(All of my Right Start posts, all in one place!)
We have been using Right Start Level C as part of Bruce’s afterschooling for about seven or eighth months now. We switched over to Right Start, after Bruce completed year of Horizons 1st grade math. I thought Horizons’ first grade program was okay, but that the second grade curriculum focused too much on algorithms. For more information on our experience with Horizons, please see here: http://teachingmybabytoread.blog.com/2011/05/01/horizons-math/
I believe in teaching children math through the Constructivist method, which is where they discover mathematical concepts and strategy themselves, sometiems through hands on discovery. I was very impressed by the philosophy of the Right Start program which stresses understanding over rote memorization. Additionally, I was familiar with Right Start, having used components of the program when I taught 3rd/4th grade at a Charter school.
I decided to shell out out the big bucks and bought the homeschool deluxe set for level C, and I am really glad I did. It has tons of math manipulatives that are useful for Bruce, Jenna, and other math activities we do as well. It also has all of the books, including the Teacher’s Guide. I used the Right Start manipulatives a lot to help explain concepts in Bruce’s school math program, Houghton Mifflin Math Expressions, and we have also used them to help with Life Of Fred Fractions.
The Right Start program has a teacher’s guide that is very creative, detailed, and goes above and beyond what is just in the worksheet book. If you were using Right Start as a stand-alone curriculum, you would really need the teacher’s addition. We were using the program as a supplement to Math Expressions, so we didn’t follow the lessons plans exactly, although Bruce did do almost all of the worksheets.
Since I’m a teacher myself, I read the teacher’s guide almost cover to cover, and then just “winged it”, or taught the lessons intuitively according to all the training I’ve received in teaching mathematics from a Constructivist perspective. But I would definitely recommend following the teacher’s guide, to anyone who was new to the Constructivst approach, or who was using Right Start as their child’s sole mathematics curriculum.
The hallmark of the Right Start program is the abacus, which I was really excited about when the box arrived. My husband is an engineer, who has had the opportunity to work with a lot of coworkers from China, many of whom are abacus devotes. (But a different type of abacus, I should point out.) One of these friends told my husband he could “see the abacus in his mind,” and that’s why he had such exceptional mental math skills. This is the same claim that the author of Right Start makes.
I am still super excited about teaching with an abacus, and intend to do this with Jenna as soon as she is old enough for Level A. The problem with Bruce and the abacus, was that he rejected it from the get-go. You know how there are little babies who reject the pacifier or the bottle? You think, “Did that mother really try hard enough? I mean, did she really try?” Well yes in fact, I did! Bruce would not have anything to do with the abacus at all. Probably his math skills were developed enough already that imposing the abacus into his thinking was something his brain just did not want. He was five years old at the time and had already finished the Horizons first grade workbooks, and half of Hougton Mifflin 2nd grade. This is also party the reason that we could not follow the Right Start lesson plans exactly, because so much of them are abacus based.
Not using the abacus turned out to be okay for our family, because I am not teaching the traditional algorithms of borrowing or carrying to Bruce at this point. The way the Right Start lessons set things up, they use the abacus to teach borrowing and carrying in a manipulative way. So I would have skipped over those parts in the Teacher’s Guide anyway. (For those of you thinking, “What the heck! This lady doesn’t teach borrowing or carrying?”, please see my previous post on subtraction: http://teachingmybabytoread.blog.com/2011/03/15/subtraction/.)
A final point of note. Bruce has almost finished all of Level C, and I’m still stumped by what exact grade level it is. I’ve thought about it a lot, and reread the 2nd, 3rd, and 4th grade standards in our state. I’ve also taught 3rd grade for two years, and a 3rd/4th combo for two years. And yet, I’m still a bit perplexed, because it introduces some concepts that aren’t usually taught in public school until later. In general though, I’d say Level C seems to be in the 2.5 grade – 3.5 grade range. They also have a good placement test online to help you determine which book to choose for your child.
A while back I posted about how my son Bruce (6) has been working through the Right Start Level D workbook this summer, sans scripted lessons in the Teacher’s Guide. I wouldn’t recommend this for everyone, but we have all of the materials and the geometry booklet, plus I’ve had a ton of training in Constructivism, since I use to be a teacher. In the future, I won’t attempt flying solo for Level E because I have never taught higher than fourth grade!
Summer is nearing completion and Bruce has completed 35 pages. That’s not as far as I hoped, but isn’t bad if you look at a one page a day M-F average. We’ve jumped around a lot, and now he is doing the geometry section. Are we doing this right? Hmmm… That’s a very good question. Bruce is definitely learning a lot, but I’m not sure I’m teaching this exactly how Joan Cotter would like. Please feel free to tell me what you think (or give me a geometry slap-down as the case might be). 🙂
You can see by the time we get to the last triangle which is supposed to be “free drawing”, Bruce has about had it. We’ve been working on this right before dinner time, so it’s no wonder.
Here’s how I’ve been teaching segmenting circles and drawing octagons etc. These next pictures are with my own handwriting:
That was all using the 45 degree triangle. I’m thinking maybe I should write the angles on the triangles with a Sharpie. Why didn’t I do that before? With older kids you could probably be more heavy handed about angles, and go through and label them all, match up the congruent ones etc. If you have a compass, and triangles you can do all of these activities at home. Of course, the caveat is that I might be teaching you the wrong way to do this!
