Math in Medicine: A PBL Course Outline
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can mathematical tools and models be utilized to solve real-world problems in medicine and healthcare, improving diagnosis, treatment, and public health outcomes?Essential Questions
Supporting questions that break down major concepts.- How is math used to measure medication dosages?
- How are statistical models used to understand public health?
- How do doctors use math to diagnose illnesses?
- How is math used in medical imaging?
- How are mathematical equations used to model the spread of disease?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Understand the role of mathematics in medical diagnoses.
- Apply statistical models to interpret public health data.
- Use mathematical calculations for accurate medication dosages.
- Utilize math in medical imaging techniques.
- Model the spread of diseases using mathematical equations.
- Design a 16-week course outline with PBL activities focused on the application of mathematics in medicine.
- Learn how to improve diagnosis, treatment, and public health outcomes with mathematical tools.
- Investigate how various sciences use mathematics daily in the medical field.
- Evaluate the effectiveness of mathematical models in predicting and controlling disease outbreaks.
- Communicate mathematical findings to diverse audiences.
- Analyze and interpret medical data using mathematical concepts.
- Develop problem-solving skills by applying mathematical principles to medical scenarios.
- Collaborate with peers to explore interdisciplinary applications of math and science in medicine.
- Critically assess the limitations and ethical considerations of using mathematical models in healthcare.
- Apply mathematical concepts to optimize healthcare processes and resource allocation.
- Explore career opportunities in the intersection of mathematics and medicine.
- Use mathematical tools and models to solve real-world problems in medicine and healthcare
Entry Events
Events that will be used to introduce the project to studentsThe Case of the Celebrity Patient
A local hospital presents students with anonymized patient data and a diagnostic challenge, requiring them to use mathematical modeling to determine the most likely illness. The catch? The 'patient' is a celebrity.Disease Outbreak Simulation
Students receive a cryptic message detailing a potential public health crisis, challenging them to use epidemiological models to predict the spread of a new disease and advise public officials on containment strategies. A follow-up news broadcast reveals the scenario as a simulation, but emphasizes real-world implications.Healthcare Innovation Challenge
The class is divided into 'research teams' tasked with creating a math-based solution to a healthcare problem, using limited resources. They present their solutions Shark Tank-style to a panel of medical professionals and mathematicians.Medical Imaging Forensics
Students analyze real-world medical images (X-rays, MRIs) and use mathematical algorithms to enhance and interpret them, diagnosing a condition. The images are from an actual case that local doctors consult on after the student presentations.The Drug Trial Dilemma
A pharmaceutical company presents the class with clinical trial data for a new drug, challenging them to use statistical analysis to determine its efficacy and potential side effects. The data reveals unexpected trends and prompts students to question ethical considerations.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Medication Dosage Calculations
Students will learn how to calculate accurate medication dosages based on patient weight, age, and other 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 worksheet demonstrating accurate medication dosage calculations for different patient scenarios.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Use mathematical calculations for accurate medication dosages. Standard alignment will depend on the specific mathematical operations used (e.g., ratios, proportions).Disease Spread Simulation
Students will create a mathematical model to simulate the spread of a disease in a population.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 computer simulation of a disease outbreak, based on a mathematical model.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Model the spread of diseases using mathematical equations. Standard alignment will depend on the specific modeling techniques used (e.g., differential equations, agent-based models).Medical Math PSA
Students will create a public service announcement (PSA) to educate the public about a specific medical issue, using mathematical concepts to explain the issue and its impact.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 PSA video or poster that communicates mathematical findings about a medical issue to the public.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Communicate mathematical findings to diverse audiences.Math in Medical Imaging
Students will investigate how mathematical concepts are used in medical imaging techniques to aid in diagnosis.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 explaining how math is used in a specific imaging technique (MRI, CT scan) to identify a medical condition.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Understand the role of mathematics in medical diagnoses. Standard alignment will depend on the specific mathematical techniques used (e.g., statistics, calculus).Public Health Data Analysis
Students will analyze real-world public health data to identify trends and patterns, using statistical models.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 report summarizing the analysis of a public health dataset, including statistical models and interpretations of the results.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Apply statistical models to interpret public health data. Standard alignment will depend on the specific statistical methods used (e.g., regression, hypothesis testing).Healthcare Resource Optimization
Students explore mathematical optimization techniques used in hospital resource allocation, such as linear programming to maximize bed usage or minimize patient wait times.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 outlining an optimized resource allocation plan for a hypothetical hospital scenario, including the mathematical model used and the rationale behind the allocation.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Apply mathematical concepts to optimize healthcare processes and resource allocation.Forensic Math: Crime Scene Analysis
