Writing Better Math Journaling Prompts,

 I have tried using writing prompts in the past with less than spectacular results. It might be that I have never learned to write a proper prompt and have had to rely on prompts I found in books or on the internet. A lot of prompts I found didn’t seem right but I used them anyway because they were available. The other day, I came across something that explains how to write better prompts. Ones that will help students think more deeply and not just regurgitate the lesson.

It has been suggested that teachers move towards prompts that encourage multiple solution paths and away from ones that have students simply retell everything contained in the lesson, or just rewrite the steps needed to solve a problem. Prompts should appear in a variety of formats that encourage more writing, more reasoning, and even debates or arguments. The prompts need to be carefully constructed. 

Unfortunately, this not happen in the math classroom as much as it should due to state testing and mandated curriculum and pacing requirements. What is nice, is that with a bit of adjustment, it is possible to create opportunities to engage students in higher order thinking, writing, and conversation. One can make small changes to already existing material to make them more effective. 

Instead of writing the prompt to tell students how to do it, the language needs to be changed so the student has to do more work.  For instance, rather than writing "Use a drawing to show how to add two fractions together", change the wording so it is more like "Describe an efficient way to add two fractions." This makes it more open ended which requires students to do more thinking.  

They have to decide what way to use to show how to add fractions.  This could be done by using a number line, a drawing, or even photos of manipulatives.  This leads to higher level thinking and it provides more opportunities for multiple solution paths. If there is a fear students won't write much, it is easy to rewrite the prompt so the student is asked to provide two to three different ways of solving the problem and have them include their solutions with an explanation of why all the ways are accurate.

Another problem with many writing prompts is they ask students to explain how they solved it.  This is often interpreted by students to mean they need to write down the steps they used to solve the problem.  Instead of asking students to calculate the volume of a box of cereal and explain their answer, ask the student to explain the meaning of each term in the volume formula to a friend.  Think of using phrases like "Explain to your friend how you solved......" or "Describe the meaning of........" or "Explain the patterns you found...........".

These types of prompts allow the students to communicate their understanding of a mathematical. concept in the way that they answer the question. For instance, if they use more mathematical terminology correctly rather than general English vocabulary, it shows a higher level of understanding.  If the written answers are constantly  vague, then one should talk to the individual to determine how much they understand.

Finally, look at prompts that ask students to defend the validity of their answer or friends answers to a specific problem.  This allows students to see there are multiple pathways to get to a solution, see the common errors that occur, and help them become mathematical writers and thinkers.  If you have a prompt which asks if the work of a student is correct, rephrase it as two students are debating their answers.  One has one answer, the other another answer so students have to write a text, an email, or answer to both to explain who has the correct answer and why it is correct.  

When prompts include the phrase "How do you know" offers the opportunity for students to explain how students approached solving a problem, provides an opportunity to practice mathematical writing, and argument while practicing higher levels of critical thinking.  Let me know what you think, I'd love to hear. Have a great day.