Since this project started, I’ve constantly struggled to see where math fits into a project-based learning environment. The math most of our students would naturally use in academic research is heavy in statistics, modeling, and basic Algebra/Geometry. Conversely, the standard high school curriculum devotes much more time to advanced Geometry and Algebra, setting students up for the Calculus track. Typical GHS graduates get over 400+ classroom hours devoted to Algebra-based math and only a fraction of that touches upon the math most academics use.
So what do we do when a thematic, discussion, and project-based path doesn’t hit on each and every mathematical topic? What do we do for the students for whom conics never turn up or for those who never seem to get off on a trigonometric tangent?
We acknowledge that, for some, we can offer something better.
There are two types of math out there – theoretical math and applied math. Theoretical math is the stuff the majority
hated loved in school – the proofs, the random secant and tangent theorems in circles, the way a constant affects a directrix, or the way the degree of a denominator affects end behavior. Math geeks love this stuff – it’s mind-blowing how much is out there. Applied math, however, is taking a set of population data and fitting a curve to it, tracking climate change over time, or generating an equation for the ball that you rolled down a ramp. There’s so much more to both, but for the sake of brevity, roll with it.
We teach too much theoretical math and not enough applied math to the general population. Some theoretical math is great – when done right, it forces us to extend our imagination beyond what we know, ask “what if?”, and then talk about what might be true. This is unbelievably valuable, but students do not need four ‘out of context’ years of it. Some students will want to keep at it and those should be the students foraying into Calculus with plenty of encouragement from those around them. Some will argue Calculus is a perfect marriage of theoretical and applied and I will agree that ideally, yes, this is true; in practice, however, it is much more the former.
So, back to project-based learning. What do we do when the script is taken away and students don’t interact with all the math that their traditionally educated peers do? Again, we must acknowledge that, for some, we can offer something better.
There are a list of standards students must meet through the Common Core and Connecticut’s specific interpretation of it. Specific to the GHS Innovation Lab, STEM teachers should guide students so that their work incorporates these whenever naturally possible. A student studying population change as part of a unit on the Industrial Revolution can hit on numerous standards in a more natural way than a traditional setting. Another student may encounter parabolic or exponential motion in a particular physics application. (See two real 6th and 9th grade project examples here.) It would be naive to think students would cover as many different topics as they currently do. However, they would apply what they do cover in a much deeper way – a way that, months after learning and applying it, they could still refer back to.
The CCSS topics that are left will still be covered – perhaps in discovery-based seminars or more traditional modules, as we’re calling them. It’s possible that students could ‘test out’ of a module after having learned the material via a flipped lesson or as part of a small team. If we can create a program where the critical thinking and problem solving often so sought after in the math classroom takes place across the curriculum, sacrificing the discovery of intersecting chords in a circle could be one we’re willing to make. Other schools have scheduled SAT or state test prep to offset any shortcomings. Anything beyond that will certainly be available to all, but only required of those who choose to pursue it.
We need to accept the fact that currently, students take comprehensive math survey courses, pass a variety of tests and a final, and move on. What they actually remember three or six months later goes unmeasured. Our argument is that a project-based model encourages longer-lasting learning that students will actually remember.
So what happens when a student goes to college, jumps into Calc 101, and is missing a chunk of Algebra knowledge? We find that, after talking to countless people from other PBL schools, they do just fine. They don’t fall flat on their face like many peers who have never struggled without a teacher holding their hand each step of the way. They have grit and perseverance and, countless times, learned how to solve their own problems, Google how to do something, watch a video, ask a classmate, or use any one of the numerous resources they have to figure something out. They are independent, investigative, life-long learners. And they’re better off for it.