![]() Origins of Concrete Pictorial Abstract ApproachĪnyone working in primary mathematics education can’t fail to have noticed that the word ‘maths’ is rarely heard these days without a mention of the term ‘mastery’ alongside it. Building these steps across a lesson can help pupils better understand the relationship between numbers and the real world, and therefore helps secure their understanding of the mathematical concept they are learning. Then they are asked to solve problems where they only have the abstract i.e. When they are comfortable solving problems with physical aids, they are given problems with pictures – usually pictorial representations of the concrete objects they were using. Pupils are introduced to a new mathematical concept through the use of concrete resources (e.g. The Concrete Pictorial Abstract (CPA) approach is a system of learning that uses physical and visual aids to build a child’s understanding of abstract topics. The CPA approach illustrated by one of our Third Space Learning resources What is the Concrete Pictorial Abstract in Maths? The maths curriculum is far too broad to cover in one blog, so the focus here will be on specifically how the CPA approach can be used to support the teaching and learning of the four written calculation methods. Students do not attempt to make blind regrouping moves in algorithms by crossing out numbers, writing new numbers on the top, and then looking up to me for approval like….did I do it right?Īfter this concrete and pictorial immersion with regrouping, they are able to compute abstractly, they explain their thinking in a meaningful way.The Concrete Pictorial Abstract approach is now an essential tool in teaching maths at KS1 and KS2, so here we explain what it is, why its use is so widespread, what misconceptions there may be around using concrete resources throughout a child’s primary maths education, and how best to use the CPA approach yourself in your KS1 and KS2 maths lessons. ![]() This is an awesome transition too! I listen to the kids verbally explain about trading in ones for a ten and tens for a hundred, while they point to their models. Picture models are used until the student has internalized what the concept of regrouping is before moving to the algorithm. Students are bundling tens and moving them to the next place value. As students move into adding and subtracting with regrouping, they rely heavily on the place value chart and base ten blocks at first. They are making meaning of the written language of the story problem, the pictorial model of showing what is needed to solve, and then finally the abstract portion, the equation!Įureka Math then pushes forward with the abstract thinking into more challenging concepts. They are making connections as to what the equation means. When they are solving story problems, they draw the model or number bond, then write the equation. It teaches students how to connect their models to an equation each and every time they solve. Students have to be ready to relate concrete and pictorial understanding of math to be successful with this new math language.įor example, when Eureka Math teaches story problems. This program immerses students with a very in depth understanding of what math concepts are in a concrete and pictorial way BEFORE ever introducing math abstractly.Ībstract math relies on symbols and digits as a language. Here is why Eureka Math is so different than traditional math training. I have the tools and knowledge that I need to make math meaningful for them and make sense! I EVEN have a strong abstract math concept now! I have internalized more logical ways of preforming math. Using Eureka Math to teach my students has let me start all over again. ![]() I had to break my old bad math habits and build myself a new strategy repertoire. I never want my students to feel as anxious and stressed out about math the way I always did in school. I relearned math for myself this way! I learned how to make meaning of concepts. I want my students to know how to let math help them in their life. I want to know every way to teach my students math in a productive way. I was now approaching math from a different perspective, and I dug right in. When I became a teacher, I was introduced to Eureka Math.
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