New Insights and their Implications

In this class, I feel like I have learned so much and have grown as an instructor. I used to think that math teaching consisted of lecturing, formulas, homework, tests, but now I see so far past that. I know understand how important it is for students to understand why they are doing the things that they are learning. I know that using models and diagrams greatly improve comprehension. Overall, my views on teaching math have changed completely.

Summary and Synthesis

The clinical interview taught me more about thinking about the way students think. It is important to try and understand how they think when creating your instruction. Think about what makes learning easier for them and how to explain it best at their level. Asking students why they came up with that answer and how can tell you a lot about the way they think and solve. Every students may have a different answer as to how they got their answer and how they can explain it to you. Therefore, your instruction needs to be varied enough to address all students and be open-ended so all students can take their own approach on it and the clinical interview taught me about that.

Looking Back at Math

Since my internship, I have been thinking about my past math experiences.  I went to meet the teacher I would be with for my internship and it turned out to be one of the two favorite math teachers I had while I was in school.  As I sat there and watched her teach, I tried to figure out why she was one I chose as a favorite math teacher.  Nothing she did was way different than any other teacher who taught math.  Then it struck me, she let you do the math the way you figured it out.  You would just have to show her how you came to the answer.  So many times in school if you weren't doing the math the way the teacher was teaching it, you were doing it wrong, even though you were arriving at the same answer.  Both of my favorite teachers allowed me to do that!  I was one who liked to figure it out on my own, using my own methods and they allowed me to do that.  This is a lot what reformed based math looks like.  I hope that when I teach math I give the students the opportunity to discover methods on their own and find their own way of doing the math.

Summary and Synthesis

Recently, my group presented our LPU project over the Instructional Sequence of Measurement. In some ways it was harder than I expected, but in other ways it was easier. At certain points during the lesson, I knew exactly what questions I wanted to ask and it seemed to flow smoothly. Other times we felt more forced and awkward.

I'm always concerned about time (being able to fill an entire class period). Had you asked me at the beginning of the semester to plan a lesson that would last 75 minutes, I might've had a panic attack. However, the time seemed to fly by. We started with our first activity, and it seemed like 5 minutes later we needed to wrap up because the class period was over.

Both the time management and inquiry parts of the lesson I think can be further developed with experience. It's hard to plan questions and time limits for activities that you've never done before because you don't know what kind of problems, challenges, or questions will arise.

New Insights and Their Implications

After presenting our lesson plan, I have come to realize how much work it takes to present a thought-out lesson that will make my students think critically. It takes a lot of time and even after coming up with an idea you find to be flawless and after presenting it you may find flaws. The activities you do are very important and it can be hard to find the best activity to help your students understand each concept. I don't think you can ever settle on presenting the same lesson every year because there will always be changes that could be made to make it better.

Questions and Answers

Recently our group had to present our lesson on 'Place Value' to the class. My greatest concern was if I was able to understand and relay my understanding to the rest of the class. The lesson we go over in class are by no means necessarily easy to understand, they take thought and process. As we went through out lesson I was concerned I was not doing a good job explaining the game and students would be lost, but as the lesson continued they showed that they understood and I was doing an decent job at making them understand. This gives confidence that I can explain to people in a way they will understand.

Summary and Synthesis

From the last time I posted we have finished the first part of the class and began the second. We took the final and received our grades back. I didn't think the final was too hard. It was basically what we did in class everyday. The multiple choice was, for me, the most challenging part of the test. There were a lot of concerns throughout the class about scores and the difficulty level. The first few classes were tough to get into the swing of 'thinking outside the box" but as the semester went on it became more and more familiar and easier to put your self in that perspective. Overall I think the class has made me a better future teacher.

Personal Concerns and Next Steps

After taking the exam, I think my concerns were wether or not Dr. Reins would think that if we did poorly it was because we weren't listening in class or we weren't trying very hard. I think there were many students that were worried about the test before hand. Since we didn't grow up in an education system that made us think outside of the box, it's harder to train your brain to see math problems in a new way. I think it would be nice to have just a few sample questions before the exam so we knew more of what Dr. Reins expects or would be testing us on.

New insights and their implications

I have learned that everyone solves problems in different ways; even in our classroom. Each of us solve different problems in different ways. I have learned that as a teacher I need to be open to the idea that my students will all learn in different ways. I need to be able to accept that and learn how to teach them. I have learned many different ways to teach math and to assess it.

New Insights & Implications
I still find myself struggling in the class to grasp the idea of how to teach the way Prof. Reins teaches.  I can get the concept of learning a new way, but sometimes I don't get how we came to get an answer.  It is starting to sink in little by little, but I think that it may take longer for me to understand fully how to grasp teaching math in a way that students will understand it.  It will be difficult to teach in the areas that I continue to struggle in, but I'm sure that there will be someone to give me more help along the way.
Like Emily said in her post, when the answer is given to me I have an easier time understanding the problem or if someone explains it to me in simpler terms and jargon that I understand, then it isn't so confusing to me.  So far I have learned a lot and hope I can continue to do so.

New Insights and Their Implications

I learned a lot from the house project where we needed to determine how much paint was needed. It was interesting to try to figure out the answers based off of ideas from group members, how I would have done it on my own, and how students would look at it if I presented it as a teacher. I liked the idea, that someone mentioned in class, that students could take their own photos around the school so they would have their own angles to work with. Students can then see the real-life situation that they would need to know the formulas for areas of different shapes.

