Why math acceleration?

One could also ask Why math remediation? No one questions that. We should meet everyone where they are. Also, acceleration opens some possibilities.

Here’s the normal progression of math for students in PPS schools:

• Algebra 1/2. one and two variable linear equations. function notation, interpretation. Basic function scaling and x/y shifting. Introduction to exponential growth/decay. Introduction to quadratics.
• Geometry/Statistics. Basic trigonometry, triangles, averages, mean.
• Algebra 3/4. review algebra 1/2. arithmetic, geometric, and recursive series. more advanced function concepts
• Precalculus. review algebra 1/2/3/4 and trig. more complex function scaling. logarithms. extend quadratics to polynomials and rational polynomials
• AP Calculus

That’s five years to calculus but high school is only four.

There are two PPS sanctioned paths to AP calculus

• some middle schools offer algebra 1/2 in 8th grade.
• in high school algebra 1/2 and geometry can be taken concurrently.

Cool. what’s the problem?

For motivated kids I see a couple problems.

• Until you get to precalculus, the classes are slow and boring. We’re talking about motivated kids. Doubling up means they spend twice as much time in slow and boring classrooms.
• Precalculus doesn’t really prepare you for AP Calculus.
• No possibility to take advanced calculus.

How do I define motivated

When I talk about motivated kids, I don’t mean the really exceptional, prodigy kids. For me, a motivated kid is someone who:

• shows up to class ready to learn.
• They’re able to basically sit still and actually pay attention.
• Doesn’t have large gaps in prerequisite knowledge.
• Thinks math is at least a little interesting.
• I’d guess this is at least 10% of students.1

Ready to learn as in they don’t mind being at school. Their goals don’t include sidetracking the teacher. They are still a little curious about the world around them.

Some kids, especially boys, need to bounce around and burn energy. They have difficulty focusing. There are strategies to mitigate this.

The biggest issue for many is they haven’t learned the basics. In particular, times tables and fractions. Gaps like these make it difficult for otherwise bright kids to succeed in more advanced math subjects.

Classes are slow

Algebra 1/2 and 3/4 cover mostly the same concepts, just a bit more depth. These concepts can be challenging to many or even most. Motivated kids could learn both subjects in one year. Really motivated kids could also learn precalculus in the same year.

For kids that can handle two to three times the pace, normal offerings are boring and they’ll wonder whether they like math.

I’ve heard a reason not to accelerate that I find peculiar. The reason is that kids that are accelerated early will often not take more advanced classes later in their schooling. Here’s my take on that: the kids are tired of being bored. Even being bumped up didn’t fix it. Instead, course offerings should be more compelling.

If a student excels in math, they should be rewarded with more challenging classes.

precalculus doesn’t really prepare you for AP Calculus

At some PPS schools, students can earn PCC precalculus credit… for one semester. PCC has two before their calculus. In addition to this, AP Calculus, even the AB version, is pretty challenging. So we’re expecting students to switch from a high school paced bunch of classes and then the next school year they’ll go into turbo mode to prepare for the AP exam? Hardly.

Taking an AP class and doing well (3+) on the exam are two different things.

If a student is accelerated they’ll get to more challenging classes earlier. Knowing that many students 2 will run out of coursework high schools could offer more rigorous options.

The benefits of acceleration take a while to manifest

In PPS, fifth or sixth graders can be bumped one year ahead. So a fifth grader can be in a sixth grade math class or a sixth grader can be in seventh grade math.

PPS requirements for this can be found here.

For a kid who manages to accelerate, those sixth and seventh grade math classes are just as boring as what they experienced before. No real benefit there, but…

They will be able to take algebra 1/2 as seventh graders and geometry in the eighth grade. PPS offers, begrudgingly, a self paced, Khan style course for geometry. Algebra 3/4 as freshmen, Precalculus as sophomore and AP Calculus as a junior.

They’ll have something to report on their college applications

Also, they can take advanced calculus as PCC, PSU, or UoP.

But really, acceleration should be more aggressive so motivated students can experience the joy and the rush of being in real classes much sooner.

Math is awesome, but our system tries to convince students otherwise.