How I Organize Chapter 2 | Gattegno Textbook 1
Gattegno Textbook 1 is a short book, but don't be mistaken by its brevity. Today, I will tell you how I integrate my materials into Chapter 2 of Gattegno's Textbook 1.
First, if you've ever took a peek into The Handbook of Activities for Cuisenaire Rods, you become aware at the depth that can be gained from Cuisenaire rods It is a hefty detailed book every all the additional activities and instruction most are looking for.
Too many teachers may have choked on that book. In hopes of not discouraging the educator, Gattegno wisely kept his textbooks brief. I believed he hoped that while interacting with the rods the teacher would perceive the math opportunities available for themselves.
Our first time through Gattegno Textbook 1, I blew through it with my kids and thought we nailed it. Then I read Madelene Goutard's book, Mathematics and Children, and soon realized I missed a lot. I am sure though that I am not the first to make this mistake.
My children did not come out of Textbook 1 the first time producing the works Goutard's six year old students produced. That is when I took a deeper look at the Handbook of Activities.
My eyes opened to the greatness that lie inside these magical Cuisenaire rods. Between Goutard's work, the Handbook and Sonya's classes, I began to refine how I cultivated my kids' math minds. To see how I integrate everything, first you need to understand block logic.
Block Logic, Not Linear
Linear logic is progressing steps of 1 to 2 to 3. Block logic is step 1, step 2 incorporating step 1, and add in step 3 while still incorporating step 1 and 2. This pattern continues. It maybe better perceived as concentric circles that grow and grow never leaving itself.
Basically, chapter 1 Free Play always stays with you. Rod free play gradually dissipates but free play itself remains through the freedom of number studies. It is where intuitive math knowledge, along with the child's ingenuity, grows.
Chapter 2 of Gattegno Textbook 1 is qualitative. Because qualitative is about perceiving (noticing) the mathematical qualities inherent to the rods, you never leave this chapter either. The whole journey of math is about understanding the qualities contained in numbers in order to better solve problems.
Module 1 as an Expansion of Gattegno's Textbook 1 Chapter 2
With that in mind, chapter 2 of Gattegno's Textbook 1 is not exhaustive. You can read it in half an hour, and thus, it deceives you into thinking you can complete in one or two months.
However, it is better to linger in chapter 2 and add more qualitative exercises. That is what Sonya did in Module 1 of her Manual.
Sonya Post pulled additional tasks from the Handbook of Activities and from her own experience to expand Chapter 2. I formatted the activities into Math task cards for convenience. For me, nothing makes my eyes cross than staring at too much text in the morning. Plus, I wanted tasks that could be completed without much instruction from me.
Missing from Module 1 are the staircase activities included in the Handbook of Activities. I found these activities valuable and so I created the Staircase Activities expansion pack.
Two Main Goal of Gattegno's Textbook 1
There are two main goals of Gattegno's Textbook 1. First, develop the student's math insight through Cuisenaire rod tasks and questions. Second, give the student language to articulate their new math insight.
Insight is what the child notices or discovers. A notice or discovery is any math the child is able to perceive and articulate. "I see a yellow rod is the length of a red and a light green" is a reasonable discovery for a young child.
Will they use that same language? Not likely. Their discovery may sound like this, "I ran out of yellow rods and used red and light green instead." You would validate their discovery with more clear mathematical language by repeating back, "Yes, red plus a light green is equivalent to a yellow rod."
Language Immersion with Quality Context
With those 2 goals in mind, understand that your main objective for Chapter 2 of Textbook 1 is language immersion through quality context.
Like any language immersion program, it begins with naming things and naming things in context. The exercises provided by Gattegno Textbook 1 are the beginning of that language immersion.
Children already understand a pancake by their experience, but it is you who provides the child the name for the pancake and all the yummy words to describe the pancake.
In the same way, children understand equivalency, greater than, less than, multiples and fractions by the experience of the rods. Then there is the guide who gives names and describing words for the child to use to better communicate their experience.
Tasks for the rods provide context for you and the child to communicate and discuss math. Pointed questions and language refine the child's ability to perceive and describe the math available to them through the context of the rods.
