Learn How to Overcome the Top 5 Problems in Problem Solving
As a math teacher you know that students should solve problems. But you also know getting them to solve a problem is like pulling teeth. Even some of your best students have math anxiety. What should you do as a teacher? My advice: confront problem solving head on!
Problem 1: Math Anxiety
Solution: Improve Your Classroom Culture
Face the Problem Head On
Many students dread problem solving which in turn causes math anxiety. Do you need a great way to lighten the mood and improve mathematical mindset? How about reading a picture book? Even my high school students loved it when I read picture books in math classes. What Do You Do With a Problem? by Kobi Yamada is a great way to set the tone for the year and create a positive classroom culture.
Here is one way to use the book in your classroom:
Before Reading
- Start with a pre-write. Have students write about how they feel about problems in math class. If you would rather focus on social-emotional concepts, you could talk about problems in general. Then in the post-reading you could connect it to problems in math class.
Spreads 1-10
- During reading ask connecting questions such as “Do you worry about word problems?” You can even use this as a way to talk about how they deal with other life problems.
Spread 11
- When you get to spread 11 where it says, “I realized I had to face it.” You could stop and introduce SMP.1 (See the bottom of this post for a shorter version of the SMP.1)
Spread 12
- Spread 12 states, “So even though I didn’t want to, even though I was really afraid, I got ready and I tackled my problem.” You could use this sentence to introduce some problem solving strategies that you like to use in your classroom.
Spread 13
- When you read “I discovered it had something beautiful inside,” ask the students how a problem could be beautiful. Then ask them for examples and give some of your own. Include both math and non-math problems in the discussion.
Spread 14
- On the next spread, discuss how problems can be opportunities. Then give some examples of problems in you life that became opportunities.
Post-Reading
After reading discuss how problems can be scary in math. Give them some problem solving strategies that you use such as breaking down a problem, acting it out, drawing a picture, etc. Then launch into a fun but accessible math problem.
If you decide to do a Unit 0 and start the year explicitly teaching problem solving, this book would be a great fit. Check out my blog post on Why You Should Start the Year with a Unit 0 for more information about a Unit 0.
Subscribe to my blog if you want greater math ideas sent directly to your input. Subscribe today and get a FREE Student-Facing Rubric on Problem Solving (SMP.1) for Grades 3-8.
Mistakes Are Your Friends
The best way to improve math anxiety is to create the classroom where it is a safe place to fail and make mistakes. Emphasize the learning process over correct answers. Please note that correct solutions are also important, so don’t indicate otherwise. But rather praise students for their thinking and leverage mistakes as a learning opportunities. For example, you might say, “I’m so glad you made that mistake. It’s one that lots of students make. This gives me the opportunity to show you……” You can also model this concept by intentionally (or unintentionally) making a mistake, laughing, and drawing attention to the fact that you made a mistake.
Here are some great quotes about making mistakes that you can use in your classroom:
- “I hope that in this year to come, you make mistakes. Because if you are making mistakes then you are making new things, trying new things, learning, living, pushing yourself, changing yourself, changing your world. You’re doing things you’ve never done before, and more importantly, you’re doing something.” ~Neil Gaiman
- “If you have the guts to keep making mistakes, your wisdom and intelligence leap forward with huge momentum.” ~Holly Near
- “Life isn’t about algebra and geometry. Learning by making mistakes and not duplicating them is what life is about.” ~Lindsay Fox
- “Failure is good. It’s fertilizer. Everything I’ve learned about coaching, I’ve learned from making mistakes.” ~Rick Pitino
- “The only real mistake is the one from which we learn nothing.” ~John Powell
- “If you don’t make mistakes, you aren’t really trying.” ~Coleman Hawkins
Encourage Questioning
Using open-ended and scaffolded questioning strategies defuses the pressure in the classroom. It allow students to enter the learning process without having the pressure to know the right answer.
See my blog posts How to Practically Create a Culture of Questioning and How To Cure Math Anxiety with Modeling Mondays for more ideas.
