How has this course changed or not changed your perceptions of teaching math?

This course has so far completely changed my perceptions of how I will teach math to my future students. Thus far, I never questioned how I would teach math because I never before saw a flaw in the way that I was taught. However, being that this course requires me to think so much more in depth than I ever had to in my elementary, middle, or even high school days, I have realized that I was probably not taught the best way. I personally like the new way that I am being taught to teach, because I think that it is a better way for my future students to learn. When students need to use their peers and their own mind when learning, I think that the actual learning process is then better than just having a teacher stand at the front of the class and talking about concepts. This new way of teaching will in my mind be better because it allows students to connect concepts instead of just move on front one concept to the next.

New Insights and Their Implication

I thought that this course would be way over my head at the start of the semester, but I enjoy doing activities and problem-solving strategies that are still challenging but still have a relation to teaching elementary students. I am looking forward to the rest of the semester and though the two big projects will be challenging they will be beneficial and a good way for us to stay responsible and hold leadership for ourselves in this class. I have especially enjoyed the 'laft' activity in relation to the optimal mean concept because I had no idea we would be learning about standard deviations and understanding formulas by simply estimating a spot on the 'middle' of the laft where a certain number lies. These situations will help us instruct our future students and be able to find ways of explaining various reasoning strategies and math implications in ways they are familiar and comfortable with. I believe this course will be still a challenge for me but it will be good to be forced to take the type of math we are learning to think about it as if I would be teaching my class someday!

New Insights and Their Implication

Before taking this class, I had heard some pretty interesting stories. I heard it would be one of my biggest challenges so far in my college career. So, I braced myself for quite the adventure. I really really enjoy math and all of the concepts that go along with it. This class is very different than any other math class I have taken in the past. A lot of the learning happens on our own time through reading. I have found this class to be pretty challenging because it is not straight forward like other classes and we are required to think critically and problem solve on our own. My favorite part of class so far was the activity we did last week that involved mean standard deviation with the washers and the sticks. It was a good hands on activity and it was an activity that I learned a lot about. This was an activity that I grasped very well and was able to ask intriguing questions about! I was on the top of my game this day in class! I look forward to the rest of the semester because this math class really teaches us how to get children to think about math in a different way. The class forces us to think like a kid again, and that in itself is pretty fun!

New Insights and Their Implications

Before starting this class I knew that teaching math would not be one of the easiest tasks. I especially thought it would be challenging but rewarding at the same time. Since starting this methods class I realized that it truly takes more than just knowing how to do a math problem to teach math. It takes knowing the steps, how you came to such steps, and why you chose to use those steps. As our teacher you told us at the beginning of the semester that this class would be especially challenging to us and that mahy of us may struggle for somewhat of the semester. I believe you are right. I do not think that any of us have been taught math quite like this class, and from the sounds of it many of us still feel kind of lost. Every day that I come to class I learn something new and that really makes me happy. I am tired of sitting through boring education classes learning nothing. If I wanted to waist my money this way I would be addicted to gambling. I am hoping that this class allows me to teach math in ways that teachers have been failing to do for quite some time. Hopefully this method will boost the knowledge of math and the feeling towards math, resulting in better scores and knowledge. I think this class has a great constructivist view, and I am hoping to start seeing more benifits from learning this way soon!

New Sights and their Implications

I have never been a huge fan of learning math, however when I understand how to do a math problem I tend to enjoy it. Before this class I thought of elementary math as adding/subtracting and simple concepts like that. I expected this class to be about how to teach students how to do these concepts and learn facts about math. However, Dr. Reins has a completely different take on teaching math. At first, it was frustrating to learn because I am used to being taught a formula or equation and doing the problem. We were forced to think backwards and try to make connections which is hard for me to do. I do however feel that this is a great way to teach elementary mathematics. If students learn right from the beginning how to make connections and why formulas are what they are, students will most likely understand these concepts and realize how they are relevant in the real world. I hope to take from this class what Dr.Reins is doing and be able to help my students make connections on their own in math.

New Sights and Their Implications

My experiences with have been more so up and down. I catch on to some things in math easier than others. Basically math and I have never been a good match. But I have learned recently that when teaching math to the elementary school students is that we need to have the them see the connections. Like seeing how mean can be describe differently than just adding up all the numbers and then dividing by that number. Teaching the students about mean absolute deviation, standard deviation, also even using median, and mode. I may not be explaining this well but all these things are connected to each other one way or another, but it does depend on how you present these areas to the students. Also this class is making you think on the other side rather than what you already know based on what you were taught. This kind of thinking is hard to do and does make learning a little confusing until you catch on. The important thing is to ask for help when not fully understanding what it is being taught. It is interesting to learn from a different view point that can help students better compared to the way most of us have been taught in the past.

