Summary & Synthesis

Throughout this semester, Dr. Reins has used many methods and strategies for helping us understand that the processes and reasoning students are using to solve a problem is more important than the product. The goal is for students to practice reasoning skills in order to create a deep understanding of a math concept, understand how it relates to all other math concepts, and know how to apply the math concept in real-world contexts. Also, throughout the semester we have been discovering how manipulatives and other models can help students further explore, understand, and develop deep mathematical understanding. Particularly over the past few days, we have been learning about how to bridge the gap between symbolic math work and manipulative math work. Traditionally, many teachers will try to use one or the other to help students learn math concepts. Some teachers will only use manipulatives to help students build mathematical knowledge, but when it comes time for the students to show symbolic mathematical work on paper, the students struggle. On the other hand, some teachers simply teach the mathematical algorithms, expecting students to memorize procedures in order to “show” symbolic math work. Today, a group presented a lesson on dividing of fractions. First, the group demonstrated the mathematical algorithm and taught us why we use the algorithm the way we do. After explaining the symbolic mathematical work behind dividing fractions, the group extended the learning by having us use manipulatives to demonstrate dividing fractions. Using manipulatives provided a concrete, visual picture of how to divide fractions. By demonstrating the algorithim and then supplementing the symbolic math with manipulative work, the group was able to successfully bridge the gap between manipulative math and symbolic math. After seeing seeing how well, this process can works, I now understand more clearly what Dr. Reins meant by bridging the gap between manipulatives and symbolic math work. The most successful reasoning, problem solving, and learning occur when both are used, and I believe this is true because it is provides differentiated teaching. The more ways a teacher can activate students’ brains, the more likely students will understand the concept more fully.