Dr. Chris Schunn, University of Pittsburgh, CoPI on the project
It is crucial for teachers to develop students’ algebraic thinking and engineering design skills if we are preparing them to compete in the global economy The Robot Algebra Project develops of a set of - Robotics provides unique opportunities for teachers to place engineering design and mathematics in contexts that students find engaging and understand.
- Learning is a cooperative process between the student, the teacher, and the problem; engagement must be present for optimal learning to take place. The choice of the problem is critical if the goal of the problem is to teach STEM.
- Design problems are a natural way of teaching design skills and creating a need-to-know for students to learn math and science. DBLs organize extended curriculum units around design challenges.
- Math is the language of science, engineering and technology. The mathematics in the lesson needs to be thought throughout by the teacher and foregrounded for the student.
- For STEM education lessons to have a significant impact on a students’ math understanding, the focus of the math instruction must be centered on addressing specific mathematics concepts (not general) and the mathematics in the lesson must be made explicit not implicit.
- For students to obtain a deep understanding of the focal math concepts, connections need to be made between the applied math problem and everyday math situations.
- For students to move beyond parroting the teacher’s words, ideas, and solutions, and develop deep understanding, students need the opportunity to struggle with the problem, be able to defend their decisions, and explain their answer in their own words.
- The ideal STEM curriculum gives students opportunities to solve problems that require them to work cooperatively, to use technology, to address relevant and interesting mathematical ideas, and to experience the power and usefulness of mathematics.
- Curriculum implementation is important
**. The ability to vary teaching strategies; connect what the learner already knows to what they need to know; and provide individualized feedback for students needs to be taught to teachers.**
The Robot Algebra project measures and iteratively improves curriculum that can be implemented in both traditional and non-traditional educational settings.
Over the last two years, CMU and LRDC have been guided by the following questions: “What can we do to improve Robotics’ ability to demonstrate and teach STEM?” and “Can we integrate the successes that LRDC has demonstrated in their science DBLs into CMU’s highly regarded Robotics curricula?”
Traditionally, fractions, ratios and proportions have been considered middle school topics, but testing shows that high school and college students struggle with these foundational mathematic concepts. Fractions, ratios, and proportions are arguably the most mathematically complex and cognitively challenging concepts for students to understand. In addition, ratio and proportion problems can be solved multiple ways, which often leads to student confusion. The Robot Algebra DBLs give students opportunities to work on, struggle with, and eventually solve contextually rich applied ratio and proportion problems. For example, the Dancing Robots unit asks students to create programs that allow a set of physically different robots to dance in synchrony to music. In these lessons, students will learn that there is a linear proportional relationship between: - Speed and power,
- Speed and wheel diameter,
- Wheel diameter and distance traveled,
- And, the center to center distance across the robots wheels and the angle of turn that the robot makes.
These proportional relationships, once discovered, give the student programmers the control that they will need to synchronize their robot dances. This DBL presents many teaching moments where the teacher can demonstrate proportional relationships that lead to student understanding.
Carnegie Mellon presented a scaled down version of the Robot Algebra project to a group of thirty mathematics teachers at a professional development seminar. Teachers were posed with the following challenge: Given a robot with 5.6 cm diameter wheels and wheel encoders accurate to 1 degree of wheel rotation, program your robots to travel exactly 31 centimeters (the length of a ruler, it is easier to find rulers than it is to find meter sticks The teachers were broken into teams and tasked to calculate the mathematics to solve this problem, they were shown how to enter the values they calculated into their robot to test their results. Within 15 minutes, all teacher teams solved the problem. During the debriefing session teachers were asked to explain how they calculated the number of degrees the robot traveled. Below are the results. There are slight variations due to rounding, but the answers are basically the same.
This sample group of math teachers identified five different ways to solve this simple robot math problem. And each group of teachers might argue that their method was the best one to solve this problem. At the very least, it was the method that they selected.
