How to “Read and Write” in Math: Improving Problem Solving and Communication in Mathematics

An in-depth exploration of teaching systematic approaches for solving math word problems and developing written communication skills to describe solution processes. Teachers will learn a wide range of strategies to develop students’ skills in the math problem-solving tasks of:

  • comprehending the problem and identifying relevant data
  • analyzing the problem’s internal structure to determine what type of problem it is
  • selecting a viable solution process and carrying it out
  • explaining the solution process both orally and in writing

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How to “Read and Write” in Math:

Reviews

Check out what other teachers from your area and across the country are saying about this course.

California

The key things that I have learned in this course, is that I want my students to feel less intimidated by word problems. This can be done, by letting them look for deep structures in word problems, and to train students to have the mentality of feeling comfortable not knowing the answers right away. I have started to apply the journal exercise, when the students will have to write how they solve the problems, and to also self-assess their writing. I will also make talking and writing a regular part of my lesson, through think-pair-share, group discussions, and reflective journals. So, with all these new practices, I hope my students will become much better at solving word problems. (CA)

With this class and my own experiences of seeing how emotions sometimes prevented me from viewing a word problem correctly, I see the importance of creating that effective classroom learning experience that will help my students solve word problems successfully and for them to describe their solution processes clearly. I see the importance of and will implement the four main tasks of problem solving in my class (1. understanding the problem and what it is asking; 2. analyzing the problem to determine its structure; 3. choosing a solution process and carrying it out correctly; 4. explaining that process, both orally an in writing). I have seen and will have my students see the deeper structure of math word problems. I will put in to practice Polya’s 4 basis steps (1.understand the problem for solving math word problems; 2.devise a plan; 3.carry out the plan; and 4.look back). I will introduce and have my students memorize the 10 strategies for math problem solving (a.arrange objects; b.(work)backwards; c.chart; d.draw a picture; e.eliminate possibilities; f.formula; g.guess and check; h.hunt for patterns; i.invent an equation; j.just simplify). I see the power of asking the right questions (coaching, probing, and intermediate). I have seen first hand how language arts journal writing has empowered my students, so I can’t wait to implement math journals as well. The same applies as I plan to expand using math rubrics. Again, I have enjoyed learning from this class and can’t wait to incorporate them in my own class and share them with my peers. (CA)

The key things I learned from this course is the following: It is important to help students be aware that confusion or not knowing how to solve a math problem is normal and to be comfortable with this. That there are deep structures within problems. I need to teach students a step-by-step problem solving approaching, such as Polya’s Four Steps which includes understand the problem, devise a plan, carry out the plan and look back. Included with this a list of possible strategies that can be implemented to solve particular problems. I need to model for my students how to read, comprehend, and think about problems. I also need to ask my students probing, coaching, and intermediate questions. Talking and writing need to be a regular part of my math lessons, and students need to be taught to self-assess their skills in writing explanations to their solutions. While I currently do not have access to a class I am looking forward to implementing these strategies and thereby reducing my students anxiety or affective filter when they approach mathematical word problems. (CA)

I have enjoyed learning some new strategies for teaching problem solving and look forward to incorporating them into my instruction the remainder of this year, as well as with a fresh group of students from the beginning of the year next year. One element that resounded strongly with me was Polyps four steps for problem solving. I found it enlightening to learn how to improve upon an instructional strategy that I thought I was already using. The clarity and simplicity of the process helps me to help my students to dig deeper into the problems, incorporate previous learning, and have a plan for moving forward with their solution. Another learning experience I appreciated dealt with extending word problems. I never thought it could be so easy to give students multiple opportunities to solve similar problems, not to mention the opportunities to differentiate. What a great way to get the most bang for your buck when teaching kids to recognize the structure of word problems. There are many other elements of this course that I have embraced to help kids to dig deeper, and understand more.I will continue to use the four steps for problem solving and extensions daily, and I will continue to work to help them become better “math writers”. (CA)

Colorado

“I really enjoyed this course, and feel that my math instruction will continue to strengthen because of the course. I have long used word problems, and even student created word problems, as a daily part of my instruction. However, this course has really opened my eyes to even deeper use of word problems, and has provided me with new insights in teaching communication in the context of math problems. I have read a few of Marilyn Burns’ books and have long used some of her strategies, but I was new to the steps of problem solving as laid out by Polya. I have now used and emphasized these steps daily with my fifth graders, and I feel that I am seeing solid growth with them. I also am very grateful for the persistent reminding through the course for me to ask my students if the problems look familiar, and if they do then how did they solve the similar problem last time. This is a strategy that I have long used personally, but have not done a very good job explicitly teaching or modeling. I aim to continue to improve with these steps. I gained a great deal from this course. Thank you!” (CO)

