Laying a Foundation – Chapter 2 Recap
We made it through chapter 2 of Gattegno Mathematics Textbook 1! If you followed this series, then the foundation for teaching Gattegno's mathematics with Cuisenaire has been laid. We 'll be adding a few new things here and there, but for the most part, we're just adding more details to what we've already put down. You will find the entire series by clicking Gattegno Textbook 1 in the sidebar under categories.
The Bricks of Our Foundation: Free Play, Trains, Patterns, Mats and Staircases
The end goal of book one is mastery of the 4 basic operations and fractions as operators in numbers up to 10. In this first section, the big picture goal is that the student becomes familiar with the rods and the activities, is capable of manipulating the rods, and begins to develop the language to communicate what s/he is seeing and doing.
Free Play: Don't skip this. It is the temptation of most parents to skip this part and get to the work of "real math". However, free play does teach real math. Beyond that, children develop an intuition about how math works, develop spatial reasoning, plus free play encourages problem-solving skills and much more. Intuition is not something you can teach didactically. If you want to skip free play in lesson time, give your students free access to the blocks and encourage your students to use them outside of math time.
Informal Activities with the Rods
There are 4 basic activities that make up our foundation: trains, patterns, mats, and staircases. A train is made of one block or multiple blocks placed end to end. When we make a train and compare that train to either a single rod or another train, we call that a pattern. A mat is made when we make multiple patterns and place them side by side. A staircase is made by placing rods in order smallest to largest or largest to smallest.
When Gattegno calls these informal, he means that we have not begun work with arithmetic proper. We are still in the play/game stage. Our attitude regarding this time should also be light and fun.
The following are the basic patterns for the work we've already covered. Multiplication and addition patterns can easily be turned into mat work.
Patterns that are the Foundation of Addition
Patterns that are the Foundation for Subtraction
Patterns That Are the Foundation of Multiplication, Division, and Fractions
What I Wish I Would Have Done Differently
When I found Gattegno, I had started with another base ten program that was good but even harder for people to implement. I kind of did this back and forth sort of thing instead of just choosing a pedagogical approach and sticking to it. I didn't settle on Gattegno for several months. There was some wasted time there. Once I made up my mind, things started to click.
Having come from another program that did not emphasize workbooks, I didn't read through the textbooks in the beginning. I read Johnny Can Now Do Arithmetic and A Teacher's Introduction to Arithmetic. I had watched some video and then just took the plunge. It worked ok. But had I read the textbooks I would have gotten a better feel for how Gattegno puts it all together. I would have better understood how Gattegno creates awareness in a student and slowly builds from awareness to awareness.
The last thing I would have done differently is to spend more time getting to know my child/student. It is because I am an impatient observer that I don't understand the cues he is giving me. I mistake hard thinking for frustration which makes me quick to intervene when I should be patient and let him think it out. I've missed a lot of his aha moments because I thought he knew/understood something when he had only a partial understanding.
What We Did Right
One thing that has been hammered into my thick skull, and I think I'm starting to catch on, is to provide information in small bites. We are not sprinting to the finish line; we have time to take the slow route and enjoy the journey. My habit was to take a large serving spoon with information piled on top and shove it down my child's throat. Having done that, I would then immediately become peeved when he choked, complained or stopped breathing.
My work with Crewton Ramone primed the pump for everything Gattegno has to say about creating awareness. We take things slow. We play games. We enjoy the journey. I am actively cultivating a love of math in my son. But this couldn't have happened unless I had loved math first.
I have this thing about studying that which is beautiful and lovely. There are some areas where I succeeded when we homeschooled the first time. Math was my big failure. It was beyond a failure. It is that failure that caused me to look for another plan. In that search, I managed to reteach myself math. What I discovered is that math is a wild and wooly thing. It is a shockingly beautiful, fun, and simply amazing world. That world deserves our love and attention.
But what if you haven't taken the time to reteach yourself math and all you know is a scary place that contains a bunch of symbols that you don't understand. I get it. My answer: Play blocks. You have time. Play blocks.
Do you have a kindergartener? You have lots of time. Read Now Johnny Can Do Arithmetic and chapters 3-4 in The Cuisenaire-Gattegno Method of Teaching Mathematics. Once you have done that, start at the beginning and play blocks with your kids. They're a lot of fun.
Do you have a 3rd grader who already hates math and thinks they can't do it? You have lots of time. Read Now Johnny Can Do Arithmetic and chapters 3-4 in The Cuisenaire-Gattegno Method of Teaching Mathematics. Once you have done that, start at the beginning and play blocks with your kids. They're a lot of fun.
Do you have a 6th grader who hates math and is math resistant? You have some time. Read Now Johnny Can Do Arithmetic and chapters 3-4 in The Cuisenaire-Gattegno Method of Teaching Mathematics. Once you have done that, start at the beginning and play blocks with your kids. They're a lot of fun. You'll move quickly through the lessons. You can finish the entire curriculum in 2 years, at which point your student will be ahead of his/her peers.
Do you have a special needs child? Great, so do I. Read Now Johnny Can Do Arithmetic and chapters 3-4 in The Cuisenaire-Gattegno Method of Teaching Mathematics. Once you have done that, start at the beginning and play blocks with your kids. They're a lot of fun.