New Insights and Their Implications

I have disliked Math ever since I was a little kid.  I have dreaded every math course because they are always alike; completing problems out of the book or worksheet.  However, this is the first math class that I find somewhat interesting.  It requires us to use metacognition and deeper thinking.  This is a challenge for almost everyone because it is so much different than what we are used to.  My head was spinning the first couple of days but after I believe that I am now beginning to fully grasp that all mathematics connect to one another.  This new concept will help me become a better teacher and hopefully allow my students to understand mathematics better.  

New Insights and Their Implications

Math has never really been my favorite subject ever. So when I signed up for this class, I was a little hesitant and really didn't want to have to take it. I wasn't really sure what we would be doing and just expected everything to be out of the textbook and not really doing problems and activities in the classroom. I have learned a lot of different fun activities you can do with your classroom dealing with math. And the input from other classmates really helps me to understand a concept I maybe wasn't too certain about. That is an aspect of this class that I do like. Not everything is done by the teacher, he expects us to do the work and even go up to the board like today and explain ourselves. My favorite activity to date is the one we did with mean. By first having to figure out without any math what we think the mean is and then putting the washers on them and hanging them up to see where it was even. This is something I learned a lot from and was fun to work on too. Sometimes some of the stuff we do in this class are way over my head, but continually doing activities like that, I think should really help with my understanding of math so I can teach it better to my students.

New Insights and Their Implications

Math has always been a subject that I have struggled with. I think it is in large due to teachers making me memorize formulas and ways of solving problems, but not putting any meaning behind it. So far in this class we are learning the process of math problems and the reasons why we get the answers we do. Explaining how we come up with methods of solving problems is helping me understand why and how we come up with the correct answers. Learning this in class will help me to teach my students, so they can understand the process of math and hopefully have a better time learning it than I did!

New insights and implications

Math was never my strongest subject. I believe it is because I was taught to plug numbers into formulas without ever knowing the why or how of math. Throughout this course thus far, I have gained the perspective that math can be figured out without just being handed a formula. For example, today (9/22), we learned how to find the area of a triangle without just being handed the formula and told to plug in the numbers.

New Insights and Their Implications

Math has always been a subject that has come easily to me. Throughout my education, I have memorized formulas, and use them correctly to find the answers. After starting this class, I have found out that formulas are not everything. There needs to be a reason for the formula and an explanation for why. I understand that everything connects to each other. This class had made me think of different ways to solve problems, and sometimes it may take more work for me to understand because I am not used to this kind of concept. However, through learning these new concepts, I will be able to teach children at a younger age. When the concept actually comes up in later grades, they already have some understanding and it will be easier for them.

New Insights and Their Implications

Math is a subject that has always taken me a little more time to grasp than it may have for some others. I was never a bad student in math, I just had to work harder than some other people who, I felt, just 'got it.' Within the first few days of taking this course, I began to realize why I did not immediately understand the new concepts that I was taught in school. We were always supposed to memorize formulas, that all looked similar to me, and were never told why the formulas were that way. We just had to know them. I realize now that math was difficult for me because I struggled to make connections from one concept to another in higher math education. I have learned in this class that these connections are what gives a person the ability to truly understand math. The implications of this simple concept are huge. Learning how to help students form these connections will likely help me to become a better teacher in the subject of math, and will help my future students to become more proficient in the subject as well.

New Insights and Their Implications

I came into this class expecting to work out of the textbook or with worksheets, completing various math problems while also discussing how to teach these types of problems to K-8 students. It has been a little bit of a frustrating transition to thinking of math problems in this way because it is totally out of my comfort zone. I am a math person. I love math and I have always been relatively good at it, but this class makes me rethink that all together. It makes me realize that I really only learned math on a single level. So far, I really like this way teaching math. I am also a SPED major, so I am also thinking of how this type of teaching would help SPED students. Though it's tough for my brain to switch gears, I am really enjoying this new way of thinking about math problems.

New Insights and Their Implications

When I first started this class, I assumed it would be how to add/subtract, multiply/divide, and maybe go into fractions and decimals. I have learned that math is much more than the simple concepts I learned when I was in school. Learning math is so much more such as doing projects and activities that attract learning and intensify the potential to retain the information learned. When Dr. Reins was doing the lath project, I sort of tuned out thinking it wasn't really a math activity. When he went into more detail and showed what we learned in mathematical terms, I completely understood. I am now looking at this class with a different eye looking for the hidden message in a fun activity.

Personal Concerns and Next Steps

I have always been fairly good at math. Sometimes I would need a little extra help to understand something, but I was in accelerated math during high school and elementary school math was simple for me. In this class, it is hard for me to understand the project base method. I get confused at first, but after doing different problems, I am starting to understand this way of teaching. I know teaching through project base will help many students; it will just take some time getting used to. If I keep working hard in class, I feel as if I will understand how to teach my students, by the end of this class.

