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Carnegie Mellon University & University of Pittsburgh Collaborative Badge Research

CS2N is involved in research in collaboration with Carnegie Mellon University and the University of Pittsburgh’s Learning Research and Development Center.

Ongoing Studies

1. Building Theory of Badges for Computer Science Education

2. Changing Culture in Robotics Classrooms (CCRC)

3. Teaching Robot Programming Through Simulation

• Robot Virtual Worlds Fall 2012 Study Results

4. Robots in Motion Robot Algebra Project

Teaching Programming through Robotics

• Witherspoon, E., Higashi, R., Schunn, C., Shoop, R (December, 2017) Attending to Structural Programming Features Predicts Differences in Learning and Motivation in a Virtual Robotics Programming Curriculum Journal of Computer Assisted Learning, DOI.10.111/jcal.12219 [ PDF ]

• Witherspoon, E., Higashi, R., Schunn, C., Shoop, R., Baehr, E. (October, 2017) Developing Computational Thinking through a Virtual Robotics Programming Curriculum. ACM Transactions on Computing Education, Vol. 18, No. 1, Article 4. [PDF]

• Higashi, R., Schunn, C., Flot, J (May, 2017) Different underlying motivations and abilities predict student versus teacher persistence in an online course. Education Tech Research Dev DOI 10.1007/s11423-017-9528-z [PDF]

• Flot, J., McKenna, J., Shoop, R. (2016) Helping Students Build Conceptual Models – the Lost Manual. Carnegie Mellon Robotics Academy, Pittsburgh, PA. [PDF]

• Flot, J., Higashi, R., McKenna, J., Shoop, R., Witherspoon, E. (July 2016) Using Model Eliciting Activities to Engage Students in Computational Thinking Practices Presented at the High Impact Technology Exchange Conference (2016 HI TEC), Pittsburgh, Pennsylvania. [PDF]

• Flot, J., Friez, T., Schunn, C., Shoop, R., Witherspoon, E. (March 2016) Can Computational Thinking Practices Be Taught in Robotics Classrooms? Presented at the International Technology and Engineering Education Conference, National Harbor, Washington DC. [PDF]

• Liu, A., Schunn, C. D., Flot, J., & Shoop, R. (2013) The role of physicality in rich programming environments.. Computer Science Education, 23(4), 315-331., [PDF]

• Flot, J., Shoop, R (November 2013) Foregrounding Math, Engineering, and Computer Science using Robotics.. Presentation given at the Technology Education and Engineering Association of Pennsylvania Annual Conference, Camp Hill Pennsylvania., [PDF copy of PowerPoint]

• Flot, J., Shoop, R (November 2013) Teaching Programming with Robot Virtual Worlds.. Presentation given at the Technology Education and Engineering Association of Pennsylvania Annual Conference, Camp Hill Pennsylvania., [PDF copy of PowerPoint]

• Liu, A., Newsom, J., Schunn, C., Shoop, R. Learn to program in half the time!. Robot Magazine , 49-51. [Author Proof (PDF)]

• Soldaat, X., Friez, T., Flot, J. Pointers and Data Structures in ROBOTC. Robot Magazine , 59-61. [Author Proof (PDF)]

• Liu, A., Newsom, J., Schunn, C., Shoop, R. Students Learn Programming Faster through 7. Robotic Simulation. Tech Directions , 16-19. [Author Proof (PDF)]

• Flot, J., Lui, A., Schunn, C., Shoop, R. (November 2012). Learning How to Program via Robot Simulation.Robot Magazine , 68-70. [Author Proof (PDF)]

• Avanzato, R.,Choset, H., Friez, T., Shoop, R. Veloso, M. (2011, December). Programming and Multi-Robot CommunicationsRobot Magazine ,74-77. [Author Proof (PDF)]

• Atwood, T., Shoop, R. Carnegie Mellon Launches a Mega Million Dollar Robotics Education Initiative. Robot Magazine , 70-71. [Author Proof (PDF)]

• Shoop, R. (2011, May). FIRE Unveils Robot Virtual World GamesRobot Magazine , 78-81. [Author Proof (PDF)]

• Shoop, R. (2011, January) Computer Science Student Network Project. Presented at the Computing Education for the 21st Century (CE21) meeting, New Orleans [Handout]

• Higashi, R., Shoop, R. (2011, November) Organizational Expectations Presented to Propel School System Teachers and Administrators, Robot Algebra Partnership Kickoff [Handout]

