Non-Routine Questions-Preferred Math Learning Styles

Navigating MathLand: A Guide for Parents to Help Their Kids Through the Maze followed a student’s struggle learning math from fourth grade through middle school.  At the end of grade 5, the student was placed into an advanced middle school program. The program compressed three years of math curriculum (Common Core), a rigorous program, into two years with the goal having the student take Algebra I in the 8th grade. The only issue was that the student repeatedly scored a level 2 on the state assessment exam in grades 3 through 5. The parents of the student were given no feedback as to what their son’s gaps were in learning math concepts and skills for his entire state testing experience in elementary school.

Fast-forward two years: the student enters eighth grade, but is advised not to take Algebra I; instead, repeat the compressed math curriculum of grades 6 and 7 (the student had again scored only a level 2 on the state exams for grade 6 and 7 and no feedback to the student or parents on what math concepts and skills were deficient). However, a level 2 for the past 5 years indicated that the student was not ready to learn Algebra I.

I suggested to the parents that I administer the Math Learning Style Inventory (MSLI) for Secondary Students Grades 6-12 (Silver, Thomas, and Perini, Thoughtful Education Press, LLC, 2008, The profile takes about 20 minutes to answer and identifies four preferred ways (domains) that students learn math. The goal of the profile is not meant to pigeon-hole students; but to help students recognize different styles of thinking and learning to help them understand how best they engage in learning mathematics. There are four domains: Mastery, Understanding, Self-Expressive, and Interpersonal.

Mastery students want to learn practical information and procedures. They like problems that they have solved before and use set procedures to produce a single solution. Understanding math students want to understand why the math they learn works. They like problems that ask students to explain, prove, or take a position. Interpersonal math students want to learn math through dialog, collaboration, and cooperative learning. They like problems that focus on real-world application and on how math helps people. Self-expressive math students want to use their imagination to explore mathematical ideas. They like math problems that are non-routine, project-like in nature, and allow thinking “outside the box.”

I administered the MLSI to the young man who now really hates math and does not feel successful, especially having to repeat math that he already had learned, (such as, the step-by-step algorithms for solving two step equations). Then I reviewed the results of the MSLI with him and his parents (note: students have all learning styles and one that is dominant).

His dominant style was Mastery, with a second strength in the Understanding style. His weakest math learning preference was the Self- Expressive style. He agreed with the results of the profile and validated that he did not like to do non-routine problems. In fact, he shuts down when confronted with a non-routine problem.  An example of a non-routine problem: A set of data is provided in a problem where high and low tides have been recorded for an entire month. The problem asks the student to create a function (equation) that represents the high and low tide data. Then the problem asks the student to use the equation to find out the time of the highest tide for the following month.

Here was a very bright young man who just did not prefer to work on non-routine problems; which are on state tests. A student who does not choose to answer the non-routine assessment problems scores a level 2 and misses achieving a level three (which is passing). His level 2 results on the state exams have prevented him from partaking in a math class he could have been prepared for. However, had the student been aware in grade 6 that he does not like to solve non-routine questions that would be the first step in helping him develop strategies to problem solve, such as rewriting the question to identify what it’s asking, drawing a diagram to illustrate the problem, and listing what is known about the problem (formulas, rates, measurements).

From my experience as a secondary math consultant, here is a case where the industrial model for schools, the lack of required mastery of math concepts and skills, and the inadequate training of teachers all contribute, like a perfect storm, to low student achievement on the state math assessments. The forty-five minute periods do not provide the time needed for students to strategize solutions to non-routine problems, especially if students have not mastered the skills and concepts required to solve the problems. In order to identify the correct equation to represent the tide table, students would need to have mastered the attributes of families of non-linear functions.

It makes me wonder if the drastically poor results on the state math assessments are a result of poor mastery of math concepts and skills; that and the limited time that students have to work on non-routine problems.

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