The solution is easy to find, but not so easy to check

“The solution is easy to find, but not so easy to check.”

While visiting one of the BSME (mathematics education) university courses on Wednesday 10/11/17, two students agreed to demonstrate their completed geometry homework solutions on the board. Their explanations were both conceptually and procedurally well done.   Upon completing some additional problems from the homework, the professor said: “the solution is easy to find, but not so easy to check.”

These words resonate around my discussions on equity, access, and actions for all students in the process of learning mathematics. No one seems to argue about the value of learning math, in fact, in New York State, the high school Advanced Regents Diploma requires Algebra, Geometry, and a second Algebra course. While the argument for more math classes is that students have more career opportunities, we have to take into account that some students may become more alienated through two more years of negative experiences (insert research). So we want learners to understand the breadth of mathematics through our curriculum choices, but the system is not always interested in the quality of the average student’s experiences. So back to the quote.

The quote is an admonishment of my loud proclamation that we have to do a better job of teaching mathematics for all students, but the solution may not be so easy to implement.

Is it about resources? Yes.
Is it about teacher expectations? Yes.
Is it about the lack of technology? Yes.
Is it about the stratification of who gets good math teaching and who does not? Yes.

George Polya (Heuristics around problem-solving in mathematics–see notes below.) might say, to solve any problem the first step is to “Define the problem.” I am not really past the first step yet. My journey has been about making sense of the problem through my interactions with colleagues in another part of the world. I will not step back (or step off as young people might say) without a plan for equity, access, and actions around mathematics learning. What is different,

Geometry Spheres Workshop
Lenart Istavan Workshop on Spheres

is that I realize that I cannot just ram the access mantra down your throat, but I have to figure out how to add you to the conceptual framework of equity in mathematics.

Maybe I have defined the problem.

Polya’s four-step approach to (math) problem solving

  1. Preparation: Understand the problem.
  2. Thinking Time: Devise a plan.
  3. Insight: Carry out the plan.
  4. Verify: Look back.

2 thoughts on “The solution is easy to find, but not so easy to check

  1. Last year, when my son was in middle school, his algebra teacher approach to teaching incorporated flexibility into the classroom-learning environment. Now you must be thinking, how can this be possible? When mathematics is a rigid subject (you either get a problem right or wrong). This teacher would allow students to re-take quizzes or exams for a higher grade, without any penalizes. The re-take would be a different test but contained the same types of problems. Yes…by offering students the opportunities to take another test is more work for the teacher. But, I believe by being flexible helped students to gain confident in their math abilities and opened the door to be successful in their own learning environment.

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