As David Wees shares in his blog entitled, Make Mathematics Fun, “too many students spend a lot of time not enjoying themselves when learning mathematics.” He challenges mathematics educators to make math accessible and more easily learned for their students. Being up for the challenge, here is a suggestion.
Angry Birds is the largest mobile app success the world has seen so far. It is an interactive, animated projectile launcher that creates parabolic motion. The parabola is traced by the flight of the projectile (the bird). In the app players use a slingshot to launch birds at pigs stationed on or within various structures. The goal is to destroy all the pigs on the screen. The game is such a huge hit that The MIT Entrepreneurship Review predicts that the game will be bigger than either Mickey Mouse or Mario. If kids are that into it, let’s change it from a mindless game to a vehicle for learning math.
As evidenced by several of my recent blog posts, I am an advocate for using Jerome Bruner’s concrete-representational-abstract (CRA) approach to learning. So, introduce parabolas using the CRA model and Angry Birds. Activities with concrete materials come first, followed by activities using representational forms such as pictures, drawings, diagrams, charts or graphs (animated or static). Finally, abstract activities, with symbols such as numbers and letters, are introduced.
For a concrete activity, use a beanbag toss or shoot basketball hoops to create projectile motion. Once the activity is finished, have students draw the path of the beanbag or basketball. Once the concrete activity is completed, students are ready for the representational part of the model.
With iPads, students play the Angry Birds app. Students create parabolic motion with the birds while exploring launch speed, launch angles, launch angle with the maximum range (45 degrees), complementary launch angles (the range will be the same say for a 60 degree launch and a 30 degree launch), and the impenetrability of various construction materials used to shelter the pigs. Because the program traces the path of each projected bird, students can see a wide range of parabolas. See video below.
The teacher connects the concrete activity to Angry Birds by having the students discuss the similarities in the two. Discussions as to how the various arcs are used to achieve goals, such as getting the beanbag on the target, the basketball in the hoop, or the bird on the various shelters help establish the relationship. Students now move on to the Elevated Math lessons that use the representational part of the model as a bridge to the abstract.
The Elevated Math iPad app lesson A14.1 introduces several new terms: quadratic relation, standard form of a quadratic relation, parabola, vertex, axis of symmetry, and summetrical. Students learn to represent quadratic relations graphically as parabolas by finding five to seven points on the graph. Then, they graph a quadratic relation by finding the vertex and using symmetry. The lesson’s teacher, Mr. Frogan, explains “besides graphing lines, we can graph curves.” He asks the students “to think about a nice fly ball in baseball. The ball follows a path that arcs up to a highest point and then falls in a path that mirrors its rise into the air.” That path is a U-shape that is very important when learning how to graph quadratic relations. Diagrams and illustrations are used in the lessons to help students learn what U-shaped curves or parabolas are, how to graph them, and how to graph quadratic relations in standard form. Then, the lessons provide abstract activities for students to practice newly learned skills.
In lesson A14.2, students apply their knowledge of translation and reflection first introduced in M11.1. Students inspect equations y = ax2 to determine the direction and width of the opening of a parabola. They translate or shift parabolas horizontally, vertically, or both horizontally and vertically before graphing equations in the form y + a(x – h)2 +k. In Elevated Math lesson A14.3, students use quadratic equations and their graphs to solve problems. They learn that the path of a projectile can be represented with a quadratic equation.
From tossed-beanbag parabolas to Angry Bird parabolas to graphing-quadratic-equation parabolas in Elevated Math, the students follow Bruner’s CRA approach. Follow that up with the parabolas found in the real world — cables on a suspension bridge, reflectors, satellite dishes, and driving golf shots — and we have a very tidy and effective approach to learning that is accessible, more easilty learned, and downright FUN.
So, what do you think, David? Did we meet the challenge?