Badges, Motivation, and Assessment

• Abramovich, S., Schunn, C.D., Higashi, R. (2013) Are Badges Useful in Education?: it depends upon the type of badge and expertise of Learner. Educational Technology Research & Development, March 2013. DOI: 10.1007/s11423-013-9289-2. [Paper PDF]

• Higashi, R., Abramovich, S., Shoop, R., Schunn, C.D.(2012, June) The Roles of Badges in the Computer Science Student Network. 2012 GLS Conference [Paper PDF]

• Abramovich, S., Higashi, R., Hunkele, T. Schunn, C.D., Shoop, R. (2011, July) Achievement Systems to Boost Achievement Motivation. 2011 GLS Conference [Paper PDF]

Approaches in Teaching Mathematics and Robotics

• Alfieri, L., Higashi, R., Shoop, R., Schunn, C.D., (2015, February). Case studies of a robot-based game to shape interests and hone proportional reasoning skills. International Journal of STEM Education. [Paper (PDF)]

• King, S., Stein, M., Schunn, C.D., (2012, May).Designing Educative Guides: Reconceptualizing Teacher’s Role in Teacherless Cognitive Tutor-based Robotics Instruction.Paper presented at the 2012 annual meeting of the American Society for Engineering Education, Vancouver, BC. [Paper (PDF)]

• Silk, E. M. (2011).Resources for learning robots: Environments and framings connecting math in robotics(Doctoral dissertation, University of Pittsburgh). Available from D-Scholarship at the University of Pittsburgh. (No. 8607) [Paper (PDF)] [Presentation (PDF)]

• Silk, E. M., Higashi, R., & Schunn, C. D. (2011, June).Resources for robot competition success: Assessing math use in grade-school-level engineering design. Paper to be presented at the annual meeting of the American Society for Engineering Education, Vancouver, BC, Canada. [Paper (PDF)] [Presentation (PDF)]

• Silk, E. M., & Schunn, C. D. (2011, June).Calculational versus mechanistic mathematics in propelling the development of physical knowledge. Paper to be presented at the 41st annual meeting of the Jean Piaget Society, Berkeley, CA, USA. [Paper (PDF)] [Presentation (PDF)]

• Silk, E. M., & Schunn, C. D. (2011, April).Resources for learning robots: Facilitating the incorporation of mathematical models in students’ engineering design strategies.Paper to be presented at the annual meeting of the American Educational Research Association, New Orleans, LA, USA. [Paper (PDF)] [Presentation (PDF)]

• Silk, E. M., Schunn, C. D., Shoop, R., & Stein, M. K. (2011, March).The Robot Algebra Project. Poster presented at the eighth annual NSF ITEST Summit, Arlington, VA, USA. [Poster (PDF)]

• Silk, E. M. (2010, August 25). Can math help in LEGO robotics competitions? [4-part web log post]. Retrieved from [Part 1] [Part 2] [Part 3] [Part 4]

• Silk, E. M., Higashi, R., Shoop, R., & Schunn, C. D. (2010). Designing technology activities that teach mathematics. The Technology Teacher, 69 (4), 21-27. [Paper (PDF)]

• Silk, E. M., Schunn, C. D., & Shoop, R. (2009).Synchronized robot dancing: Motivating efficiency & meaning in problem-solving with robotics. Robot Magazine, 17 , 74-77. [Author Proof (PDF)]

• Silk, E. M., & Schunn, C. D. (2008, June).Using robotics to teach mathematics: Analysis of a curriculum designed and implemented. Paper presented at the annual meeting of the American Society for Engineering Education, Pittsburgh, PA, USA. [Paper (PDF)] [Presentation (PDF)]

• Silk, E. M., Schunn, C. D., Higashi, R., Shoop, R., Dietrich, A., & Reed, R. (2007).The use of robotics to teach mathematics. Robotics Educators Conference, Butler, PA, USA. [Presentation (PDF)]

Other Notable Research

Badge Research

• Antin & Churchill, Badges In Social Media: A Social Psychological Perspective – In this short paper Antin and Churchill describe badges from a social scientist’s perspective. [PDF]

National Studies around CS-STEM

• National Science Board (2010). Preparing the next generation of STEM innovators: Identifying and developing our nation’s human capital. Publication NSB-10-33 of the National Science Foundation.

• Gal-Ezer, J. & Stephenson, C. (2009). The Current State of Computer Science in U.S. High Schools: A Report from Two National Surveys. Journal for Computing Teachers, Spring 2009

• CSTA (Computer Science Teachers Association) (2009). CSTA National Secondary Computer Science Survey: Comparison of 2005, 2007, and 2009 Survey Results.