Students will analyze forensic data (e.g., blood spatter patterns, time-of-death estimations) using mathematical principles to reconstruct events and assist in investigations.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 report analyzing a simulated crime scene using mathematical techniques, including calculations, diagrams, and a narrative reconstruction of the events.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Analyze and interpret medical data using mathematical concepts.Math in Nursing: Essential Calculations
Students investigate how nurses use math in medication administration, IV drip rates, patient monitoring, and other essential tasks.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 infographic illustrating the various ways nurses use math in their daily practice, including specific examples and calculations.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Understand the role of mathematics in medical diagnoses.Math in Orthopedics: Surgical Planning and Biomechanics
Students will study how orthopedic surgeons use mathematical principles in surgical planning, implant design, and biomechanical analysis of movement.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 model demonstrating the mathematical principles behind a specific orthopedic procedure or implant design, including relevant calculations and biomechanical analysis.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Apply mathematical concepts to optimize healthcare processes and resource allocation.Math in Radiology: Image Processing and Analysis
Students will explore how radiologists use mathematical algorithms and image processing techniques to enhance and interpret medical images.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 explaining the mathematical principles behind a specific radiology technique (e.g., image reconstruction in CT scans, signal processing in MRI), including examples of how math improves image quality and diagnostic accuracy.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Utilize math in medical imaging techniques.Pharmaceutical Calculations: Compounding and Dilutions
Students will learn about calculations specific to compounding medications, adjusting concentrations, and converting units in a pharmacy setting.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 report solving complex pharmacy calculation problems, demonstrating proficiency in compounding, dilutions, and unit conversions.Alignment
How this activity aligns with the learning objectives & standardsLearning Goal: Use mathematical calculations for accurate medication dosages.Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioMath in Medicine Portfolio Rubric
Medication Dosage Calculations
Evaluates the accuracy, clarity, and completeness of the medication dosage calculation worksheet.Dosage Accuracy
Accuracy of medication dosage calculations.
Exemplary
4 PointsCalculations are consistently accurate, demonstrating a sophisticated understanding of patient-specific factors and unit conversions. Demonstrates leadership in ensuring accuracy and safety.
Proficient
3 PointsCalculations are generally accurate, demonstrating a thorough understanding of patient-specific factors and unit conversions. Contributes effectively to ensuring accurate calculations.
Developing
2 PointsCalculations show some inaccuracies, indicating an emerging understanding of patient-specific factors or unit conversions. Requires support in ensuring accuracy.
Beginning
1 PointsCalculations contain significant errors, demonstrating a limited understanding of patient-specific factors or unit conversions. Requires significant support in calculation practices.
Worksheet Clarity
Clarity and organization of the worksheet, including the presentation of patient scenarios and calculation problems.
Exemplary
4 PointsWorksheet is exceptionally clear, well-organized, and visually appealing, enhancing the understanding of the calculations and scenarios. Innovatively organizes patient scenarios.
Proficient
3 PointsWorksheet is clear, well-organized, and easy to follow, facilitating understanding of the calculations and scenarios. Organizes patient scenarios effectively.
Developing
2 PointsWorksheet is somewhat disorganized or unclear, making it challenging to understand the calculations or scenarios. Shows partial organization of patient scenarios.
Beginning
1 PointsWorksheet is disorganized and difficult to understand, hindering comprehension of the calculations and scenarios. Requires significant work to organize patient scenarios.
Worksheet Completeness
Completeness of the worksheet, including a variety of patient scenarios and dosage calculation problems that cover different factors (weight, age, etc.).
Exemplary
4 PointsWorksheet is exceptionally comprehensive, covering a wide range of patient scenarios and dosage calculation problems that demonstrate a sophisticated understanding of various factors. Integrates all skills to cover every possible patient scenario.
Proficient
3 PointsWorksheet is comprehensive, covering a range of patient scenarios and dosage calculation problems that demonstrate a thorough understanding of various factors. Integrates multiple skills effectively.
Developing
2 PointsWorksheet is somewhat incomplete, missing some patient scenarios or dosage calculation problems that would demonstrate a broader understanding of various factors. Integration of skills is partial.
Beginning
1 PointsWorksheet is incomplete, lacking a variety of patient scenarios and dosage calculation problems that would demonstrate an understanding of various factors. Lacks integration of skills.
Disease Spread Simulation
Assesses the accuracy, implementation, and presentation of the disease spread simulation.Simulation Accuracy
Accuracy and validity of the disease spread simulation, based on the chosen mathematical model.
Exemplary
4 PointsSimulation is exceptionally accurate and valid, demonstrating a sophisticated understanding of the chosen mathematical model and its application to disease spread. Shows advanced integration of skills to create a simulation with highly accurate results.
Proficient
3 PointsSimulation is generally accurate and valid, demonstrating a thorough understanding of the chosen mathematical model and its application to disease spread. Integrates skills successfully to create an effective simulation.
