ALEKS and Adaptability
So, what does work? I've been interested in ALEKS for a while now, and my university has begun using it for placement testing. The idea is that students take an adaptive assessment to assess their math knowledge. Then it provides them with “prep and review” modules based on the problems they got wrong on the assessment.
I think that, generally, this is the right model for students, especially those with major gaps in their prior math knowledge. It is nearly impossible — given the current state of class sizes at both the secondary and post-secondary level — for one instructor to meet each student where they are and give them the personalized review they may need. In our current “one size fits many” model, we put a big group of students into, for example, a “college algebra” course (which is really high school algebra, but I guess we want to make them [and us] feel better about it). Many, if not all, of the students in this course only really “need” at most half of the material the course covers. The trick is that they don't all need the same half.
A co-requisite model of a college algebra course would allow students to spend time in a self-paced adaptive system like ALEKS alongside the main thread of course content. This would hopefully keep students from getting bored when that main thread covers material they already “know.” The logistics aren't trivial:
- How much in-class time is spent with students working on ALEKS in a "lab" setting? All? Some? None?
- What do you do if/when students "finish" ALEKS significantly before the end of the semester?
- How do you filter the ALEKS material to not force students to "waste" time on topics that you don't think are relevant to their future coursework? Is this even a good idea, given that you don't know what their future instructors' expectations may be?
This also doesn't address the issue of students who need “just in time” math review outside of a class environment, which is a primary role that Khan Academy fills.
What would a “just in time adaptive” math review website look like? Is such a thing possible?
The Biggest Challenge Isn't the Math
One of the biggest challenges with helping students understand the “why” behind algebraic rules is often the attitudes about they bring with them to the discussion.
These are not attitudes that exist in a vacuum. These are attitudes that have built over time, often year after year in math classes throughout their pre-college schooling. A student may have had years of caring, compassionate, and considerate math teachers, but it only takes one bad experience to knock many of them off track. This is not to mention the very real systemic issues (including underfunded schools and systemic racism — not that those are particularly separate issues) that can get in the way of students' learning.
When you talk to someone who “hates math” (and trust me, I hear from a lot of them whenever I tell them what I do for a living), they usually tell a story of a particular teacher who made them feel dumb, or flawed, or “less-than” just because they “weren't good” at math. That one experience sticks in the minds of far too many students. It begins a snowball effect where a few less-than-perfectly grasped math concepts lead to frustratingly confusing math concepts, which in turn lead to an impenetrable barrier between the student and understanding.
Breaking down those barriers is difficult. It requires convincing the student to believe in themselves. That they should trust a process of learning that often involves failure. And it involves breaking down preconceived notions of mathematics as a binary field of study where everything is either “right” or “you're not smart enough to understand this.”
Any program or methodology that hopes to raise the bar and improve math aptitude, especially one that hopes to do so anonymously and asynchronously, must first accept that the math usually isn't the root problem.
What's wrong with Khan Academy?
Don't get me wrong; Khan Academy is, in many ways, not bad. It's simple to use, accessible, and well-known among students. The amount of content is not the problem, it's the way in which the content is presented that I have a problem with.
Over the years, as I've taught students with weaker math skills, I've noticed a common theme. Many of them have trouble making algebraic concepts (including “pre-algebra” concepts like order of operations and fractions) make sense. What I eventually realized is that many of these students don't think algebra CAN make sense. They truly believe that some people “just know” what algebra steps come next in a particular problem, and that they don't.
For example, a student might struggle to solve an equation like this:
$$ 2x-5=9 $$
To students familiar with algebra, this is likely an extremely easy problem: add 5 to both sides, and then divide both sides by 2. But to a student who struggles, they might recognize that they need to do those two operations but not understand why they need to be done in that order.
It is possible to explain this using order of operations (“PEMDAS”), but many math instructors simply do not understand that it is something that may need to be explained for some students.
What Khan Academy does well is showing students what to do to solve a problem. A Khan Academy video for the equation above would definitely tell students to add 5 to both sides and then divide by 2. But it doesn't tell them why. Without the why, that same student will be just as lost when you ask them to solve
$$ 3x+7=4.$$
My vision for a new KA-like resource would focus on building that understanding. It would give students the tools they need to build on that understanding. And I have a bunch of ideas for how to do it.
Khan Academy, But Good: A Manifesto
A couple of days ago, I posted a “toot” on Mastodon saying “What if Khan Academy, but good?” This is something that I've thought about a lot, ever since I first encountered Khan Academy videos several years ago. In this and subsequent posts, I hope to flesh out my ideas and lay out my vision for a KA-like resource that I'd like to someday create.
This is going to be somewhat stream-of-consciousness, and I don't expect many folks will ever read it, but here goes nothing.