Getting Ready for Level A
Last week’s exploration into determining whether or not Jenna(2.5) could visualize the quantity three sent me searching in my Right Start Level C box, to see if I could find any literature about the subject. Bingo! I rediscovered Math and the Young Child, and fell in love with Dr. Joan Cotter and her work all over again. (The link takes a little while to load btw.)
On page 3 of the Transitions Lessons book, Dr. Cotter writes about Dr. K. Wynn’s paper “Addition and Subtraction by Human Infants” and the experiments she did with babies and teddy bears. She would show a baby a teddy bear and then put the bear behind a sheet. Then she would show the baby another teddy bear and put that bear behind the sheet. When she lifted the sheet, the baby expected to see two teddy bears. If the adult added a third bear behind the sheet and the baby saw three teddy bears instead of the expected two, then the baby looked at the bears longer. By tracking infant eye gaze she found that five month old babies could tell the difference between 1, 2, and 3 bears.
Does that really mean that infants understand the quantity 3? Or does it mean that infants understand 1, 2, and “more”? I’ve played the chocolate chip game several times with Jenna now, and she still can’t consistently name the quantity three even though she is 31 months old. But I hadn’t been measuring her eye contact. Maybe she was looking at the quantity three longer and I hadn’t realized.
So I tried my own version Dr. Wynn’s teddy bear experiment. I recreated it as best as I could by myself using a pizza box and some Calico Critters.
It really did seem to startle Jenna when there was an unexpected number of Critters behind the pizza box! I was witnessing the very foundations of addition and subtraction development in her brain! This experiment would seem to indicate that Jenna can visualize and recognize when something is “more than two”. But when it came to articulation, she still hits a brick wall. If I asked Jenna to name a quantity, she could verbalize one and two, but started wildly guessing when I showed her three Critters.
This lack of ability to name the quantity is not immutable; it is only a matter of time before Jenna will be developmentally ready to start quantifying objects. Once she can name quantities up to five, I’m going to be starting her on Right Start Level A. I have no idea when this will be, but I am really excited about using Dr. Cotter’s methods from day one with Jenna, instead of floundering around with other programs like I did with my son Bruce. (And no, I’m not a paid spokesman for Right Start! I’m just a passionate Constructivist.) 🙂
Does Your Two Year Old Know the Quantity 3?
In case you are wondering, I’d offer a hesitant yes to this question regarding Jenna(29 months). She correctly identifies quantities of three about 80% of the time. There is no way she is ready to move on to four yet, despite her ability to “count”, i.e. rattle off numbers without correspondence. I got a pretty accurate understanding of where my daughter’s thinking currently resides, by trying out lesson 1 from Right Start Level A. You can download the first few lesson plans yourself for free and give it a try with your own two year old.
I wish I had known to try this experiment with Bruce (6.5) when he was two, because of course I’m now uber-curious what his thinking was back then. When did the quantities three and four really solidify for Bruce? When will they solidify for Jenna? The Psychology major in me is going to be periodically checking to figure this out. Looking forward in lessons 2 and 3 of Right Start Level A, the other two abilities to monitor are A-B-A patterns, and sorting.
The reason why I decided to investigate all of this to begin with, was that I have just finished reading Keith Devlin’s wonderful book The Math Instinct: Why You’re a Mathematical Genius (Along with Lobsters, Birds, Cats, and Dogs). This book was well written, meticulously researched, and thought provoking. The final chapters reaffirmed everything I learned about Constructivist math in my professional development as a teacher. The research he presented about young infants understanding the quantity of two was especially fascinating. I had previously been proud of Jenna understanding the quantity two. Now I realize that’s no big deal!
I’m going to continue on reading more of Keith Devlin’s books. I’m not a “mathy” person myself, but he writes in a way that is easy to understand… even for someone who hasn’t studied Calculus since 12th grade. 🙂
Visualization and Not Just Counting
Day after day of watching her big brother Bruce sit at the dining room table working on Math Expressions and Right Start, Jenna has now started regularly asking to “do math” too. She is 23 months old now, and I’m still trying to work on visualization with her in addition to counting.
Jenna can count with correspondence from 1-3 and can also rattle off her numbers to 14. However, I’m trying to phase that part out and work on saying “ten and one, ten and two, ten and three etc.” This is what is suggested in the Right Start literature, and is a new idea to me as an educator. I’m really interested in trying it out, so my poor little girl gets to be my experimental guinea pig!
With Bruce at this age, we worked on counting and that was about it. All of his early math skills were learned at Montessori, and I didn’t begin any formal instruction with him until he was four.
Here are some of the difficulties I’ve encountered trying to teach math to an almost two year old. First of all, Jenna keeps trying to eat the math manipulatives! They are all choking hazards, so I really have to watch her and put them away up high when we are done. The other problem is her eternal asking of the question “Why?” Our most recent math session looked like this.
Me: “Can you give me two?”
Me: “Because Mommy wants two squares.”
Me: “Umm… because one square is not enough. Mommy wants two. Can you count out two?”
Jenna: “One’s nough. One’s nough Mama.”
Me: “No, one’s not enough. Mommy wants two. Please give me two.”
Jenna: “Why? Why Mama?”
At this point in the lesson I decided to just switch back to counting with correspondence. I’ve been using the counting song from Sesame Street and Jenna can now sing along. I’m not sure how much she is learning from all of this, but at least it’s a fun activity to do with Mom.