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Standard 2: The lesson teaches the abstract concept of the Pythagorean theorem through a robotics project-based lesson.
Standard 6: In the creation of this activity I participated in a learning group with two other teachers and input from the course instructor.
Standard 3: The lesson is written to ISTE standards.
Goal 2: This lesson was designed to respond to difficulties I have had in teaching students the very real implications of the Pythagorean theorem.
This week for CEP 811, we are designing lesson plans for our maker kits. The goal of my lesson plan is to give students an engaging problem to solve using 8th-grade math concepts, especially the Pythagorean theorem. The activity is student-centered with more than one way to complete the task, so there are a number of concepts that will likely come into play including ratios, calculating circumference, identifying angles, and using equations to solve real-world problems.
The premise is this: Your colony is threatened by an approaching monster. You have to program a robot to make an indirect approach to the monster in order to subdue it with a tranquilizer. Here are the major players in our story: the monster, the outpost, and the robot.
The items are arranged to form a right triangle, like this:
There are a number of problems the students have to solve. They need to identify the shape as a right triangle. They will need to use the ultrasonic sensor to measure lengths of sides a and c ( the distance from the robot home to the outpost and the monster, respectively). They will then need to calculate the distance from the outpost to the monster using the Pythagorean theorem. They will also need to figure out how many centimeters the robot travels per rotation and set up a ratio to correctly calculate how many rotations will be needed for each side.
Rather than instructing the students in all of the steps, I took a problem-solving approach that has them spending the majority of their time trying to solve the problem themselves. This, of course, leaves the possibility that they will arrive at a solution in a way that is different from what is intended. In one of the papers, I read last week, Krista Francis and Michael Poscente (2017) pointed out the possibility of different solutions in a project where students made triangles with EV3s: “With multiple possible solution methods, there is no wrong way for the robot to move around the triangle. There are, however, ways that are more efficient and that use deeper mathematical understandings and fluency” (p. 311).
For example, you can calculate how far the robot travels in one rotation by having the robot travel one rotation and measuring the distance, or you can measure the diameter of the wheel and calculate the circumference, or you can have the robot travel four rotations then measure the distance and divide the distance by four. You also don’t have to use a ruler to measure the distance traveled, you can use the sensor to find the distance to an object and then calculate the change. Perhaps, the most sophisticated approach would be to predict the distance per rotation based on the circumference, then do multiple tests at various rotations using the sensor to record the change in distance, and average all of the observed results. The uber-sophisticated student could even come up with a correction function that would account for the variable nature of the EV3. On the opposite end of the spectrum, there is nothing that says students cannot use the sensor to program the robot to stop a given distance from the (say 5 cm) from the object. What this strategy lacks in mathematical sophistication, it makes up for in programming prowess.
A successful attempt would look like this:
I am looking forward to trying this lesson out. I am a little concerned that students might not have enough information to effectively program the robot, so I tried to build a number of scaffolding options into the lesson plan. But my preference would be to avoid using them unless absolutely necessary. The hope is that by beginning with a mini-lesson and moving into small group work with a teacher floating from group to group we can achieve what O’Donnell (2012) described as, “The adults or other children operate(ing) in the child’s zone of proximal development to assist the child to perform in ways that he or she could not do without assistance” (p. 64). Leaving open the possibility that little or no help is needed.
While the common core math applications of this activity are self-evident. I also tried to incorporate the following ISTE standards (2000).
ISTE 5. b Students collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making.
The ultrasonic sensor and gyroscope are used to measure the length of the two sides and the size of the right angle, respectively. The students use this data to program the robot.
ISTE 5.c Students break problems into component parts, extract key information, and develop descriptive models to understand complex systems or facilitate problem-solving.
While there is a single task, it requires a number of steps to solve. Students must:
- Measure and record distances
- Calculate distance using Pythagorean theorem
- Determine distance of single rotation and create a ratio to determine program parameters
- Identify and program a right angle
ISTE 5.d Students understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions.
Students will need to sketch out a plan and write pseudocode for their plan. Then program the plan into robot and test and fine-tune the parameters until the plan works.
In designing the lesson, I also tried to think of Dr. Yelon’s (2001) six components of instructional design discussed in this week’s LEARN section. While there is an element of science-fiction to the story, the lesson still represents a real-world problem and performance that is based on a clear instructional objective that is tied to a content standard. I tried to include the essential information needed for the students to succeed before beginning active group participation in the lesson. The task itself provides feedback to students—do they succeed or not? Finally, I built time for reflection and assessment of objectives into the schedule of the lesson.
I am looking forward to teaching this lesson. You can read the plan here. I’ve set the share settings to can comment so you can tell me what you think!
Francis K., &l Poscente M. (2017). Building number sense with Lego Robots. Teaching Children Mathematics, 23(5), 310-312. doi:10.5951/teacchilmath.23.5.0310
International Society for Technology in Education. International Association for Computing in Education International Council for Computers in Education. (2000). ISTE national educational technology standards (NETS). Eugene, OR : International Society for Technology in Education, https://www.iste.org/standards/for-students
O’Donnell, A. (2012). Constructivism. In APA Educational Psychology Handbook: Vol. 1. Theories, Constructs, and Critical Issues. K. R. Harris, S. Graham, and T. Urdan (Editors-in-Chief). Washington, DC: American Psychological Association. DOI: 10.1037/13273-003.
Yelon, S. L. (2001). Goal-Directed Instructional Design: A Practical Guide to Instructional Planning for Teachers and Trainers. Michigan State University: Self-published, Not in electronic format.