Learning mathematics requires deep-rooted intrinsic motivation, motivation to learn, to problem solve, and to discover the best methods for solving those problems. When we, as educators, attempt to offer doing well on assessments or being prepared for college algebra as intrinsic motivators, we often find that the results are marginal and superficial.
The role of mathematics educators is to promote reflective practices that promote connections within the realm of mathematics, as well as prepare students for the mathematical elements that are the foundation of so many aspects of the daily lives of citizens, consumers, and workers in their communities.
Mathematics teachers need as much training as possible promote discussion and reflection in their math lessons. Some considerations for best practices include the following:
- Rather than expecting the teacher be the source of knowledge, a mathematics classroom should offer opportunities for the students to explore, collaborate, and make decisions on methods to solve problems. Such guided interaction among the students will add excitement to the development of student problem-solvers.
- Instructional feedback needs to be more than whether the answer is right or wrong. Students need guidance on which elements of the process were misguided, help with identifying the flaws in judgment, and what adjustments need to be made. In solving most puzzles, we need to step back and determine where we are missing some information or going in a wrong direction. Working in the mathematics classroom can offer the similar intangible gratification when the problem is solved.
- Problems can be solved using different approaches. Allow time for students to discuss in whole group activities or in small groups to share the different methods and styles of thinking. In the social studies or science classrooms, many discussions lead to the phrase “I never thought of it like that.” Sharing tactics in the mathematics classroom can certainly lead to such discoveries, also.
In order to develop mathematics classrooms that foster reflection, discussion, engagement, and discovery, math educators should be trained at every level. Teachers without strong insights about the reasons for the various algorithms in mathematics will not have the confidence to promote dialogue that might go in unexpected directions. Even the teachers in the lower grades need to understand how topics in mathematics are interwoven so that “math talk” promotes that connectivity. Students who become engaged in learning become life-long learners. This should be the case in all content areas, including mathematics.