Blog #4: How Children Learn (Better!) in Algebra

As a middle school mathematics teacher, I often struggle with the fact that over 90% of the eighth grade students enroll in Algebra 1 or Algebra 2. Are all of these children ready to learn this complex mathematical language at the ages of twelve or thirteen?

This past summer, I reconsidered my approach to grading. In my nine years as an algebra teacher, I came to the realization that some students are simply not ready for the rigorous curriculum involving variables, systems, and the quadratic formula, and other complicated concepts. This school year, I decided to place a larger weight on practicing algebraic skills than I ever had in the past. My new policy is that if a student completes every homework assignment in the marking period (following guidelines such as showing all steps of work), he or she will earn at least a B- in the course, regardless of the accuracy or correctness of the assignments. My modification in the grading scale supports the findings outlined in Bransford, Browning, and Cocking’s “How Children Learn” chapter in which the authors not only emphasize the importance of experience, but assert that practicing is also a critical component of skill development.

I have already noticed positive changes in my algebra students’ approach to learning. Students demonstrate increased motivation and determination, as well as higher homework grades than ever before. I have made very few calls home this year due to a lack of effort. A shift has occurred: My students have transformed from entity theorists to incremental theorists. The students have learning goals and understand that if they put effort into attempting the problems, they will be rewarded. Additionally, a surprising effect has surfaced: the averages on the first three assessments are significantly higher than in past years.

Although I modified my grading scale, I have not changed the responsibility placed on the students, nor have I changed the curriculum. Each student is expected to complete homework and perform well on assessments. I believe the focus on the practice aspect of algebra has reduced the so-called math fear or test anxiety within the classroom environment and allowed the student to concentrate on what is really important in math – skill development and independent problem solving. I find that the students ask better questions and are motivated to explore and understand the processes, rather than simply getting an answer.

I encourage the students to “find a better way” to solve problems and I look forward to receiving emails from proud students wondering if their particular method of solving has been used before and/or if it is allowable. These senses that learning is a process and practice is as important as experience have proven successful thus far.

My students are participants in their own learning, no longer spectators, as stated by Bruner in Bransford, Browning, and Cocking. I only hope that the persistence continues throughout the school year while the students set out to improve their mathematical abilities, one practice opportunity at a time.