Constructivism

I think of Constructivism as Student Directed instruction. Concepts that keep gaining more discussion on. The students are engaged and keep discussions going and getting to the depper meaning of ideas.

Constructivism

Constructivism is building knowledge by using prior knowledge. Through constructivism, students learn new information by building upon their prior knowledge. A classroom that uses constructivism is student centered. A student centered classroom consists of hands-on projects, group work, field trips, etc.

Constructivism

When I think of Constructivism, I think of a building on to prior knowledge. Students learn by connecting new information with what they already know. A teacher who runs a Constructivist classroom tends to focus on student centered instruction. The classroom is hands-on and deals with a lot of group work. Constructivist teaching actively involves students. They are adding on to what they already know.

Jessica Murphy

What is constructivism?

Please comment to this post (by clicking on the "comments" link below), do not start a new post. Write your initial feelings as to what constructivism is to you. Do not ask anyone, look up anything, or read your colleague's comments. It is important that these are YOUR preconceived notions of what constructivism is to you!

Personal Concerns and Next Steps

You may blog about genuine personal concerns created as a result of the experiences in this course.

These last few weeks of class we have been listening to different peers present about different topics. We have mostly followed a progression from beginning number sense to learning about different probabilites. While everyone has done an excellent job at their presentations, I still feel like I do not have a full understanding of the different topics. I tried my hardest to follow what they were saying and complete the different activities. I would have liked a little more. I'm not exactly sure what, but something could be changed. At times everything felt very disorganized. We also nine times out of ten ran out of class time for further clarification.

Using the constructivist approach to teaching seems very important in this class. For me to feel comfortable teaching somewhat in a constructivist approach, I need to feel comfortable with the materials presented in the classroom. I know I am going to have a variety of students and that I am going to have to present a variety of levels to a topic. I will have to review materials and hope that they sink in. I almost feel that there was too much material and not enough time.

Personal Concerns and Next Steps

Now that we are starting the last week of classes this semester, I find myself looking back at the semester. My views on math have changed along with how I will teach math. Especially after conducting the clinical interview, I feel that my views on teaching math have changed. I never realized how huge a process it is. I always thought it was a bunch of memorization. It was either you got it or didn't. I would like to conduct some sort of clinical interview on my students someday. I think it would be very beneficial for teachers to do this with their students. I sure wish one of my elementary teachers would have done a clinical interview. I wouldn't have struggled so much with math my whole life had one teacher realized the way I was thinking about math was wrong or needed clarification!
After teaching a lesson to our class, I have also realized how hard it is! You really have to know your stuff. How can you effectively teach without knowing the material. That scares me. I'm scared I won't be able to teach math in a way that my students will truly understand and comprehend. I know it will take a few years to get into my groove of teaching math and other subjects. But what about those poor students who get those first years of teaching?

Personal Concerns and Next Steps

I have had a lot of thoughts about class today (we talked about the Equity Principle) and I just wanted to talk a little about that topic. It very clear to me that much of what we do in teaching is better "said that done" and one has lots of ideas about what should be fixed or what should be done, but when it comes down to it, it's really hard to implement. I find this to be a struggle within my heart and my head because I have a true passion for helping students get to their full potential. I was watching a program last night about a district in Washington, D.C. and they were talking to a principle in this district that said if he could he would fire over half of his staff. I found this to be very interesting and he said his main reason is because they don’t set high standards for the students (they teach in an impoverish neighborhood) and they don’t believe the students can achieve high. To me that was very upsetting those teachers think and believe that way. In that case maybe it would be a good idea for him to fire them. It is important for people would WANT to help students and who CARE about students and take this seriously to be teachers. It really bothers me to see people who could careless TRYING to become teachers and passing some how... I think it would save our school districts a lot of headache and stress if we weeded out the teachers who don’t actually care about the students and being a good teacher. Teaching is a life changing experience and by that I mean we have the ability to change lives. We can all recall a time when we have had a "bad" teacher and it scars us or helps us, but either way it affects us. I just want everyone to stop and seriously think about why we want to be teachers and do what it takes to be the best that we can be, not only for ourselves but for our soon to be students also.

