Final thoughts on intermediate math

Prior to taking this first math methods class, I had neither idea nor experience in how to teach math. Everything presented in this class was new to me and I soaked it up like a sponge. In conjunction with this class, I took the opportunity to teach only math lessons in my Dyad placement this quarter in order to use what I was learning in class in my own lessons. I found this to be very beneficial in helping me to see how what we were learning worked for me as I taught, worked for my students and aided in my retention of this new knowledge.

There is a lot that I have learned during my time in this class. The foundation of my knowledge began with the constructivist view on teaching math; where we help students build connections in their math learning by meeting them where they are. This is view allows for lots of discussion, questioning and exploring, and is different than the drill and kill method. Then, I gained some helpful criteria for group worthy tasks; ensuring that everything we give to student to accomplish in groups is both worthy of their time and allows each student to contribute their strengths. Learning about math discussions and sequencing student presentations that scaffold important mathematical ideas in a way that is most beneficial to students was fascinating. My dyad partner and I even tried this in one of the lessons we taught together. It was challenging, yet engaging for the students and I know the students gained from this experience. I also learned about the value of integrating other subjects and resources, such as manipulatives, into math lessons. This integration invites all students to be successful in the lesson and can increase engagement. I could go on and on with all that I have learned, but there are two important pieces I will take away from this class. One, we should never to answer questions that students can figure out on their own. Instead, using excellent questioning strategies we can aid students in reaching understanding on their own. They may struggle, but in the end this will be more beneficial for them than for us as teachers to simply give them the answers. Second, each student has his or her own math identity and each student is good at math in some way. I was that student who always thought I was bad at math. I am looking forward to helping all students find their math identity and understand that they all have a brain for math.

Much of what I have learned I have already begin applying or plan to apply to my own teaching. In fact, practicing what I was learning this quarter while teaching myself was very helpful. When it comes to questions I may have following this class, I cannot think of any at this moment. Due to the fact that everything I learned this quarter was new, I am still taking it all in and I know I have so much more to learn. What there is for me to learn I am not sure of.

I think this class was beneficial and I thank you for the time you have taught us. One thing that would have been helpful for me this quarter would have been to have some sort of objective for the day’s lesson. While I was enjoying class, and learning much from my reflections on class and readings, during class I often found myself wondering what I was supposed to be learning specifically from what was being taught. I do not mean to be harsh by any means, I loved this class, and I know that you enjoy going with the flow of the class. Although, I would have liked to hear from you what it was that you wanted us to receive each day from the lessons you provided us (implications for teaching). I wanted to gain more from your knowledge and not just my peers. Again, I appreciate you and your wealth of knowledge. Thanks for this quarter!

Making writing regular, enjoyable and worth it

Through much of my readings in literacy this quarter I seem to continue to come across the same three ideas: regular, enjoyable and worth it. These are in my own words of course. I keep circling back to these ideas for a few different reasons. For one, these would not have been the three words I would come up with when asked about teaching writing. Secondly, I have not seen these modeled in my current placements so these ideas stood out to me as something very different than I am seeing. I love these ideas because I think they are critical to teaching students how to write and I think they tie together much of what we have been learning.

Regular & Enjoyable

In Routman’s book she discusses how writing needs to happen on a regular basis. In addition, writing needs be completed in varying contexts. This can be a writing response, a free write, writing for another subject and so on. Something in this past week’s reading that stuck with me was how Routman explained that students need plenty of time practicing reading without being tested, and the same goes for their writing. Students need to have plenty of practice writing without it being graded. This was a major aha moment for me. I was under the impression that every piece of writing needed to be checked or graded; in the past this frustrated me when teachers did not follow through on this. Now, I understand that students need to practice without the pressure that they are being graded. Granted, students still need to practice good writing skills and the writing process even though the piece may not be completely checked. As for enjoyable, if writing is more regular I believe students will come to love writing. Additionally, if students are given options during their regular writing, they may find an outlet of writing they love. Celebrated student writing is also more likely to help students enjoy writing!

Worth it

In my observations, and my time as an elementary student, student writing is rarely celebrated or published in some way. Writings are usually published at least twice a year. Students need to have a sense that their writing is important and that it is worth it. I believe with worthwhile assignments, many opportunities for publishing and still more opportunities for celebration of writing will help students to feel like writing is worth it. In the end, this too will improve student writing.

Here I am now

Looking back on my thoughts on the use of iPod Touches or other similar hand held technologies, my thinking has not changed too much. I think in the beginning I was more skeptical as to whether or not these were actually being used in the classrooms and now I have arrived at the understanding that they may not be in full use but they are being used. In addition, their use is spreading.

In my previous post on the iPod Touch, I was missing real life examples of how a class set of these are being used in classrooms today. I am struggling to find this information, although I am definitely on the look out. I plan to keep my eyes and ears open in the months to come for more practical uses. The reason why I am still searching is because I do not think the way in which we have used the iPod Touch this past quarter is realistic for an individual teacher to do on their own. Each interaction we have had with students and the Touch is one on one. Granted there have been some helpful applications, such as being able to record students as they read. On the other hand, I am still searching. I have been checking out professional blogs and YouTube videos for answers.

Lastly, I am interested in the funding of a class set of iPod Touches. I am sure there is some grant out there that would help pay for something like this for classroom use. I would love to be the teacher who has them in her classroom. Maybe then I can experiment with more uses. Therefore, I am on the hunt to find funding for a project like this because even though I am searching for uses, I do believe the ipod Touch can have a positive impact on student learning.

