Students today seem to only understand concepts when it is beneficial for them. They only learn the concepts for a short period of time, and seem to have a tough time retaining information. As future teachers, it is important for us to teach mathematical reasoning to help students recall information needed in future classes. We need to help create habits for our students to help relate concepts together.
We need to create situations in which the students are allowed to work through the problems. A big example I was able to experience this last week, was the complete the square lesson. The professor told us that we would be using different algebra tiles to relearn concepts we learned in high school. He began it by giving us an explanation of how to use the tiles. He then gave us a problems and let us, in partners, work how to solve them. He didn’t interject much, which allowed us students to recall past concepts he explained to us as well as our own ideas to figure it out.
As future teachers, it is important for us to bring this type of learning into our everyday classrooms. I think lectures and notes have their place in a classroom, but the biggest way students can learn is by reasoning and coming to the solution by working through the problem and critically thinking about past concepts.
According to Strategies for Mathematical Reasoning, through reasoning the student is able to evaluate a problem, understand a problem, and create a solution. This handbook provides a lot of different ideas to help create more situations for students to mathematically reason. The biggest one that stood out to me was the idea of using manipulatives in the classroom. This concept means that the teacher provides objects from the real world that the students are able to play with and manipulate to understand a concept. While learning graphing, it means seeing how to manipulate the graph by changing one variable or number. In geometry, it means bringing in objects representing each shape/theorem so the students have a visual representation of what they are learning. In the lesson explained above, the professor knew that using the manipulative of algebra tiles gave us a chance to manipulate and change how to get different equations.
They say in the handbook that “there is a proverb that states, ‘What I hear, I forget; what I see, I remember; what I do, I understand.’” I think this is a great way to prepare for lessons as future teachers. We need to provide more chances for the students to learn by using objects to understand. Instead of being the teacher that talks at the students, we need to be the teachers that allow the students to be doing the learning and teaching, while we facilitate and point them in the write direction.
Overall reasoning is necessary in the mathematics classroom. Students don’t just need to remember the different concepts. They need to learn how to understand and retain information. Through manipulatives the students will be able to mathematically reason and continue to grow in their math skills.