New Insights & Their Implications

I want to talk about Cognitively Guided Instruction and how much I love it. My internship teacher used this approach with her first graders. So I have seen it modeled several times. When she first asked me about it I was very unfamiliar with it and felt so behind. Little did I know that I would learn about it soon.  The principal asked my field based supervisor to go toa a training workshop and teach it to the other staff in the school. I remember one day she got a substitute and I observed her teaching math to other classes other than her own using the CGI approach.  I watched her use CGI with her students and demonstrate it for other teachers but never really understood until this class. What I particularly like about this approach is how students have a choice for which strategy they want to use in solving the problem. I also like how they can choose to use or not to use manipulatives. What I really like about this program is how all the students come together at the end and a select few will share how they worked through the problem. It helps us as teachers know their understanding of the content and helps kids think of other ways work. One thing that I loved is that my teacher used Math Journals. She would print off a story problem for each child and they would glue them in their notebook. These stories were made fun by using different the names of her students.  She would then ask them to write in marker because she wanted to see their thinking and that it was okay to make mistakes. I would never have thought of that! It is a great idea! I feel so fortunate to have been able to learn about this approach in class and to be able to see it in action. I know that a lot of teachers out there are now just learning how to implement CGI. As future teachers we will be able to go into the schools with the training already under our belts! This is something that we are going to need to know because Math will most likely not be taught the traditional old way. More and more schools are adopting this approach. 

New Insights and Their Implications

I have learned a nimber of things in this class. I think that it has been helpful to see different ways that we can teach the students. I really enjoyed the CGI approach. This approach has really made me think about the different ways I can teach in my own classroom.
I really liked how the CGI approach allows the children to work on their own ways to solve problems. I think this makes this task more interesting to the children, rather than just having the answer told to them. I also liked how they can share their ideas, so they can see what else may work, and also that there may be a better way to solve it than what they had done.
It was interesting to see the videos about this approach. This helped me to see a real example of this, making it more understandable and usable than just reading the text. I was also given the opportunity to see this approach used in a real classroom in my internship. The children really seemed to enjoy using this in their classroom, and using the children's names in the problems really got them interested in the problems. The children also were able to keep these problems in a journal, so they can look back at the old problems and explore other ways to solve problems. I think that this will be something that I can use in my own classroom that the children can carry on with them as they continue through their schooling.

New Insights and Their Implications

What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?
First, I just want to say that I feel that I have a new appreciation towards math in general. I really had a "math fear" for a very long time and this class has helped tear away at that fear. I can't say I love math, nor can I say I love learning about it quite yet, but I think in time I will eventually feel that way. I can say for certain that I have an amazing group of classmates. They have all made me feel like I was part of the group and I feel comfortable speaking out in front of the class because they have made me feel like what I have to say is important. In the past that would have been hard for me to do. So I want to thank you all for that. Also, I have learned so much from all of you and everyday I keep on learning more. Dr. Reins has taught me to become a very deep thinker. I have never had to think so much on a math problem in my entire life before. I like his way of teaching and I think he does a remarkable job doing so. Finally, I hope that I can someday teach in a way that my students will be able to not only know and do a formula to get an answer, but have a deep understanding on the significance of that formula. Plus, I hope that my students will be excited to learn math and that they don't develop a "math fear" like me.

Questions and Answers

Questions and Answers - Questions raised as a result of the experiences and your personal thoughts on a solution/answer to your question. (These could be inquisitive questions, musings, wonderment questions, or future research questions.)
My partner and I have been continually working on our LPU. One question that has come up is how detailed does the lesson script actually get? We have looked at previous LPU's and there is a wide-range. Some students described almost everything and others kept the script concise. How in-depth should they truly be?
I know what I DO NOT want as an answer for this question (ex) "It should be however long you think it should be or take."). The reason being is that this kind of answer will not help me. I am confused by how much actually should be typed into this section of the LPU or what main characteristics this section needs to have. Does anyone have any solutions or suggestions from they have already done on their LPU or are planning to do? Let me know! Thanks!-Kristin

New Insights and Their Implications

During this class we have worked with different types of manipulatives that I have not been in contact with before. I remember working with rods but not the many different types that we have encountered in class: Cuisenaire rods, pattern blocks, etc. I have learned that it is important to provide many different options for students to be able to learn fractions. I do not have fond memories of learning fractions when in elementary school myself but now I think that it would be easier if students were presented with the many different manipulatives and strategies to find the solution to fraction problems.
Reading the blue CGI book has also presented many different ideas to work with in the classroom. I never knew that the CGI program even existed before reading the book. I never realized that problems needed to be categorized even within the category of the type of problem, for example addition having the different types. From reading the book I now know that it is important to have a variety of different problem types and structures. Also, the foundations of a CGI program are things that I would like to be able to incorporate into a math class that I may have in the future. Through this method I believe students would learn best. It would definitely have been better than some of the math classes that I have had.

