Transferring Knowledge from Concrete to Abstract

Brick Math is the leading math manipulative program for K-8 students, no matter the students’ experience or previous understanding of math. Brick Math is so successful because it incorporates several key teaching strategies proven by research to help students achieve success.

Today we’ll explain the first teaching strategy: Transferring knowledge learned from concrete to abstract.

​Math is abstract. A number is actually a concept – not really a thing in the physical world. Students need to learn what the idea of “1” means before they can begin to do anything with numbers like count, add, or subtract. A concrete tool like a LEGO® brick is a physical representation of the concept of the number. One stud on a brick represents the number 1, for example.​

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​The Brick Math methodology starts with students using LEGO® bricks to make models of the numbers and the math problems. Students say they can “see” the math when they model with the bricks. Here’s an example of modeling the sum 4 + 3 with bricks:

​Students touch the bricks, feel the studs on the bricks, and can count each stud to understand what 4 means, what 3 means, and then, what 7 means.
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The next step in the Brick Math method helps students begin to transfer that new knowledge from concrete to more abstract. Students draw the model they have just built. Using another tactile sense, students move away from the physical bricks by creating a drawing of the bricks.

​The final step that cements the learning is using words and numbers to explain the model they have just built and drawn. Students write or tell why the model describes the math problem, and they write the math sentence that the model is showing. In our example, they would write “4 + 3 = 7” and explain in words that the model shows four studs on one brick and three studs on another brick, and when they are brought together, seven studs in all. This last step of explaining the problem in words reinforces the concept.
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​This three-step teaching method is very effective in building deep, true understanding of the math. The physical representation with bricks helps students learn what the math means, and the steps that transfer the learning from concrete to abstract ensure that students really comprehend the math.

Brick Math is a K-6 math curriculum that uses LEGO® bricks to model  11 different math subjects: Counting, Addition, Subtraction, Multiplication, Division, Basic Fractions,   Basic Measurement, Fraction Multiplication, Fraction Division, Advanced Measurement and Geometry, and Decimals. It works well for homeschooling, math intervention, enrichment, and as a whole-school program. Materials are simple and affordable.
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If you teach math or have a student at home who is learning K - 6th grade math, check brickmath.com. The website includes videos for both teacher training and direct instruction of students. You can learn more about how Brick Math improves students' math test scores and hear what people who are using Brick Math have to say about the program. ​