The Struggle for New Math Instructional Technology

This article by Jack Smith IV (mic.com) says what I’m thinking better than me. Matt McFarland (Washington Post) has a similar argument most focused on the price (which mysteriously hasn’t followed the trends of any other piece of personal technology by staying quite high).

The argument: Texas Instruments has some kind of a stranglehold on secondary mathematics here in the United States and it certainly isn’t that it is the best tool for the job.

The arguments that I most often hear from teachers in support of sticking with TI are that it is the tools that have been in place so long that they are the easiest for teachers to teach. It’s just easier to have the students all using a single tool that the teachers are really familiar with.

In an article written in The Atlantic, Alexis C. Madrigal argues that there is very little need for an update in the technology if there hasn’t been a corresponding update in the math content requiring the technology. “After all, the material hasn’t changed (much), so if the calculators were good enough for us 10 or 15 years ago, they are still good enough to solve the math problems.”

And also that these tool are the tools that are allowed on the SAT or the ACT. For some teachers that I talk to, this is kind of a big deal. And there is a reasonable logic to it. Those tests are pretty important (especially in Michigan, where school accountability for math is connected to student outcomes on the SAT). So, why confuse a student’s brain with a variety of tools that, when the rubber hits the road, they won’t be able to use?

It’s worth noting, however, that College Board (the designers and publishers of the SAT as well as the Advanced Placement exams) have a particular target audience in mind. In states where the SAT isn’t the state-mandated accountability measure (meaning every single high school junior statewide will take the test), which students are likely to take a test designed by College Board? Students who are college bound and/or enrolled in advanced placement classes. For many, many of these students TI Calculators have “worked out fine”. Also, they’ve likely been the only tool made consistently available. And it’s better than graphing all of your parabolas by hand.

But, have you ever watched a group of students in an algebra class for the second time trying to remember those key sequences and explore images on those tiny, granulated screens? And by now, they know there are technologies out there that are easier to use.

I am certainly not accusing College Board of being deliberately prejudiced. I am not accusing TI of being deliberately prejudiced. I’m simply accusing them of having goals that are different than “100% of math students will learn math at the highest possible level”.

But that’s my goal. And it should be the goal of all of our classroom teachers. And the question should be whether or not TI calculators fit within that goal.

Well, in Michigan, there might be a couple of potential cracks in the shell through which the light of better technologies (like Desmos and Geogebra) could potentially shine through to teachers previously unwilling to explore them.

The Redesigned SAT, which launches in March 2016, has a math portion that includes two sections. There is a significant portion that prohibits calculators completely. Then, there is a section that allows calculators, but the College Board includes questions “for which calculators would be a deterrent to efficiency.” D’ya catch that? That’s our window. This allows for an entirely different message than simply “TI’s are allowed on the SAT, so we’ll use them.”

You could reasonably guess that AT LEAST half of that test should be able to be done with no calculator at all. This could potentially leave a huge hole in one of the most stubborn supports for the TI-status-quo. Now, we are potentially keeping these clunky, expensive devices as the primary tool because of possibly 25 questions that they’ll use it on for a single testing sequence. That’s a much tougher sell.

The other main issue (teacher familiarity) is is a matter of exposure. The teacher prep courses could support this for our preservice teachers. (In 2004, when I was a preservice teacher at WMU, I had one “instructional technology in math” course that has a TI-89 or Voyage200 as a required purchase. Luckily my girlfriend (now my wife) had one.)

Instructional technology in math should be way, way more than a semester-long how-to on a single TI device. Desmos and Geogebra and other available technologies that are free for use in the classroom provide valuable opportunities to give students different experiences with problem-solving in mathematics. But teachers, like all people, are going to stick with what they are familiar with.

And most of these young math teachers (most born in the early 90’s), we raised in the classroom as math learners with TI calculators. Given no other experiences, they aren’t going to have just their familiarity to build from. Especially when, for most of them, the TIs “worked out fine.”

As for the teachers already in the classroom, that’s part of the work of math-minded instructional techs… like me. I’ve got two sessions coming up that are focused on Desmos as a tool to engage math learners.

The SAT did it’s part and I intend to do mine. Our students deserve better than TI or nothing.

Advertisements

Don’t forget Geometry when teaching Algebra

Right now, Michigan educators are trying to sort out the implications of the state switching to endorsing (and paying to provide) the SAT to all high school juniors statewide instead of the ACT as it had previously done. The SAT relies very heavily on measuring algebra and data analysis. This leaves plane and 3D geometry, Trig and transformational geometry under the label “additional topics in mathematics.” The new SAT includes 6 questions from this category. Compared to closed to 10 times that from more algebraic categories.

This comes up in every SAT Info session I lead. Should we just stop teaching geometry? All Algebra? Could geometry become a senior-level elective? If it’s not going to be on the SAT, then what?

These questions reflect a variety of misconceptions about the role of testing in curriculum decisions. In fact, these are the same misconceptions that are driving an awful lot of the decisions that are being made. And in this case, I think there’s more at risk than simply over-testing our students.

It would be a real shame to see Geometry become seen as an unnecessary math class. Because it’s not.

And to illustrate that, I’m going to tell you a story about a conversation I had with my daughter. She’s 6.

She wanted to try multiplication. She’d heard the older kids at school talking about it. So, I taught her about it and let her try some simple problems to see if she understood. And she did, for the most part.

So, I started to not only make the numbers bigger, but also reverse the numbers for some problems that she’d already written down. She had already computed 2 x 3, and 4 x 2, and 5 x 3, but what about 3 x 2, and 2 x 4, and 3 x 5. Were those going to get the same answers as their reversed counterparts?

She predicted no. So, I told her to figure them out to show me if her prediction was right or wrong. To her surprise, she found that switching the factors doesn’t change the product.

“Daddy… why does that happen? It should change, shouldn’t it?”

Translation: Daddy, how do you prove the Commutative Property of Multiplication?

How would you prove it?

The geometry teacher in me thinks about area when I see two numbers multiplied. We can model (and often do) multiplication as an array. It’s just a rectangle, right? A rectangle with an area that is calculated by it’s length and width being multiplied.

What happens if we rotate the rectangle 90 degrees about it’s center point? Now it’s length and width are switched, but it’s area isn’t. Because rotations are rigid motions. The preimage and image are congruent. Congruent figures have the same area.

If l x w = A, then w x l = A. 

Geometry helps prove this. Geometry also helps support a variety of other algebraic ideas like transformations of functions within the different function families. Connections between slope and parallel and perpendicular lines. There’s also the outstanding applications of algebraic concepts that geometric situations can provide. Right triangle trig, for example, is often a wonderful review of writing and solving three variable formulas involving division and multiplication. (A consistent sticking point for lots of math learners.)

As a teacher who spent years watching how Geometry presents such an environment for real, effective and powerful mathematical growth, eliminating it will leave a lot of holes that math departments are used to geometry content filling.