Small Tweaks for Big Gains
As long as I can remember, multistep problem solving has been a struggle for students. The problem that we are actually seeing is that students are not able to sit with their thoughts and have some concrete things to do in order productively process their thoughts and persevere. Here are a few small tweaks we can make in order to get students to think on their own and develop skills that go far beyond math problem solving.
Students Can Write an Answer Statement and Label Their Representations
This is a great place to start. As students notice the question, have them write an answer statement. See image below.
This helps them to check in after they have solved to see if they have answered all of the parts and if their answer is reasonable. They can even do this in K and 1st. Just have them put a blank and a letter or word. They don’t need a whole sentence. Also have them label their representations so they remember what in real life they are doing. It’s all about making sense the whole time. This really helps you to see where their thinking breaks down. Is it in the context or is it computation?
2. Students Can Keep the Context Alive
When students are reading a problem, they are in the context, the story. Once they decide what operation they want to do to solve it, their brain switches over to the math piece. They decontextualize and solve with the numbers. Many students stop there. This is why you might see that students only solve the first part of a multistep problem or that their answer is unreasonable. We have to teach students to be able to switch back to the context or to keep it alive while they are solving. For example, They can think about how many steps are in a problem as they are reading and think through what they will be solving for in each step. See the image below.
This also allows them to have a workspace set up for each step so they don’t forget to go back into the context once they solve the first or second part. If you think this is too hard for your students, I promise they will get better and better at it, but they will need a lot of practice. This is a skill that really deepens their comprehension around the problem and the math that goes with it. It will grow them exponentially. You will also see how students solve problems differently and will be able to celebrate that. To be able to do this, students will need to go deeper with fewer problems instead of solving many problems. Quality over quantity.
3. Students Can Justify Their Thinking
Students justifying their thinking is a part of every content standard in Texas and probably every other state. It is a life skill being able to slow down your thinking and to be able to communicate your steps and defend your reasoning. This does not always mean this will be in writing. Actually, I would highly recommend that students get their thoughts out by talking first. Have you ever needed to write an email to a parent and you wanted to run it by your teacher friend first to ensure that you communicate in a way that makes sense, is in the right order, hits all of the important information, and uses just the right words to convey the meaning of what you want to get across? In a training from Teacher’s College, a staff developer called this “writing in the air", and I love it! Students need to process out loud, just like we do in order to communicate their thinking well in writing. The revising process goes so much faster when done this way.
Another important thing to remember when students are exposing their thinking is to give them some guidelines or components on what to include. One year, when I was teaching 5th grade math, I remember my class had a common justification. “I’m right because I solved it.” So I had to back up and really teach them how to bring their thinking to life. Then we got to where they could tell me what they did mathematically, but they still struggled to involve the context. So I started to give them these components and could even do very specific small group lessons based on what specific part of the justification they needed to focus on. The Components are:
Includes a sentence with the answer.
Includes the context and how it supported what you did mathematically.
Includes what you did to solve mathematically.
Includes mathematical vocabulary.
This gave them parameters and helped me as a teacher to figure out what they needed to grow in their communication skills.
I hope you got some tips from today’s post that can provide some small tweaks you can make to continue to put the thinking on students and see gains in problem solving skills. These will not be overnight success, but will create lifelong communicators and thinkers. Small steps for big gains. Quality over Quantity. If you want lessons to help you to teach these skills, subscribe below!