• “Enrollments and Degree Production at US CS Departments Drop further in 2006/2007”, CRA Bulletin, March 2008.

• “Fastest Growing Occupations”, Monthly Labor Review, November 2007.


Robot Algebra

“This project positions mathematics as a thinking tool.”
Dr. Chris Schunn, University of Pittsburgh, CoPI of 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. Algebraic thinking involves identifying patterns, relationships, and functions between one or more objects and being able to find the interrelationships between the variables that make up the objects; it is the beginning of symbolic reasoning.  Engineering design skills provide students with a systematized methodology for solving complex problems; it is rigorous creativity. The Robot Algebra project uses classroom-friendly technologies to develop students’ algebraic thinking and reasoning skills by placing them in technology-rich problem solving situations where they must find the mathematical rule or principle to unlock the solution to the problem and then apply that rule across multiple contexts.  The goal of the engineering design portion of the project is to teach students a research-based systematized method for solving engineering design problems. The project places mathematics and design engineering in contexts that students understand, encourages teamwork, integrates a systems ways of thinking, and most importantly makes salient, supports, and connects the math with the engineering design activity.

Robot Algebra Project

The Robot Algebra Project develops of a set of Design Based Learning Units (DBL) that use a combination of the motivational effects of robotics, music, dance, and student success, combined with foregrounded mathematics lessons, engineering design, and competition to promote algebra readiness.  The project is a partnership between Carnegie Mellon (CMU), the University of Pittsburgh’s Learning Research and Development Center (LRDC), and a consortium of industry, government, foundation and education partners committed to improve both the quality and quantity of students pursuing science, technology, engineering, and mathematics (STEM) careers.

Across the region and nation, many schools and community-based organizations are proposing to use robotics to address STEM competencies. Yet, our research has found that most teachers miss the key STEM “teaching moments” that a robotics project places into a real-world context.  Often, teachers working with the robotics will allow students to be haphazard in their design process, avoid mathematics when possible (e.g., using guess-and-check strategies), which leads to weak solutions and reduces student learning.  Building from decades of research on instruction and learning, our project team believes that:

• 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.

Initial Robotics Education Research

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?”

In year one, we evaluated the mathematic concepts taught in a middle school level robotics curriculum.  CMU and LRDC began by performing a content analysis on CMU’s “Introduction to Robotics Engineering, Volume 1” LEGO curriculum, which is currently being used in thousands of classrooms. In this analysis, researchers identified many types of mathematical topics that students would have an opportunity to learn, and investigated the extent to which those topics were aligned with national mathematics standards. They found that the robotics lessons aligned well at the category level, but not as well at the individual math topic level. Simultaneously, the group conducted a case study analysis of an implementation of the robotics curriculum in an eighth grade technology classroom to assess whether mathematics ideas were salient as students were engaged with the tasks. Indeed, when prompted by the teacher during whole-class discussion, students brought in a wide range of formal mathematics ideas. However, because of the multitude and diversity of those ideas (e.g., measurement, algebra, geometry, statistics), we were not able to develop significant gains in math understanding with so little exposure to any one mathematics concept.  Similar findings were uncovered during a second test in a ninth grade technology classroom.  Our initial research suggests that robotics provides a promising engineering context to teach STEM concepts and that we can use this organizer to teach meaningfully relevant algebraic mathematic concepts in ways that make sense to students but this will take a redesign of the curriculum.

After the end of the first year, the CMU/LRDC team decided that to improve the curriculum’s ability to teach math, that we would need to focus on a narrower set of mathematical principles. The mathematical focus of the Robot Algebra curriculum is to teach ratio and proportion; the ultimate goals of the curriculum are to develop algebraic reasoning skills, support the development of technological literacy, and to teach engineering design to students.  We chose ratio and proportion because research supports that these foundational mathematical concepts are not understood by students and these concepts are found in every math class that a student will study from middle school through college. We chose to teach engineering design to provide students with a systematized methodology to solve complex problems. We chose LEGO because of its ease of implementation into the conventional classroom as well as its ability to allow our project to scale. This project will focus, support, and align a set of robotic engineering activities with algebraic concepts that will effectively enable students’ mastery of algebra thinking skills.

Fractions, Ratios, and Proportions

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
• 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.

Lessons Learned with Teachers

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.

