects of manipulative materials in mathematics instruction’, Journal for Research in Mathematics Education

Stigler, J.W. and Hiebert, J.: 1999, The Teaching Gap, The Free Press, New York. Strauss, A.: 1987, Qualitative Analysis for Social Scientists, Cambridge University Press, New York.

Uttal, D. H., Scudder, K. V., & DeLoache, J. S. (1997b). Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics.