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.

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.

Changing the conversation about testing and data

What if I told you have I know of schools that run through their first grade students through just over an hour of math and reading exercises while recording their results to get a sense of their strengths and weaknesses? These exercises are done a little bit at a time in the first three weeks of school. They do this so that they can make accurate decisions about the ways that each of these students will be properly challenged. This way, each young person gets exactly what they need to grow as learners.

What are your thoughts about these schools? Would you say they care about their students? Would you say that this is a nice approach to education?

Pause here for a moment…

I’m going to start this blog post over again. This time I’m going to tell the same story in different words. I want to see if different words paint a different picture of these schools. Keep in mind that the second set of statements are equally accurate.

Ready?

What if I told you that I know of schools that will give their first grade students eight different standardized tests by the end of September? They do this so that they can record a bunch of data about the students so that they can group them based on the data on those tests.

Sounds a little bit different, doesn’t it? Eight standardized tests sounds like a lot. (Even if the longest of them 8 minutes long. Some are as short as 1 minute.)

So, we’re faced with a decision. Is the first one unrealistically rosy? Or is the second one unnecessarily cold? Your bias will determine which of those viewpoints speak to you most. My bias certainly is.

What isn’t based on a bias is that “standardized test” and “data” have become hot-button, divisive words. And there’s been some backlash. That backlash is captured by posters like these.

important-things-black-flowers-300

Sharing encouraged by Marie Rippel

The message is that our young people are more than a few data points. And that, no matter how much data that we collect, there are important elements to these young people that no test can reveal. That is absolutely correct and if you don’t agree, I’m curious to hear your argument. Post it in the comments and we’ll explore it together.

But that doesn’t mean that the poster (and the related sentiment) are safe from push back. First, there are some things on that list that tests actually could measure. It would be fairly reasonable to collect some data on “determination”, “flexibility”, and “confidence” provided we could all agree on the definitions and manifestations of them.

But secondly, that poster includes items like “spirituality”, “wisdom”, “self-control”, and “gentleness”, which are items that different groups would argue aren’t really the job of the American public school system. That isn’t to say that these groups wouldn’t consider these valuable qualities, just qualities that the schools aren’t on the hook for teaching.

To me, this is an important point. Because there’s a variety of other things your garden variety standardized tests don’t measure. For example, they don’t test a student’s ability to drive a car, their ability to write a cover letter or resume, or their ability to cook a decent meal.

These fit largely into the same category as the items on that poster. Important qualities that are common among successful people, but not qualities that are tested on any of the standardized tests that the students take in the K-12 education. Yet, I’ve never heard anyone use their absence as a support to discount the value of the tests. What makes these qualities different that the ones on the poster?

It could be that the American public and teaching professionals agree that those things are not the job of our public schools. It isn’t their job to teach young people how to drive a car or write a resume, or cook a meal. So, clearly we should be inspecting their ability to do so.

So, would I be safe in assuming that if we could all agree on the job of public schools, then some of the fervor over tests would cease?

Would the authors of that poster be more satisfied if we were collecting data on students compassion?

What are the jobs of our public schools? Frame your answer from the context of what should all students be expected to do when they leave the educational systems after spending 13 years in it.

And how are we going to know if the system is doing it’s job? Listening to a discussion regarding those questions sounds like a huge upgrade compared to listening to hours of endless back-and-forth about whether or not to test, how to test, which tests to use, or what to do with the results of the tests.

What are our goals and how are we going to know if the system is doing it’s job? It’s fine by me if testing students isn’t part of that. But, our educational system has a vital job to play and somehow or another, we need to develop a way to inspect what we expect from the system.

Perhaps the first step of that is coming to consensus on what we expect.

Should we test them? or not test them? (Hint: Those are the wrong questions…)

This time of year in Michigan, standardized testing is on everyone’s mind. This year is a little more frantic than others, I’m afraid. Michigan’s Department of Education is piloting the online version of a new state test. In my role, I’ve spent a lot of time contributing to support all over the state trying to help concerned educators prepare themselves and their students for this transition.

Besides that, every Michigan HS Junior is given a chance to take a college entrance exam. Since the inception of this practice, this exam had always been the ACT. Then, just after the new year, news broke (somewhat out of nowhere) that Michigan was going to switch to giving the SAT.

Now, each of these tests has a whole machine surrounding it. There are practice tests, prep sessions, special activities put in place to prepare for both the look and feel of the testing items as well as for the content. In many ways, “teaching-to-the-test” has become a foregone conclusion. This is especially true in districts who are working very, very hard to improve the test scores for evaluative or punitive reasons. (More on this later.)

All of this fervor can really make a guy wonder whether or not this testing is worth all the hassle. Are we doing good things to education by instituting all of this testing? Are frequent assessments the right way to go?

And I think those are the wrong questions.

Consider a person who is hyper-interested in his or her weight. Like dangerously so. This person steps on the scale several times a day. And makes aggressive changes for the sake of gaining or losing 10 or 20 lbs very, very quickly. On what can we blame this problem?

Lots of things, I suspect. This person may have a background with some experiences that need to be reconciled. This person may have anxiety issues that need to be resolved. This person may be in a personal or professional relationship that puts unrealistic pressure on his or her appearance. This person may spend too much time focusing on and associating with other people who have similar habits. There is a culture that he or she has become a part of that feeds into this point-of-view.

