Notice and Wonder with Play Mats | Chapter 2 Gattegno Textbook 1 Part 1
Chapter 2 of Gattegno's Textbook 1 is the start of the student's immersion into the language of math, but they too can begin to notice and wonder.
Notice and wonder is a way to see what interests the student and to take the student's lead in math. I wouldn't make it more than that.
Chapter 2 is segmented into 8 concepts with various activities for each concept. Sonya's Manual for Module 1 lists these activities in greater detail and my Math task cards pair with each of these activities.
What a student notices and wonders as they play with the rods depends on where they are in the Chapter 2 and the student's interests.
This posts covers the first 4 of the 8 concepts in Chapter 2 of Gattegno Textbook 1. I give examples of what a student could notice and wonder based each concept. First, let's examine how not to do it.
How NOT to Notice
In notice and wonder, the temptation for the educator is to lead the student to notice what they want the student to notice. An educator might be tempted to say "What do you notice about such and such?" Leading questions like that can misled the educator to think a student notices what they notice.
Instead, take turns noticing with the student. The following example is for a student who has completed all exercises in Chapter 2. Student has been instructed to build 3 trains side by side. The first train is 3 reds, the second train is a dark green, and the last train is 4 light greens.
Educator: "What do you notice?"
Student: "I notice 3 reds."
Educator: "I notice 3 reds are the same length as a dark green."
Student: "I notice 3 reds are the same length of 2 light green."
Educator: "I notice a red is shorter than a light green."
Student: "I notice a pair of light greens is the same length as a dark green."
Educator: "I notice 4 light greens are shorter than the dark green."
Student: "I notice dark green is longer than 2 reds."
If the educator wants the student to expand on something a student notice, the educator could phrase the question, "Tell me more about such and such." The question avoids the temptation of leading the student to notice what they want the student to notice.
The key is to get the student in the habit of observation and the habit of prediction.
In the beginning, be content if the child only notices the color of the rods, the number of each color rod, the narrative of their free play activity and sizes of the rod. Focus on the activities in Module 1 which contain the various ways of naming, describing the rods and observing the rods.
How Often to Notice and Wonder
It depends on the student. Model notice and wonder every day, but remove expectations that the student should notice and wonder with you. Also remove expectation of what you want them to notice.
The habit of observation takes time to build as well as their language to describe what they observe. To avoid anxiety, be content if the child doesn't notice very much. Continue to do the simple tasks in the module 1.
Our family notices and wonders every day. It is my children's favorite activity and often guides our lessons. They are in Textbook 2 though.
My children didn't notice and wonder much in the beginning. However, I did model it, and it soon caught on. Early on we noticed more than we wondered. Their ability to wonder developed as they noticed more about the qualities of the rods and numbers.
Module 1.1 Discovering Rod Names and Qualities
For module 1.1, the student is getting acquainted with the color of the rods. Notice and wonder can be done in the context of free play.
Educator: Can you tell me about your picture?
Student: It is you and me.
Educator: Oh, how sweet. Am I the taller one?
Student: Yes. You are the yellow one. (valid notice)
Module 1.2 Recognition by Size
Expectation should be kept to a minimum. Students are just beginning their immersion into the language of math. The only activity for this module is the several versions of the blind find.
I suggest to conduct notice and wonder at the end of free play. You may chose to conduct free play before the blind the find or after as personal choice.
Student's notice and wonder is limited to size recognition. If you take a picture of a recent Cuisenaire rod art, bring it out to notice and wonder. Notice and wonder may look as follows.
Educator: "What do you notice?"
Student: "I notice two people."
Educator: "I notice a red rod is shorter than a light green rod."
Student: "I notice a yellow person is taller than the light green ."
Educator: "I wonder what rod you could use to make an even taller person."
The student may take you up on that wonder. That is great. If not, move on.
Module 1.3 Bigger, Smaller, Equivalent
In module 1.3, students get acquainted with tasks that develop their language and insight for greater than, less than and equal to. The following play mat is from Math Task Cards for Module 1.
Before notice and wonder, ask the child to find a few rods smaller, larger and equal to the dark green rod. Have them sort the rods on to the mat. Don't ask them to find all of the rods.
Educator: What do you notice?
Student: I notice a red rod at the top.
Educator: I notice the red rod is shorter than a light green rod.
Student: I notice the black rod is larger than the red rod.
Educator: I notice the dark green rod is smaller than the tan rod.
Student: I notice the red rod is shorter than the dark green.
Educator: I wonder what other color rods are larger than dark green.
The student may or may not take you up on that wonder. But if they do, great.
Module 1.4 Staircases
I love staircases. There is a lot available to notice and wonder. The following concepts for Module 1.4 is taken from Sonya's manual.
- Rods are separated by a common difference
- The rods have an order of size
- If we add the same colored rod to all steps in the staircase, the difference between the steps remains the same.
- If we reduce the staircase by a given amount, the difference between each step also remains the same.
- If the height between the steps of the staircase is filled with the same rod on each step, an new staircase is produced.
The following play mat comes from the Number Building Staircases also found in the Interactive Math Notebook Bundle.
Educator: What do you notice?
Student: I notice a white rod at the top.
Educator: I notice the bottom stair is made of 2 reds and a dark green.
Student: I notice the blue step.
Educator: I notice a white rod added to the blue step makes it the same length as the bottom step. I wonder if I add a white rod to the step above it will equal the step below?
The student may or may not test out your idea. Give them time to consider the idea. You may demonstrate your idea with a white rod. Then give them more time to consider. If nothing happens, continue with the exercises in module 1.4.
There area a few important concepts in Module 1.4. Remember what I said in the previous post about integrating modules 1.4 thru 1.8 together. Rotate the tasks from each module throughout the year for young children until they have gained fluency for each concept Sonya lists in the manual of Module 1.
What if my student notices nothing?
Every had expectation or even the feeling of expectation breathing down your neck? Give kids space to answer.
Space includes time and physical space. Maybe walk away and do the dishes while they think and work with the rods. Time may even include weeks of having no expectation that they notice anything at all. Just keep modeling.
Remember language building takes time. Remember how much time it took for your child to start using their native tongue. Remember that they babbled things incorrectly, Remember that you had to point and name things over and over again. The same is true for math.
You may need to repeat the tasks in the module to help the student become comfortable using the language. However, if the student is fluent in the tasks but not noticing or wondering about those concepts, it might be that those concepts do not interest them at this point. That is okay.
My kids went through a period where all they noticed or cared to notice were fractions. That is all that interested them and that was fine. Differences between rods never interested them and yet, they were fluent in the concept. They enjoyed differences between squares but never rods.
Notice and Wonder is Not a Test
It is worth repeating that notice and wonder is not a test. It is a tool for you to connect with your student's thinking. It can also be a tool for student-led exploration into math.
This concludes part 1 of Notice and Wonder for Chapter 2 of Gattegno Textbook 1. Next post, I cover module 1.5 thru 1.8.