This week we were given the task of finding 5 scholarly articles that pertain to our current teaching practices and to write an annotated bibliography for them. This has been one of my favorite tasks for this class so far because I agree with Eileen Bender and Donald Gray “that the demands of teaching and research are counterforces fiercely contending for control of our time” (1999). There are so many resources in the world today about good teaching practices, wonderful educational questions, and how to best meet the needs of our students and yet with everything that is asked of us as teachers, really diving into these resources generally loses out in the battle over how we spend our time. This week also gave me a wonderful chance to get back in touch with the MSU library and it’s abundant resources; a quick online chat with a librarian opened me up to wide variety of articles surrounding middle school mathematics and just a quick glance at all the titles had me literally jumping out of my seat in excitement over some of the ideas that were presented. Below is an annotated bibliography of just a few of the many articles that I found, printed, and will keep in my arsenal of amazing teaching resources. These articles discuss different approaches to problem solving and eliciting productive mathematical conversations in my classroom, which are two big ideas that I continue to struggle with this year. Each article brought up interesting ideas and solutions that I plan on taking back to my classroom tomorrow in order to get my students growing even more.
References:
Bender, E and Gray, D. (1999). The Scholarship of Teaching. Research & Creative Activity, XXII(1). http://www.indiana.edu/~rcapub/v22n1/p03.html
Annotated Bibliography:
Bicer, A., Capraro, R., and Capraro, M. (2013). Integrating Writing into Mathematics Classroom to Increase Students’ Problem Solving Skills. International Online Journal of Educational Sciences. Vol. 5 Issue 2, p361-396.
This text was more or less a summary of various research that points to the fact that incorporating more and more writing in math classrooms directly effects a students ability to be more successful in problem solving. The article notes that writing helps improve student’s problem solving abilities because the writing requires them to demonstrate how and why they know things as well as the information they already know. The authors also dive into a discussion about what makes something difficult versus complex, which opened my eyes to the kinds of questions I’m asking my students, and how I can restructure them to make them appropriately rigorous. This text broke down the levels of cognitive capability to: visualize, analyze, generalize, deuced and rigor and then gave mathematical examples of what each level would actually look like. Seeing this distinction has gotten me thinking about where some of my students are cognitively and if my expectations of them in my classroom are appropriate. As I’ve been trying to utilize the iPads I have in my classroom and make more self paced units, I think this kind of information would perfectly align to my planning and help me to structure lessons that help each student show growth. The article also gave various examples of structures that can be put into place for students to write in math. These examples include, writing out their answers in detailed sentences, keeping a math journal, and using a graphic organizer to keep track of prior knowledge. The examples and data they present make it clear that writing in mathematics is crucial to improving a student’s problem solving skills and makes me want to try to find spaces in my class that students can write even more than they do now.
Billings, E., Coffey, D., Golden, J., and Wells, P. (September 2013). Teaching with the Mathematical Practices in Mind. Mathematics Teaching in the Middle School, Vol. 19, No 2, p. 100 – 107.
This article outlined a professional development opportunity offered to a group of middle school teachers that introduced them to the workshop model. I chose to read this article because I myself have attended a couple professional developments that have addressed the workshop model and I try to implement these strategies in my classroom once a week so any more research or information about how to use it in my classroom is always helpful to me. In addition, I was instantly attracted to this article in particular because the content was surrounding proportions which is one of the biggest standards we cover in 7th grade. The article highlighted each of the components of the workshop model (Make Connections, Focus, Engage in the Activity, and Reflect on the Process), in plain, easy to comprehend language and allowed me to dive a little deeper into how I approach each in my classroom. In my experience I haven’t put much emphasis on the “think aloud” as a lesson’s focus, but that was the biggest part of this article’s example which got me thinking about how I could restructure my classroom to allow for my students to participate in think alouds more often. One of the biggest deficits my students have, according to our data, is that they cannot read a math problem and appropriately pick a strategy to execute the problem. Unfortunately, one of the only ways to help students improve in this area is to have them working with examples and talking to each other about their thoughts. Even if my students can do that on a regular basis, it is difficult for me to judge their individual progress because I cannot be a part of every group, every day. With having access to the iPads in my classroom, I believe this is a perfect opportunity to have students record their thoughts so that I can go back later and listen to each of their thought processes. If I can be a part of each student’s learning on this deeper level it will also make conferences that I have with each of them more meaningful and ideally they will improve even faster.
