Helping Your Child Explain Their Math Thinking
Explain your thinking...
Make a model and explain your thinking...
Explain how you know this isn't the right answer...
On every math assignment that my students get, one of these sentences is bound to be attached to at least one problem, and often these short sentences can frustrate and confuse my student and their parents.
Why explain thinking if they already got the answer right? Why model something when they know how to get the answer mentally? Most argue that it just seems like educators are trying to make kids do more work.
Most adults didn't grow up explaining their thinking when doing math. I vividly remember not being allowed to show work in the margins of my multiplication drill tests. So, why are most schools requiring kids to explain how they thought about the problem, when it worked just fine for us to just "know"?
One reason is to help students learn how to show what they know. Often in lower grades, students may rely too heavily on procedure, and might not understand why or how the math is actually happening. In these cases, encouraging students to explain or show their thinking with words, pictures or charts can not only help the teacher understand what the student knows and doesn't know, but also helps the student further their understanding of the math concept.
Explaining, modeling, and justifying answers also helps students learn to think critically about problems and the problem solving process. Often students are asked to explain their thinking in group discussions. When justifying answers and explaining methods of thinking in a group setting, students are able to learn from each other's ideas and mistakes. A student who is still working at a basic level may hear the explanation of a student at a higher level and change some of their methods.
At times teachers may require that a student model their thinking in a certain way, such as modeling a division problem with a bar model. These requirements are placed at times to help students learn to envision what is happening with the problem instead of just memorizing a rule or procedure. Memorizing a procedure may work at first, but may not work in the long run, when the student needs to apply their knowledge to a unique situation.
I also understand that at times rules on showing work can be restricting depending on the situation. Some students think in pictures, while others think in words. In general, I believe that a student should be allowed to show and explain their work in whatever way works for them.
Whether you agree with this new trend in education or not, your child will be expected to justify their work. To help curb the frustration, and increase the learning, try a few of the suggestions below to help your child become a pro at explaining their thinking.
Use sentence stems
If your child has a hard time putting pen to paper, sentence stems are a great place to start. Often students who already have a hard time with writing (whether it be handwriting, coming up with the words, or a combination of both) have an extra hard time writing to explain their thinking. Having a few sentence stems printed out and on hand can help get them started.
What are sentence stems? Sentence stems are the beginning of a sentence that can get students started writing. An example of a sentence stem to help your child explain their thinking might be "I know that _____ is the answer because....". Though it seems simple, giving your child the first few words can help launch them into a good explanation because they don't have to think about how to start their sentence.
Here are a few more sentence stems you might use to help your kiddo get started...
I used_______to solve my problem because________
I know this because___________________________
The strategy I used was _______________________
I know this is right because____________________
The steps I used to solve this problem were__________because__________
Help with models
When your child is asked to use a model to explain their thinking it can be difficult to help them if you don't understand the model yourself. Different schools use different kinds of modeling for the same subject, so even I run into this problem from time to time as a tutor. The best place to go to understand different modeling techniques is the internet. My preferred place to start is because they usually model problems in many different ways. After Khan, I usually will search YouTube videos for examples of the modeling technique.
If your child doesn't understand the way they are being expected to model a problem, don't be afraid to ask their teacher for a different way of explaining and doing the same problem. Not all students learn the same way, and not all visuals will click with every child.
Explain your own thinking
Take the opportunity to explain your own thinking whenever possible. Our students learn from our examples, so seeing us explain our thinking can be very helpful as they learn to explain theirs. When helping with math homework or practicing with word problems, do the same problem as your child and then compare answers. As you compare, each of you can explain your thinking to the other. This gives you a great opportunity to model explaining your thinking as well as to listen to your child's thinking.
Help with frustration
At times, students can get frustrated when they are asked to explain their thinking. Sometimes thoughts are hard to put into words or pictures. When frustration hits, you can help ease the pressure by offering a few different options to help your child release their thoughts. Offer up a white board or piece of paper for your child to draw out what they are thinking. Offer to let your child explain orally what they are thinking while you act as their scribe. If things are getting too frustrating, never be afraid to solve the problem and come back to the explanation later.
What do you think about students being asked to explain their thinking? I'd love to hear your thoughts in the comments.