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How can we get students to reason and make sense of numbers when they learn operations? Math Solutions Professional Learning Specialist Ivan Alba walks ICLE Senior Fellow Weston Kieschnick through some common issues students face when learning mathematics, and how we can help students move beyond digits and see numbers as quantities.
Ivan outlines the challenge math instructors face as we encounter students who are missing crucial foundational understanding. “One of the biggest things we have to combat is that students aren’t making sense of the math they’re learning. When I was in school, my teacher taught me lots of rules, and I was one of the good students who could remember a lot of rules. Without making sense, eventually those rules start to cave in. Around middle school and high school, students say ‘I don’t really care how it works, just show me how to do it’ because they think that’s all that math is–rules.”
“One of the biggest things we have to combat is that students aren’t making sense of the math they’re learning.”
Why is memorizing rules and algorithms without understanding so harmful? “The problem is if we boil math down to a series of steps and rules, the best you can do is memorize those rules and eventually just mimic the teacher. That’s not good enough when the students get older and go to high school and have to take algebra. In algebra, it’s almost as if they’re learning a completely different language. Students who don’t have a strong understanding of the arithmetic they do in elementary school have nothing to hold onto when they get to algebra and it falls apart. That’s the beginning of the end for them. Most of them don’t go into higher mathematics or have to take remedial courses.”
Students have to understand what we’re talking about is numbers. Not the numerals my teacher taught me to write, but it’s really about the quantities we’re working with.
How do we teach math in a way that’s different, so students know the “why” and the process? “Students have to understand what we’re talking about is numbers. Not the numerals my teacher taught me to write, but it’s really about the quantities we’re working with. When teachers start to teach operations, the teachers are not focusing on the quantities, but on the algorithm or set of steps that turn the numbers into a string of digits.”
Watch Ivan break down arithmetic problems into a language students can understand that will give them the algebraic reasoning they need for success in later mathematics.
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