Math in Scoliosis Patients
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we use mathematical modeling and statistical analysis to understand, predict, and optimize treatment strategies for scoliosis patients?Essential Questions
Supporting questions that break down major concepts.- How can mathematical models be used to represent the curvature of the spine in scoliosis patients?
- What statistical methods can be applied to analyze the progression of scoliosis?
- In what ways can mathematical concepts be utilized to optimize the design of braces or surgical interventions for scoliosis patients?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to create mathematical models to represent spinal curvature.
- Students will be able to apply statistical methods to analyze scoliosis progression.
- Students will be able to use mathematical concepts to optimize scoliosis treatment strategies.
- Students will understand the real-world applications of math and science in healthcare.
Entry Events
Events that will be used to introduce the project to studentsThe Crooked Man Challenge
Students are presented with anonymized 3D scans of spines with varying degrees of scoliosis. The challenge: use mathematical tools (geometry, trigonometry, statistics) to quantify the curvature, predict potential health risks, and propose non-invasive treatment options. This entry event connects math to real human health and sparks immediate interest in solving a tangible problem.Spinal Architect
Students receive a brief from a fictional medical device company tasked with designing a new brace for scoliosis patients. They must use mathematical modeling to optimize the brace's shape, pressure distribution, and corrective force, considering patient comfort and mobility. This combines creativity with mathematical precision and exposes students to engineering design principles.Scoliosis X-Games
Students participate in a simulated competition where they use mathematical algorithms to guide the placement of spinal implants during a virtual scoliosis surgery. The goal is to achieve optimal spinal alignment with minimal invasiveness, judged by a panel of simulated medical experts. This gamified experience makes complex surgical decisions accessible and emphasizes the critical role of math in precision medicine.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Curve Capture: Spinal Geometry
Students will begin by exploring the geometry of spinal curves, learning to measure and model the curvature of scoliotic spines using angles and geometric shapes. They will use these models to quantify the severity of scoliosis from 3D scans.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA geometric model of a scoliotic spine with quantified curvature measurements.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to create mathematical models to represent spinal curvature. Essential Question: How can mathematical models be used to represent the curvature of the spine in scoliosis patients?Progression Prediction: Statistical Analysis
Students will delve into statistical methods to analyze how scoliosis progresses over time. Using patient data, they will learn to identify trends, calculate rates of progression, and predict future spinal curvature based on various factors.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA statistical report analyzing scoliosis progression, including trend analysis and future predictions.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to apply statistical methods to analyze scoliosis progression. Essential Question: What statistical methods can be applied to analyze the progression of scoliosis?Treatment Optimization: Brace Design
Students will focus on optimizing scoliosis treatment strategies by mathematically modeling the design of spinal braces. They will explore how brace shape, pressure distribution, and corrective force impact treatment effectiveness, considering patient comfort and mobility.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed mathematical model of an optimized scoliosis brace design, including considerations for corrective force and patient comfort.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to use mathematical concepts to optimize scoliosis treatment strategies. Essential Question: In what ways can mathematical concepts be utilized to optimize the design of braces or surgical interventions for scoliosis patients?Math in Medicine: Real-World Applications
Students will investigate the broader applications of math and science in healthcare, focusing on how mathematical models and statistical analyses are used to improve patient outcomes and advance medical knowledge.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA presentation or report highlighting the real-world applications of math and science in healthcare, with a focus on improved patient outcomes.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Students will understand the real-world applications of math and science in healthcare.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioScoliosis Portfolio Rubric: Mathematical Applications in Healthcare
Mathematical Modeling
Evaluates the student's ability to create and apply mathematical models to represent and analyze spinal curvature in scoliosis patients.Model Accuracy
Assesses the accuracy and precision of the mathematical model in representing the spinal curve.
Exemplary
4 PointsThe model accurately represents the spinal curvature with precise measurements and demonstrates a sophisticated understanding of geometric principles. All calculations are correct, and the model is highly detailed and refined. The student can explain the model's assumptions and limitations clearly. The model could be used in a real-world medical context. Reason: Demonstrates sophisticated understanding and accuracy in modeling.
Proficient
3 PointsThe model accurately represents the spinal curvature with clear measurements and demonstrates a good understanding of geometric principles. Most calculations are correct, and the model is detailed. The student can explain the model's basic assumptions. Reason: Demonstrates thorough understanding and accurate representation.