The scale that he or she steps isn’t the problem (provided the scale is accurate). The scale is the tool that provides the information. The information is then getting abuse by the recipient. The solution to this problem is NOT to dispose of the scale. The abusive recipient is still going to seek for information and they will find it in perceived tightness of clothes, or calories consumed or duration of a workout.

What we need to adjust is the response to the information.

Right now, we are asking our schools to step on the scale too frequently, and making too much of the number we get.

Look, changes in policy and curricula often show effects slowly. And we should look for slow, sustained improvement. This is evidence of a cultural change that is becoming a new standard. Just like the dieter who is looking to lose 50 pounds. A two-year journey losing a three or four pounds per month doesn’t make for an exciting, story. It doens’t get you on NBC Shows, but it’s healthy. It’s sustainable. It is evidence that a real change has taken place.

It is with this in mind that I will assert that the tests aren’t the problem with our educational testing culture. While I suspect that we are testing too much. If the person from the analogy has a scale in every room, then it might be useful to reduce that number to one, but it would be wrong to blame the tests. They are giving us information. And we in the educational community aren’t handling the influx of information very well.

So, I have some thoughts about this.

What if we only formally and decisively tested students every other year? When it comes to state tests that determine school ratings, funding, oversight, and evaluation, how about we get on an every other year plan. We aren’t looking for quick-hitting solutions. We are looking for culture changes. The most effective instructional and curricular changes take time to go from implementation to fruitful improvement anyway. So, if the 2013 testing cycle revealed content weaknesses in a certain area, then you have 24 months to implement an update to your system that will improve it. Then in 2015, we’ll see how it’s going.

Taking a standardized test well is NOT a meaningful life skill with which to send students away from school. I’ve heard this one from a variety of different angles. The “they’ll-need-it-to-get-through-college” argument, to the “managing-test-anxiety” argument, to the “we-need-our-scores-to-jump-30-percentage-points-in-3-months” argument. This has been the most troubling development I’ve seen. This goes beyond “teaching-to-the-test”. This is downright teaching test-taking strategies as though the skill of taking a test has any application. It doesn’t. Students need to take tests well because we choose to test them. When we change our focus, we change this skill set. It is completely dependent on our choice. EVERY SINGLE other skill we want students to leave school with are determined by appealing to some outside need. Critical thinking, basic math skills, reading, obedience, playing well with others, healthy eating, tolerance for diversity, etc. These are things that you can EASILY give reasons for students leaving school with these skills in their hip pockets. So, why are we spending one second teaching standardized teaching strategies?

I’ve never seen a school or educational department include students (or even suggest it) in the process of collecting or analyzing the formal and decisive testing data. Why not? When it is becoming more and more evident that there are huge gains to be made by putting students in a position to self-monitor and to train them to be competent in doing so, why are we allowing this opportunity to pass us by. (I don’t think our decision-makers trust young people as much as you and I do.) Perhaps while we are training them to be effective self-monitors, we see minutes that they could be spending practice math problems ticking away. It’s too bad that we have begun to operate on such a short-sighted view of efficiency.

Look folks, I’m not any more excited about this hyper-evaluative testing culture than anyone else, but I think that we need to take a step back from our repulsion and really look at what the problem is so that we can really solve it.

Why aren’t more people talking about this?

About a week ago, Common Dreams reported on growing boycott of standardized testing coming out of Seattle.

I heard about it through an e-mail from a former professor of mine. When I posted it to Facebook, it got 2 likes, 1 share and a single comment (that also got 2 likes). Not a lot of interest.

There is also a growing number of post-secondary institutions that are shying away from ACT and SAT results when making admissions decisions. You can read the list of schools here. It isn’t a short list.

So, why isn’t this story of more intrigue to people? Standardized testing has become the means through which we make most of the decisions across the country. Whether you support them or not, why isn’t a growing boycott a bigger story?

To me, this is a great opportunity. If more school’s get on board and some momentum can be  built, this a fantastic chance for conversation to begin. Not a conversation about which test to give, or what content to test, but instead whether or not standardized testing is an effective means of evaluation.

I’ve talked about this before. In The Growing Case Against Standardized Testing, I reveal my hand as a skeptic of testing as it is currently done. I would love the conversation to get going because I think that educational community needs to produce answers to some key questions:

1. Do we have an agreed upon definition or description of a “successful” school? Have we done any studies to demonstrate the standardized testing process is an accurate predictor of a school’s “success”?

2. Why do we have so much faith in the standardized test results? What have we done to ensure the fidelity of the results?

3. Why is important that students get tested so often?

4. Do we have an agreed upon definition of a “successful” student? Are we convinced that test results are a predictor of current or future success of an individual student?

All of these questions get at the heart of Standardized Testing. There is a growing body of evidence that is piling up against the standardized testing model as an effective means of evaluating anything… a school, a student, a teacher, a leadership team, or a community, but policy makers seems to be taking no notice.

So, I ask again: when a major public school system has schools that are boycotting the tests and major universities are ignoring the results, why aren’t more people talking about this?