XQ Competencies

Computational Thinking (FL.MST.1)

This competency focuses on using mathematical tools and computational thinking to solve problems strategically. Learners:

• Represent quantities in multiple ways (e.g., different expressions or visual representations)

• Choose and adapt appropriate mathematical tools (algorithms, formulas, concepts)

• Identify patterns, create algorithms (through prose, flowcharts, code, or oral explanation), and check results using different methods

• Leverage equivalence among expressions, describe and adapt strategies, and recontextualize algorithms for varied situations, aiming for efficiency and clear communication of solutions.

RoboTrig:

Students use mathematical and computational tools strategically to design precise robot motions.

RoboTrig Alignment (Sharpened):

• Multiple Representations: Students express the same quantity as a geometric configuration, a trigonometric relationship, a numerical calculation, and executable code, moving flexibly among representations to understand and solve the problem.

• Selecting Mathematical Tools: To reach a target point, students choose appropriate tools (e.g., trigonometric ratios, the Law of Cosines) to solve for joint angles in the robotic arm.

• Pattern Recognition & Algorithm Design: Students identify regularities in inverse kinematics solutions (e.g., consistent “elbow-up” vs. “elbow-down” configurations) and translate their mathematical reasoning into step-by-step motion algorithms.

• Checking & Refining Solutions: When a robot’s behavior does not match predictions, students debug by recalculating angles, inspecting logic, and testing alternate inputs. They refine methods for greater efficiency, accuracy, and reliability.

Mathematical Modeling (FL.MST.2)

Mathematical modeling emphasizes mathematizing real-world situations to build and manipulate mathematical models for understanding and prediction. Students:

• Identify quantities and variables in a scenario, describe model assumptions, test if models make sense, and compare outcomes with real-world data

• Clearly state limitations of models, select appropriate units, and communicate how a model could be improved

• Create, refine, and justify models, clearly noting assumptions, variables, and the relationships among them, and apply models to explain or support predictions for specific audiences or stakeholders.

RoboTrig:

Students mathematize a real situation to predict, test, and refine robot motion.

RoboTrig Alignment (Sharpened):

• Identify Quantities & Assumptions: Students define relevant variables (coordinates, arm lengths, joint limits) and construct a coordinate-based model of the task scenario.

• Compare Model Predictions with Reality: Students evaluate the accuracy of their model by comparing calculated positions to the robot’s actual movements, using discrepancies to drive revisions.

• State Limitations: Students identify physical constraints, such as self-collision, reach limits, or calibration error, that restrict the validity of their mathematical model.

• Refine & Justify Models: Students adjust their models to better fit observed outcomes and justify improvements by demonstrating increased consistency between predicted and actual robot behavior.

Problem Solving (OT.PS.2)

Problem Solving is defined as generating and implementing creative solutions for non-routine or unfamiliar problems. Problem Solvers:

• Develop solutions by redefining problems, applying diverse tools and processes, and synthesizing multiple strategies

• Innovate by analyzing regularity and repeated processes, checking results with various methods, and justifying solutions with evidence

• Present clear algorithms and adapt solution processes for analogous challenges, promoting deep understanding and effective application of their problem-solving approaches.

RoboTrig:

Students generate creative solutions to non-routine, human-centered robotic challenges.

Develop Solutions for Audiences: Students design robot actions to help a specific person, requiring them to balance mathematical feasibility with user needs.

Redefine Problems (The "Elbow" Problem): When simple point-to-point motion fails (e.g., elbow collision), students reconceptualize the problem—shifting to path planning and managing the full arm’s swept volume.

Innovate and Check Results (Iterative Path Planning): Students build solutions using waypoints, run motion trials, analyze outcomes, and iterate based on evidence.

Justify with Evidence: Students demonstrate that their final motion algorithms meet human-centered success criteria and explain how their refinements improved performance.