Most math practice assignments are a waste of time. They don't teach problem-solving skills, but instead reinforce the idea that math is a matter of pattern recognition (if you see this, then do that, etc.). It's why so many straight-A math students flounder on the SAT or why students are utterly terrified of word problems.
Why does this happen? Because practice assignments create an illusion of learning without challenging students to find the right solution strategy. Ask yourself, is there any fundamental difference between these problems:
Bigger numbers, scarier exponents, same solution strategy. For sure, it is extraordinarily tedious to enter the third problem into a calculator. But there's no real learning happening here. Here's a simpler, yet more effective set:
But they don't know algebra! Or PEMDAS! Or the power of a power rule!
But you don't need algebra to plug numbers in. In fact, plugging numbers in is a great way to develop the basic intuition behind exponents ("Woah, things get big really fast!"). Second, just tell them to do the parenthesis first. That's all you need to say. They can do it!
Interleaving is a teaching technique that arranges problems so that they require different solution strategies, even if they seem similar. It challenges students to choose the right strategy before tackling the problem, developing their meta-cognitive skills in planning and problem solving. It also improves retention by encouraging students to revisit concepts in different contexts.
Interleaved practice forces students to choose a strategy based on the problem itself, just as they would when working on cumulative exams and high-stakes tests (Dedrick et al., 2017).
You can read more about it in this guide by D. Rohrer, R. F. Dedrick, and P. K. Agarwal.
Submit a math problem below. The AI will create an interleaved problem set that targets different but related solution strategies. (This may take up to a minute, as the system runs multiple prompts to create the problems). Each problem includes a "Generate Step-by-Step Solution" button that produces an AI generated, detailed guide to solving the problem.
Examples: