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Julia Steiny: 5th Graders Having a Blast with Algebra
by Julia Steiny I was forewarned, but still, it was a lovely surprise to spend a solid hour with a class of students constantly popping off with “I got it!” And “Ooooohhhhh!” And “I see!” These yelps of satisfaction sound just like the ones you hear from boys playing video games. Except that this is [...]
by Julia Steiny
I was forewarned, but still, it was a lovely surprise to spend a solid hour with a class of students constantly popping off with “I got it!” And “Ooooohhhhh!” And “I see!”
These yelps of satisfaction sound just like the ones you hear from boys playing video games.
Except that this is math class at Dawson Elementary School in Holden, Massachusetts.
Julia Steiny
No, worse: it’s algebra, the academic subject that more than any other strikes fear in grown-ups’ hearts. But these are 5th graders. And some are struggling learners.
The lesson is plenty rigorous, as you’ll see.
But the kids get a useful assist from the “manipulatives,” concrete objects — pawns and blocks — that support a program called Hands-on Equations. Kids use the objects to build and break down algebraic equations.
Six years ago, teacher Lori St. Germain jumped at her district’s offer to train her in Hands-on Equations. She shrugs, “I was always interested in algebra. So I took a one-day, easy training, and later showed it to the other 5th grade teachers who were able to pick up the rest on their own. For a while we were sharing one set.” Each now has her own.
St. Germain also acquired the digital version so she can demonstrate the day’s concept on a whiteboard. Students talk her through moving the pieces to solve the problem.
They start with a warm-up: 2(x + 4) + x = x + 12.
On the board, and in a packet in front of each students, are red cubes showing the constants, or actual numbers. An oversized blue pawn represents the oft-feared “x.” Kids build their equations on a “scale,” really a laminated placemat with a picture. The fulcrum is the equals sign.
Borrowing from game language, “legal moves” are the mathematical rules for how to make an equation balance. The equivalent of winning is solving for “x.”
St. Germain reviews a recent lesson about how to handle multipliers that are outside parentheses. With the kids’ help, she builds two versions of x + 4, one on top of the other, on the left-hand side of the scale. And adds the extra x. On the other side, they put a pawn and a cube marked 12. Kids whittle down the equation by subtracting equally from both sides, first a pawn and then the value 8, from each side. What remains are 2 pawns on the left and a 4 on the right.
“So what’s x?” The kids shout “2!” The visual makes it painfully obvious.
“Let’s check our work.” Again, the kids talk their teacher through plugging 2 into the places where the x had been. It’s become a simple arithmetic problem.
After teaching the new concept, St. Germain cuts them loose to work the problems out on their own. The worksheets each had four examples of the new problems, six from recent lessons, and ten review equations on the back. Math smarties finish quickly and go back for sheets of word problems.
St. Germain explains, “Some kids can see the problem in their heads and don’t need the manipulatives. Some just draw. Eventually you want them all to solve without the manipulatives, making drawings or using letters. But the one or two who still need the manipulatives in June will have them.” The objects wean the kids from concrete to abstract, the way training wheels support learning to ride a bicycle.
Several kids struggle. St. Germain hovers nearby, helping. After she got a lollygagging, impeccably-dressed girl through the first problem successfully — with one of those big “Ohhh!”s — the little fashion-plate quit fooling around and got to it. By the end of class, she was proudly booking through the practice problems. She nudged her neighbors for clues here and there. A little lazy, but she was getting it.
St. Germain’s colleague Marie Horton says “This program takes a complicated concept, like a variable, and turns it into something they can take apart and put back together. Like a puzzle. So this is incredible for 10, 11-year-olds because of how much it makes them think. They get such a sense of pride instead of looking at a problem and rejecting it as ‘stupid.’ Kids go at their own pace, so the learning is differentiated. But the best part is seeing the little light bulbs pop, that sense of happiness.”
That is the best part.
At one point, St. Germain firmly told a squirmy boy to look her in the face. She had to ask him twice, but he finally swiveled around and complied. Without impatience, she repeated a sentence she’d already said several times during the lesson. This time, not only does he get it, but a chorus of eavesdroppers who’d been struggling with their own work bellowed their version of “Oooooohhhhh!!!”
That’s what algebra class looks like when we’ve got it right.
Next week we’ll meet the program’s inventor, Dr. Henry Borenson, to understand the thinking that went into this work, the only algebra manipulatives program to merit a patent.
Julia Steiny is a freelance columnist whose work also regularly appears at GoLocalProv.com and GoLocalWorcester.com. She is the founding director of the Youth Restoration Project, a restorative-practices initiative, currently building a demonstration project in Central Falls, Rhode Island. She consults for schools and government initiatives, including regular work for The Providence Plan for whom she analyzes data. For more detail, see juliasteiny.com or contact her at juliasteiny@gmail.com or c/o GoLocalProv, 44 Weybosset Street, Providence, RI 02903.
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February 7th, 2013
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[...] by EducationNews.org – Making algebraic variables child’s [...]