We have found that teachers see robotics as offering great opportunities to teach STEM. We also found that many teachers miss these opportunities because solving the robotics project becomes the focus of the class and the STEM concepts in the lesson are either assumed or implied instead of foregrounded, scaffolded and made explicit. In order to foreground the academic STEM content, our team has developed a concept that we call an abstraction bridge. Abstraction bridges are easy for teachers to implement and are designed to: - Refocus the teacher and student’s attention to the academic component of the problem.
- Provide a set of everyday problems designed to develop generalized set of problem solving strategies across multiple contexts for the student.
- Provide formative assessment tools for the teacher enabling individualized remediation.
- Tie the lesson to outcomes measured by NCLB standardized tests.
An added benefit to the development of the abstraction bridge concept is that it can be used by all STEM teachers who are using project-based learning and authentic assessment to teach. Robot math demonstrates specific mathematical principles in a focused-applied setting. Students apply ratio, proportion, conversion of units, and measurement when they program their robots; the robot math context is much different than what is being taught in the mathematics classroom and assessed on NCLB-required state standardized tests. The abstraction bridge concept is designed to enable students to form a cognitive bridge between what they learn in a focused-applied robotics setting and the types of mathematics that students encounter everyday. The Robot Algebra abstraction bridge model is a tool that the teacher will use everyday. Students will be required to solve at least one non-robotic math problem per day for the duration of the project. Initially, the problems will be solved in class as a group; eventually the problems can serve as warm-up activities checking student understanding or will become homework assignments. Students will be required to both solve the problem and also explain how they derived their answer. Documentation will be kept in the student engineering journal. Example Problems are below: ______________________________
Books on a Shelf Halloween Better Deal Proportional Equation Example Functional understanding
- p = 2n
- p = 0.5n
- p = n – 2
- p = 6 – n
- p = n + 1
Scale Factor Problem Example 5 inches by 7 inches 5 inches by 7 ½ inches Proportional Reasoning Example There are limitless numbers of ratio and proportion problems that can be developed as part of this project. Below are the strategies that we will use to create a user friendly database for teachers to access: - Continue to build, sort, and qualify the database of ratio and proportion problems that currently reside at the Robot Algebra site. (This database will have many potential users as it is can be used by all teachers incorporating authentic assessment STEM challenges ensuring that math is covered in their lessons.)
- Develop a structure in the database that helps teachers to quickly identify different types of problems in the database i.e. ratio word problems, graphs, tables, proportional algebra problems, fractional relationship problems…
- Rate the problems from basic to sophisticated
- Provide ongoing teacher training in the form of webinars, seminars, and multiday classes that will enable teachers to become expert math teachers.
- Continual upgrade of the database based on teacher usage and research.
Design Based Learning Units (DBLs) According to the Standards for Technological Literacy published by the International Technology Education of Association, “All students need to develop an understanding of Engineering Design.” Design projects are being used to motivate and teach science and technology in elementary, middle, and high-school classrooms across America: they can serve to open doors to possible science or engineering careers. Over the last six years, the University of Pittsburgh’s Learning Research and Development Center (LRDC) has spent a considerable amount of effort researching and refining how to teach “engineering design”. They have developed a particular methodology called the Design-Based Learning Unit (DBL). The DBL is a well thought out design-project where the student develops a technological solution using limited resources. The DBL is carefully designed and orchestrated so that students feel that they have a lot of choice and freedom in their design, but the DBL is designed so that the student can only successfully solve the problem by applying the mathematical concept that the teacher intended to highlight. The DBL, a highly scripted but open-ended engineering design problem, has the dual benefit of being able to teach academic concepts in rich interactive environments as it develops the students’ problem solving, scientific inquiry skills, and engineering design competencies. - Defining the problem, including thorough research enabling the formulation of well developed potential solutions
- Establishing clear objectives and criteria enabling the development of a requirements document
- Systems decomposition - break the problem down into granular modules
- The use of time management tools like PERT and Gantt Charts
- Ideation, brainstorming, and design reviews
- The development of working prototypes
- Iterative testing, evaluation, and improvement of the prototype
- Selecting the best solution based on established criteria
- Iterative improvement based on research and testing
This methodology is valued in the workplace and needs to be taught to students. |