Math in Medicine: A High School PBL Experience
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Math in Medicine: A High School PBL Experience

Grade 11ScienceMath29 days
This project-based learning experience explores the applications of mathematics in medicine to enhance patient care and medical advancements. Students will use mathematical models to understand physiological processes, determine treatment efficacy, measure medication dosage accurately, and interpret medical conditions through graphs. Through activities like disease spread simulation, clinical trial data analysis, dosage calculations, and medical graph interpretation, students will learn to apply mathematical and statistical tools to solve complex problems in medicine, ultimately improving patient outcomes and advancing medical knowledge.
Disease ModelingMedical ImagingPharmacokineticsStatistical AnalysisClinical TrialsDrug DosageMedical Graphs
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can mathematical tools be applied in medicine to improve patient care and medical advancements?

Essential Questions

Supporting questions that break down major concepts.
  • How are mathematical models used to understand physiological processes in the human body?
  • How is math used to determine the efficacy of a treatment?
  • How do we measure medication dosage accurately?
  • How do graphs help doctors understand patients' medical conditions?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Students will learn to apply mathematical models to predict disease spread.
  • Students will learn how statistical analysis informs medical decision-making.
  • Students will learn to accurately measure medication dosage.
  • Students will learn how graphs help doctors understand patients' medical conditions.
  • Students will learn how to use mathematical and statistical tools to solve complex problems in medicine.
  • Students will improve patient outcomes.
  • Students will advance medical knowledge with math and statistics tools

Entry Events

Events that will be used to introduce the project to students

Introduction to Mathematical Modeling in Physiology

Week 1: Introduction to Mathematical Modeling in Physiology. Students explore basic mathematical models of physiological processes, such as heart rate variability and respiratory mechanics. This includes understanding differential equations and their application in modeling dynamic systems within the human body.

Statistical Analysis in Clinical Trials

Week 2: Statistical Analysis in Clinical Trials. Focus on statistical methods used in clinical trials, including hypothesis testing, p-values, confidence intervals, and sample size calculations. Students learn how to interpret statistical results and assess the efficacy and safety of new treatments.

Pharmacokinetics and Drug Dosage Calculations

Week 3: Pharmacokinetics and Drug Dosage Calculations. This week covers the mathematical principles underlying pharmacokinetics, including drug absorption, distribution, metabolism, and excretion. Students learn to calculate appropriate drug dosages based on patient characteristics and drug properties.

Medical Imaging and Signal Processing

Week 4: Medical Imaging and Signal Processing. Explore the mathematical techniques used in medical imaging, such as X-ray, CT scans, MRI, and ultrasound. Students learn about image reconstruction algorithms, signal processing methods for noise reduction, and image enhancement techniques.

Epidemiology and Disease Modeling

Week 5: Epidemiology and Disease Modeling. Students delve into mathematical models of disease transmission, including compartmental models (e.g., SIR model) and network models. They learn to analyze epidemiological data, predict disease outbreaks, and evaluate the effectiveness of intervention strategies.

Resource Allocation in Healthcare

Week 6: Resource Allocation in Healthcare. This module focuses on mathematical optimization techniques for resource allocation in healthcare settings. Students learn to apply linear programming, queuing theory, and simulation to optimize hospital bed allocation, staffing levels, and emergency response strategies.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Advanced Disease Spread Simulation with SIR Model

Students will construct a basic SIR (Susceptible, Infected, Recovered) model to simulate the spread of an infectious disease within a population.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research the SIR model: Understand the basic assumptions, variables, and equations involved in the SIR model.
2. Collect data on a specific infectious disease: Gather data on transmission rates, recovery rates, and initial population sizes. Consider factors such as population density, vaccination rates, and seasonality.
3. Implement the SIR model: Use a spreadsheet program (e.g., Excel) or a programming language (e.g., Python) to create a simulation of the SIR model using the collected data. Experiment with different parameter values to observe their effects on disease spread.
4. Analyze the results: Run the simulation and analyze the resulting graphs of susceptible, infected, and recovered individuals over time. Discuss the impact of different parameters on the spread of the disease.
5. Write a report: Summarize the methods, results, and conclusions of the SIR model simulation. Discuss the limitations of the model and suggest improvements, such as incorporating additional factors like age structure or spatial heterogeneity.
6. Present findings: Prepare a presentation summarizing the project, methodology, results, and conclusions. Present the simulation to the class, highlighting key insights and challenges encountered during the modeling process.