Hands on Equations has made algebra effortless and intuitive for my 7 year old (who yesterday helped my 10 year old multiply and divide polynomials in his Algebra 1 class, just by watching him do it a couple of times!). My 10 year old thinks HOE is just plain fun, asking for it by name (we have a lot of mathy activities here). Thanks to HOE, they easily translate their understanding of abstracts into other areas of critical thinking, letting something represent something else and deducing new information or answers from there. Basically we are BIG FANS of Hands on Equations!
I have been borrowing a set of Hands On Equations this year and using them with my third grade gifted students. I liked this sentence from the article, “the objects wean the kids from concrete to abstract, the way training wheels support learning to ride a bicycle.” My students are very successfully solving problems. Some understood the process faster than others but they are all loving doing the problems and taking turns demonstrating or being the teacher.
I used Hands-On Equations with elementary school children and was sold on its ability to make algebra fun. I now teach adults who are studying for their GED. One of the most difficult lessons for my classes has been learning the Distributive Property. I remembered Hands-On Equations, and the lesson became easy!
We use Hands on Equations at home with all of my children. They love to solve the problems and are so excited doing it.
I borrowed a copy of Hands on Equations and within minutes my son went from completely confused to total understanding. I was amazed how quickly he started to catch on by having a visual!
I used Hands On Equations on my I Pad at the airport and had a couple of children from other travellers interested in my “game” they asked their parents if they could get the app to play the game too. I gave them the information. I love using the App to exercise my brain. Who says you are too old to learn new things.
We use this great program with students in grades 4 and 5. The concrete experiences build such adeep understanding of algebraic concepts. The students love the program. We have students from the middle and high schools come back and tell us how the program jas helped them in their classes.
I’ve used Hands On Equations several times. I’ve used this great program with my 7th graders who struggle with math. Many of them had a poor self concept regarding math. They had a blast as they figured out algebra problems that they thought they never would have gotten! I’ve also used it with my developmental prealgebra adults (at the community college) who struggle with math. They thought it would be silly at first, but gave it a try and were very successful with it… and in the process actually had fun doing math! Just recently, I tried it with my 5th grade nephew who was willing to try some math with her “Geeky Aunt”… he treated it as a challenge and totally understood what was going on. I told him to tell his teacher that he was doing Algebra with his aunt over the weekend & he couldn’t wait to tell her! I love this program and can’t wait to start working with my own 2nd grade daughter when she’s ready!
I started with my 9 year old daughter and am surprised how quickly she has grasped the algebraic process. I use this in a Home School setting and highly recommend it. It is fun engaging and she likes doing it.
I taught Hands on Equations last year to a group of 6th grade boys with learning disabilities during our RTI time. Common core requires 6th graders to solve one step equations. One particular boy picked it up quickly and wanted to do it all the time.
This year we have a school just for 5th & 6th grades and we didn’t have enough kits for all teachers to have a class set, so I went to the middle school to borrow some. This particular boy’s teacher approached me to let me know how well he did when she taught two step equations. She did not use Hands on Equations, and he told her many times that I should come back to teach them.
Hands on Equations made a difference in the way I teach. It’s made a difference in my students’ confidence levels. And most importantly, it made a difference in his life. Thank you to everyone who had a hand in creating such a phenomenal product!!
Just saw it last week and intend on purchasing it for next year’s math. It looks like a great program for our iPad.
The first time I saw Hands-On Equations was at an NAESP convention and Dr. Borenson was demonstrating it in the exposition hall. I remember how impressed I was with the product in that it made understanding the basic mechanics of algebra so simple! I ended up purchasing all three levels of the program to use with our third, fourth and fifth grades. Third grade began with Level One, Fourth grade used Level Two and Fifth, Level Three. During one of our school corporation’s cross-grade level administrator meetings, the middle school principal to which our students would go to shared that it was important that students come to him ready to learn algebra. Hands-On Equations equipped us to be able to do just that…our state test results for the students who had just exited our building showed them having strong skills in algebra.
Later, I went to a different elementary as principal and also purchased all three levels for that building as well. Hands-On Equations was received well by both staff and students. Because it was a small building, I ended up having to teach half-days during my last four years there. While teaching sixth grade math, I was able to teach Level 3. The sixth graders quickly understood the process, especially since they had Level 2 in the fifth grade. They looked forward to the math periods during which we used Hands-On Equations and caught on quickly to new concepts.
Now, as a retired educator of thirty-eight years, I work part time in the tech department for a local Christian school. I downloaded the iPad version of Level One Hands-On Equations and enjoyed the review as I finished it. I shared it with the high school algebra teacher and she is looking into having the elementary purchase some kits and possibly the SmartBoard software. I look forward to doing Levels Two and Three on my iPad and sharing it with my 7th grade granddaughter who attends the same school where I work.
Well, it’s the best teaching program on the market to introduce many algebra concepts to students as early as 3rd and 4th grades. Students immediately feel success and that motivates them to want to solve more examples. They can take the concepts learned in solving equations, and apply that knowledge to word problems. They are amazed at how easy it can be to translate English into algebraic equations.