Hutchison Math Teacher, National Expert in Illustrative Math, Explains the IM Advantage in Classroom

By Conchita Topinka
Middle school teacher Joe Koelsch loves quadratic equations like only a math teacher can. He wants his students to spend time understanding the equations before they rush to solve them. Koelsch, a national expert in Illustrative Math (IM), wrote in a leading blog for educators that IM’s focus on understanding processes, not just the pursuit of a right answer, can be a game-changer for math students.
Joe Koelsch, a certified IM facilitator, enjoys challenging his Algebra I students to understand quadratics patterns and applications before jumping in to solve the equations. He recalls his own experiences with quadratics differently.

“As a student, I followed the teacher’s instructions, which led me to the desired solutions, but I had no idea why the steps worked or why the work mattered. In Algebra 1, I could factor one quadratic expression after another and “FOIL” my way through any pair of binomials. I couldn’t say, however, what made an expression like x2+11x+24x2+11x+24 “quadratic” or what it was for,” wrote Koelsch for his recent blog in a national newsletter for educators.

Freedom to Be Curious

Illustrative Mathematics uses relatable language and problems to engage students with math beyond memorizing rules and formulas, which only creates a superficial understanding of concepts. Here is Koelsch’s observation of how that approach is applied in an Algebra I unit.

“They are simply asked to notice and to wonder. By removing the pressure of a right or wrong answer, students are free to be curious about the relationship in the last table and to observe that it is distinct from the linear and exponential relationships in the first two tables,” Koelsch wrote.

Hutchison teachers in grades K through 7th use the problem-based curriculum known for balancing rigor, usability, and comprehension of fundamental math standards. In the earlier grades, the IM approach teaches students how mathematical concepts build upon one another.
“It’s all about making connections across grade levels. In math, a coherent curriculum is one where girls understand that the math topics we present in a certain grade are connected. We encourage them to apply the concepts they have already learned to think about the lesson at hand,” said Katharine Kent, Lower School Division Head. “Mastering this fundamental skill allows girls to grow their math skills from one grade to the next.”
Even as the curriculum evolves based on research and best practices, it is always fundamentally anchored by established national standards.

Click here to read Mr. Koelsch's blog for Illustrative Mathematics.

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