New Insights and Their Implications

Since I decided to major in education, and more recently during our class periods, I've been concerned that I won't be able to give my students a quality math experience, or the experiences that they need. I'm not trying to be arrogant, but I understand math, and I like math. Although I'm nowhere near perfect at it and it does take some work, it usually clicks fairly quickly for me. I'm concerned that because of this, I won't be able to help the students who need it. I don't know if I'll be able to explain the concepts to them, when they don't get it the first or second time.I'm not sure I'll have an answer to this until I get into a school and experience it.

Summary and Synthesis

After today's class period, I have come to the realization that no matter how much I think I understand something, I never really do until the answer is given. It is easier for me, and I'm sure a lot of other people, to understand a concept when you are able to work backwards after given the answer. I know that fully defeats the purpose of everything being taught in the class so far, but today I just could not understand how 1/3 of a cup could make half of the batch when 2/3 cup was said to make a full batch. Although Shari had tried to explain it, I just could not understand it right away until I thought about it for awhile. I wish things were easier and I could just get it quickly, but that hasn't been the case with almost every topic we've covered. I guess my biggest issues that I am most concerned with at this point and with the experiences I've had in this class are thinking of ways to teach using this approach, even if I don't understand it fully myself. It's very difficult sitting in class and thinking I understand the concepts being taught then struggling to do the homework outside of class. I'm not sure why I'm finding this class as challenging as I am, but I want to fully understand what is being taught and how to teach it well in a way for my students to develop the deepest understanding. I hope my struggles, in turn, make me a good teacher so that I can help those students who face these similar challenges.

Personal Concern and Next Steps

I have always been pretty good at math. I like the calculating and solving and the feeling of accomplishment you get when you can correctly solve a math problem. I hope to get a better understanding of why we do math and teach all the disciplines to our students. I hope that I can better grasp the hows and whys of math calculation and be able to better understand how to teach my students. I hope this class can contribute to my teaching skill set and help me be a better teacher.

Personal Concerns and Next Steps

Math has always been a decent subject for me. There are some concepts that come easier than others, but overall I have done pretty well. A concern of mine is that throughout my previously schooling, I was never taught the way that we are being taught now. It is a whole new concept for me do I think it takes some getting used to. In the beginning of class I typically feel frustrated, but by the end of class, things usually click. I am going to try my best to better understand this way of teaching in order to teach my students this way, as I feel it is very beneficial. Other next steps include asking for help when needed so I can get the most out of class.

Math so far.

In this class, I hope to gain a better understanding of why math problems work the way they do. I agree with some other in the class about how I enjoy math and believe for the most part I am fairly good at it however the way it has been broken down so far is one that has never been explained to me. It makes me look at other math problems in a way of breaking them down too. I hope through out this class we continue to grasp a deeper understanding to formula's and math problems. I believe this will then help us to teach our students as well as our peers to look at task from many different angles not the one that presents itself as the easiest or quickest solution. This concept will be able to be used across many curriculum we may encounter as teachers.

Thoughts on Math

I have always enjoyed math and was usually pretty good at it; however, I don’t feel that I ever actually understood it on the level that is being taught in this class. If I was asked to do more complex math tasks that I learned in high school, I probably would not be able to complete them today because I lack the understanding of the concepts that is necessary to retain what they are and how to complete them. Throughout this course, I hope to deepen my understanding of concepts in math as well as learn how to teach my students so they will have a deeper understanding of math. Without a good understanding, math can be difficult for anyone, so I hope to teach my students to overcome their struggles and understand math better.

Personal Concerns and Next Steps

This course is helping me to deepen my understanding of math concepts, as opposed to other math classes. Other math classes are more traditional and only teach factual math and only show you how to find solutions to specific problems. I like how this course is forcing me to use hands-on problem solving.  I like how the mathematics is being shown in generalization and being shown using real world examples.  It was difficult at first, because this learning style is not what I was used to.  I think it will be beneficial for me to be able to solve problems myself, so that I can more effectively teach others how to solve math problems.  I like how we are able to discuss and build on each others' ideas during class discussion, because we can come up with different solutions for math teaching techniques.  My largest struggle with this class has been adapting to the new learning style, but I think in the long run it will be beneficial to me. 

Personal Concerns and Next Steps

Math for me has been an up and down process. I struggled a ton while in elementary but I had a good instructor in middle school and began to catch up and really understand it. I then excelled in math through high school. Now that I'm coming back to it I feel as if the "use it or loose it" statement is really true. This is class was overwelling the first few class periods but now that we have gotten into it and really started to examine how important math is to students and how teaching it is crucial to their learning I have new perspective on it. I know that one day I will be teaching these students so I need to value what Dr. Reins says and put it to use and remember this is what will be best for my students when I get into the classroom.

How it's going

I have always been up and down with math. In school I understood math well until Jr. high and in high school I got it half of the time. College was pretty easy but it's only when I had a great teacher that I truly understood it. Right now I'm having a hard time understanding because this is a new way of thinking. It's hard to change your ways and learning habits and we as teachers are expected to do this to our students. I think that by going through this class will help me understand my students and help them figure out different ways to get an answer. I am excited for the moment that I truly get it I just hope it comes soon.