Mathematics as a Thinking Tool
According to the National Council of Teachers of Mathematics, real-world problems are not ready-made exercises with easily processed procedures and numbers. Math educators need to place students in situations that allow them to experience math problems with “messy” numbers or too much or not enough information or that have multiple solutions, each with different consequences, then students will be better prepared to solve problems they are likely to encounter in their daily lives.
Robot Dance Goals
• Provide an academically-foregrounded, contextually-stimulating design problem that improves student understanding of ratios, proportions, and fractions which are foundational mathematical concepts that are essential for success in higher level math and science.
• Make cognitive bridges for students between the type of mathematics students learn in robotics and the type of mathematics assessed on NCLB tests.
• Teach students research-proven best practices in engineering design.
Introduction to the Problem
In the Robot Dance DBL, students are given a robot, asked to select a musical piece, and then develop a set of dance steps to “teach” their robot to dance. Students are told upfront that once they teach their robots to dance, they will pair up and be required to teach other student’s robots to dance their “dance”. The pairs of robots will be required to dance in a choreographed synchronized way. To ensure student ownership of the problem, students are asked to develop a requirements document that can be used to determine what a good dancing robot looks like; i.e. is the dance choreographed, are the robots synchronized, does the dance contain all of the required dance steps, what degree of accuracy must the dance step adhere to, will more complicated steps allow teams to score higher in the dance competition rating system?(similar to rating systems in ballroom dancing or ice skating). Students are encouraged to make the requirements document rigorous, enabling the judges to fairly evaluate each dance team. The requirements document discussion will be facilitated in a whole group setting by the teacher.
When the students begin to develop their dance they are asked to break the dance into a series of steps that involves forward, backward, right, and left movements. Students are asked to choreograph their dance in human movements and then lay them out on a sheet of paper so they have something to reference when they begin programming their robots. Students will make one copy of their choreographed dance and turn it into the teacher for future reference. Each movement (straight, backward, right, and left) needs to be calculated mathematically so that the dance step can be reproduced as needed. Students are required to keep all documentation in their engineering journal including the math involved in each dance step.
When the students complete their robot dance, the teacher will grade the robot’s dance according to the class developed requirements document and the pre-planned choreographed dance that was turned in before they began programming the robot. After the robot dances are completed and evaluated, students are randomly paired and are required to teach each other's robots how to do their synchronized dance routine. For the learning experience to work as intended, students are placed in teams so that their paired robots have a different set of characteristics i.e. different diameter wheels, different wheelbase, caster versus four wheels, etc. Initially, it appears to be a trivial task to teach another robot to dance; upload the code to the robots and watch them dance. Students quickly find that a variation in the robot’s physical characteristics leads to multiple problems, and they will soon discover that these problems all have proportional relationships.
There are two components to a well-designed DBL. First, the engineering problem needs to allow student creativity and has an unlimited number of ways to solve the problem. Second, the problem can only be solved by applying teacher-specific academic principles. The quickest way to solve the Dancing Robot DBL is to apply mathematical proportional reasoning. Students will discover that it is nearly impossible to solve this problem using a guess and check strategy; there are too many variables involved. Students will discover that it is easier and to do the math than to attempt to guess and check their programming values.
Our observations have led us to believe that students are motivated by:
• Fun assignments
• Direct linkage between subject matter and real-world applications
• Success (student’s personal success leads to confidence and further success)
• Involved, interesting, and knowledgeable teachers
In order to meet the aforementioned goals and build a robust STEM understanding for students at the same time, the Robot Algebra project has the following attributes:
• It consists of a series of DBLs that include opportunities for student choice.
• Robotic lessons are STEM foregrounded; the actual connections to the math and science must be made by, with, and for the students. The current model that many robotic programs employ, a policy of an “open door” where students discover the STEM is not sufficient for a learner who is not yet inclined to walk through the door.
• The DBL units must include opportunities for both authentic and traditional assessment.
• Includes high levels of teacher professional development (PD) that are guided by research-based best practices in PD. The PD should help teachers to recognize student misunderstandings and how to correct them.