New Insights and Their Implications

So far it has been quite interesting to learn about how to teach students math. A lot is stressed on how to connect, how to understand, and how to implicate, rather than how to come to the correct answer. Math can certainly be a hands on activity; which I think could help the students a lot. More hands on learning can create an enjoyment of math in students. This can also help students understand math. Math can be a lot of abstract thinking rather than right or wrong.

New Insights and Their Implications

So far in this course, I have learned how to create activities that students will enjoy to help them learn more about math. I never would have thought about using some of the demonstrations that were given in class to develop the concepts we have talked about, such as the mean or scale factors. The math classes I was exposed to offered little hands on activity and more worksheet or practice problem format. This seemed to be ok, because I was interested in math, but I could not imagine doing that day after day if I did not like or understand math. These are great tools for getting all students interested in math and developing knowledge that they can use later in the class or in the following school years.

Questions and Answers

Before this class the role of the teacher seemed to be the all knowing that would provide steps for the students to take to accomplish a goal. I know see that the questions are just as important to as the answers and that what students learn while getting the answers can be more valuable in the end. If students questions themselves during the learning process and focus on how they are going about the process of getting the answers they will end up with an answer and a better understanding of how they got their answers. This new process of asking questions to help student find answers, though takes time and hard work, is an exciting process that i truly look forward to implementing in my class.

What knowledge have you gained about how children learn mathematics from this course?

1. I have gained a lot of knowledge about learning math in this course. Children all learn differently, we all already knew that, but what was unknown was different ways to teach how to solve a problem so that many different children can find the correct answer based on what they already know. Children can come to the same conclusion, same answer, even if they start at a different spot of the problem because it depends on where they are at and how they are attacking the problem. It is important to let students know that they can make mistakes and that's ok, it is also important to let children explore a problem before you give them too many limitations, the "correct" way to solve the problem or the answer. It is also valuable to let children discuss and verbalize what it is they are thinking, how they are getting to their solution.

What knowledge have you gained about how children learn mathematics from this course?

What knowledge have you gained about how children learn mathematics from this course? I have learned that children truly learn in different ways and those ways have to be met the best way possible. There is more to mathematics than showing students "this is how to do it" and then hand them a worksheet to work out similar problems. This procedure or way of teaching makes future math teachers to underestimate their students abilities because they only know how to think of a problem one way. Teachers need to become aware of what their kids know and then go further indepth on the topics that need to be. Children are really curious at different ages and I think teachers need to take that into consideration as well. When using manipulatives, question the students about them and about how they are thinking. Who knows how many ways will turn up to solve one problem.

How has this course changed or not changed your perceptions of teaching math?

I originally thought that math was as basic as introducing a basic formula to students and building on that. I never thought much about using manipulatives past the younger ages of students. I liked how the class forced me to look at problems the way my students would and break them down in order to be able to teach them to my students. This class frustrated me several times because it took me so long to understand the importance of breaking problems down the way Dr. Rein's did. Students need to be challenged and given opportunities to approach problems in different styles. Each student learns a different way and at a different rate, which means that my instruction should cater to the differences of my students. In order to teach a problem, it is important to start with the basics and work my way up.

Last two Questions--Kendra Lundeby

1. What knowledge have you gained about how children learn mathematics from this course?

• While being in this class I have learned many important aspects on how to teach math. I learned that is important to teach students the strategies and steps to reach the understanding and solution rather than just stating a formula. Explain why the formulas are set up the away they are and plan many activities to learn the stages of the problem. Teach students the foundation of the math so they create a strong foundation of the material before they need to use it in their worksheets and activities. I have gained a better ideas on how to properly teach math so that more students are understanding the material. In this course I have gained an understanding on how the teach math better while being in this course.
  

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How has this course changed or not changed your perceptions of teaching math?

This course has changed everything I have thought about math and doing math. I now know that helping students to reach inside to help themselves build on prior knowledge is a great way to learn math. Once given a problem, students are able to figure out a problem with out equations that they would have memorized in the old way of teaching math. Often students, if given time to think and struggle, will find a way to solve a problem.In the same classroom, with the same problem, there will often be many different ways that will be shared for solving the problem. Students will then learn that with the different ways to solve a problem, they can use other strategies to check their work. One of the things that really stuck out to me was that students should be praised, even if their answer is wrong. I think this is a great concept, because if a student is afraid of making a mistake, they will not try very hard. Overall, I think this class was great because it helped me see a whole different outlook on teaching math.