Strategy 1 (direct proportion)

360 degrees / 17.59cm = (x)degrees / 31cm =
17.59 * x = 360 * 31
x= 634 degrees

Strategy 2 (unit ratio)

31cm / (.0488cm/degree) =
31/.0488 = 635 degrees

Strategy 3 (unit ratio)

31cm * 20.408 degrees/cm =
31 * 20.408 = 632 degrees

Strategy 4 (scale factor strategy)

31 cm is the distance to travel
17.59 is the distance traveled per rotation
31 / 17.59 = scale factor

360 degrees * scale factor = new number of degrees;
360 degrees * 31 /17.59 = new number of degrees ;
360 degrees * 1.76  = 634 degrees

Strategy 5 (iterative testing – guess and check)

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.

Students arrive in class with an intuitive understanding of proportional reasoning. Imagine a less than confident math student sitting in a classroom being taught a strategy to solve the problem that was incompatible with the student’s cognitive model.  If the intuitive understanding that the student has is incompatible with the way that the teacher presents the solution to the problem, and if the teacher insists that their way is the best or only way to solve the problem, then the student may experience uncomfortable levels of cognitive dissonance which can lead to low self esteem and a less math confident student. It is important that teachers recognize and position mathematics as a thinking tool and that the tool can be used many different ways to the same problem similar to the way that a person driving car can go from point “A” to point “B” using many different routes, but still getting to the same destination.

Abstraction Bridges

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:

Robot Problem: Faster Robot

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Dontay has the choice of placing two different diameter wheels on his robot; 5.6 cm or 8.15 cm. Which robot wheel will go faster? Explain your answer using math and words.

Generalized Problem: Better Deal

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Two girls got into the theater on State Street for $3. Five boys got into the theater on Main Street for $6. Which group, the girls or the boys, got the better deal? Explain your answer using math and words.

So for the above robot problem example, in the physics problem you can ask the exact same question, and then follow up with a question on how much more torque is needed. This teaches conservation laws and a deeper lesson that you don’t get something for free.  In fact, the latter, the deeper life lessons, is the final thing I like to get out of the robotics courses. So for me, robots:

1) captivate the students
2) provide a vehicle to learn math and science
3) can teach deeper lessons, even if they are design ones

Books on a Shelf

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: If 6 books are 2/3 of all the books on Robert’s shelf, figure out how many books are 5/9 of the books on his shelf. Explain your answer using math and words.


Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Suppose you are making treats to hand out on Halloween. Each treat is a small bag that contains that contains 5 Jolly Ranchers and 13 Jaw Breakers.  If you have 50 Jolly Ranchers and 125 Jaw Breakers, how many complete small bags can you make?research_halloween

Better Deal

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Who gets more pizza, a girl or a boy? Explain your answer using math and words.research_betterDeal

How Far

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Car A and Car B are leaving the same place and going in the same direction. If it takes Car A 6 hours to get to the destination driving 20 miles per hour, how long will it take Car B to get to the same destination driving 50 miles per hour? Explain your answer using math and words.

Proportional Equation Example

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Write an equation for the following statement: There are six times as many students at this school as there are teachers at this school.  Use “S” for the number of students and “T” for the number of teachers. Explain your answer using math and words.

Functional Understanding

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Angela makes and sell special-occasion greeting cards.  The table below shows the relationship between the number of cards sold and her profit.  Based on the data in the table, which of the following equations shows how the number of cards sold and the profit are related.  Explain your answer using math and words.


1. p = 2n
2. p = 0.5n
3. p =n – 2
4. p = 6 -n
5. p = n + 1

Scale Factor Problem Example

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: Roxanne plans to enlarge her photograph, which is 4 inches by 6 inches. Which of the following enlargements maintains the same proportions as the original photograph? Explain your answer using math and words.

5 inches by 7 inches | 5 inches by 7 ½ inches

Proportional Reasoning Example

Directions: Show all work, describe how you got the answer using mathematics and words, and circle your final answer.

Problem: A giraffe moves forward 10 meters every step that she takes.  A lion moves forward 2 meters every step that she takes.  If the giraffe takes 80 steps, how many steps must the lion take to cover the same distance? Explain your answer using math and words.

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.

