The Meaningful Task of Math Journals
Keeping a journal is an exercise in storytelling, that is narration. We are wired for storytelling. We remember and store information in stories.
Storytelling is also that internal dialogue that shapes our thinking. It takes place both in pictures and words. Keeping a journal gives structure to where we've been and where we are headed.
This is why math journals play an important role in math for us.
Math Journals Give Structure
Much of the stress of math is because there is this arbitrary timeline that we place ourselves and students under. This timeline is very linear and often there is no room to linger or deviate.
The reality is that learning is very circular. Even more so, these circle overlap. Think of spirographs. Of course, this is frightening because we don't like to plan out our life in such crazy beautiful circles. We plan in lines, that forward linear movement of to-do lists and calendars.
Because journaling provide structure in a linear timeline, I use math journals to chart progress without the constraint of an arbitrary timeline. We are always moving forward, but like the seasons, we circle back to old stomping grounds and look a little closer at fractions then we did before.
Math journals help me plan too. I find a rhythm of circling back to old stomping grounds to observe more without beating a topic to death and boring my children. When they quite enjoy a topic or game, I make note to linger a few more days longer.
Anytime I notice a concept is solid, I review journals to find opportunity to extend their understanding. I also note to send a question to a trusted math friend when I feel we have a problem.
Math Journals in Pictures and Words
Much like a nature journal, math journals happen in both words and pictures. When I create a math journal, there is space both to draw or color and write down observations.
One might find it redundant to draw a math manipulative. But one who keeps a nature journal doesn't find it redundant to both draw and write observations. Drawing a picture of our observation enhances our understanding. It has a way of slowing us down to observe more deeply what is before us.
We see, then we see, and then we see see. It each instance our insight of what is before us grows. But we have to slow down to see it and that is what drawing does for us.
But we can't forget how language adds an even deeper level of understanding. The search for the words we need to describe what we see drives us towards clarity. It is in that strive for clarity that understanding takes a firmer grip on the mind.
Most worksheets do not provide the opportunity to strive for clarity. Neither do these worksheets acknowledge what is known to the child. I design math journals to do both, share what they know and deepen their understanding using both pictures and words.
Math Journals as Starting Points
Math journaling can also create student-led opportunities to explore mathematics. As you learn to connect with student-thinking, you will see opportunities to encourage their interests and expand their observations.
PDL's Math Journaling pages are starting points that I created to help me encourage student-led explorations of math. It begins first by creating a structure with the rods. The student observes the structure and wonders about the structure. Sometimes there are opportunities to create similar structures.
Cultivate Internal Drive
The pages offer structured choice for the student. Structure to guide but not to stifle. Students have autonomy and control over their education. This is important for it cultivates an internal drive in the student.
Develop Student Confidence
Math journaling also builds the confidence of the students. Student need an environment that validates their innate math mind.
Validate Student's Innate Math Mind
Journal pages cultivate confidence by allowing the student to explore and validate their own math ideas. It also encourages the student to extend their own thinking through wondering about math.
Challenge Student Thinking
Journal pages challenge students to validate their math ideas by moving the student to the abstract by changing the value of the rod or extending their thinking with the right kind of questions. Does their idea remain true if they change the value of the rod? Can they replicate this idea in other contexts?
Develop Self-corrective Thinking
Students need to develop the habit of self-corrective thinking and these journal pages provide the environment for students to cultivate that habit. Is this true? How do I know?
When to use PDL's Math Journaling Pages?
These journaling pages are great for after completing Gattegno Textbook 1. Both educator and student need to first develop the language of math before using these pages. Gattegno Textbook 1 prepares students and educators to use the math journaling pages.
Blog posts on PDL's Math Journaling Pages
Math Journals | Notice and Wonder Math Tables (coming soon)
Math Journals | Notice and Wonder Math Expressions (coming soon)
Math Journals | Noicte and Wonder Compare and Contrast (coming soon)