Developing
2 PointsThe model partially represents the spinal curvature with some inaccuracies in measurements and demonstrates a basic understanding of geometric principles. Some calculations are incorrect, and the model lacks detail. The student struggles to explain the model's assumptions. Reason: Shows emerging understanding but needs improvement in accuracy and detail.
Beginning
1 PointsThe model does not accurately represent the spinal curvature, and measurements are largely incorrect. The student demonstrates a limited understanding of geometric principles. Calculations are mostly incorrect, and the model is incomplete. The student cannot explain the model's assumptions. Reason: Shows initial understanding but requires significant improvement in accuracy and comprehension.
Application of Geometric Principles
Evaluates the appropriate use of geometric principles (e.g., Cobb angle measurement) in quantifying spinal curvature.
Exemplary
4 PointsApplies geometric principles flawlessly and innovatively to quantify spinal curvature, demonstrating a deep understanding of their relevance and limitations in the context of scoliosis. Provides insightful justifications for methodological choices. Reason: Demonstrates sophisticated application of concepts and insightful analysis.
Proficient
3 PointsApplies geometric principles accurately to quantify spinal curvature, demonstrating a strong understanding of their relevance. Provides clear justifications for methodological choices. Reason: Demonstrates thorough understanding and appropriate application.
Developing
2 PointsApplies geometric principles with some errors or inconsistencies in quantifying spinal curvature, demonstrating a basic understanding of their relevance. Justifications for methodological choices are superficial. Reason: Shows emerging understanding but needs more consistent application.
Beginning
1 PointsStruggles to apply geometric principles to quantify spinal curvature, demonstrating a limited understanding of their relevance. Provides inadequate or incorrect justifications for methodological choices. Reason: Shows initial understanding but requires significant support.
Statistical Analysis
Evaluates the student's ability to apply statistical methods to analyze scoliosis progression and make predictions.Data Analysis and Interpretation
Assesses the student's ability to analyze patient data, identify trends, and interpret statistical results related to scoliosis progression.
Exemplary
4 PointsAnalyzes patient data comprehensively, identifies subtle trends with insightful interpretations, and explains the statistical results with exceptional clarity and depth. Demonstrates a sophisticated understanding of statistical significance and potential biases. Reason: Demonstrates sophisticated analysis and insightful interpretation.
Proficient
3 PointsAnalyzes patient data effectively, identifies clear trends, and interprets statistical results accurately. Explains the statistical results clearly and demonstrates a good understanding of statistical significance. Reason: Demonstrates thorough analysis and accurate interpretation.
Developing
2 PointsAnalyzes patient data partially, identifies some trends, and interprets statistical results with some inaccuracies. Explains the statistical results with limited clarity and demonstrates a basic understanding of statistical significance. Reason: Shows emerging analysis but needs more accurate interpretation.
Beginning
1 PointsStruggles to analyze patient data, fails to identify meaningful trends, and misinterprets statistical results. Explains the statistical results poorly and demonstrates a limited understanding of statistical significance. Reason: Shows initial analysis but requires significant support.
Prediction Accuracy
Evaluates the accuracy and reliability of predictions made using statistical models.
Exemplary
4 PointsPredictions are highly accurate and reliable, with clear justifications based on robust statistical models and a deep understanding of underlying factors. Demonstrates a sophisticated understanding of predictive modeling limitations. Reason: Demonstrates sophisticated modeling and accurate prediction.
Proficient
3 PointsPredictions are accurate and reliable, with clear justifications based on statistical models and a good understanding of underlying factors. Reason: Demonstrates thorough modeling and accurate prediction.
Developing
2 PointsPredictions are somewhat accurate but may lack reliability, with limited justifications based on statistical models. Shows a basic understanding of underlying factors. Reason: Shows emerging modeling but needs more reliable predictions.
Beginning
1 PointsPredictions are inaccurate and unreliable, lacking clear justifications and demonstrating a limited understanding of underlying factors. Reason: Shows initial modeling but requires significant improvement in prediction accuracy.
Treatment Optimization
Evaluates the student's ability to apply mathematical concepts to optimize scoliosis treatment strategies, such as brace design.Design Innovation
Assesses the creativity and innovation in the proposed treatment optimization strategies.
Exemplary
4 PointsThe proposed treatment optimization strategies are highly creative, innovative, and well-justified with mathematical concepts. Demonstrates a deep understanding of the trade-offs between corrective force, patient comfort, and mobility. Addresses previously unconsidered aspects of brace design. Reason: Demonstrates exceptional creativity and innovative problem-solving.
