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.

Personal Concerns and Next Steps

I've talked to other students that have taken this course and some described it as frustrating. I've always enjoyed Math and been able to understand it fairly well so this didn't concern me. Being farther into the course, now I know what they meant. I felt a little lost in the beginning, but now I am starting to feel better. I know it is because we are having to think about the math like I never had to do in any math class before. I can tell that this way of teaching is much more beneficial for students and plan to teach more like this and less like I was taught. I do feel better about this course now, but I know that I may struggle with it throughout the semester. I get frustrated when it doesn't click for me right away. I know that I have to keep putting in the extra effort and maybe start spending more time on assignments and even visit some office hours to fully understand what we are covering.

Personal Concerns and Next Stages

I have always struggled with Math. The first few classes that we had were extremely overwhelming and stressful. I completely agree with certain concepts that Dr. Reins has spoken about. One major thing that I took to heart is taking time on each topic and not rushing it. For some people, including myself, I need more time for professors to go over the material and I need time to process it. In this class I hope that I get the information that I need and have plenty of time is taken on each topic.  As the semester has gone on, I am starting to understand the concepts-which is promising and is starting to build my confidence in this difficult subject. If and when challenges arise I will try different solutions to answer questions (looking outside of the box), I will collaborate with my peers, and also go to Dr. Reins.

Personal Concerns and Next Steps

I'm not sure when or why I lost interest in math, but when I left elementary school I feel that math became more challenging every year. When I was younger, every day after school I would sit at home and practice my math flash cards, not as punishment but for enjoyment. I loved the board races, "Around the World," and other forms of competition that our teacher would let us do to help us to remember math facts both quickly and correctly while having fun at the same time. I've always been someone who likes a little competition, and when I knew I would have to participate and race against my classmates, I would practice that much harder to make sure that I was the best in the class. When I started middle school, I feel like the fun was taken away from learning. Not many teachers would incorporate excitement into their daily lessons. Direct teaching was most certainly the top method of instruction, with the teacher writing the notes on the overhead as we copied them down before completing an assignment with twenty of the same types of problems over and over again.

When I lost interest in math, I would not try to fully understand the material, but simply memorize the steps so I could do well on the exams. I've always done fine in math, but it hasn't come easily. So far this semester I have realized how much deeper my understanding would be if I had been taught by the method of instruction we are learning in class now. To help me find my strengths again and to be successful in this class, I will need to participate in class by asking questions, push myself with every topic by reviewing the material daily, and really look at the big picture instead of just memorizing how to do the problems.

Questions and Answers

One of the things I've been thinking about during this semester is the effectiveness of this type of mathematical instruction. I really do believe that this method is effective and could really make a difference in many students' learning. However, I wonder the effect it will have if the students only work with math this way for one year. At best, everyone in our class will leave this semester after having mastered this method. Since we won't all be teaching together in the same elementary school, though, will this kind of instruction be advantageous when surrounded by years of direct instruction?

I realize that the teacher after me would then need to spend less time on the topics I covered the previous year, but I'm still concerned that the curriculum plans wouldn't match up between years of problem-solving instruction and direct instruction. My personal solution would be to teach middle school mathematics so that I could continue with the students for two to three years rather than just one. That seems like an easy way out, but the alternatives are risking a disconnected curriculum, submitting to direct instruction, or trying to persuade other teachers to use this method.

Math has never been an easy subject for me.  I have struggled with it all of my life and coming into this class I started to feel more defeated.  Hopefully throughout this semester I will be able to understand the concept of how to teach math a new way. So far I have struggled a little but it is becoming easier to understand.

Personal Concerns and Next Steps

So far I have found this class very challenging. I have never been in a class that has been taught in this way. I have always done fairly well in math growing up but this class makes me feel like I know nothing. Hopefully, I begin to understand the teaching methods used in this course. It is a great challenge and really gives me a new way to look at both learning and teaching math in a classroom. I think I will grow a lot from the experiences in this course.

Personal Concerns and Next Steps

Math has always given me trouble throughout my school years. It started when we first learned how to subtract numbers with two digits in elementary school, and got worse from there on out. I am afraid that this class is going to give me trouble because of my history with math, and I'm afraid that I won't be able to teach it well to my students. There are some math topics that sometimes click right away and I understand them, but others take a long time for me to grasp. If I keep having trouble with understanding concepts, my next step will be to ask Dr. Reins and/or my peers in the class for help with the problems.

Personal concerns and next steps

I find this course very interesting, but I do think it will become more of a challenge for me. Math has never been my strong point. I think it is because I had very bad teachers all throughout junior high and highschool. My personal concerns are that I will fall behind and not understand the information before the test. I hope that if I get help from Dr. Reins, from my peers, and pay attention in class then I will be able to be successful in this class. My next steps are to keep up with the homework and get as much help as I need to keep up with everyone else.

Questions and Answers

When comparing the United States to other countries in Math. I was wondering if the tests have the exact same questions. Are they questions asked in a way where the students need to think and discover the answer (as the way we are being taught in class) or are they well defined so the students know exactly what they teacher/test is asking of them? I think it would be fair to compare our progress with other countries if the questions were the same, but I'm more curious about wether or not it's how we were taught math or how we were taught to thought process.

As a kid, I remember having problem solving questions that I could go one way or another if this…or if that… but I never knew what the teacher would be grading me on, so I would spend my time trying to guess what the teacher wanted. Then time would be running down because I had spent all my time trying to think of different senerios. Finally, I would just have to guess on following questions because I ran out of time. Which leads to another question: If the tests are going to be timed and determine someones math ability, shouldn't the questions be well-defined? I personally like problem solving questions and could sometimes spend forever trying to figure out different possible answers, so I think it would be nice if tests questions were either ill-defined and have no time limit or well-defined if there is a time limit.

My Thoughts on Math

I have always loved math.  It has been my favorite subject since middle school, where I had a great math teacher who actually challenged us in math.  She taught us how to think on our own and come up with our own way of coming to a solution.  My freshman and sophomore year in high school our teachers were very procedural based which did frustrate me because I like things to make sense why I am doing it rather than just do what they are telling me to do.  Then my junior and senior year I had another great teacher who also challenged us to think on our own and it that it is okay to go outside of the box.  My only problem with math is I know how to do it in my head, but when I try to explain it to others I don't think it makes sense to them.  This class, however, is teaching easier ways to put what I am thinking into words for others to understand.  It was crazy that I have actually seen that this class has allowed me to express myself in math after only being in it for a short time.  The students in the youth group I help out with know that I love math, so they often ask for help; last week I was helping a girl with some advanced math and she was so confused.  Before I would just give them the answer because I didn't know how to explain it to them, but this time we actually had a discussion about it and it was like a light bulb went off in her head.  So it was encouraging to see, and I am looking forward to see how much more this class with help me stretch and grow in teaching.
April Buse