Week 3: Building Students' Mathematical Thinking

Watching the videos of the three students solve the mathematics problems I was amazed by how students can use their partial understanding of mathematics in order to solve problems that they may not be familiar with. For example the boy who was asked about the six dozen eggs may not have known from memory that six times twelve equals seventy two but he was able to recognize that it was a multiplication question and then use his understanding of ten and five facts to find the answer. It is interesting to see these videos as we discuss looking at student artifacts because the students work did not give the information that they shared orally, when prompted. This makes me wonder how I can promote a classroom environment in which students freely give their explanations instead of just their answers and make their thinking known in their written work.  

The articles on Dylan’s work also made me think about how I can promote students mathematical thinking. Even though Dylan was not taught how to solve multi-digit subtraction problems he was excited to try. I would love to build that excitement and perseverance about mathematics within my students. The article also made me wonder about the value of teaching students algorithms in mathematics as it mentions that once students know the procedural method there is no further need for them to think mathematically. On the other hand I don’t think it’s practical for students to only learn conceptual mathematics and have no fluency with basic math facts and functions. I’m really curious about how to balance the two in my mathematics instruction.