Bolyard, J., Lynch, S., and Lynch, J. (August 2013). I-THINK I Can Problem Solve. Mathematics Teaching in the Middle School, Vol. 19, No 1, p. 10-14.
This article takes the idea of a traditional Think-Pair-Share as a way for students to think about and discuss a mathematical problem and adds on another dimension. Most of my students are struggling to determine which procedure or strategy will allow them to correctly answer story problems and the I-THINK structure asks students to talk about all aspects of the problem before trying to solve it. This is something I’ve been trying to do in my class for the past few weeks, however I have been doing it without actually naming the actions that I expect my students to do. This article presents a perfect framework for putting words to the actions I want my students to be doing; it also provides suggestions for questions and suggestions I can provide to students who continue to struggle with the idea of talking about mathematical ideas. The authors bring up the point that the new Mathematical Common Core Standards call for teachers to provide instruction in communicating mathematical ideas in problem soling, making connections, and justifying solutions. As a teacher, these are obviously my goals, but actually putting structures in place for my students to follow will help me as I track their growth and improvements in these areas.
Brydges, C., Erlandson, K., Howard, K., Karpie, M., and Plumb, M. (2012). Build Like an Egyptian – The Perfect Pyramid: A STEM Project for All Egyptian Ages. New York State Mathematics Teachers’ Journal, Vol. 62 Issue 3, p. 132-136.
This article beautifully sums up a STEM project that really allows students to act as creative individuals while engaging in a rigorous, cross content assignment. The article points out that there are not many STEM projects available to math teachers, especially projects that are classroom ready, which is something I know to be true. Having the students create a perfectly square pyramid, maintain a budget to erect the pyramid, and create a mummy to be placed in the pyramid opens up so many opportunities for students to deepen their understanding of geometry, basic finance, and humanities topics while having good old fashion fun. The article provides step by step instructions and advice to execute the lesson which is highly beneficial to teachers considering the juggling act of increased responsibilities they’re already working with.
Imm, K. and Lorber, M. (August 2013). The Footprint Problem: A Pathway to Modeling. Mathematics Teaching in the Middle School, Vol. 19, No 1, p. 46 – 54.
This article emphasizes the importance for students to solve word problems by modeling; it also brings up very valid points about how students are traditionally taught to solve problems. The author presents the idea that generally when students are asked to solve problems they are set up to solve them in a certain context. We first teach them certain skills, and then give them big ideas, and only after they have demonstrated a certain level of mastery of these insolated skills do we give them a problem to practice the application of that skill. Even then, as they point out, most teachers give students isolated word problems that practice the given skill, not necessarily problems that they will have any true connection to or see as legitimately real-world applicable. There are two points that the authors brought up about this idea that really hit home with me. The first is we need to teach our students to be problem finders before they can be problem solvers. This one idea highlights one of the biggest issues I’m currently having in my classroom; students are so intent on just doing something with the numbers and words given to them that they don’t take a step back and really determine what the problem is. In my current class, students can’t even articulate what they’re trying to solve for in the problem, let alone do the correct math. The second point that really resonated with me from this text was that when we are creating “real-world” problems for our students to solve, we need to be more intentional about making them imaginable, believable, and intriguing to the students. This seems so basic and obvious, however when I’m trying to create word problems that are more rigorous and test multiple skills at once I struggle with making them meaningful to my students. It is common knowledge that students will perform better or try harder when they feel connected to the material, so hopefully making this small adjustment in my classroom will help my students to be more engaged.