In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission again comes from my former student Haley Higginbotham. Her topic, from Pre-Algebra: absolute value.
A2. How could you as a teacher create an activity or project that involves your topic?
A fun activity to do would be to have a graph on the floor taped out and divide people into pairs and give them sets of points to graph. Then, they would have to measure how far away they were from origin. I would ask if it mattered that the x and y values were sometimes negative, and why or why not. Hopefully they’ll respond that since they were measuring distance, and distance isn’t negative, then it didn’t matter if the x and y values were negative. And that would lead into the idea that absolute value refers to the distance from origin, and it doesn’t just “make the negative a positive number.” If I were to teach absolute value, I would very much want to emphasize this point because even though it seems like the absolute value just magically gets rid of negative signs, it is important to know what it actually is.
D2. How was this topic adopted by the mathematical community?
Originally, the term absolute value came from Jean-Robert Argand’s term ‘module’ (unit of measure in French). The term wasn’t commonly used in English until about 1857. The standard notation of vertical bars came from Karl Weierstrass in the time intermediate time. Now, the notation of vertical bars is used for different purposes in other areas of mathematics, like determinants and cardinality, which don’t relate to distance. However, the idea of absolute value (or magnitude) extends to the realm of physics, and science in general. Generally, when you want to know how far an object has traveled, but it has returned to its original position, you take the magnitude of the distance. In physics, you often want to find the magnitude of a vector, in order to know the distance. It’s also helpful because you can extend this idea into multiple dimensions, even though the calculations can become longer than just removing the negative sign.
E1. How can technology be used?
GeoGebra’s graphing calculator is fantastic for math in general because it has a wide range of functionality besides just graphing. In terms of absolute value, you can graph the absolute value function easily and it will actually pop up with the vertical bars next to it and not just abs(x) which is good since then student can get more familiar with the notation. GeoGebra allows you to measure distance between points, which is really the important tool in this case. You can easily plot different points and measure the distances to verify more accurately that the distances are the same regardless of sign. GeoGebra is also fairly intuitive to use, which is good if you have students who aren’t very familiar with using technology. Plus, it’s just plain fun to play with and students will love the fact they don’t have to graph a bunch of points and functions by hand.