Concept Rich Chapters 3/4

I anticipate that there will be systematic errors, preconceptions, under and over generalizations and possibly some counterintuitive concepts.I think that the reason that I will have so many of things things happen in my unit is because it is a subject which students often times have a hard time understanding on many levels. The book often used creating equations as an example of where students struggle in each of these categories and I that makes me realize how prevalent a lot of these are in the beginning of Algebra. I don't think that some of these would have automatically been something that I would have said I would have in my unit so the examples which they used in the book were actually a helpful tool to put me into the mindset I needed to be in and to help me realize the many misconceptions that students can have about variables and creating equations. I did come up with one specific example outside of the ones which they gave in the book and that is with solving inequalities. One thing that I remember having a hard time coming to terms with when I was learning this and that I have seen students at MBMS struggle to remember is the fact that your symbol changes direction when you are dividing by a negative with inequalities. I think that would fall under the counterintuitive piece because to many students it doesn't make sense as to why this would be done. I think that flexibility and alternative mental representations would help with these issues because if there are misconceptions being flexible enough to go back and talk about them with your class will help correct those misconceptions, or at least to put the proper concept ideas into their heads for them to think about, and alternative mental representations will help those students who don't understand the way that the concept was taught, leading to them having these misconceptions.

I think that I would use the problem solving process throughout all of my unit. When it comes to creating equations you are usually given a word problem and asked to create an equation from that which is very difficult for many people. I think that it is important to make sure that when doing word problems, especially when it comes to an outside the box concept such as creating equations, it is extremely important that they know how to interpret and understand the question so that they are able to use the important information in them. I think this would be the part that has the most weight in this process for me because I feel that since many teachers don't like word problems, and students very vocally don't like word problems, it is not taught so in the future when students see them they're automatic reaction is to not want to do them. The other parts of this process are very important too but I think that because this first part seems to be often times left behind for students it is extremely important to make sure it gets included.

Citation: Meir, B. (2006) Concept-Rich Mathematics Instruction. ASCD: Alexandria, VA. ISBN 978-1-4166-0359-7