A Blog on Problem Solving & Word Problems

Problem solving is a life skill, as we all problem solve everyday - what to wear, what to eat, where to sit at lunch, how to schedule our day, which homework assignment to complete first, how to manage our budget, etc. Students often don't realize how much problem solving they do on a daily basis. It's helpful to connect problem solving in math to everyday problem solving. Students know and use more tools for problem solving than they realize!

Problem solving integrates critical thinking. Problem solving is as much about the method, approach, and thinking as it is about the correct answer. Plus, good problems may not have only one correct answer. Problem solving is also a great way to support students in being comfortable with making mistakes and learning from their mistakes. Making mistakes is part of learning and we need to allow for that in our classrooms (Boaler, 2016). Problem solving additionally provides opportunities for explaining and justifying our methods and solutions - all of which supports higher order thinking and understanding. Problem solving shouldn't conclude with simply the correct answer. It should focus on the method, the thinking, the explanation, and the understanding, among other aspects (Boaler, 2016).

Problem solving isn't just about the steps followed. It's about the thinking underlying the steps and the process. Too often, when we teach problem solving, we focus so much on the steps that students memorize the steps but don't truly understand the process or develop the critical thinking necessary with strong problem solving. Consider that every textbook series has its own problem solving process. Is one process truly better than any other? Every time we change textbook series should we change our approach to problem solving? Any of the approaches provided by the textbook series have value. But the emphasis is on the thinking and the process - not a list of steps. Any problem solving method can be used. We all have our preferred methods. Teaching and developing problem solving skills is about consistency with how we teach the thinking that is necessary with the steps. I argue that it is more important for there to be consistency across grade levels within a school about how problem solving is taught and fostered than it is on ensuring that students can regurgitate steps. If the steps don't involve any critical thinking, then what is the point?

Word problems are a common way we integrate problem solving in math classes. Word problems can provide real-life context and application of math concepts - particularly if the context is one in which students can relate and/or have experienced. One key factor often overlooked with word problems is the underlying literacy skills that are required for supporting student success in solving word problems (Leinwand, 2009). By the time a student reaches third grade, if a student is struggling with reading, the student often begins to struggle in math because the complexity of word problems typically increases in third grade. Essentially, the student's struggles with reading impact their success in math, not because of lack of understanding of math concepts, but because of challenges with reading complex text. It is critical for literacy skills to be explicitly addressed and applied in math class, especially with word problems (Leinwand, 2009).

Reading in math is technical reading. Comprehension strategies taught in ELA should be referenced and applied in math class. In ELA while reading a text, if students are expected to annotate what they are reading, they should also be annotating when they read in math. The comprehension strategies and skills taught in ELA do not apply only to ELA - they apply to anything students read. These cross-curricular connections are often overlooked. We need to explicitly connect these ELA strategies to math and other subject areas (Leinwand, 2009). These strategies can provide important scaffolding for students as they develop their problem solving skills, particularly with word problems. If your school is departmentalized, collaborate with your ELA teacher to ensure consistency in language and strategies in breaking apart technical text. If you are self-contained, review the strategies you are teaching and applying in ELA and directly connect them to reading in math.

With the application of literacy skills, students learn to read word problems for context. Solving word problems is premised on understanding the context of the word problem itself. At times, students are taught to look for key words and numbers. From my experience, I find this approach to not be effective for teaching students to solve word problems because students typically then focus on locating the key words and numbers without fully reading and understanding the problem. Many words in math have different meanings based on the context of the problem. Give me a "key word," and I'll provide at least two different computational operations that can be used with that word. Focusing on reading for context is more effective.

Writing in math is also helpful for strengthening student understanding of concepts and skills. It also builds on the writing strategies and skills students are learning in ELA for technical writing. If a student can explain their thinking verbally or in writing, they can show their depth of understanding. Below I provide some suggestions for integrating writing into math, such as with math journals. I additionally provide suggestions for integrating more literature into math as the literature can provide context for math as well as provide practice for strengthening reading comprehension with technical text.

References

Boaler, J. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass.

Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.