Summary & Synthesis

During the last month we have been talking about fraction concepts, which is definitely not my favorite subject but I feel I have learned a lot through the class activities. I think many children don't like dealing with fractions because of the way they were taught and they don't have the relational understanding as to why it must be done the way it is. This class has shown me a variety of ways to learn and understand fractions, yet our schools are all teaching in the same manner, it doesn't make much sense to me. I really liked using the pattern blocks and cuisenaire rods to complete those worksheets because I could see how the problems made sense instead of just completing the problem in the way I was taught. I think many students enjoy working with manipulatives but teachers need to ensure that that is not the only way students can solve problems, they need to reach the symbolic stage of working. I was a little confused when using the dot paper to solve fraction problems but I can see how it may be beneficial for some students.
I really like the blue CGI book that we are reading because although I have used these types of problems and can teach it, I didn't realize that each strategy has a name. The error patterns book that we did some problems out of was also really neat and gives some great ideas for helping struggling students. It seems like the past month we have been doing a lot more hands-on activities that could easily be used in the classroom and I feel like I get a better understanding of the concepts by doing these activities.

New Insights and Their Implications

What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?

While we have begun our foray into writing the lesson plan for understanding, I have learned a lot about myself. This lesson is very difficult for me to write because I want to fall back into my comfort zone and the way I have always been taught. In writing this lesson, I know it is more beneficial to my students and their learning to use the approach that we have learned thus far in class. While old habits die hard, new and improved ideas are popping out of my head. I am using and adapting the ways that I was taught into my new way of thinking.

Kami and I are working together to create a lesson for the order of operations. I distinctly remember my teacher writing the order on the board, making us copy it, and then telling us we had to memorize it. We were to use what we memorized (Please Excuse My Dear Aunt Sally) to complete different problems in assignments and test now and in the future. She never explained why we had to use them and why specifically in that order. It was just something we were expected to know. In our lesson, we have realized that we need to let students discover the order (Thanks Dr. Reins) on their own and also the importance of knowing why they have to do it. We have looked into a variety of sources and our just now discovering the why's. Hopefully our students will not have to wait ten or more years to discover this.

Summary and Synthesis

So, I found myself pushing outside of my confort zone and attempting to use and look for ways to incorporate construvism within my teaching philosophy. Working with my partner on the LPU, I have found myself working hard and trying to use this approach. It does take a lot more time, however, as a student I found that learning this way is effective. Each day in class when are taught using this approach the concepts sort of stick in my head. Even taking the Praxis, I used some of the information we learned. I know how to find the area of different objects because I learned the process of developing the formula instead of just memorizing the formula! I found that part of the exam to be less stressful because the way I view math and math problems has changed.
I also find myself applying this approach in science. With all the reflecting we do with reading and daily activities, I can see the transfer of teaching this way into science also. I'm not exactly sure how to apply this to other content areas but its cool to see how it can be used in science too. As much as I complain and whine, I know this class will have a big impact on my teaching ability, strategies, and overall philosophy.

Questions and Answers

My partner and I have been working on our lpu and it has raised a few questions.  First, do teachers really have to write lesson plans that are like our lpu assignment?  Do teachers mostly get their lessons out of the teachers’ manual and follow that or do they write their own lesson plans?  The past few days we have been working on our lpu and it seems me a teacher should take ideas out of the teachers’ manuals, but have the main ideas and activities be their own.  It maybe difficult and time consuming to write lesson plans as multifaceted as we are, but I feel the students will get a lot out of our lesson plan. 

As I have been looking through 5^th grade teachers’ manuals I have noticed that there are worksheets for different leveled math students.  My question is when handing out a worksheet for homework do you give each student a different worksheet, one that has questions that fits the level they are at, or do you give everyone the same worksheet.  I don’t ever remember not having the same worksheet as my classmates when I was in grade school. 

Deanna

            

Questions and Answers!

I am interning in Yankton, SD in the Special Education room and find the view point of this class and the view point of the SPED classroom to be clashing. We are learning how to be constructists teachers, in which we help students obtain knowledge, in Math Concepts. In the SPED classroom they do direct instruction where the answers are practically handed to them on a silver platter. My question is can the constructivist way of teaching be modified for SPED students or do I need to stick with direct instruction? I comtimplated this idea for awhile and even talked with my intern instructor at Yankton Middle School. She told me that most SPED students do not have the patient's or background knowledge to be able to use the constructivst way of teaching. She than preceeded to metion that if they had been started out learning in that way they probably would be able to now, but since direct instruction is the easiest and only way they have been shown than introducing something like that now would only be a set back. It makes me sad that these students are being pushed along and forced to memorize information just of pass the standarize testing. Anyway, I kind of would like you thoughts on this!

Ruthie

Summary and Synthesize

Over the past month, I have really come to understand what I need to do in order to teach math effectively. First of all, it can be said the the majority of us in this class (not all, but a lot) came into this class with strong dislike of math. I myself have always disliked math and struggled with many concepts. What this class has taught me thus far is that students can NOT continue to come out of math instruction feeling this way. We as educators need to adapt to the new methods of math instruction that we are being taught and implement them into our classrooms even if we are planning on teaching lower grades. The traditional mathmatics approaches that we have been taught are not effective and we (myself included) are all the perfect example of this. I now understand why I struggle with some math concepts, because I was just given a concept and I memorized how to do it (or at least that's what I want to think). I enjoy learning new ways to teach different concepts, and have taught myself to keep an open mind with learning new techniques. I have finally come to terms with the idea that teaching math traditionally is not going to work. I will be cheating my students. The things we have learned about fractions has really helped me with the idea of not teaching traditionally. I honestly can say that I have never thought about fractions this way, and I hope that I will continue to see ways to teach students the right way.

New Insights and Their Implications

What did you learn from your peers, from the instructor, and/or the readings, about elementary school students, and/or about yourself, and the teaching and learning of math and what are their implications to teaching and learning mathematics?

Recently in class, we have been working with a variety of manipulatives to assist in student understanding of various concepts. Prior to our working with manipulatives, we were to read an article by Deborah Ball entitled, Magical Hopes: Manipulatives and the Reform of Math Education. She begins the article by discussion a particular situation in which she has asked educators what they would do in a situation regarding student exploration about even and odd numbers. Many of the educators responded by asking whether or not manipulatives had been used prior to the student presenting their ideas. Educators, on the majority, also suggested that manipulatives be used to help further student discussion. Ball's point in mentioning what educators said is that many have the misconceptions that manipulatives are the answer for EVERYTHING! She continues on to state that the difficulty in educator's relying on manipulatives is in their misinterpretation of the standards. There is a clear discrepancy in what the standards say and what educators say with regard to "concrete objects" as vehicles for teaching and learning.

Due to reading this article and my experience in our class using manipulatives, it has made me much more aware of how educators are actually using them in the classroom. I recently observed a teacher using Base Ten Blocks (ex. shown above in yellow) to help a student understand addition of three digit numbers. As I sat and watched, I wondered whether or not having the student use the manipulatives was really helping to reinforce what the teacher wanted the student to learn. It seemed as though the student was able to understand the concept when using the blocks, but when it came time to solve the problem on paper, the student struggled. I feel that this is a clear example of the disconnect that we have talked about in class between differing understandings.

~Kristin

P.S.) I hope everyone has a wonderful week and safe SPRING BREAK!

Summary and Synthesize

This class has brought forth new ideas for dealing with fractions and the explanation of why certain techniques are used. I knew how to work with fractions but when asked in class I was not sure why I was doing some of the things that I was doing to solve fractions. I even answered some questions with “because they told me to”. Discussions in class helped me to realize that I need to know why certain rules exist and that sometimes you can come up with your own method that will work. I knew to find the LCM when adding and subtracting fractions but I never knew why that was the way to do it. Working the different manipulatives in class helped me to learn why we use that process. I know now that having students work through these different ideas on their own is important because then they will understand a concept better. I do believe that working through these methods has helped to improve my understanding and my belief that I can help others understand. I am worried that I may not be positive of the best methods to teach with the manipulatives.

Personal Concerns and Next Steps

I have grasped every concept to date with a little reviewing and rereading of troublesome areas.  Some concepts have been learned very easy, while others were definitely a struggle.  When we started working with manipulatives such as: the paper fraction strips and pattern blocks I was lost somewhere out in left field.  I could not see how using fraction strips were any help to solving a problem and if anything it made it harder.  I was having a hard time getting from concrete work to symbolic work.  I tried to use the semi-concrete model, but I was struggling!  During the next class period we continued our discuss on using manipulatives and we went through the session notes and Dr. Reins put a new spin on learning with manipulatives.  We used the pattern blocks again but we added the Cuisenaire rods and to my astonishment it all came together for me.  This may seem somewhat meaningless, but I took a lot out of this experience.  I learned that not every student is going to understand what I am talking about, and that I may have to take a little extra time and teach a concept multiple ways before every student understands.  I now see how manipulatives can really impact a students learning techniques in a positive way.  

Deanna Smith

Personal Concerns and Next Steps

Coming in to the class, I prepared myself to be faced with even more math concepts, but looked forward to learning how I could actually apply some of the concepts I knew already and new ones I gathered, in the classroom. After going through a couple of sessions, I realized this math class would require me to know large amounts of information, being able to understand how to complete math problems as well as how to teach them. When I came in to this class, I felt I would maybe be given much more insight and comprehension about the teaching aspect of math, but like others have said, I feel like I am just re learning and learning new math concepts. Some concerns of mine deal with the knowledge from the book. When taking the quizzes and reading from the book, I feel like I am learning about students and how they learn, therefore, becoming knowledgeable about how to teach students math. I wish we could focus more on this type of content. I do enjoy, after having gone through a session and going over concepts I've done previously, having the feeling something "clicks" and the light bulb goes on. I feel like this type of epiphany actually will benefit when teaching math, but only if I am performing each step precisely and understanding how I got to the solution in the problem. I hope to learn more about the teaching aspect of math in the classroom as this class goes on. It'd be extremely useful to have more practice with lesson plans.

Personal Concerns and Next Steps

I really enjoy math but I am becoming really confused on how to teach it. I am placed in an eighth grade math class for internship, but it seems so different from what I am being taught. I read it on someone else’s blogspot, and I agree with there statement that I feel like I am learning math all over again and not how to teach it. Maybe I am not seeing the connection from what we are doing to how to teach math. How should I transfer this information to teaching math? I am kind of scared to teach math, but then I go to my internship and it gives me some confidence again.
I am kind of worried about my test. I think I well but on the other hand I am not so sure. I think I had most concepts down but then applying them to the test makes me wonder if I really understood them. I do appreciate the time that you gave for the test. I finished in class but with the thought of the extra time kind of gave me a little relief. There just to be so much information that I needed to know and understand for the test. I know I had notes but they were only there for a little help. I needed to understand the concepts of the notes, and to a point I did. I do appreciate the use of the notes because they did allow me to go back and re-look and understand some of the material again. I hope I did well on the test.

