In previous posts, I encouraged parents, homeschoolers, and teachers to explore the world of math and introduced one of my favorite learning tools, the math journal. Then I shared several of my favorite types of journaling prompts to get your kids started writing about math.
Math journal prompts offer a wide range of options for students to explore. Most of the prompts do not have a “right” or “wrong” answer. Our goal is to root around in some small corner of the world of math, to lift a stone and peek underneath it, just to see what we can find.
The idea that being good at math means finding the right answers is a huge myth. Of course, many problems in math do have a single right answer. But even for those problems, the answer is not the real math of the problem.
Math is all about thinking.
It’s like taking a road trip. You may have a destination, but there are many paths you could take to get there. Different students may take different paths — they may think about the problem in different ways.
It’s this reasoning that is the real math, and the right answer is just a side effect of reasoning well.
An Example from Geometry
Our goal in the journaling activities is to get students thinking about the different paths they can take in any problem, so they can explore what interests them.
Let’s look at an example. Consider this geometry prompt:
“Draw a large circle. Draw its diameter. Connect both ends of the diameter to any other point on the circle. Do it again, connecting the diameter to another point, and another. What do you notice? What questions can you ask?”
Young children will find the construction itself a challenge. They may be surprised to see a triangle appear. Depending on its shape and orientation, they may not consider it a proper triangle. After all, in most picture books, triangles are usually equilateral and almost always rest flat on a side.
Young students might also see that the diameter of the circle is longer than either of the triangle’s other sides. But it’s not as long as both of them together.
Elementary and older children will discover they can create many quite different triangles following these instructions. They may wonder which of these triangles is the largest. They might guess (correctly) that it’s the one with the third corner point as far as possible from the diameter, but they may have no idea how to prove that fact.
They may also wonder what fraction or percent of the circle is contained in the triangle, though answering that question could be beyond their skill.
Middle school and older students might wonder about the angles produced by this construction. They may notice the smallest angle is opposite the shortest side, and the largest angle is opposite the circle’s diameter. Some may even manage to prove that the largest angle measures 90° (a right angle) for all possible triangles.
Or they might go in a completely different direction, deciding to add more lines to their construction and create an artistic design.
The point of the journaling exercise is not to discover any specific piece of mathematics. Rather, we want our children to play with the ideas and explore whatever connections they find interesting.
Hierarchy of Editing Comments
Because journal writing is so personal, students are easily overwhelmed by criticism. If you make too many comments, your student may feel like you are trying to seize control of their expression.
Build your students’ confidence by pointing out whatever you admire in their work: clear statements, vivid word pictures, clever phrasing, imagination, and so on. Then limit yourself to at most one or two critical comments. Focus on meaning, on understanding what the student is trying to communicate. Help them make that as clear as possible.
Honor the student’s work by not marking up their paper. If you must make corrections, put them on a sticky note. Leave the child in control of which changes to incorporate into their writing — or whether they want to let the paper stand as it is, a record of their understanding at the time.
Consider these areas for improvement, beginning with the most important.
1. Purpose: Did the student make the central idea, experience, or theme clear? Is this primarily an exploratory piece? Or is it written to inform a reader? Does the student need to summarize, analyze, or argue their point?
2. Development: Does the piece hang together? Can the reader easily follow the student’s logic? Did the student use evidence, examples, data, etc. to support the explanation or argument?
3. Audience (optional): To whom is the student writing? For most journaling activities, the audience is the student’s own self, along with perhaps a teacher or peers. If the piece will be shared with a wider audience, the writer may need to put extra effort into defining terms and elaborating on ideas.
4. Readability (even more optional): If the piece will be shared, does the student need to proofread for language mechanics?
It’s easy to find mistakes in spelling, grammar, or punctuation. But these areas have little to do with mathematical understanding. If we want our students to think about the math, then that’s where we need to focus our attention as well.
If you find it impossible to ignore the minor distraction of spelling or punctuation errors, ask your students to read their writing to you. That will allow you to focus on the higher levels of conceptual understanding.
As teacher and author Marilyn Burns explains, “Writing in math class isn’t meant to produce a product suitable for publication, but rather to provide a way for students to reflect on their own learning and to explore, extend, and cement their ideas.”
Journal writing is a first draft, not a finished product. Even professional writers often ignore the mechanical details in a first draft. They focus on organizing and expressing their ideas. The grammar and punctuation can be fixed later, before they submit the piece for publication.
Proofreading and clean-up is always the final step, after all the real thinking is done.
The Most Important Tip
Have fun with math journaling prompts. If an activity doesn’t make sense or feel playful to your students, move on to something else. You can always try again another day.
I encourage you to participate alongside your children. Math often works best as a social endeavor, whether we bounce ideas off each other or simply work at the table side by side.
Play. Discuss. Notice. Wonder. Enjoy.
If you enjoyed this series of posts about math journaling, you may also like:
- Math Journals and Creative Reasoning
- Your Student Can Be a Math Maker
- Notice, Wonder, Create
- Math Makers: Write a Poem
This post is an excerpt from 312 Things To Do with a Math Journal, now available from Tabletop Academy Press. You can buy the ebook at my store (Thank you for cutting out the middleman!), or get the ebook or paperback through many online retailers. Read more about my playful math books here.