Q and A

Most of the math classes I have been in have pertained the normal method of teaching math.. show you the most common way to complete the problem and that is how you do it. From Math Methods I have learned that this teaching style is hightly looked down upon, and I am happy about that. I feel that it is very important that multiple approaches to the same problem are displayed for students. I also think that students should be encouraged to come up with new approaches and really try to look at the problem in a new/different way. I like how this is stressed in our class and although there are times when I feel there are no more possible ways, there always seems to be a hidden approach out there just waiting to be discovered. Encouraging students to explore the possibilities of how the different problems may be answered in numerous ways will also force them to use prior knowledge and relate tasks that they have learned in approach previous problems in order to advance in their learning and develop different learning approaches to problems.

New Insights and Their Implications

This class really opened my eyes to learning math. I always thought of math as something that was really cut and dry you either got it or you did not. And I generally got it so never really struggled with it or worked with it or thought more about it, I just knew what I did. I never really realized that there was so much more in math to explore and so much of a deeper understanding to work with, and to know a couple of main concepts and be able to solve pretty much anything. The instructor and working with my peers through some problems really made this realization clear to me. I have gained a very different perspective of math through this class.

Q & A

Like many, I was hesitant about taking just another math course. However, this math course has been unlike anything most of us have ever experienced. I did come into the class with many questions, such as “How am I going to start out with limited materials and teach math in an innovative way?” and “How long will it take students to adjust to this new way of doing math?” and “How much better are students actually performing?” I have found that there are many schools starting to incorporate this new way of teaching math and I am excited that these students are no longer being drilled for hours on sets of math questions that they will learn how to do after the test.

The way my past teachers and professors usually teach math is by the though, “There is only one right answer and only one correct way to find the answer.” I have had high school and college professors both take points off for not solving the problem right [a missing minus sign, numbers messed up]. I think this is unfair I strive to never do this to my students. I always wanted to know why it mattered about making little mistakes when I knew how to solve the problem and I got the answer right. I do not know if I will ever find out an answer to that, but I hope I never make my students wonder the very same thing.

Question and Answers

How will I find time to do the constructivism method when I am a teacher? 

I have thought about this question a lot because I know that this method is hard to find time for.  I would like to do this for every period of the day, every school day but I know that in the busy world of a teacher, that is not possible.  What I will do so that I can incorporate it a little into my lessons is try doing it once a week, for one or two periods of the day.  Throughout the week I can do discovery learning and provide lots of tools that will encourage the constructivism method.  

I do wonder how all of that will work out.  It is easy to plan for something when you are not actually in the field, with all of the work that is involved with being a teacher.  Once you are actually out in the field many things come up and you may have to cut back even more then I already have on, the constructivist way.  I will have to wait and see if this can become a reality.  

Personal Concerns and Next Steps

My first concern with this course is learning the different strategies and styles of teaching. I was taught the traditional way which has resulted in me being stuck with the procedural way of learning and knowing mathematics. This class has challenged me, and made me think about mathematics in a different way. I feel the techniques we have learned in this class are preparing us tremendously for our future teaching. My next steps for this class are to take the concepts we have been learning and apply them in my student teaching and continue to learn more in the future. I really enjoy this class and I feel it is preparing me for my future teaching career.

Questions and Answers

When I started this class I had a negative view of what math and did not want did not want to have to teach it. I never understood why fractions are inverted when dividing. Why can't we just multiply across? Through the fraction bars and cosine air rods I was able to understand more about fractions and why we have to do invert and multiply. I also learned that pictures and representations of the fractions can help students understand fractions better then just given them a formula. After doing the activities in class I feel better about fractions. I am also nervous that I will not have time to to do CGI with my students and my question is how do teachers fit it into the day? I definitely want to make sure that I am using CGI with my students because I believe that it is one of the best ways to teach math. I may not be able to do CGI with my students every day but I know that I will make a great effort to do CGI with my students at least twice a week.

New Insights and Their Implications

I feel as though over the course of this class I have really come to have a new understanding of mathematics reform. I see where it is coming from (TIMSS studies)and why it is necessary to change how we are educating our students. The only issues I have with the new reform are that I think it is somewhat out of context to compare ourselves to Japan and China because we allow our children to be children, we give them summers and we want them to learn, but our cultures are very different and we cannot expect to "catch up" with those countries just by changing our methods. I think it is worthwhile to reform our mathematics I just hope that it is not expected for us to be even with Japan or China in the very near future. I will be interested to see the results of the latest tests. The other insight and implication I have is that I am training to become a special education teacher. Yes, I will be certified to be an elementary educator as well, but I want to be a SPED teacher. What I am learning in my SPED classes is that inquiry learning is not effective for students who are struggling. Direct instruction has been found to be the most effective for struggling learners. So my question is, will I be prepared to teach the traditional way if that is necessary for my students? I think I will, and I think it has been worthwhile to learn the different methods of teaching. Those are the implications and insights that I have been dealing with lately.

Personal Concerns and Next Steps

I am concerned about teaching mathematics in a constructivist manner. I was taught in a different way and I think it will be extremely difficult to get away from teaching that way. This class has really taught me the importance of teaching in a constructivist manner and that is how I want to teach my future math classes. However, I feel like I am not completely prepared for that just yet. I suppose to take the necessary next steps I will study more about constructivism. I will try to learn as much about it as possible so that I can apply my knowledge to teaching math in the future. I have already learned so much on constructivism, but I feel like it is not enough to prepare me for teaching in that way. I suppose I will just have to give it a try when I get out there and hope that I can teach in a constructivist manner. I hope that I am able to be a good constructivist teacher because I know that students learn much better through a constructivist classroom.