# Math Journals Notice and Wonder | Structures

While Gattegno’s free textbooks serve as our math spine, it is math journaling that gives us a place to individualized learning. It is where we notice, wonder and explore math.

Math journaling is much like nature journaling. The habit of observation is honed while the student's curiosity is cultivated. It is the side trails of math to explore and discover as the heart leads.

Math journaling helps make math a personal experience. It isn’t about what the teacher wants the student to see or learn but instead, it is about what student wants to see.

Math journaling meets the student where they are in their journey. This is unlike a textbook which sometimes drags students about on a hurried agenda.

Through math journaling, the educator sees what interests students and gives students permission to linger and be curious. There is a lot to love about math journaling.

But what does math journaling look like?

### The Inspiration of Math Journaling Pages

Gattegno's free math textbooks, "Mathematics and Children" by Madeline Goutard and Arithmophobia No More's online live math classes are the sources of inspiration for my math journal pages. All these sources understand the power of student choice and student-led exploration.

Juggling the homeschooling of 3 kids and a toddler leaves me in desperate need of pre prepped activities that offer meaningful choice and encourage student-led exploration. I created PDL's Math Journals for Cuisenaire Rods to do just that.

There are various journals that give students a sense of choice while providing meaningful math exploration. Some journals explore structures. Others focus on exploring expressions. There are opportunities to compare, contrast, notice, and wonder. There are opportunities to predict, test ideas and gain satisfaction in student-led discoveries.

This is the beginning of a series of blog posts on how I use these math journaling pages. Let's look at simple math structure journal that focu

There are a variety of Cuisenaire structures that Gattegno uses. Some structures emphasize differences, multiples, equivalences and fractions. Almost all structures can do all that but some more than others. The structure above emphasizes multiples and quantitative equivalences in different shapes.

### Notice and Wonder

First, begin with notice and wonder. Depending on the child’s awareness, what is noticed and wondered about varies. My children noticed the equivalency, but they have been working with rods for a while. This may not be apparent to a child just working in chapter 3 of Gattegno’s Textboook 1.

The student might need to use rods to build the structures. Then they can stretch the structures out into trains to compare and see. Otherwise, the student may just color the page according to the rod colors.

Wondering doesn’t always come naturally to a child who is used to traditional textbooks and worksheets. It is important to model wondering. What do you wonder? One of my children wondered if each structure could be divided by 2.

Another wondered if other numbers build twelve. In his own language, the child asked if there is another multiple of twelve.

It is important for students to use their own understanding to articulate their idea. Their own understanding entails their own limited vocabulary. This requires you to listen to what the student is saying carefully.

Students want to be understood as much as you want them to understand math. Once you understand what they mean, then provide them richer vocabulary to express their idea.

### Pursuing a Wonder

One child wondered if the structured doubled in value, would it double the number or rods used? Delving into the distributive property, the child decided to test their idea.

Intuitively, they believed the number of rods would double if the value of the structure doubled, but were they certain? It is great to see them test out their ideas.

This is an important life skill being built. It’s great to have ideas and wonder, but there is greater value in testing ideas to be certain they are true. It’s truth that matters. Encourage students to pursue the validation of their ideas.

This is the benefit of the math playground. It's a place that cultivates the importance of validating ideas.

There is much more that a student may notice and wonder about. I like to use graph paper to insert between journals. This allows us the opportunity to come back to these pages and explore more.

## Composing Math

I try to leave room for the children to translate the structures into mathematical notation. This often helps to emphasize equality of structures that may not appear to be equal.

Children write the equations as addition or multiplication. For older students, you can play with rewriting the equations using only prime numbers. Or you can change the value of white from one to two to one half of six to 100 to whatever. The opportunities are endless.

The danger of manipulatives is letting them leave children in the concrete. Mathematics is a playground for the mind. We want to use manipulatives to move children to the abstract. Changing the value of the rod is one way to help students move from the concrete to the abstract.

### Don’t Do It All

There is plenty to wonder about but set a timer. It is easy to be so excited by what students notice and wonder that you will find yourself pushing math class beyond the reasonable time limits. Tell me how I know.

There is so much that one page has to offer. Cuisenaire rods have that unique ability to offer a lot of math with very little. When that time is up, put away and return to it tomorrow to pick up where you left off. Maybe there was a wonder not pursued or more to notice. Just don’t do it all in one day.

Whether you are in Chapter 3 or Chapter 4 of Gattegno Textbook 1 or have completed the entire textbook, these are great starting points for math exploration.

These activities provide students choice and it helps them take responsibility for their own education. It also gives students confidence in their own thinking and exploration of math.

Even if you don't use Gattegno's Textbook, these are still great starting points for students to notice and wonder about math. The page featured above is part of PDL's Math Journals for Cuisenaire Rods.