 Abstraction Bridge Examples

Warm Up 1
Super Bowl Commercials

Warm Up 2
Super Bowl Commercials

Warm Up 3
Robot Sizing

Warm Up 4
Building Robots

Warm Up 5
Halloween Candy

Warm Up 6
Wheel Dispute

Warm Up 7
Splitting Degrees I

Warm Up 8
Splitting Degrees II

Warm Up 9
Tony Hawk’s Landing

Warm Up 10
Red Team vs. Blue Team

Warm Up 11
Wheel Diameter

Warm Up 12
Big Wheels

Warm Up 13
Basketball Court

Warm Up 14
Sentry Calculation

Warm Up 15
St. Patrick’s Day

Warm Up 16
Calvin’s Robot I

Warm Up 17
Calvin’s Robot II

Warm Up 18
Calculating Circumference

Warm Up 19
Board Game

Warm Up 20
Swing Turns

Warm Up 21
Circumference Equations

Warm Up 22
Laser Range Finder

Warm Up 23
Faster Robot

Warm Up 24
Better Deal

Warm Up 25
Introduction to Ratios

Warm Up 26
Ratios to Robots I

Warm Up 27
Ratios to Robots II

Warm Up 28
Ratio to Distance

Warm Up 29

Warm Up 30
Synchronizing Distance

Warm Up 31

Warm Up 32

Warm Up 33
Best Buy

Warm Up 34
Books on a Shelf

Warm Up 35
Better Deal

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.

For the DBL to motivate students and teach core concepts effectively and efficiently across a variety of settings, the units must be developed in very particular ways. Just giving students a design challenge produces chaos. Telling students exactly what to do at every step produces boredom and little learning. A well designed DBL begins with an engineering design problem with clearly defined rubrics that define what a successful solution looks like, coupled with seemingly unlimited student choice about how they might solve the problem. The engineering design process systematizes the thinking and the learning issues that must be supported. Thus, students practice a real design process but also receive carefully designed lessons that foreground the STEM concepts the teacher has pre-determined important to teach. The figure below shows the typical macrostructure of a DBL unit. The DBL teaches systematic design process while motivating and supporting STEM learning.


The DBL provides a working, tested framework upon which Robot Algebra design problems are built. They provide a natural mode for teaching the topics which are inherent to robotics and technology and have proven success in the classroom over several years of research and refinement.

The fundamental elements of the engineering design process include:

• 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.


Robot Dance

Robot Algebra, Robot Dance (Example Design Based Learning Unit)

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 of engineering design.


The Robot Dance project blends robotics, choreographed dancing, music, ratios and proportions, and a highly-structured open-ended problem designed to teach proportional reasoning and engineering design. The fundamental premise in the Robot Dance DBL is that if students are placed in an engaging design problem where they have choices and are given properly scaffolded instruction, they will learn. The Robot Dance DBL requires students to think deeply and struggle to solve mathematical and technical problems across multiple contexts.  Their struggle will lead them to discover a set of rules and principles that will prepare them to apply algebraic reasoning, technical problem solving, and engineering design in the future.

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 in to 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 others 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 different set of characteristics i.e. different diameter wheels, different wheel base, caster verses four wheel, 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.

Video Examples

These examples are designed to stimulate creativity and generate student enthusiasm for the project.  A number of the videos, such as the excavator ballet, provide “steps” which may be directly imitated. Others, such as the treadmill dance, while not perfectly translatable to LEGO robots, may inspire and motivate through its innovative and fun use of synchronous dance.

NXT Robots Dance
Excavator Ballet
Treadmill Dance
Dancing Shoe
Vacuum Cleaners Dance
Three Robots
Keepon Dance
Four Robots
Tractor Square Dance

ROBOTC Software Selection

The team chose ROBOTC software because it is by far the best software available to teach mathematics using LEGO MindStorm robots.  Our team uses functions in the program to make it easier for beginning programmer.  The program uses an “include” file that enables student programmers to use programming language like moveForward, moveBackward , turnPointRight, and turnPointLeft to program their robots to move point to point.  In program example 1 see that moveForward used parameters to control the number of degrees of rotation as well as the powerlevel that the robot travels. This enables the student programmer to control how far the robot travels as well as the robot’s speed. Note in program example 2 that the variable degree has be changed to 360 in the moveForward command line and is 360/(2*.45) in the moveBackward command line.  ROBOTC allows the programmer to write their numbers in whole numbers or algebraic expressions.



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 fore grounded; 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.

For information about the Robot Algebra project please contact:

Robin Shoop at (412) 681-7160 or  email_rshoop

Robots in Motion

The Robots In Motion (RIM) research project stems from The Robot Algebra Project. The Robot Algebra project is a collaborative project the University of Pittsburgh’s Learning Research and Development Center (LRDC) and Carnegie Mellon’s Robotics Academy (CMU) to develop instructional materials designed to significantly improve robotic education’s ability to use robotic project based learning activities to increase students’ mathematical competency. The goals of this project are to:


• Test and iteratively improve project based instructional units which, when implemented effectively in educational settings, significantly increase students’ algebraic reasoning abilities

• Design the units & support materials in ways that are educative to both the educator and the student

• Evaluate the extent to which the unit & support materials have met goals one and two

• Increase the field’s understanding of how policy and organizational features shape instruction and learning outcomes.

