Doing Math

Doing Math: I believe doing math means students are understanding the thinking behind the process they are taught. The act of doing math means students are not just plugging in numbers to an equation they were taught but actually knowing why they put the numbers where they do in the equation and where those numbers came from. Sometimes doing math means students will have to struggle through a problem to arrive at the final answer. They need to investigate different strategies to arrive at the final answer. By trying a number of strategies the student will make a genuine connection with the problem and finding a way to solve it. By trying different ways to solve the problem students make sense of the math they were taught and this is what I believe it means to be “doing math”.

Personal Concerns and Next Steps

Personal Concerns and Next Steps: After being in this course I am very concerned about how teachers are teaching mathematics to their students. I discovered that in many cases teachers show how to do a problem and give the formula and then students just mimic what the teacher did and plug numbers into the formula they were given. Unfortunately this means many times the students do not actually know the reasoning behind the way they figured out the problem. They have the formula and know how to plug the numbers in but they have no concept of why they are solving the problem that way. This really concerns me because I am one of those students. I know the formula but not the reasoning behind doing the formula. I can find the right numbers to plug in to get the correct answer but don't really know where the reasoning is coming from. The next step for me is to try to not teach mathematics to my students in this way. I will make a conscious effort to give students the extra push to try and work through and solve the problem on their own. I will encourage them to struggle a little and try different methods to arrive at the answer. By doing this they will truly understand the why behind the problem.

Questions and Answers

As a results of taking this class lots of questions have been raised. The main question I have is how do we go about finding the time to teach using different techniques then we were taught. One of the reasons we were taught math the way we were had a lot to do with time. Teachers are given a whole list of standards they have to meet and not nearly enough time to teach everything they need to. When you throw in new teaching techniques it does not seem like there would be enough time to teach your students that way even though it is a better way. You want to give your students the best possible education they can get and that means creating a deeper understanding of math for your students. Instead of just showing students formulas and how to plug in numbers you want students to have a deep understanding of why math processes work the way they do. It will be interesting to see how teachers teach this way for deeper understanding and still have to to fit in all the standards they are supposed to teach. My question is how do we as upcoming teachers do this in our classrooms?

New Insights and Implications

After talking about manipulatives in class, I can not believe how many manipulatives are available to teachers to use in the classroom. I think that they more a student is able to work with the manipulatives and use them the more they will understand what is being taught to them. I wish that when I was in grade school that my teachers had the manipulatives or used the manipulatives that were available to them, I think that if I was able to use them learning math that I would understand some concepts a lot better today. So this makes me understand that when I am in a teaching position that I should use the manipulatives available and let my students use them and learn new concepts with using the manipulatives.

New Insights and Implications

After the past week of class I have realized an important aspect of teaching, especially in mathematics. In is essential, for teachers, to know and understand all the terminology located in the standards. At first glance, the standards seem simple; although after this week of class I have realized that the standards are full of loaded terminology and are complex. As a teacher, I need to be able to understand how to appropriately dissect each standard in order to effectively teach students. I think standards can be extremely confusing and complex, so as teachers, we need to make sure we understand what is expected of us in order for our students to learn what is expected of them and perform well on state and national standardized tests.

New Insight and Their Implications

In class we were discussing fractions and how to divide the candy bars equally for a certain number of kids. I have not thought about breaking away from the halving strategy. It is the easiest thing to do, so I have always just done it. I also thought that looking through that book was interesting because I would have never guessed that there were so many different types of manipulates that we could use to teach fractions, and some of them are not very expensive. I never would have realized that buying the ones without the fractions labeled will be more worth while.

New Insights and Their Implications

On Tuesday, we discussed using manipulatives in the classroom for a variety of reasons, one of which is fractional understanding. I've always known manipulatives are useful, but have been wary of them because some times they seem to be overused. But many are very helpful to students. When we were talking about them, it was mentioned that the manipulatives with the fraction written on them aren't very good to use. At first I didn't understand it, but now it makes sense. Though the size of the manipulative piece doesn't change, the fractional value does, depending on what is considered a 'whole'. Using it the other way would confuse students in the future. I think it is also good to not label them so the students can experience creating the fractions on their own. They can 'construct' in their mind how fractions work, and relate that to which ever manipulative piece they are working with. Students understand better and longer when they discover the solution on their own, through their own strategies. I'll definately remember this when teaching.
Mary Fink