“Many of the elements I was already using but here is what I am incorporating now and into the future. I acquired a comprehensive list of the problem solving strategies that is posted in my room (I have been looking for this for years!) not just posting the ones that I designed lessons around. I had the students use the rubric to assess a writing sample to deepen their understanding of how it worked — I never did that before! I am consistently spending time in class to take the time to really focus on the deeper structure of the operations and the number systems I am finding that this helps the students with the conceptualization of problem solving. Last, I modeled for the students my thinking—this went over fairly well and many of my students do think out loud.” (CO)

South Carolina

“This course has been very inspirational to me. I have found significant value in applying the strategies studied. Partner talk, thinking out loud and all the strategies to engage students proved useful in promoting understanding. When students gain a command of the four task of understanding, analyzing, selecting and carrying out an appropriate process, and explaining what was done both orally and in writing, they will master the key components for problem solving. The process of modeling for the students and, in turn, allowing them to model builds confidence. These strategies all help students to become effective communicators, a skill necessary for career success. I utilized these strategies with the students and found success with the methods. Sharing was used in groups and as whole class experiences. Through applications of the strategies, student learned to relate problems to previous learning and to realize that there are optional ways to solve problems. I will continue to use these strategies with developing and utilizing problem solving strategies.” (SC)

Texas

“In this course, I have learned a lot about the importance of reading and writing in math. As a math specialist I have known the importance of being able to explain the process, but this course has helped me to grasp the idea, “If you can talk it you can write it.” I will be implementing more writing into my strategy for teaching mathematics. I have also gained more insight into the problem solving process. In university and in many staff development trainings, I have been given tools and specific strategies to teach my students. Through this course, I have learned a broader idea of how I can teach problem solving that will reach students of many learning styles. With Marilyn Burn’s 10 Big Math Ideas and Polya’s four steps of problem solving I am confident that I can reach all of my students at their various skill-levels and learning styles. Modeling and questioning have also been vital strategies that I’ve used. I am thankful that I have my notes from this course as a resource that I can refer back to, in order to broaden the questions I use my classroom. The self-assessment rubrics are still difficult, but I plan to implement them alongside the writing. This way the students can better evaluate themselves and thrive in their problem solving skills. As I implement these ideas and get my students more comfortable with reading and writing in mathematics, I am sure to send my students up to the next grade-level better prepared and confident in problem solving.” (TX)

Virginia

“I have enjoyed taking this course because it has helped me to help my students. Word problems have always been a struggle for my students because of their English language abilities as well as their below grade level math skills, but through this course I have learned some new ways to approach word problems to help them. I have slowed down the process of solving a word problem and now we read the problems 2 or 3 times before we even start to write. I now have laminated cards for each student that outlines Polya’s 4 steps for them to use when solving word problems. I have begun to have my students “talk out” the problem to each other and in their writings, which as encouraged them to slow down and be sure they have included all the steps necessary to solve the problem correctly. It has also helped them to be able to explain it to someone else and then perhaps repeat it in the future if needed. I have learned that students do not think alike and they need multiple strategies to solve the problems. I have begun to do more partner work where students share their strategy for solving the problem with another student so that they can compare what was similar and different about their strategies. The writing has been the slowest piece to develop, but it is a work in progress that we will continue to work on. I have learned a lot of valuable strategies to help my students through this course and will continue to implement them in my classroom.” (VA)

“This course has been extremely beneficial in trying to help students meet the rigourous expectation of the new state testing as well as prepare them to be successful and confident in math. I teach the “below” grade level math students, so word problems are especially daunting for them. I have always taught them to solve in step by step ways, but often they cannot make a decision about what to do with the problem or solve too quickly. Through this course and Polya’s 4 steps, I have been able to create dry erase cards that the students can use when solving problems. This has helped them to slow down and improved confidence because they have the steps there to work with. Creating a chart listing strategies to try has also helped them not feel lost when they see a problem and they are starting to learn their “favorite” strategies. These things have helped improve their perseverance with problem solving so they don’t quit in the middle or just write something down to be done. Moreover, the idea of writing and talking as essential to math has proved to be a tremendous asset in the classroom. Setting the expectation that they explain their work in writing has improved the level of thinking about problems tremendously and I am already beginning to see them doing this on their own without prompting after just a few weeks of writing. I am currently working to find ways to incorporate more writing into my math lessons as well as using the self-assessment rubric. These things have added a new enthusiasm to the class with both myself and the students. I have seen a great rise in the confidence level, which inevitably produces better results. Overall, it has also made me more aware of how I am teaching and that the lessons I am teaching are including depth and better questioning (especially intermediate questions). I am looking forward to the success my students will have on the end of the year assessments due to the ideas in this course.” (VA)

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