With the shift to common core standards and concept-based learning, we are asking students to do more and more written work in math. They are expected to perform in writing on assessments to complete error analysis tasks, explain problems, justify solutions, and more.
But, I've noticed that if we do not take a full day (or more) to explicitly teach this and practice it in context immediately, then we cannot expect our students to know what results we are looking for in their writing.
They really are not comfortable writing out full responses in math until we model it, show them specific examples, and explicitly outline what is required.
One of the best ways to do this is to offer a full class period or two in which you only cover writing expectations specific to math classes. Here are what I have found to be the basics to go over with kids during this lesson:
Complete Sentences. Always.
You can ask them to offer at least three sentences (or more) when you are looking for a complete explanation of something. At first, they probably will not know how to finish those sentences, but that is why we go on to the practice afterward.
Give students examples of the different forms of "WHY" that we see in math explanations, and ask them to come up with samples on their own as you go forward. Remind them that each sentence can be followed up with a justification answering the question "why." Here are a few sample justifications that they could embed into an explanation:
• Why did you use that process?
• Why does that answer seem reasonable or not?
• Why did you choose to do that?
• Why do you think that?
• Why is it an error?
• Why will you start with that step?
Include Examples and Counter-Examples or a Picture / Diagram if Needed.
However, the full sentences must always be present. Any pictures or examples are just supplements.
Now, Practice It!
- Explaining a mathematical relationship
- Explaining a method, approach, or thinking process
- Explaining a problem
- Explaining a choice
- Explaining an answer
You can practice each of these types of written explanations with your students.
Explaining a Mathematical Relationship
Explaining a Method, Approach, or Thinking Process
Explaining a Problem
Explaining a Choice or Answer
My favorite approach for this "Writing in Math" lesson is an introductory doodle note that goes into the characteristics of a good math explanation followed up by stations where students practice right away (using the above prompts and additional ones as well). The full lesson pack for that is available for purchase here if you want it all fully assembled and ready to go.