It didn't seem like math

What I loved most about our math class last week was that it did not seem like math. Now, when I say this do not intend to negate the necessity of math. Instead, this made me think about how we teach math to our elementary aged students. This past week in our math class we were able to explore Gapminder.com, which offers important world statistics in graphical form. This site is fascinating and instantly the whole class became engaged in manipulating this graphical information to display information that was most interesting or important to themselves. What I loved about this particular activity was that it did not seem like math, this was not your typical direct instruction lesson where the teacher gave us a new topic, demonstrated it, we practiced it together, then we were sent off to work it out on our own. Instead, we were set out to discover, interpret and essentially play with math.


Thinking back on this specific class made me think about how many teachers teach math today. Many teachers simply use the direct instruction route and this leaves many students fearful of their lack of what they think are math skills and they simply check out. What if we taught more math like this? With discovery. I do not mean to say here that there is never a need for direct instruction in math classes, instead I think there needs to be less of it. I personally would say that I do not like math. I am one of those people who never had the "math class" skills. Although, if you read one of the articles we previously read this quarter about math identities, I have many other mathematical skills. It was encouraging for me, with my lack of "math class" skills, to feel like I succeeded in class this last week, that i had something to offer my group and that I was interested in the content. Nevertheless, this class made me think about how I want to teach math, what to consider, and and how math should not only be taught in "math class".

Pattern Making Machines

In class we often hear that our brains are pattern-recognizing machines. When it comes to adding single digit numbers, my brain is admittedly not so great at recognizing patterns. In fact, when I was growing up I was constantly getting in trouble for using my fingers to add and subtract. I even remember the math tutor I had to go to who would make me sit on my hands when drilling me with single digit addition and subtraction to avoid using my fingers. Little did she know I was still able to make it work.

        

Growing up, teachers were constantly telling me not to use this method, so I switched to a new method – counting up or down from the highest number. For example I saw that the number 3 has three points on it. If I were to add 3 + 8, I would start by saying 8 then count up three by touching the three points on the 3 one at a time. It was at this time that I was not taught to see that 8 +2 = 10 + one more = 11. This would have been much more efficient.

I bring up my personal story because I have been enjoying what I will call “pattern training” by my Dyad teacher. To begin a math lesson each day he puts virtual dice up on the smart board. He “rolls” the dice and asks students to add the numbers shown on the dice. He begins using two dice and progressively moves up one at a time until students are adding 5 dice. After asking the students to respond with the answer, all dice added together, he asks students to share any patterns they found. The patterns this teacher is looking for specifically are double numbers or combinations to make fives or tens. The students are very excited to share their own methods on how they have added the given numbers to get their answers. We know already that this method of having students share their own methods helps them to understand more about why they did what they did and allows other students to learn from their peers.

At first, when observing this part of the math lessons I thought “drill and kill”. Weeks have passed and I am now beginning to appreciate the pattern recognizing aspects this has to offer. In fact, I myself am seeing my single digit numbers in new ways. This experience has taught me that we do not need to get rid of all of the “kill and drill” methods we once learned, although an addition like this can enhance student learning. 

Making math relevent

One discussion we had in class last week was about making math relevant to students. So often we give students completely abstract or adult focused examples of how to use the mathematical idea we are attempting to teach and so often we completely lose our students to utter boredom and dislike of this “useless idea”. This is something I focused on while creating a lesson to teach with my dyad partner this last week. Our goal was to teach students different approaches to solving two-step word problems and help them to see that there are many ways to arrive at the same correct answer. For this lesson we could have stood up and taught straight from their textbook or the teacher’s curriculum guide. But, after looking at the direction the curriculum was going and the examples it wanted us to use, we realized this lesson would quickly become mundane and not applicable to our students. Therefore, we began our lesson by telling our students about a recent problem we had where we had to use math to solve and fix our problem. More simply, we told our students a real life story. Then, we helped them connect our story to the idea that math word problems are like real life problems where ordinary people need to use math to solve. We involved students in the word problem examples we used; all of the problems involved students’ names and were real problems that the students were or could be experiencing. We noticed that our students were highly engaged in solving these “problems” for their peers. When it came time to have students write their own real life word problems, they were excited at the chance to share a problem they had that involved math. We did not use silly stories. There was never an example like “There are two frogs in the pond, five frogs come to the pond and three frogs leave. How many frogs are left in the pond?” Who cares! Our students definitely do not. This is just one example of how we as teachers need to make our lessons applicable to our specific students.

Mathematical identity and our students

This week I read Exploring Our Complex Math Identities by Keith R. Leatham and Diane S. Hill. This article was fascinating to me personally because of my own view of math. I have never enjoyed math yet I always seemed to get good grades – telling me that maybe I am pretty good at it. This article discusses how our beliefs about math affect the way our students engage in math and the way we as teachers teach math. This I knew already, but I did not now how to tackle these views we all carry in order to benefit a classroom of students. The article defines mathematical identity as an individual’s relationship with math, this includes the way the person learns, thinks about, retains, does and associated with math (Leatham & Hill, 2010, p.226).  Some of our mathematical identity is observable and some is not. A classroom discussion focused on mathematical identity can help students determine their mathematical identity and that of their peers. The main questions used to facilitate this discussion include: 1. What does it mean to be good at math? 2. What is mathematics? How useful is it? 3. How do we feel about our own ability to do math?

I enjoyed reading this article because it put something I always thought of as very abstract, how we feel and think of math, and put it into describable words. I see how a discussion such as this can be very beneficial to a teacher – understanding more about our students. Although, after reading this article I am left wondering how early is too early to have this discussion with students. I wonder this because it seems as though many of the student examples in this book are from middle school, high school and college aged students. In reality, most of us are beginning to form and cement our thoughts about math when we are in early elementary school. How can we create discussions around the three main questions to determine mathematical identity in a way that is age appropriate for younger students? Do you think it is too early to begin discussing math in this way at this age?