Why Keep Math Journals

Observations in her journals began simple and mundane, but I noticed her engagement increased.  When she was asked to draw, it slowed her down to observe more details like how many, position, and comparisons of size. 

I didn’t leave her to just observe though.   I asked her to wonder.  This encouraged her to take an even deeper look.   Could she see any connections that gave her questions?  

To extend her wonder, I asked her questions that caused her to predict.   What would happen if I flipped the structure?   What would happen if the structure grew?   Over time, her observations became more detailed.

Math Journals Improve Communication Skills

With all the observations, I found all my children searching for clearer language to describe what they noticed.  This was language I was ready to hand them as they required it.

“It’s higher than this one,” soon became “the difference between the red and purple is one-half of purple.”  

Math journals simply created opportunity to develop math vocabulary in a more natural way.     

Math Journals Encourage Organized Thinking

As I read Goutard’s “Children and Mathematics,”  I noted her use of tables to organize information for further observations.

So we too began to organize information into tables.   This served us well.  It allowed us to observe as we filled the tables and we made predictions about what would happen next. 

My children also came back to the tables to observe new patterns not previously seen.  

The patterns they saw unveiled by the tables made math table journals popular in our home.

Math Journals Improve Critical Thinking Skills

I noticed with the right questions my children began to think about the implications of their observations.   Questions that encouraged my children to manipulate the information helped them to think more clearly about the implications of their observations.  

For example, when my children observed the effect of parentheses in certain situations, they began to better understand when and when not to use parentheses.

Math Journals Encourage Research Based Learning

One day my oldest noted the difference between the two structures, a purple cube and a light green cube. He wondered what the difference of an orange cube and blue cube would value.

He didn’t have enough rods to figure it out.   This became a beautiful research opportunity that forced him to use what he already knew to find the answer.

He was ready though.   He had built up a storehouse of knowledge.  All his observations of rod structures taught him how numbers behaved.  

He broke apart the structure to help him work out the algebra.  Then he plugged in the values for each number if white equaled one.    He was so proud.

Math Journals Meet Students Where They Are

Have you ever just had someone jump in mid-conversation and start talking about something random?   Textbooks have that kind of effect on my children.  Math journals let my children begin the math conversation instead of me or a textbook.

There was no judgment about what their first observations were about. Every thought and observation is worth the pursuit, worth consideration, worth the time. Math journals provided my children individualized learning experiences.    

For the classroom, this may be more frightening to a teacher, but I know notice and wonder has really leveled the playing field in classrooms like Anne’s.  

My daughter is so confident in her math now that she isn’t afraid to tackle hard problems.  

Math Journals Provide Documentation for Learning

Keeping a math journal has helped my children to see how far they have come. It has also helped them to go back and tackle those big ideas they had that they weren’t ready to conquer before.

How encouraging to see that they had big ideas worth pursuing even if they weren’t ready to pursue it.

Math Journals Provide Structure and Planning

Math journals gave me clues for planning. To ensure I tapped into their passions, I took note of what interested them most in their observations.  Then I looked for opportunities to extend their thinking.

When they took note that the structures were getting larger, I would ask them by how much?   If they noted the difference in growth between two structures, I would ask them if they noticed any fractional relationships between the two growths. I worked only to actively engage what interested them during journal time.

Sometimes, the absence of certain observations told me that one of my children was not comfortable with a topic.  Early on this was fractions.   It wasn’t that fractions weren’t interesting though.  It was their lack of familiarity with the language.

Math journaling is a lot like nature journaling.   It isn’t observing that is the hardest part for a child. It’s the describing.  How can a student articulate and compare tree leaf structures if they don’t know the different names for leave structures? 

Much of math journaling and nature journaling can be improved simply by spending time naming and describing things in a straight forward fashion.  We played lots of games and created lots of stories that gave my children the confidence to name fractions.

Math journals Reveal Misconceptions

Often my children see patterns that aren’t there.   Instead of just saying so, I often ask them to show me.   This is key.   Often in the process of showing me, they discovered why they were wrong.

This has also created a habit of self-corrective thinking.   They aren’t unsettled by the idea of explaining their work to me.  On many occasions, they have had victory over me.  

It is so important to take this defeat with joy and humility.  The reality is that when given the opportunity to explain themselves, you learn that you as a teacher are just as bad at paying attention as the student.

Don' be afraid to ask this question even when you know they are right.   This will help them to be more confident in their thinking.

Math Journals Allow for Creativity

Math journals have allowed my children to see how math is creative and how diverse the opportunities are for exploration.

Their favorite activity is to create art with Cuisenaire rods and explore the math that lies hidden within it. This cultivates curiosity and curiosity is required to fan the fire of a self-driven education.

Math Journals Instill Math Confidence

Math journals validated to my daughter that she does have a math mind.   Her math observations tend to be more interesting than her brothers who never really struggled with traditional math.   This has assured me that I am on the right path with her. 

All my children have gained confidence in their ability to think and draw conclusions.   Math has proven to me more than once that math is the best playground for teaching critical thinking.   

Because we have had so much fun and progress with math journals, I have tried to recreate that experience for you in almost all the products I sell.    I do follow Gattegno’s textbooks (free online) as a structure to introduce math language and Cuisenaire rod tasks.   (However, we do a lot of discovery-based/inquiry based explorations.) 

Gattegno's textbooks are just enough to show you depth of the rods, but I find that it helps to have a friend to reconnect you with your math curiosity.   I am thankful for Sonya at Arithmophobia No More’s online classes.   A lot of journal pages were created based off the many light bulb moments I had in her interactive class.    She ignited my math curiosity and gives me constant encouragement in our math journey.