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Making Math Real

Mathlete at work

There is a difference between learning and learning with understanding, especially when it comes to math. If math understanding is limited in scope to a certain circumstance and cannot be applied or utilized outside of that, then it has little merit. For example, take the scenario many parents have experienced. In the middle of seeking help from his or her parents, the child exclaims, “That is not the way my teacher taught me!” Clearly, this indicates little understanding with very limited depth or breadth.  

To learn with understanding, students need to experience a setting in which knowledge is connected, knowledge is generative, students dialog around their mathematical thinking, and students see themselves as mathematicians capable of making sense of numbers. Whether adding single-digit numbers or factoring polynomials, connecting new knowledge to something already known helps with retention and brings forth some familiarity. Then, students extend this to novel problems, seeing what strategies might work. Comparing strategies with one another and explaining the whys or why nots are critical steps to making sense of mathematical concepts. Student discourse in the math class has the added bonus of helping the teacher assess and address misperceptions and alternatively, to see the more sophisticated strategies that some students are ready to deploy.

The National Council of Teachers of Math indicates that “...many high school students have experienced mathematics as a set of rules that are disconnected from underlying mathematical reasoning (e.g., “flip and multiply” for dividing fractions; “minus a negative is plus” for integer subtraction) (Schoenfeld 1988). This procedural view of mathematics without connections to underlying concepts can lead to gaps in knowledge of basic number operations that can impede understanding of high school content.” 

What we now know from the field of neuroscience is that there is a positive impact on the brain when it must struggle. The brain grows and changes best when the student is challenged, makes mistakes, tries again, and so on. Our impulse is to lead directly to the right answers, but that takes away the very cognitive demand that results in deeper learning and brain growth. 

Let’s make our math classes places of inquiry where the struggle to develop new concepts is not feared but embraced as something the students and teachers do together and as part of the path to learning with understanding.


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