In my previous post I talked about how variety is a key component of math acceleration. But what does that look like in practice? For my last two years of elementary school I was lucky enough to attend an innovative full-time gifted program that did an incredible job of covering the basics while simultaneously doing creative project-based learning. Math for that program was split into two parts: 1) regular math class which was a standard program but entirely self-paced and 2) a math laboratory class which covered unusual topics like probability, different base number systems, graph theory, and cool projects like visualizing a million. I loved this idea so much that I decided to use it with my own student. On a weekly basis we spend approximately 2/3 of our time working in our main math book (currently Art of Problem Solving’s Introduction to Algebra) while another 1/3 of our time is spent on fun and interesting topics outside of the mainstream. A typical day might look like this:
Morning Main lesson: AOPS Algebra – 10 minute challenge problem from a previous chapter, 10 minutes of easier review exercises, 20 minute lesson on new material such as factoring quadratic equations.
Mid-morning break: 20 minutes working on a Scratch programming project that draws a line based on user inputed point and slope.
Most evenings: 30-60 minutes of discussion about Venn diagrams, logic, probability, triangle numbers, geometric drawing, playing with Zometool, or whatever strikes our fancy. These discussions are led by me but not forced and usually start out with “Have you ever heard of…?”
I have a math-loving student and provide a rich educational environment at home so access to fun books, games, apps, toys, and videos are also part of his math education. All of this often adds up to 2 hours or more of daily mathematics, and it adds up effortlessly. Even for a student like mine who absolutely loves math, plodding through pages of standard exercises and working until mastery in every area would be an uphill battle. For students who are working ahead of grade level, keeping their chronological age in mind and being realistic about attention span is essential. Changing topics, interleaving review with new material, and combining difficult problems with easier questions keeps attention and interest high which allows us to work for a longer period of time and cover more material. It also has the added benefit of helping the student make new connections. Despite what we’ve been told, mathematics is not a single lane track leading from arithmetic to calculus.
The idea of a math laboratory is also perfect for parents who want to supplement their child’s school work with something at home. After a long day of school and homework trying to pile on more math learning during evenings and weekends can be a tough sell to a worn out kid. However, if the topics are fun and unusual, it can be a natural and joyful activity. Most of my math laboratory activities are lesson plans that I put together myself, but a few of my favorite off-the-shelf math enrichment resources are listed here:
I plan to review some of these books and resources in the future, but all are excellent. With Scratch programming I like to challenge my student to make math related programs that review a previous concept or explore something interesting like finding prime numbers or perfect numbers.
The main thing is don’t be afraid to mix things up, head off course, backtrack, and follow those rabbit trails of learning wherever they might lead. You’ll be surprised at how much material you can cover when you don’t stick to a single minded plan or curriculum.