Personal Concerns and Next Steps

I have always enjoyed doing math and taking math classes. I think the reason I liked math was because the problems had a set of steps and as long as you followed those steps in the order you were told you would get the correct answer. I have always been good at following steps and therefore received good grades in math. Until this class, I never thought about the reasons behind doing the steps and having to follow them in certain order, I always just did them. I memorized the rules and followed them. After taking this class, I am now concerned about all the things I really didn’t know about math all along, the “why.” Why do the steps result in the correct answer or why does that rule work? For so many years, I have done math the traditional or instruction way without really knowing why. I know habits are hard to break and I want to make sure my future students know the reasons behind why math works and be able to construct their own rules. I want math to be relational for them not instructional like it was for me. In class, it has been hard trying to reconstruct what I already know about math and not resort to just using the formulas to find the answers. So far I have been able to follow along pretty well and after taking a look at the processes of why the steps and rules work and multiple entry points of problems I now have a deeper understanding of math. I am just afraid I won’t be able find a way to make all math relational to my students. I now know how to make the things we learned in class relational but what about math topics we didn’t cover. Will I be able to teach in a relational way or will I resort back to what I already know and teach the traditional way. How will I know what to do or how to teach? This class has really opened my eyes into a math world I didn’t know existed and now it is up to me to find the confidence to re-teach myself and find out more of the “why” behind the rules.

Summary and Synthesis

Well, I have learned things the hard way and sometimes that is the best way to learn them but sometimes it shakes you right down to the bone. I really have learned a lot about Math in a more relational way which is how Math should be taught. Kids will learn better especially when they relate and make connections to the material. It is hard to go from a way of learning you learned throughout school and just all of a sudden switch. That is why it is SO important for children to have this type of relational learning from the beginning. This class has given me a new insight into Math (one that I honestly didn't even look at because of the way Math was taught to me). Even though the traditional route is the most common form of teaching; it doesn't make it the most influential! I am still scared that my fears about Math will cause problems in my future class but it is a challenge I am trying to face and conquer (somtimes it is not as nearly successful as I want it to be). Finally, I think it is important for children to know the HOW and the WHY when learning Math. I honestly don't remeber wondering why we invert the second fraction when dividing; I think that is because of how long I was taught through an instrumental way. Tons of children ask this question though and what do teachers say; honestly? After this class, I do have a better understanding of why to do certain steps.

New Insights and Their Implications

So far, this course has given me some great insights as to the new way of teaching math. I have learned that we need to work towards giving our students more of a relational understanding instead of an instrumental understanding. It is imperative to make connections between what they are doing and why they are doing it. From the discussions from my peers and from Dr. Reins, as well as the research I have done through the LPU, I have learned that students learn math best when concrete experiences are worked into symbolic experiences. This can first be done by first working on concrete examples through manipulatives and visuals. Then once the students obtain and understanding of the concept, they can move into semi-concrete examples by still working with manipulatives but by adding number sentences, etc. Then finally, once the students have grasped the concept, they can learn the symbolic meanings of what they have already learned. By doing this step by step, the students can gather their own conclusions and meanings on that topic and develop their own understanding--rather than it just being given to them. All of this is going to be extremely helpful to when I teach in the future. Since I am used to more of a instrumental way of understanding, it is important for me to switch my ways and develop my own teaching into a relational way of understanding. By doing this, my students will become successful learners in mathematics.

Personal Concerns and Next Steps

Upon entering this class, I really enjoyed Math. It has always been one of my favorite subjects and I felt as though I understood the basic concepts. For my internship, I helped in a 7th grade math classroom and I loved it. After that experience I had positive intentions of teaching Math in my future. Before taking this class, I was excited to learn how to break down math and learn more about teaching it to younger kids. After participating in this class, it has really made me look at math a whole different way. Some good, some bad. It makes so much more sense to teach kids on a relational basis rather than an instrumental basis. I came into this class strictly knowing only an instrumental basis of math. To me, the instrumental understanding makes sense because that is how I have always learned it. It also makes much more sense to teach kids a relational understanding of math. I am definitely more concerned now about teaching Math in my future because even I struggle with understanding a lot of what we are currently doing in class. If I have a hard time understanding it then I am worried about teaching it to my students. My concerns have been lessened a bit by understanding the process of teaching through concrete, semi-concret, and symbolic ways. I now understand better how to teach in those ways and how beneficial they are to students. I still struggle with it, but it is beginning to make sense. My next steps include trying to work harder in our math class to understand your styles of teaching and understanding the "why" part of mathematics. I think it is important for us to understand why we do stuff so I am going to continue working hard to understand that. Since this class I have developed a lot more concerns with teaching math in general as well as my own knowledge in math, but my next steps will include working hard to develop a more thorough understanding.