Project Description

Robotics education has the ability to excite and engage students in science, technology, engineering, and mathematics (STEM). Robots are intrinsically motivating to students and introduce a rich range of STEM concepts. Mathematics is a fundamental component of STEM careers and that is our focus. Our team has a multiyear collaboration studying robotics education and has observed how a single 30-minute robotics activity designed for middle-schoolers can in rapid-fire touch upon measurement, geometry, algebra, and statistics concepts. In such an activity, there is no time to focus instruction on any one mathematical concept, and we were not surprised that students made no mathematical progress over a full semester of engagement with such activities even though the instructor attempted to focus student attention on the mathematics. Our approach is to focus on one foundational mathematical construct, proportional reasoning, for an entire robotics unit, and indeed build it up over multiple robotics units. Proportional reasoning is a foundational mathematics concept that relates to a wide range of situations in everyday life and in the workplace, such as those that involve unit rates, mixtures, or scaling. Proportional reasoning is also central in understanding how a robot’s movements can be controlled, as the relationships between the physical construction of the robot, the values used to program the robot, and how the robot actually moves are often proportional in nature. Moreover, students need to understand rates, ratios, and proportions to develop algebraic ways of thinking.

Testing Initiatives

During the summer of 2012 a set of teacher support materials were developed for teachers using the curriculum. The development team believes that teachers using the materials should participate in certified professional development programs to learn how to use the teacher support materials. The Robotics Academy includes training on RIM in their LEGO NXT training programs. During the fall of 2012 we will test the materials with 10 regional middle schools. This testing will be used to inform the next round of curriculum improvements.

Project Development and Resources

This project developed three instructional units designed to foreground measurement, direct proportionality, and indirect proportionality through robotics activities.

research_rim• Unit 1 B-U-G – In this unit, students learn about the iKnowMATION Corporation, a company that makes robots and needs to develop a process to ensure that their robots drive straight, turn accurately, and travel the correct speed. Students are required to develop testing methodologies that insure that a new robot travels the correct distance, turns the correct angle, and travels the correct speed. In this activity measurement is foregrounded.

• Unit 2 Asteroid 2012 JN4 – In this unit, students are tasked to program a robot on an asteroid that needs to explore specific areas of the asteroid. The robot has a limited power supply and therefor students need to program the robot accurately on their first attempt. The lessons focus on direct proportional relationships involving distance, turning, and speed. While solving the challenge students will explore the difference between using a unit rate or scaling strategy to solve the challenge.

• Unit 3 Bots-in-Sync – In this unit, students are asked to program several robots with different physical characteristics, different size wheels and different robot sizes, to dance in synchrony. Students will use lessons they learned while solving the B-U-G and Asteroid units to solve this challenge. Students will quickly find that they need to solve both direct and indirect proportional relationships to make the robots dance synchronously.

Abstraction Bridges

Through our Robots In Motion units, students are exposed to core mathematics ideas and problem solving strategies in ways that build upon and extend their mathematical thinking. However, we believe addition intervention is required to develop mathematical fluency because of the following issues with the problem-based units:

• Insufficient time to develop fluency with these mathematical concepts

• Lacking direct connections with what they are learning in their mathematics classrooms.

• Lack of easy assessment opportunities for the facilitators to evaluate individual student progress

• Lack of connections with high stakes testing (of importance to some informal organizations)

We believe that robotics units can build up a core understanding, but additional work is required to generalize the learning. In particular, we believe additional assessment/practice opportunities are required. These paper-based word problems are called Abstraction Bridges—they act as a bridge from contextual mathematics in robotics problem solving to generalized mathematical problem solving abilities. They have the following form:

• Activities that can act as warm-ups as students are shuffling into the after-school setting, or as simple challenge problems to work on at home between sessions. Only one would be assigned at a given time (i.e., not worksheets filled with problems), but they would be assigned every day for regular practice.

• Some of these paper-based activities will involve robotics contexts, and many will make connections to other problem situations.

• Although not as complex as the problems to be solved in our robotics units, neither will these units be rote, mindless kind of mathematics worksheets. More formally within the mathematics education framework, these problems will involve Procedures with Connections, a kind of problem generally associated with better learning outcomes (Stein, et al., 2007).

Abstraction Bridge Example Problems

Below are sample problems, drawn from existing mathematics education resources.

Abstraction Bridges Problem 1:

About how big is 4/5 of this rectangle? Show your answer by shading in the rectangle.


What other fractions are near 4/5 in size? Explain your answers.