Personal Concerns & Next Steps

First off...I am terrified of math and then at times I love it, that is if I know how to find the correct answer. I can't make up my mind as to whether I have a firm grasp on this constructivist approach. When I did the worksheet on the polygons I had it all down to the key. Then I took the polygon quiz and got so worried about time and the length that I did not do as well as I should have. I was so happy that we got to re-take it. I did amazing compared to before and I believe the atmosphere and not having a time pressure made all the difference. I also felt this way with the midterm as I know others have as well. I was not sure what to expect. I tried reviewing all the modules and sessional notes that I printed off but it was too much information to look at...so I ended up not making it all the way through the notes. Dr. Reins was right, even though you can use your notes be sure to study ahead of time. While I was taking the midterm in class I began to panic at all the detail, tricky questions, length, and time limit of the test. I began to panic as I looked up at the clock tick and know I would not be able to finish. Then I started to cry right after I handed in my test. Yes, I cried. (I am way too sensitive.) I had this gigantic feeling that I was going to fail this class. It also did not help that I am a slow test taker and get very distracted by pencil tapping, etc. As most of you already know I usually do not take exams in the classroom. However; this is the only class I did not get my accommodation signed for because my friend (in the cohort above us) told us the tests are take-home and I did not think I would need it. So my next step is to get my accommodation signed and have a proctor for the next test. Also, I will be sure to review the notes in more detail before an exam (especially the modules.) Back to the midterm. It was very difficult and I felt like there were many trick and in depth questions. I totally felt the whole constructivist approach being placed in front of me but did not know how to go about to answering the questions. It was a very different form of assessment than I have ever experienced before. I now know what the tests will be like and will be able to better prepare myself next time. 

Questions oh Questions

As we continue to go through our math class and each class we try to understand the new way of teaching math, I have to question whether or not I will be able to do it. I am still feeling very apprehensive about teaching math. I feel like right now I am learning math all over again and feeling like I'm not learning HOW to teach it. What can I do to transfer this information from not just learning this but to HOW to teach it? This is where I am struggling.
I know that this new approach is all about getting students to think for themselves and for them to be able to develop the concepts, but sometimes I just wish for a lesson or two, it could be laid out to us that "this is how you should do it". I don’t mean every lesson but I just do not feel prepared what-so-ever right now to teach math and I would like to be the best teacher I can be, in EVERY subject. I will continue to work hard at trying to learning the best I can, which is the only thing I can do right now!

Personal Concerns and Next Steps

I know for this blog that we are not allowed to vent, but I did want to bring up the difficulty of the midterm. I know I wasn’t the only one who thought it was tricky and walked out after the test thinking, Wow that was really confusing! I did think it was very nice of Dr. Reins to allow us more time to finish the test. He could have just said ok that is all the time you get and now I am going to grade it even if you didn’t finish it. Everyone tests at a different rate. I am one of those people that need an enormous amount of time to take a test, especially one like that. Also, I do think it is very kind of Dr. Reins to let us use are books and binder, but the information we have learned over the past few months and all the print outs that we have been given is a tad much. I just don’t understand why he can’t give us a little bit of a heads up on what to study for. Again, I am one of those people who will want to study everything unless I get some amount of feedback on what to focus on. As for the future, I don’t see why it would hurt if you (Dr. Reins) just gave us some points to focus on.
In addition, about the first quiz that we took. I didn’t do too well, especially when one of my points got taken away after it had been corrected. I do think that it is a great idea when teachers/professors let their students make it up. It gives the student a second chance to improve their score, and allows the teacher some insight on if the student really understands the content being learned. Plus, I liked how the second quiz was similar to the first quiz that helped me out a lot. Actually now that I have taken it a second time I know I did a lot better and feel more confident on my grade. If we have this opportunity every time I won’t be so fearful that I am going to fail the class.

Summary and Synthesis

Over the last month I have discovered a lot of things about math that I had never really thought about before. This class has shown me just how willing I was to learn whatever the teacher told me without really thinking about why this math worked. I always just figured as long as I understood the method that the teacher told me to use and got the correct answer than I didn't really have to think about why this worked.
In the last month we had been learning about areas. We started out with simple areas that we already knew, like the rectangle and triangle. We then branched out into more complicated figures. We found ways that we could use what we already knew from these two figures and combine our knowledge for these figures, some of which we did not even know the names of. We were pushed to find how to use our previous knowledge on these new figures. In the end we were able to generate our own formulas to use on figures to find their areas.
One thing that I thought was important about our using this knowledge was that many of us knew the formula for rectangles and triangles already, some people even remembered the formulas for other shapes. So our knowledge was very different from the students that we are going to have to teach in the future. To me this meant that at some point we are going to have to tell students some formulas.
Pick's theorem was an interesting assignment. I really struggled to find the relationship between the formulas I was able to find, but once I was able to find the correct connections that they each have I was able to really see how I could apply this formula in other cases.
I really liked the assignment for finding the formula of a quadrilateral. I thought this really helped me to see the process that students would have to go through to understand this information. I also thought that, while at the beginning it was difficult for me, once I just concentrated on it I was able to understand the information and would be able to relate the information to students to help them understand.
Overall, I learned a lot this month. I really think that its really imporant for me to understand these concepts in order to make me a better teacher.

