I’ve been reflecting on the first Standard for Mathematical Practice (MP1 – Make sense of problems and persevere in solving them) and wondering how to build perseverance in our students.
Traditional View of Perseverance in Mathematics
In order to build perseverance in our students, we must first understand it in the context of mathematics. Perseverance describes the effort made to achieve some goal despite adversity. In mathematics, the “effort made” refers to our students’ application of mathematical reasoning and the “goal” refers to the solution they provide. Given any mathematics problem, there is an underlying presumption that a solution exists (i.e. the “goal”). Our students are expected to assess the problem, determine the most effective path to the solution, and attempt to solve the problem (i.e. “effort made”). Considering this scenario, they may not assess the problem correctly or they may not understand the problem well enough to assess it at all. They may also experience a poorly planned path to the solution. At this point, the students must reassess the problem and determine another path to the solution. This is the traditional view of perseverance in mathematics.
Comprehensive View of Perseverance in Mathematics
Let’s consider a more comprehensive view of perseverance in mathematics. Assume a similar situation, but instead of having to reassess the problem, the students selected the most effective path to the solution. Is it enough to settle with the most effective solution? In what context is this solution regarded as “most effective?” Perhaps we need to dig deeper and have our students analyze their solution further by considering other possible solutions. After producing a number of possible solutions, the students could compare and contrast their effectiveness depending on different situations.
Here’s a sample of a solutions analysis chart that I created to help students compare and contrast their effectiveness. The students write the given question/problem in the top row. They assess the question/problem and prepare up to four different possible solutions in the second row. In the third row, they explore a variety of situations, for which each possible solution might be most effectively used. The bottom row allows students to take notes on key vocabulary they encountered that helped them reason through the analysis.