Abstraction Bridge Problem 2:

You are doing a scientific study of graffiti in your local park. On the first day of spring, there is no graffiti. On the second day, there are two drawings. On the third day, there are four drawings. You couldn’t check on the fourth day, but on the fifth day, there are eight drawings.

If this keeps up, how many graffiti drawings will there be on day 10? On what day will there be 40 graffiti drawings? How do you know?

A future goal of this project is to develop a larger database of ratio and proportion problems and make them available to educators. The problems will range in contexts, mathematical concept, and difficult. These problems will be distributed through a teacher-useable/managed database. More specifically, we will:

• Build a website that allows educators to add, sort, and rate abstraction bridge word problems for educators to use with students

• Develop a structure in the database that helps educators to quickly identify different types of problems in the database, i.e., ratio word problems, graphs, tables, proportional algebra problems, fractional relationship problems also sort the problems based on themes (robots, sports, shopping)

• Rate the problems from novice, beginner, intermediate, advanced

• Continually upgrade of the database based on educator usage and research (similar to the way Amazon or Netflix provides suggestions based on prior usage and rating patterns)

Building a Theory of Badges for Computer Science Education

Project Description

There is a pressing need for improvement and expansion of Computer Science education in the US. 21st Century. Industry will demand computational literacy from all workers, with an increasing shift of high-wage positions toward computational occupations. Computer Science Education needs a means to accelerate its adoption without loss of focus on the key Computer Science Principles identified by the College Board and NSF. Further, Computer Science Education needs to address issues of gender and ethnicity diversity, leveraging new methods for motivating broad participation in computer science. We therefore build on the current success of competitive robotics for attracting a broader set of learners, and seek to deepen their understanding and interest in CS.

Badges – simple, visually prominent, validated indicators of performance – have recently attracted a great deal of attention as a tool to motivate students and mark significant learning accomplishments. The badge’s dual role as both motivator and assessment marker raises interesting questions about the ability of existing theories of Motivation and theories of Assessment to fully predict, explain, and guide the design of badges for student motivation AND assessment. Carnegie Mellon University and the University of Pittsburgh’s joint project will test and refine a Theory of Badges applied to Computer Science Education, in which we divide badges into one of three categories, each reflecting a specific set of motivational and performance-shaping assessment mechanics which current Motivation and Assessment research predict will affect student performance.

We propose to test and refine this theory by investigating and experimentally manipulating the use of badges within an ongoing Computer Science education development project, the Computer Science Student Network (CS2N). CS2N contains a badge system that maps well to the three-category system proposed by our theory. We will monitor and adapt the form and content of CS2N assessments and badge representations in CS content modules to try to achieve the best possible outcomes for student participants as predicted by the current iteration of our badge theory. These modules map to different Learning Objectives identified by The College Board’s Computer Science Principles.

Intellectual Merit

We propose to develop a Theory of Badges for Computer Science Education, and in so doing, answer the following Design, Research, and Evaluation questions:

• Design: Which particular badges: Are perceived as desirable, easily understood by students, and are accurate indicators of performance?
• Research: Does our Badge Theory predict associations of particular Badges with particular motivational states?
• Research: Does our Badge Theory predict Pathways of motivational variables to larger outcomes (skills and career goals)?
• Evaluation: Does the overall badge ecosystem increase: learner persistence, CS content learning, and CS career interest?

Broader Impacts

Building on a strong partnership with very large VEX and FTC robotics competitions, the Computer Science Student Network will serve thousands of student and teacher users over the course of this study; improvements to its badge system design will directly benefit them. It can also be leveraged as a scaling platform to reach many more students in the future, and deliver additional badged CS content. Improvements to content module assessments will help to align them with the CS Principles. The Theory of Badges will help to guide future development of both CS-related badges, and of badge systems in general. CS2N can be made available as a research platform for future research in CS Education. Research results on both badges and CS learning will be published. Special attention will be given to the effects of badges on underrepresented learner populations. Some content modules feature technologies believed to particularly benefit low-resource learning environments.

 Changing Culture in Robotics Classrooms (CCRC)

Dear Robotics Teacher,

img_ccrc1Thank you for showing interest in our Changing Culture in Robotics Classrooms (CCRC) project. This is a three year project supported by the National Science Foundation that begins September 2015 and runs through June 2018. The CCRC project will use a combination of robotics competition activities, a modified autonomous only competition that we will design each year, and curriculum and training from the Carnegie Mellon Robotics Academy designed to help teachers to teach programming in their robotics classrooms.

