by Barry Garelick and Katharine Beals

Tuesday, May 12, 2015

At a middle school in California, the state testing in math was underway via the Smarter Balanced Assessment Consortium (SBAC) exam. A girl pointed to the problem on the computer screen and asked “What do I do?” The proctor read the instructions for the problem and told the student: “You need to explain how you got your answer.”

The girl threw her arms up in frustration and said “Why can’t I just do the problem, enter the answer and be done with it?”

The answer to her question comes down to what the education establishment believes “understanding” to be, and how to measure it. K12 mathematics instruction involves equal parts procedural skills and understanding. What “understanding” in mathematics means, however, has long been a topic of debate. One distinction popular with today’s math reform advocates is between “knowing” and “doing”. A student, reformers argue, might be able to “do” a problem (i.e., solve it mathematically), without understanding the concepts behind the problem solving procedure. Perhaps he has simply memorized the method without understanding it.

The Common Core math standards, adopted in 45 states and reflected in Common Core-aligned tests like the SBAC and the PARCC, take understanding to a whole new level “Students who lack understanding of a topic may rely on procedures too heavily,” states the Common Core website. “… But what does mathematical understanding look like?” And how can teachers assess it?

- See more at: http://www.educationnews.org/k-12-schools/math-problems-knowing-doing-and-explaining-your-answer/#sthash.tbDjEwup.dpuf

Tuesday, May 12, 2015

At a middle school in California, the state testing in math was underway via the Smarter Balanced Assessment Consortium (SBAC) exam. A girl pointed to the problem on the computer screen and asked “What do I do?” The proctor read the instructions for the problem and told the student: “You need to explain how you got your answer.”

The girl threw her arms up in frustration and said “Why can’t I just do the problem, enter the answer and be done with it?”

The answer to her question comes down to what the education establishment believes “understanding” to be, and how to measure it. K12 mathematics instruction involves equal parts procedural skills and understanding. What “understanding” in mathematics means, however, has long been a topic of debate. One distinction popular with today’s math reform advocates is between “knowing” and “doing”. A student, reformers argue, might be able to “do” a problem (i.e., solve it mathematically), without understanding the concepts behind the problem solving procedure. Perhaps he has simply memorized the method without understanding it.

The Common Core math standards, adopted in 45 states and reflected in Common Core-aligned tests like the SBAC and the PARCC, take understanding to a whole new level “Students who lack understanding of a topic may rely on procedures too heavily,” states the Common Core website. “… But what does mathematical understanding look like?” And how can teachers assess it?

- See more at: http://www.educationnews.org/k-12-schools/math-problems-knowing-doing-and-explaining-your-answer/#sthash.tbDjEwup.dpuf