New Insights and Their Implications

This last month I have gotten a better understanding of shapes and how they relate to each other. I have had past experiences using Tangrams but haven't really analyzed and classified shapes into groups by their properties. I am not good at identifying shapes by name but the class discussions have helped me understand why shapes fall in the category that they do. The book also talks about using Tangrams and other manipulatives for discovering shapes and their properties.
Usually when it comes to math if I don't understand a problem the first time I see it, I am never going to get it. In my College Algebra class I relied on a friend who is a math minor to explain things to me, so I definitely agree that peer tutoring is a great way for students to learn from each other. In this class it has been fairly easy for me to understand the concepts and even if I don't completely get it right away, after I see a few examples and work it on my own it becomes a lot clearer. I just have to have time to think about it and see why it makes sense.
I was unfamiliar with the van Heile levels but I can definitely see how the concepts that take place in the first two levels are essential for students in the elementary grades. The book also gave some great examples to demonstrate students' learning. Overall, I feel that I am getting a lot out of this class because although I am familiar with the concepts we discuss such as area and problem solving, it is being presented in a new way that really gives meaning to why I use certain strategies when solving problems.

Summary and Synthesis

Summarize and synthesize of the impact of recent experiences, ideas, and/or issues encountered on the Tuesdays and Thursdays in class thus far from your perspective.

Math in and of itself has never been extremely hard for me. I have always taken for granted that I had a formula that led me to an answer. This class has challenged my view of mathematics. I no longer just randomly apply a formula and spit out an answer. I think about the different things we have done in class. For instance when we found how the area of a triangle connects to the area of a rectangle or how we found different ways to find an area formula for different trapezoids and the algorithm to back it up. While these things were not necessarily difficult, they challenged me to look beyond what I have been taught and look how they connect in my own world. While this may be sad to say, I had never realize the connection between the area of a rectangle and triangle. I was never taught how to or expected to prove my algorithms or answers.

Today in class we were working on fractions. While we did not get far into the lesson, I am already doing things that I would never have thought to do before. While I am still somewhat confused with why we were doing some of things we were doing, I made a better connection with fractions that will hopefully help me understand what my students will have to go through to understand what they are doing. While I am still confused I already know more than just rote procedures!!!

Questions and Answers

I am going to admit that sometimes this class scares me. I never know what to expect and I'm the type of person who likes to be prepared. Does anyone else feel this way? I sometimes feel like the material we cover is going way over my head and then sometimes I feel like I GET IT (which is exciting because that doesn't happen often for me in math).

I have a lot of questions about how using the constructivist approach to teaching math would work in a classroom. Wouldn't all teachers have to use this approach and implement it K-12? What happens when a student has been taught traditionally using the rote approach and then is thrown into a completely different learning environment? Won't it take time and effort out of learning time to get students to adjust? My little brother (1st grader) transferred to Austin Elementary half way through the school year last year. The way math was being taught at Austin was entirely through problem solving. He had never experienced this before and I remember my Mom finding the whole process pointless. My little brother struggled with this transition. This brings me back to one of my prior questions. What happens when students move from a constructivist approach to traditional and vice versa?

Look at me. I have never really learned in this matter. I agree with Lauren when she was talking about just wanting answer or a formula. I think when we are so used to things being "concrete" and without explanation it is truly hard to step outside and see the big picture. Math has always been a struggle for me. I am terrified of messing some student up because of my lack of math knowledge. The other day I was reading either chapter 20 or 21 and I realized I didn't know that you are supposed to count the spaces in between marks on a ruler not the actual marks. How I am supposed to teach students the right way when obviously don't know the right way?

I guess it is good that I am questioning my level of knowledge because it makes me aware of my short falls and where I can improve. I think that will make me a better teacher because I will be forced to keep learning more and more. Perhaps that is the problem with some teachers. Some are so sure of their own knowledge and are never willing to question themselves to grow as educator. I don't think a person can ever know all the answers and once that person thinks they have all the answers they should stop teaching.

Sorry this kind of went all over the place!