Changing Culture in Robotics Classroom’s Project Goal

is to develop and test curricular materials that extend robotic curricula’s ability to teach computational thinking (see table 1). The Carnegie Mellon Robotics Academy will post new materials online as we have done in the past (ROBOTC Graphical for VEX IQ, ROBOTC for VEX Cortex, ROBOTC Graphical for MINDSTORMS, ROBOTC for LEGO MINDSTORMS, and Introduction to Programming LEGO MINDSTORMS EV3), enabling all teachers to take advantage of the lessons that we develop. Our goal is to develop robotics curriculum that integrates the emerging Computer Science Principles concepts into your robotics course.

Students and Teachers will earn a Robotics Programming Certification. In the CCRC project, our research is testing the ability of badges and certifications to motivate students to learn computer science concepts in robotics classrooms. Students and teachers that complete the course materials and pass the checkpoint tests will have the opportunity to earn a Carnegie Mellon Robotics Academy Robotics Programming Certification. Students that are led by “Certified Teachers” will be able to earn a higher-level certification. Certified Teachers will have the opportunity to track their students’ progress using our Learning Management System.

In the 2014-2015 school year, our focus is on testing and improving entry-level curriculum for new programmers. The programming environment that we will begin testing with is based around the new ROBOTC Graphical Interface. Students and teachers can join the project at any time during the school year by signing up at this link:

Table 1. Changing Culture of Robotics Classroom’s projected year-long class
Fall Winter These materials will not be ready for testing until Spring 2016
Activity Robotics Competition (this could be an official competition or a teacher led in-class competition) Modified Autonomous Competition (MAC) CS Principles Robotics Unit (CSPRU) – This Unit is scheduled to be developed during the spring and summer of 2015. It will be tested locally in the fall of 2015 and be ready for national implementation in Spring 2016.
What Students Do Students compete in an existing robotics competition such as FLL, FTC, VEX, or VEX IQ Students compete in a MAC version of an existing competition designed to stress sophisticated autonomous operation Students engage in design-based learning units in which they design algorithmic solutions to robotics problems
Primary Content Mechanics and Basic Programming, ideation and creativity Autonomous Programming with an emphasis on decision-making logic High-level problem solving, abstraction, and algorithmic design
Relevant CS Principles Focus Areas Creativity, Programming (Basic) Creativity, Abstractions, Programming Creativity, Abstractions, Algorithms
RVW Role Direct simulation of robotics challenge to support teams in competitions Primary activity platform: modified challenges are played through RVWs Primary activity platform: problem is presented in virtual space, and solutions must function in RVW environment
Curriculum Supports Use existing Robotics Academy ROBOTC for MINDSTORMS, ROBOTC for VEX, and VEX IQ Curriculum Advanced lessons will be developed this fall and tested as they are being developed New problem scenarios that include appropriate instructional supports

The 2014-15 Modified Autonomous Competition (MAC)

This year’s Modified Autonomous Competition is the VEX IQ Beltway competition which is based off of the VEX IQ Highrise challenge. There are two modes: a 5 Minute mode, and a 2 Minute mode.

• Download VEX IQ Highrise (which includes Beltway)
• View the VEX IQ Beltway User guide PDF

Robot Virtual Worlds System Requirements

Internet Access
A PC or MAC* capable of running the ROBOTC & Robot Virtual World software

PC Compatible OS: Windows XP, VISTA, Windows 7, or Windows 8
Processor: Intel Core 2 Duo processor family or better, AMD Athlon X2 processor family or better
Memory: 2 GB RAM
Graphics: NVIDIA® GeForce® 8800GTS or better, ATI Radeon™ HD 3850 or better
DirectX: DirectX® 9.0c and DirectX® 10
Hard Drive: 500 MB free hard drive space
Sound: Standard audio device

*ROBOTC will work on a Apple/Mac computer with most Windows Virtualization/Emulation software packages available today including Apple’s Boot Camp, Parallels Desktop, and VMWare Fusion. Once the software is installed, the ROBOTC installation and usage is exactly the same as it would be on a normal Windows PC. Please see your software’s documentation regarding connecting your USB devices to your virtual environment.

img_ccrc2For more information on various Virtualization software:

• Bootcamp
• Parallels Desktop
• VMWare Fusion

If you are still unsure, both the ROBOTC and Robot Virtual Worlds software come with free trial periods for you to evaluate. If you have additional questions please email me.

Robin Shoop
Director, Carnegie Mellon Robotics Academy

Robin Shoop, one of the Principle Investigators on this project owns part of Robomatter Inc. which owns ROBOTC and Robot Virtual Worlds.

© 2018 Carnegie Mellon Robotics Academy. All rights reserved.