Proficient
3 PointsThe proposed treatment optimization strategies are creative, innovative, and justified with mathematical concepts. Demonstrates a good understanding of the trade-offs between corrective force, patient comfort, and mobility. Reason: Demonstrates thorough creativity and justified strategies.
Developing
2 PointsThe proposed treatment optimization strategies show some creativity but may lack innovation or strong mathematical justification. Demonstrates a basic understanding of the trade-offs between corrective force, patient comfort, and mobility. Reason: Shows emerging creativity but needs stronger mathematical justification.
Beginning
1 PointsThe proposed treatment optimization strategies lack creativity, innovation, and mathematical justification. Demonstrates a limited understanding of the trade-offs between corrective force, patient comfort, and mobility. Reason: Shows initial creativity but requires significant development and justification.
Mathematical Justification
Evaluates the strength and clarity of the mathematical justifications provided for the treatment optimization strategies.
Exemplary
4 PointsProvides exceptionally strong and clear mathematical justifications for the treatment optimization strategies, demonstrating a sophisticated understanding of the underlying principles and their impact on treatment effectiveness. Presents a comprehensive analysis of the design's impact on patient outcomes. Reason: Demonstrates sophisticated understanding and exceptional justification.
Proficient
3 PointsProvides strong and clear mathematical justifications for the treatment optimization strategies, demonstrating a good understanding of the underlying principles and their impact on treatment effectiveness. Reason: Demonstrates thorough understanding and clear justification.
Developing
2 PointsProvides some mathematical justifications for the treatment optimization strategies, but they may lack clarity or strength. Demonstrates a basic understanding of the underlying principles and their impact on treatment effectiveness. Reason: Shows emerging understanding but needs more clear and strong justification.
Beginning
1 PointsProvides weak or unclear mathematical justifications for the treatment optimization strategies, demonstrating a limited understanding of the underlying principles and their impact on treatment effectiveness. Reason: Shows initial understanding but requires significant improvement in justification.
Real-World Applications
Evaluates the student's understanding of the real-world applications of math and science in healthcare and their ability to communicate these applications effectively.Application Relevance
Assesses the relevance and significance of the real-world applications presented.
Exemplary
4 PointsPresents highly relevant and significant real-world applications of math and science in healthcare, demonstrating a sophisticated understanding of their impact on patient outcomes and medical advancements. Connects applications to personal reflections on the role of mathematics and science in healthcare. Reason: Demonstrates sophisticated understanding and exceptional relevance.
Proficient
3 PointsPresents relevant and significant real-world applications of math and science in healthcare, demonstrating a good understanding of their impact on patient outcomes and medical advancements. Reason: Demonstrates thorough understanding and significant relevance.
Developing
2 PointsPresents some real-world applications of math and science in healthcare, but their relevance or significance may be limited. Demonstrates a basic understanding of their impact on patient outcomes and medical advancements. Reason: Shows emerging understanding but needs more relevant applications.
Beginning
1 PointsPresents irrelevant or insignificant real-world applications of math and science in healthcare, demonstrating a limited understanding of their impact on patient outcomes and medical advancements. Reason: Shows initial understanding but requires significant improvement in relevance.
Communication Effectiveness
Evaluates the clarity, coherence, and persuasiveness of the presentation or report on real-world applications.
Exemplary
4 PointsThe presentation or report is exceptionally clear, coherent, and persuasive, effectively communicating the real-world applications of math and science in healthcare with compelling evidence and engaging delivery. Includes a compelling call to action for further exploration or innovation. Reason: Demonstrates sophisticated communication skills and exceptional clarity.
Proficient
3 PointsThe presentation or report is clear, coherent, and persuasive, effectively communicating the real-world applications of math and science in healthcare with clear evidence. Reason: Demonstrates thorough communication skills and clarity.
Developing
2 PointsThe presentation or report is somewhat clear and coherent but may lack persuasiveness or supporting evidence. Communication of real-world applications is basic. Reason: Shows emerging communication skills but needs more clarity and evidence.
Beginning
1 PointsThe presentation or report is unclear, incoherent, and unpersuasive, failing to effectively communicate the real-world applications of math and science in healthcare. Lacks supporting evidence. Reason: Shows initial communication skills but requires significant improvement in clarity and persuasiveness.