If you’re anything like me, you’ve noticed that while students may appear to understand what we teach them during a lesson, they often struggle to apply that knowledge in real life. Early in my career I didn’t think I could do anything about it. However, with more experience and lots of trial and error I found a technique for helping students develop the real-world problem-solving skills they desperately need.
Spies and Analysts
I developed a structure called Spies and Analysts that’s useful in helping students understand their roles during problem solving. To better understand this structure, let’s imagine that students were trying to figure out how to create stronger passwords that hackers could not guess.
The spy’s job is to figure out what information is need. In real life, we aren’t given all the information we will need to know. We have to seek out information and decide what we want to use. Do we need to know how long a password is? What characters are available? Whether words will be used? How a hacker is guessing passwords?
Too often we skip the step of letting students be spies. Instead of having to figure out what information is needed and acquiring it, they are usually given all the information they could possibly need in a pre-printed sentence for their convenience. If only that was the way real life worked!
Once students have the information they need, then it’s the analyst’s turn. The analyst needs to take the available information, determining which of it is helpful, and use it to create a model which can solve the problem.
In reality, it’s rare that you wind up having everything you need and creating a perfect formula on the first try. Usually you get closer, but then realize you need additional information or need to tweak your formula. So, this process of acquiring information (spy) and using it to create a mathematical model (analyst) often has many iterations.
Tips to Improve Students' Problem Solving Skills
To put this into practice, I came up with four tips to improve students’ problem solving skills that I wish I knew when I first started teaching:
- Present the problem like people experience it
- Don’t give students information until they ask for it
- Have students make estimates
- The journey is the destination
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The views expressed in this article are those of the author and do not necessarily represent those of HMH.
Robert Kaplinsky is one of the authors of Into AGA, our solution to transform math students in Grades 8–12 into budding mathematicians.