Reys Chapters 6 & 14

Reys: Chapter 6

Focus Question # 1: What is the difference between solving problems and practicing exercises?
           
        Reys mentions that the difference with solving problems and practicing exercises is the kind of level of thinking that is involved. With solving problems a higher level of thinking is required versus with just doing exercises the only challenge as Reys puts it is “ doing the computation. Solving problems does not mean doing traditional textbook word problems because a lot of these type of problems are just stories with words here and there not really causing the student to really think critically. From experience with tutoring and even in my own mathematics I have learned to spot the difference between exercises and problems that require solving. The routine problems as Reys calls them are literally just numbers that students can skim through the words and simply add, subtract, multiply, or divide the numbers without really having to think on a higher level. It is not to say that routine problems are not good exercises for students because they can also be used to build algebraic understanding. It is true that so many people underestimate the abilities of children and as a future teacher I have to make sure to provide my students with true problems and those resources needed to be able to solve these non-routine problems. Teachers should introduce problems that will help students survive in the real world as opposed to just problems that are conveniently set up to make the problem easy to compute.


Reys: Chapter 14

“ It is often difficult to get into the minds of children, so having them explain their thinking is crucial.”

            While doing the reading on chapter 14 I stumbled upon this phrase that made me think about how important it is to give students the chance to explain themselves. I actually learned more about math from getting the chance to explain how I arrived to a solution. I can’t remember if in elementary school I had the chance to explain myself, but in high school I did especially when I would help my sister with her math. No one can get into the minds of others; therefore in order to understand what the other has grasped we need to give them the opportunity to explain how they solved the problem and even how they feel about the problem. It could be that a student arrived to the solution in a different way that what the teacher explained and they could get the chance to explain why their way made more sense. This quote does not only apply to math, but I can see it being applied to life. Like I mentioned on Reys chapter 6, children are always being underestimated and it should be our duty as teachers to make sure that our students are active and have the opportunities to make themselves be heard. If we allow for our students to explain their thinking not only could they help themselves, but they can help other classmates and even help the teacher.