Guest post by Andrew from Match Next
Andrew here from Match Next. Our 4th graders are currently in the thick of their ‘fractions’ unit. They’re now doing all sorts of practice problems, converting improper fractions to mixed numbers, placing mixed numbers on a number line, etc. These are either created by Ryan (our math guy) or done via TenMarks (the math practice software I reviewed a couple weeks back).
But getting students to this point of doing actual problems was tough. Fractions are notorious for being one of the hardest math topics to teach, and diving headfirst into the numbers and symbols of fractions is a surefire way to make kids’ heads spin. So a question for you all: what’s the best way to introduce fractions?
There’s a program we found and we love. But we aren’t using it. It’s a story of big fish vs little fish. Let me explain.
Enter: ST Math (aka Spatial-Temporal Math)
It’s a software that first teaches math concepts visually, before introducing any math language or symbols associated with a topic. Students are gradually exposed to the language and symbols as they progress through the program. ST Math refers to this as its ‘learning progression.’ Here’s how the developers diagram this spectrum:
What do they mean by visual vs. symbolic? Something like - do you bring in pizzas and have kids start cutting them up, or do you show them “⅞” and explain to them what each number means (“the bottom number is the ‘denominator,’ it’s total number of parts…”). Obviously a student needs to understand both to understand fractions, but it’s debatable where to start and how much time to spend doing each. If a kid get tripped up on cutting pizzas, do you stick with it before teaching him about denominators? How long? A day, a week, a month?
So how does ST Math ‘teach’ math concepts visually?
Students help the penguin pictured above, named JiJi, navigate a series of obstacles. They need to use the spatial reasoning at the root of certain math concepts in order to successfully pass the obstacle. These early obstacles fall on the ‘Visual’ side of the programs learning progression. As kids move through the program, the obstacles get harder, and more numbers/symbols are introduced. These types of obstacles fall more towards the ‘Symbolic’ side of the progression.
Here’s an example of a ‘learning progression’ for number lines.
In the ‘problem’ above, JiJi sits on top of 2 whole circles, located at the ‘0’ mark on a number line. The student needs to move the balloon apparatus to the point on the number line where JiJi will end. In this case, the student needs to click on the ‘2.’ When she does, JiJi’s ‘bicycle’ will move the distance represented by the number of circles, then JiJi will fly away on the balloons. Since JiJi’s sitting on 2 circles in the problem above, he’ll move 2 units. If he sat on 3 circles, he’d move 3 units, etc. Basically, this level is just trying to get students comfortable with the idea that you can use whole circles to correspond to units on a number line.
Still visual, but a little harder:
Once students learn the basics from problems like the one above, they’ll move on to harder problems that incorporate fractions of a circle, like in this problem below:
In the problem above, JiJi will move the distance of 1 unit because JiJi is sitting on two half-circles. After all, ½ + ½ = 1.
Students really need to understand that one half the circle will only move JiJi one half of a single unit on the number line. This is a great way for a young fraction-student to learn how about ‘pieces of a whole,’ and how they correspond to actual numbers. Once they get the hang of this level and type of problem solving, the program will begin to incorporate more numbers and symbols, like in this problem below.
In the question above, the program doesn’t even try to use a ‘fraction’ of a circle. It just gives the fractions to the student straight up, and the student needs to add the numbers herself and move the balloons to the correct spot. By this point, students are very near the end of the ‘learning progression’ spectrum the program utilizes, having gone from using visual representations of fractions, to using the symbolic (aka numerical) representation of fractions.
How would we rate it?
In terms of raw content quality, ST Math is a 9/10 in my book. The only complaint I’ve really heard from other tech folks is that it can be tricky syncing the ST Math sequencing of math concepts with their class sequencing, but those complaints are really soft. Mostly, people just gush.
Big Fish vs Little Fish
MIND Research Institute, the company that created and sells ST Math, seems to have focused its sales strategy on landing the whales. They seem to sell mostly to huge districts, and as a result, have one of the most popular programs in the country. According to their website, over 600,000 students are using ST Math in over 2000 schools across the country. And every blended learning person I’ve talked to who uses it raves about it. 5 out of the 11 blended learning specialists I’ve talked to on the phone this past semester use ST Math in their schools, and they all give it rave reviews. The other 6 out of 11 that don’t use it said that they’d seriously consider using it, but can't because of the prohibitive cost (more on this in a bit). One person even told me, “it’s one of the only programs out there that I’d pay for right now.
Here’s the problem: they won’t sell us any fewer than 200 student accounts at $50 a pop. Simply won’t do it. The rep that I’ve been talking to is a nice guy, seems to really feel bad, says he’s gone back to his bosses and tried to convince them to make an exception. But nothin’. And other small blended learning schools like ours are having the same problem. Message to MIND Research: I get that you’re fishing with harpoons, but you can’t catch an anchovy like us with those.
We like this program so much we even considered just eating the $10,000 it would cost us. But that’s more than our entire tech budget for the year. Maybe if they threw in a new set of computers…
They did say they would help schools find grant money to help subsidize the cost, though I haven’t heard back from them on that.
Tough tomatoes, I guess.
I did find another potential tech solution to this problem, though. It’s called ‘Fraction Planet.’ It’s sort of the JV version of ST Math, not as clever and not nearly as comprehensive, but pretty good. And it’s free (for now). More on that in a couple weeks after we really test it out.
PS: Without ST Math, how did our math guy, Ryan, approach fraction visualization?
He went old-school: Cuisenaire rods
These are small wooden blocks used to help students begin conceptualizing fractions. Rods of one color are compared to rods of another another color. For example, it takes 10 of the white pieces above to make a rod of equal size as an orange rod.
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