Developing
2 PointsSimulation shows some inaccuracies or limitations, indicating an emerging understanding of the chosen mathematical model or its application to disease spread. Shows partial skill integration.
Beginning
1 PointsSimulation contains significant errors or is invalid, demonstrating a limited understanding of the chosen mathematical model or its application to disease spread. Shows limited skill integration.
Model Implementation
Effectiveness of the model implementation, including the use of computer software and calibration with real-world data.
Exemplary
4 PointsModel implementation is exceptionally effective, demonstrating innovative use of computer software and meticulous calibration with real-world data. Demonstrates leadership in calibrating data with real-world data.
Proficient
3 PointsModel implementation is effective, demonstrating appropriate use of computer software and careful calibration with real-world data. Contributes effectively by calibrating model with real-world data.
Developing
2 PointsModel implementation shows some limitations, indicating an emerging understanding of computer software or calibration techniques. Requires some support with real-world data.
Beginning
1 PointsModel implementation is ineffective, demonstrating a limited understanding of computer software or calibration techniques. Requires significant support with calibrating real-world data.
Presentation Clarity
Clarity and completeness of the presentation explaining the model, including the mathematical concepts and simulation results.
Exemplary
4 PointsPresentation is exceptionally clear, complete, and engaging, demonstrating a sophisticated understanding of the mathematical concepts and simulation results. Consistently shows leadership in explaining the model and results.
Proficient
3 PointsPresentation is clear, complete, and engaging, demonstrating a thorough understanding of the mathematical concepts and simulation results. Effectively communicates the model and results.
Developing
2 PointsPresentation is somewhat unclear or incomplete, making it challenging to understand the mathematical concepts or simulation results. Requires support to explain model and results better.
Beginning
1 PointsPresentation is unclear and incomplete, hindering comprehension of the mathematical concepts and simulation results. Requires significant support to communicate model and results effectively.
Medical Math PSA
Evaluates the effectiveness, clarity, and creativity of the Medical Math PSA.PSA Effectiveness
Effectiveness of the PSA in educating the public about a specific medical issue, using mathematical concepts.
Exemplary
4 PointsPSA is exceptionally effective, demonstrating a sophisticated understanding of the medical issue and innovative use of mathematical concepts. Demonstrates leadership in creating an impactful and educational PSA.
Proficient
3 PointsPSA is effective, demonstrating a thorough understanding of the medical issue and appropriate use of mathematical concepts. Effectively educates the public about the medical issue.
Developing
2 PointsPSA is somewhat ineffective, indicating an emerging understanding of the medical issue or a limited use of mathematical concepts. Partially educates the public about the medical issue.
Beginning
1 PointsPSA is ineffective, demonstrating a limited understanding of the medical issue or a lack of mathematical concepts. Requires significant improvement to make an impact.
Mathematical Clarity
Clarity and accuracy of the mathematical explanations in the PSA, ensuring that the public can understand the issue and its impact.
Exemplary
4 PointsMathematical explanations are exceptionally clear, accurate, and accessible, demonstrating a sophisticated understanding of the concepts and their relevance to the medical issue. Innovatively explains concepts in the PSA.
Proficient
3 PointsMathematical explanations are clear, accurate, and accessible, demonstrating a thorough understanding of the concepts and their relevance to the medical issue. Effectively communicates mathematical concepts in the PSA.
Developing
2 PointsMathematical explanations are somewhat unclear or inaccurate, making it challenging for the public to understand the issue and its impact. Requires support to clarify math in PSA.
Beginning
1 PointsMathematical explanations are unclear and inaccurate, hindering comprehension of the issue and its impact. Requires significant work to explain the math in the PSA.
PSA Engagement
Creativity and engagement of the PSA, ensuring that it captures the audience's attention and effectively conveys the message.
Exemplary
4 PointsPSA is exceptionally creative, engaging, and memorable, effectively capturing the audience's attention and conveying the message with innovation. Demonstrates leadership in engagement techniques.
Proficient
3 PointsPSA is creative, engaging, and memorable, effectively capturing the audience's attention and conveying the message. Captures the audience effectively.
Developing
2 PointsPSA is somewhat uninspired or unengaging, failing to fully capture the audience's attention or effectively convey the message. Requires support to engage the audience.
Beginning
1 PointsPSA is uncreative, unengaging, and forgettable, failing to capture the audience's attention or convey the message. Requires significant support to captivate the audience.
Math in Medical Imaging
Evaluates the accuracy, clarity, and depth of research in the Math in Medical Imaging presentation.Mathematical Accuracy
Accuracy and completeness of the presentation explaining the mathematical principles behind the chosen imaging technique.
