Instruction Dynamics II Final Reflection

Katie Forand

December 10, 2012

Reflections on Instruction Dynamics 2

   Instruction Dynamics is probably one of the most beneficial classes that I have taken here at Johnson State College. The course really helps to show how mathematical learning takes place in a classroom and how to encourage students to think mathematically. The important thing to remember about thinking mathematically is that it is not important to memorize formulas, but to be able to understand what a problem is asking them to do. Thinking mathematically is being able to understand the idea of the problem and how to go about it, even if it may not be the “correct” way. A big part of mathematical thinking is being able to understand basic mathematical ideas without having a formal mathematical understanding.

   Math has always been a strong suit of mine, and I had never really thought of how difficult it could be for someone. This class has helped me to understand that it can be really hard to teach math. The books that we read for the course, especially “Learning Mathematics in Elementary and Middle Schools” were very helpful. This text has a lot of good ideas and activities to teach in a variety of ways. We used many different ideas in class of how to solve problems of the same type in multiple ways. We spent the whole semester focusing on ratios, fractions, percents, etc. and we saw word problems, visuals, and many other types.

   By doing multiple different types of problems, we were able to see how we all thought about math in different ways, which helped in showing how children could think about math in different ways. We all came up with different ideas, and being able to explain and discuss the problems really helped to show that people really think about math in different ways. It helped to open up my mind at least to accepting different types of work, and possibly thinking about just starting out teaching the students multiple ways that they can then choose from later on. Also, this course really showed me that children can completely come up with their own math ideas. The videos that we watched of classrooms, and being in a classroom, helped me see that sometimes it is best to just let students go on their own and not give them a ton of instruction, at first at least. Eventually, they will probably need the formal instruction, but they also need time to explore the work and come up with their own thoughts.

   We have worked a lot with learning how to develop lesson plans and it really has helped me. I developed two math lessons on my own, from the work that we discussed in class and implemented one of them in my practicum classroom. I was able to base them both on mathematical standards and by learning about the multiple means of representation, expression and engagement, I was able to integrate all the students’ needs into the lessons. Through the course work that we did with ratios and such, and the books we read, I was able to make lessons that fit for all students. Also, in class we discussed numerous theorists, such as Sharma, which helped when grounding the lesson and entry four in research. In many education classes I have taken, these are things that just get glossed over, but I feel in this class we really discussed them and were able to learn what the ideas are.  

    As we learned, there are many ways that math can be instructed and it is important to make sure to use many of these different ways. However, the ways that you use depends on the school and the classroom. Every child learns differently, and every new group every year will need to be taught in some different way. The school helps to figure out what math program is being used, bridges, thinkmath, or something else, and that gives the basic way for instruction. However, depending on the students, there always need to be a back-up, another way to successfully teach the same material so that they can get the most out of it. Also, the more interested  the students are in mathematics, the more likely they are to listen and actually soak in numerous ways of doing the work, or even come up with their own. Students who don’t like math are not going to want to come up with their own solutions or spend a ton of time trying to understand other ways. It is important to recognize the classroom and teach to the students that are in the classroom. It is very important not to make lessons for what you think the students should be doing, but to make sure that the lessons are based for the student’s levels that are in the class at that time. Sometimes, things need to be changed based on the students understanding, and even if you have something planned for the next day, it will not work if the students don’t understand today’s work. Part of teaching, especially in math, is being flexible and open to changing up your plans for the good of the students. This class showed us that. One day a classmate had a hard time believing that students could come up with some of the math answers they did all on their own, so we spent the next class discussing this, we looked at student work and watched a video showing a student coming up with their own ideas. This was not what was planned for the day, but a “teachable moment” was used. We got to experience many of the ideas of a smooth running classroom in the course, which was something that was very beneficial as a future teacher. I finally got to see how I could actually implement the ideas that I have being taught about for the last three years. This is the first education that I have been in where we actually did work with the ideas and got to see how they were used with us, it’s always just been reading out of a book. This class gave a lot of practical work and that really helped me.

   I know that many people struggled with Instruction Dynamics 2 because it is a math course, but that really made it more appealing to me. I am doing a double major with mathematics here at JSC and have always really enjoyed math. I find it to be very fun, and I do not allow myself to get intimidated by math problems, because I know that they are solvable, even if it may take a long time. I have always been strong in math, and I feel that this will help me when I become a teacher. I really can understand math and I’m one of those people that will work on a problem until I fully understand it, no matter how long that takes. This will help me when I’m a teacher, because I will be sure that I fully understand it before I try to teach the material to someone else. I feel that my love of math will reflect on the students. I will go in wanting to teach math, enjoying math and not having a fear of math, like so many people do. I will encourage the students to give math a chance, and I will have a positive attitude about the math classes, because I truly do have a passion for math. I find that when I have teachers who you can tell love what they are teaching; I learn better from them and want to enjoy it as much as them. I know that I am able to be this way with math and I hope that I will be able to encourage students to love math as well and really do well in it, not to get test scores that they need, but to help them. Math is everywhere in the world and it is crucial that everyone has a basic understanding.

    This class was definitely one of the best education courses I have taken. The work that we did was very field based, and we actually were able to do the work, rather than just discuss how to do it, which I really enjoyed. From this course, I was able to learn that thinking mathematically is about much more than just knowing the answer to a math problem. It is about understanding what problems are asking and how you can solve them, not necessarily actually solving them. If a student can look at a problem and know what it is asking them and know that they could solve it in many different ways, and understand why, then they are a strong mathematical thinker and the answer doesn’t really matter as much as that. I hope that I can take these ideas into a classroom of my own and teach children to truly like math, rather than just have to do it, and to be able to think mathematically in their own lives.

References:
*Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk,

 N. S. (2011). Learning mathematics in

elementary and middle schools. (5th ed.). Boston,

MA: Pearson Education

 

*Twomey Fosnot, C., & Dolk, M. (2001). Young

mathematicians at work. Portsmouth, NH:

Heinemann.

 

*Improving Mathematics Instruction for All: Professor Mahesh C. Sharma