Creating More Context for Language Immersion
I created materials for Cuisenaire rods to create more context for this language immersion. Many have asked how to integrate the other materials I have created into Gattegno's Textbook 1. The following is an outline for how I intergrate some of my material into Gattegno's Textbook 1 Chapter 2 as well as how I progress through the material.
Getting started, begin with reading Module One Manual by Sonya Post. It will walk you through all the basic activities that occur in chapter 2 of Gattegno Textbook 1.
I work through Module 1.1, 1.2, 1.3 in order. After that, I mix up the daily activities and pull task cards from 1.4, 1.5, 1.6, 1.7 and 1.8. That is I work from 1.4a, 1.5a, 1.6a, 1.7a and 1.8a in no particular order for a while. Then move to 1.4b, 1.5b and so on. Sometimes, I even return to 1.1, 1.2 and 1.3 as needed.
Don't do only 1.4 all week long or all month long and then move to all of 1.5 and then all of 1.6.
Remember, it is not linear but block. Just mix it up until you work through all the tasks. Never skimp on variety. This improves the child's interest. Biggest and hardest tip: always quit before the child wants to. Things tend to go better this way.
How I Integrate the Interactive Math Notebook Bundle into Module 1
The Interactive Math Notebook Bundle is a great way to add variety and create more context for immersing the child into the language of math. The following activities are included in the Interactive Math Notebook Bundle and how I integrate them into chapter 2.
At module 1.3, introduce the Search and Find for Cuisenaire Rod Activity. This is a fun activity that will build upon their knowledge and perception of equivalency. It is a favorite with my kids.
At module 1.4, introduce the Number Building Staircase Play Mats. I would refrain from using the task cards and just use the play mats for exploration and discussion. The Staircase Extension Task Card Activities fit here as well.
At module 1.6, introduce the Building Equation Play Mats. Again, I would refrain from using the task cards in Building Equation Paths. Just use the play mats for language immersion opportunities.
At module 1.6, introduce the Fraction Exploration Play mats. Again, don't use the task cards found in this packet yet.
At module 1.8, introduce the Odd and Even Play Mats. Again, the task cards are not needed yet. Just use the play mats for added language immersion opportunities.
Tips for Using the Play Mats for Math Language Immersion
What do I mean just use the play mats for language immersion? At first, just describe to the child what you see as they build with the play mats.
- "I discovered that if you add a red rod to each stair, the stair becomes the same height as the next stair."
- "I notice your train is made up of a red, orange and purple."
- " I see your hiking trail is made up of one orange, 3 light greens, a yellow, etc."
- "I wonder which path is longer?"
- "Is this staircase made of odd or even rods?" "How do you know?" "Can you show me?"
Remember, Chapter 2 is about equivalency, less than, greater than, complements, odd, even, transformations and simply reading trains. Limit your discoveries (aka observations or noticings) to just these concepts for this chapter.
Don't expect children to articulate well what they know and how they know. Instead, ask them to show you first how they know with the Cuisenaire rods. Then provide the language to them.
So when do you use the task cards from the Interactive Notebook Math bundle? The task cards are better for the end of Gattegno Textbook 1 Chapter 3 to reinforce the mathematical notation and the expanded language of operations.
That is a lot of material but it allows you to linger in Chapter 2 of Gattegno's Textbook 1 and get all that is available in that chapter.
Considerations for Older Children
For older children (ages 9 and up), you won't really need to do all this. In fact, they may be insulted by it all. I think for older children the activities in Gattegno Textbook are sufficient for qualitative work.
The goal of the chapter is for children to be able to verbally articulate the following ideas:
- Equivalency
- Greater than, Less than
- Complements
- Rod Partitioning (Mat building)
- Comparing Single Color trains
- Transformations
- Odd and Even
There is no sense in lingering here if older children can do this with ease.
Last Key Notes on Gattegno Chapter 2
Remember how many times you had to name the pancake to baby before he babbled it? How many times did he roll it off his tongue with little to no understanding? And how many more times did you repeat the correct way to ask for the pancake?
Yes, that is your math journey too. So relax if they struggle to name things correctly or at all. Just focus on naming the rods and refining their limited math language. Provide the child with quality input and context through simple rod tasks and language immersion. The output will come.
In addition to this, there is a video below to show you how I organize my notebook. I emphasize many of the same points I made in this blog post.
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