Exemplary
4 PointsPresentation is exceptionally accurate and complete, demonstrating a sophisticated understanding of the mathematical principles behind the imaging technique and their role in medical diagnoses. Shows advanced integration of skills to explain accurate and complete math.
Proficient
3 PointsPresentation is accurate and complete, demonstrating a thorough understanding of the mathematical principles behind the imaging technique and their role in medical diagnoses. Integrates skills effectively to produce accurate and complete math.
Developing
2 PointsPresentation is somewhat inaccurate or incomplete, indicating an emerging understanding of the mathematical principles or their role in medical diagnoses. Partial integration of skills.
Beginning
1 PointsPresentation is inaccurate and incomplete, demonstrating a limited understanding of the mathematical principles or their role in medical diagnoses. Shows limited skill integration.
Presentation Clarity
Clarity and organization of the presentation, including the explanation of the imaging technique and its use in diagnosing a specific medical condition.
Exemplary
4 PointsPresentation is exceptionally clear, well-organized, and visually appealing, enhancing the understanding of the imaging technique and its diagnostic use. Presents in a novel and creative way.
Proficient
3 PointsPresentation is clear, well-organized, and easy to follow, facilitating understanding of the imaging technique and its diagnostic use. Presents clearly and concisely.
Developing
2 PointsPresentation is somewhat disorganized or unclear, making it challenging to understand the imaging technique or its diagnostic use. Presentation could be improved for clarity.
Beginning
1 PointsPresentation is disorganized and difficult to understand, hindering comprehension of the imaging technique and its diagnostic use. Presentation needs significant improvement for clarity.
Research Depth
Depth of research and understanding of the chosen medical imaging technique, including its advantages, limitations, and applications in medical diagnosis.
Exemplary
4 PointsResearch is exceptionally thorough and insightful, demonstrating a sophisticated understanding of the medical imaging technique, its advantages, limitations, and applications. Demonstrates leadership in research.
Proficient
3 PointsResearch is thorough and comprehensive, demonstrating a strong understanding of the medical imaging technique, its advantages, limitations, and applications. Comprehensive and thorough.
Developing
2 PointsResearch is somewhat superficial, indicating an emerging understanding of the medical imaging technique or its applications. Could be improved with further investigation.
Beginning
1 PointsResearch is limited, demonstrating a lack of understanding of the medical imaging technique or its applications. Requires significant additional research.
Public Health Data Analysis
Assesses the accuracy, validity, and clarity of the Public Health Data Analysis.Model Accuracy
Appropriateness and accuracy of the statistical models applied to the public health data.
Exemplary
4 PointsStatistical models are exceptionally appropriate and accurate, demonstrating a sophisticated understanding of statistical methods and their application to public health data. Innovatively uses statistical models to create reports and analysis.
Proficient
3 PointsStatistical models are appropriate and accurate, demonstrating a thorough understanding of statistical methods and their application to public health data. Produces solid reports and analysis.
Developing
2 PointsStatistical models are somewhat inappropriate or inaccurate, indicating an emerging understanding of statistical methods or their application to public health data. Reports and analysis needs some additional improvements.
Beginning
1 PointsStatistical models are inappropriate and inaccurate, demonstrating a limited understanding of statistical methods or their application to public health data. Needs significant additional understanding.
Interpretation Validity
Validity and reliability of the interpretation of the statistical analysis results, including the conclusions drawn about public health.
Exemplary
4 PointsInterpretation of results is exceptionally valid and reliable, demonstrating a sophisticated understanding of the statistical analysis and its implications for public health. Demonstrates leadership in interpreting the statistics.
Proficient
3 PointsInterpretation of results is valid and reliable, demonstrating a thorough understanding of the statistical analysis and its implications for public health. Effectively interprets statistics.
Developing
2 PointsInterpretation of results is somewhat questionable or unreliable, indicating an emerging understanding of the statistical analysis or its implications for public health. Some support is needed.
Beginning
1 PointsInterpretation of results is invalid and unreliable, demonstrating a limited understanding of the statistical analysis or its implications for public health. Significant work and support are needed.
Report Clarity
Clarity and completeness of the report summarizing the analysis and findings, including the presentation of statistical models and interpretations.
Exemplary
4 PointsReport is exceptionally clear, complete, and well-organized, enhancing the understanding of the statistical models and interpretations. Innovatively organizes data and presents information.
Proficient
3 PointsReport is clear, complete, and well-organized, facilitating understanding of the statistical models and interpretations. Effectively presents data and information.
Developing
2 PointsReport is somewhat disorganized or unclear, making it challenging to understand the statistical models or interpretations. Report needs some revisions for clarity.
Beginning
1 PointsReport is disorganized and difficult to understand, hindering comprehension of the statistical models and interpretations. Report needs significant revisions for clarity.