Have you ever heard your students say, “Ugh, why do I have to write about how I solved the math problem?” If students can TELL you what they did to solve the problem, they can WRITE about it. It seems like a daunting task to get students writing, but step by step you can do it. This blog post is lengthy, but worth the read if you are serious about helping students explain their thinking with confidence.
Why Students Need to Write About Their Thinking
Let’s think about the big picture of why we ask students to share their thinking when they are solving math problems. Fast forward to the employment years. When businesses hire employees, the employee will never be given a math problem to be solved. They will be given a PROBLEM to be solved. They will need to defend their thinking with their boss to convince him/her of their findings. Students are in training for their future.
Give students a structure when problem solving.
Ask students to restate or tell in their own words what the problem is asking. Students will tell what they know and what they need to figure out.
Next, have students draw a picture, diagram, sketch, T-chart, table, or whatever helps show their thinking. Encourage students to draw arrows and underline things that help them explain what they are thinking. Students should show what they are thinking in this space.
Then ask students to write using words, sentences, lists or whatever it takes to explain the steps they took to solve the problem. Encourage students to pretend the person reading their explanation does not understand at all so they need to be very clear in their explanation.
Have students state the answer and underline or put a box around it. Remind students to always label the units on their answer. They will also prove they are right.
Collect Student Work Samples and Practice Scoring Sample Tasks
When you being problem solving and integrating writing to the process, be patient. It takes time to help students become comfortable explaining and drawing about their thinking.
Look for great student examples so you can show students what great pictures, drawings, and explanations look like. Talk to your teaching partners and help each other find examples of student work you can use for practice scoring. Compile your stash of great examples and add to it each year. Be sure to white out student names for privacy. Label the papers, Student A, B, C, etc. Using actual student work helps students understand what they are being asked to do.
Teach Students How to Read the Scoring Guide
Teach the parts of your district or state scoring guide. Get students into groups of four. Give each student in the group a completed student math task and scoring guide. Once you’ve found a few student example tasks, give students the task of scoring an actual student math task. Ask students to use the scoring guide and score the math task. Encourage students to discuss their thinking as they score the task. In time, students will become more comfortable as they defend their thinking. After students have scored the student work, show the actual scores the task earned. Discuss and allow students to review the scores they assigned compared to the actual scores earned. If you can allow students three or four opportunities to score student work, you will see their confidence build.
Show examples as you teach students to take time drawing sketches and label them. Draw and use T-charts to organize data. T-charts are so handy and helpful to see patterns, too. Draw number lines and show the jumps needed to get an answer. Draw a map or picture. Encourage using color if that helps the visual explanation.
Writing to Explain Thinking
Have students begin by using ordinal words like, “First I …, then I …, next I …, last I…” Encourage students to slow down and explain like they would talk.
When students have the answer, insist they label the units and then either underline their final answer or draw a box around it. I love joking with students when they forget to label the units. I say, “Your answer is 14? 14 toothpicks? 14 dimes? 14 thousand dollars? 14 pickles?” Students laugh and get that units do matter.
Proving the Answer Correct
An important part of the math task is proving they answer is correct. Students may begin by saying, “I’m right because I am right.” In time, they will become better and better and eventually become masters of proving their answer is correct. You need to encourage them to think like a defense attorney whose job is to make sure their client is proved innocent and apply that method to their “proof”. Use the analogy of the story of Jack and the Beanstalk as you set the stage for proving that Jack is innocent or guilty. In the story, Jack climbs the beanstalk several times and each time he returns home with things he took from the Ogre including a goose, gold coins, and a harp. Ask students to pretend they are the attorney accusing Jack of the crimes of breaking and entering the Ogre’s house and theft of his possessions. As Jack’s attorney, you can’t say to the jury and judge, “I’m right because I know I am right.” You have to PROVE it with facts and other evidence. The same is true in math problem solving. How do you KNOW you are right? Can you prove it? What facts and details do you have? Does your picture match the equation you wrote? Did you solve the problem a different way and get the same answer? Is your sketch labeled correctly to prove your thinking? Ask your students to be the jury and give a response of “thumbs up/I’m convinced” or “thumbs down/I’m not convinced” verdict.
Be Patient! Keep Practicing!
Take it one day at a time and know that with repeated consistent practice, your students will get more and more comfortable writing to explain mathematical thinking. Remind your students that their future boss will give them a real-life problem to be solved and they need to be skilled to justify their thinking. With practice, students will have the confidence to undertake the task willingly and cheerfully.
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