Knowledge gained

What knowledge have you gained about how children learn mathematics from this course? I have learned that some educators underestimate the abilities of children to solve mathematical problems. Teachers do this by sticking to the material in the book and only assigning worksheets instead of creating a classroom where students are able to really show what they know and the processes they take. To truly learn mathematics, children need to be presented with real life problems and allowed to discover the answers on their own or with classmates or at least attempt them. Too often we are just taught the rule but are not informed of why the rule is the way it is when knowing the reason would have students understand mathematics much more. Every child has the ability to learn, but it is up to the teacher to create material that is pulls students in and has them interacting with the material.

From this class I take so much knowledge and I feel more confident not only on how to nurture every students learning styles but I also how I learn as an individual. I have gained confidence regarding teaching math. Math is one of my weakest points in school and it has always been. I was terrified to get into a classroom and teach math, I felt unprepared and not capable to introduce any sort of math. I may not be able to nurture every students learning ability but I feel confident and prepared enough to reach more than 90 percent. I have gained a tremendous amount of knowledge in this class and I cannot wait to put it all in practice.

Perceptions of teaching math

How has this course changed or not changed your perceptions of teaching math? I feel more confident about teaching math. When I was in high school all my teachers taught math pretty much the same way. They would do the examples out of the textbook and show them on the chalk board, and then give us an assignment from the textbook or worksheet. There was never an explaination of 'how' or 'why' we solved the problem that way just here it is learn it method. I now know that there are many different ways to teach math to students. It is good for the students to struggle with the material and work on it by themselves to find multiple ways to solve a certain problem. The students may also use (electronic) manipulatives to help them work out the problems intead of just paper and pencil. I will always find exciting, hands-on ways to teach math to my students so they become interested in it!

How has this course changed or not changed your perceptions of teaching math?

This course has definitely changed my perceptions of teaching math. Before taking this class, I always thought that maybe it wouldn't be so hard to teach math to young children. I have now realized that it can be quite the process. There is a huge difference between children understanding math symbolically and children understanding math conceptually. I have learned how important it is to gain a conceptual understanding of math. We need to understand why we do what we do. When I learned math, I learned it the symbolic way. It was easy for me to understand, but I know that will not be the case for all children. Some students will need further instruction when it comes to math and will need to be taught in different ways to fully understand math. I feel as though this class has changed my perception of teaching math in a good way. Sometimes this class was frustrating because I had a difficult time understanding some concepts; but I definitely understand now why the strategies that we did were important. Gaining a conceptual understanding of math and using manipulatives is extremely important and I plan on teaching students math in this way.

How has this course changed or not changed your perception of teaching math?

This course has changed my perception of teaching math in many ways. Before taking this course, I thought the way I was taught math in school was going to be the way I would also teach it to my future students. Until this course, I thought math was about rote memorization, worksheets, and formulas. This is probably why for many people who are not good at memorization do not enjoy math and therefore dread having to teach it. After taking this course, my perception of teaching math has really opened up to the possibilities of making math fun and enjoyable for students. Engaging students in hands-on activities, using manipulatives, working in groups, and having students think about what they are doing and justifying their work are all important concepts I have learned to do when teaching math. Before this course, I was also unaware of the power in using concrete, semi-concrete, and symbolic models were. If using these models helped my grasp a deeper understanding of math concepts then I know teaching it to my students will help them as well. I feel better today about teaching math then I did previous to this class.

How has this course changed/not changed your perceptions of teaching math?

This course has completely changed the way I thought about teaching math, and the way I thought about math in general. I now realize the importance of allowing opportunities for students to understand the reason why you do something in math (area formula) instead of simply telling them what to do and giving them a worksheet. I also now realize how important it is to have a few projects that are real world related. When I was in school I would often wonder why I had to learn certain math things; with opportunities like these students will know why they are learning the things they are. I have also learned that children want to be challenged. Sometimes educators think that a math concept will be to hard for their grade level of students. I believe that with the right instruction students will have the confidence to tackle some of the hard problems and even learn form their mistakes.

How has this course changed or not changed your perceptions of teaching math?

This course has changed my perception about teaching math in many ways. The prospect of teaching interests me in many ways because of my desire to engage students creatively with the material and information that they need to learn. Math has been a subject that I didn't think that I would be able to approach in that manner. Based on my history of learning math it has all been rote memorization and replication of work. The worst part of math for me is when I could find the answer but didn't follow the steps that the instructor required and was counted as incorrect for the work. This class has taught me that if I am willing to put the work into my lesson designs math can be taught in a way that it engages students and supports their actual learning, not memorization. This belief that math can be taught in a way that allows the students to construct their knowledge and possibly find enjoyment and challenge in the subject of math motivates me. This motivation will lead to creating lessons that challenge students through creating significant math tasks, creating an environment that supports mistakes, and supports students in doing math. This class has definitely changed my perspective on teaching math, but more than that has supplied me with tools and knowledge to continue to grow professionally in this area of teaching.