Problem 2: Lack of Interest
Solution: Provide Rich Tasks
When students are interested in the problem, they are more likely want to solve the problem and overcome challenges. The secret is to select interesting tasks that students can relate to. The task has to be hard enough to stretch them, but not hard enough where they get discouraged. Questioning strategies can help you scaffold tasks as well. The same lesson can be taught at a 6th grade level or Precalculus depending on what type of questions you ask.
Here are some websites where you can find rich tasks:
- Inside Problem Solving | Inside Mathematics
- Rich Tasks – Math For Love
- Activities and Tasks – YouCubed
- Search | NRICH
- Rich Mathematical Tasks | Virginia Department of Education
- Open Middle – Challenging math problems worth solving
- Illustrative Mathematics
- The Three Acts Of A Mathematical Story – dy/dan and Dan Meyer’s Three-Act Math Tasks – Google Sheets
Modeling problems are another great way to increase student engagement. See my post How to Cure Math Anxiety with Modeling Mondays for more ideas about modeling.
Problem 3: Not Knowing How to Start
Solution: Implement the Notice & Wonder Routine
The Notice and Wonder routine is an easy way to increase student engagement. Its a low risk routine for students, so all students can participate. Not to mention it causes students to slow down, notice and think which is hugely beneficial.
It’s a very simple routine. You give students a picture, diagram, or math problem and you ask students to list all the things they notice and all the things they wonder. Don’t be afraid if your students wonder things that you don’t have answers for! That’s part of the fun. Then you can take one of their “wonderings” and use it to launch a classroom lesson.
For more strategies on using the Notice & Wonder routines, see my blog post Increase Student Engagement by Using Picture Books to Launch the Notice & Wonder Routine. It’s incorporates another great book by Kobi Yamada.
Problem 4: Perseverance
Solution: Improve Your Questioning Strategies and Use Scaffolded Tasks
Questioning
Teaches are helpers—over helpers. It’s so tempting as teacher to “help” students by giving them answers. But oftentimes answers shut down the learning process. Instead help students by focusing on asking good questions.
Appropriate questioning can help produce perseverance. One of the rules we had in Ohio’s Mathematical Modeling and Reasoning Course was to always answer a student’s question with a question. Ask open-ended questions and/or scaffolded questions. Encourage students to seek out help from their classmates by asking, “Do you think one of your classmates could help you?” Or ask students how they could find the information. Of course, there are times when you need to tell students things directly, but try asking questions as much as you can. This will help their perseverance grow as they become self-sufficient learners.
Check out my posts on questioning such as How Can I Ask an Impactful Question? and How to Practically Create a Culture of Questioning?
Scaffolded Tasks
Students sometimes give up because tasks are too hard or they are bored with the task. Find interesting tasks that have multiple entry points. Don’t be afraid to differentiate by making multiple versions of the same task at various levels.
Problem 5: Assessment
Solution: Use Rubrics
Problem solving is great and all, but how do you assess it? The solution is to use a rubric. Subscribe to my blog for a FREE Printable Student-Facing Rubric for Grades 3-8.
If you teach high school, here is a link to the Standards for Math Practices Rubric I created for the Ohio Department of Education and Workforce.
Conclusion
Incorporating problem solving into your classroom can increase student engagement if done correctly. Students will thrive and see relevance in their learning. As student engagement increases so will your love for teaching! May you have the best year yet as you help create future problem solvers and thinkers.
A Few More Resources
Check the Ohio Department of Education and Workforce’s Progression on the Mathematical Standards. They also have the Math Practice Standards broken down by grade level.
Standard of Mathematical Practices #1
I’m listing both the Common Core’s version and Robert Kaplinky’s version. His is a little more readable.
| Common Core’s Version of SMP.1 | Robert Kaplinky’s Version |
|---|---|
| Make sense of problems and persevere in solving them. | Math Practice 1: Make sense of mathematics. |
| Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. | Mathematically proficient students begin a problem with a strategy in mind, but can also revise it until they get the result they are looking for. They feel comfortable representing their thinking using pictures, numbers, symbols, and/or words and can compare their method to other problem solving strategies. |
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