Final Product

What students will submit as the final product of the activityA completed SIR model simulation using a spreadsheet or programming tool, along with a written report interpreting the results and discussing the model's limitations.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Students will learn to apply mathematical models to predict disease spread.
Activity 2

In-Depth Clinical Trial Data Analysis

Students will analyze a clinical trial dataset to determine the effectiveness of a new treatment compared to a placebo.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Obtain a clinical trial dataset: Find a publicly available dataset from a clinical trial comparing a new treatment to a placebo or standard treatment. Ensure the dataset includes relevant variables such as patient demographics, treatment assignment, and outcome measures.
2. Perform descriptive statistics: Calculate descriptive statistics (mean, standard deviation, median, etc.) for relevant variables in the dataset. Visualize the data using histograms and box plots to identify any outliers or patterns.
3. Conduct hypothesis testing: Formulate a null and alternative hypothesis, choose an appropriate statistical test (t-test or ANOVA), and calculate the p-value. Justify the choice of statistical test based on the characteristics of the data and research question.
4. Calculate confidence intervals: Calculate confidence intervals for the treatment effect to estimate the range of plausible values. Interpret the confidence intervals in the context of the clinical trial results.
5. Interpret the results: Interpret the statistical results and draw conclusions about the effectiveness of the new treatment. Discuss the limitations of the study and potential sources of bias, such as confounding variables or selection bias.
6. Write a report: Summarize the methods, results, and conclusions of the statistical analysis. Include tables and figures to present the data and findings. Discuss the clinical significance of the results and implications for medical practice.
7. Peer Review: Exchange reports with a classmate and provide constructive feedback on the statistical analysis, interpretation of results, and clarity of presentation. Revise the report based on the feedback received.

Final Product

What students will submit as the final product of the activityA statistical report that includes descriptive statistics, hypothesis testing results (t-test or ANOVA), confidence intervals, and a conclusion about the treatment's effectiveness.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Students will learn how statistical analysis informs medical decision-making.
Activity 3

Comprehensive Dosage Calculations and Patient Profiles

Students will calculate drug dosages for various patients based on their weight, age, and medical condition, considering factors such as bioavailability and drug clearance.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research drug dosage calculations: Understand the principles of drug dosage calculations, including factors such as weight-based dosing, body surface area, and drug clearance. Explore different methods for calculating drug dosages, such as the Clark's rule and the body surface area method.
2. Obtain patient information: Gather information on several hypothetical patients, including their weight, age, medical condition, and other relevant factors. Consider patients with different medical conditions and demographic characteristics.
3. Calculate drug dosages: Calculate the appropriate drug dosages for each patient based on the provided information and the drug's prescribing information. Use appropriate formulas and units to ensure accuracy.
4. Justify the dosages: Provide a detailed explanation of the calculations and justifications for the chosen dosages. Explain the rationale behind the chosen dosage and any adjustments made based on patient characteristics.
5. Check for accuracy: Double-check the calculations to ensure accuracy and minimize the risk of errors. Use online dosage calculators or consult with a pharmacist to verify the results.
6. Create patient profiles: Develop comprehensive patient profiles that include relevant medical history, current medications, and dosage recommendations. Present the patient profiles in a clear and organized manner.
7. Simulate clinical scenarios: Participate in simulated clinical scenarios where you must calculate and administer drug dosages to patients. Work with a team to ensure accuracy and safety.

Final Product

What students will submit as the final product of the activityA series of dosage calculation worksheets with detailed explanations of the calculations and justifications for the chosen dosages.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Students will learn to accurately measure medication dosage.
Activity 4

Advanced Medical Graph Interpretation and Case Studies

Students will analyze medical graphs (e.g., ECG, EEG, blood pressure curves) to diagnose and monitor patients' conditions.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research medical graphs: Learn about different types of medical graphs, such as ECG, EEG, blood pressure curves, and their clinical applications. Explore the underlying physiological principles and clinical significance of each type of graph.
2. Collect medical graph examples: Gather examples of normal and abnormal medical graphs from textbooks, online resources, or clinical settings. Ensure the examples cover a wide range of medical conditions and patient populations.
3. Analyze the graphs: Analyze the graphs and identify key features, such as heart rate, rhythm, amplitude, and frequency. Use calipers and rulers to measure relevant parameters on the graphs.
4. Interpret the findings: Interpret the findings and relate them to specific medical conditions or diagnoses. Consult with medical professionals or online resources to validate the interpretations.
5. Prepare a presentation: Create a presentation that explains how to interpret different types of medical graphs, including examples of normal and abnormal patterns and their clinical significance. Use visual aids and animations to enhance understanding.
6. Case Study Analysis: Analyze real-world case studies involving medical graphs and patient data. Work in groups to diagnose the patient's condition based on the available information.
7. Interactive Simulation: Develop an interactive simulation that allows users to manipulate medical graph parameters and observe the resulting changes in patient condition. Use the simulation to test your understanding of medical graph interpretation.

Final Product

What students will submit as the final product of the activityA presentation explaining how to interpret different types of medical graphs, including examples of normal and abnormal patterns and their clinical significance.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Students will learn how graphs help doctors understand patients' medical conditions.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Math in Medicine Portfolio Rubric

Category 1

SIR Model Simulation

Assesses the student's ability to construct and interpret an SIR model to simulate disease spread.
Criterion 1

Model Accuracy

Accuracy of the SIR model implementation, including correct formulas and parameter settings.

Exemplary
4 Points

The SIR model is implemented with a high degree of accuracy, using correct formulas and parameter settings that closely match the collected data.

Proficient
3 Points

The SIR model is implemented accurately, with correct formulas and parameter settings that mostly align with the collected data.

Developing
2 Points

The SIR model implementation contains some inaccuracies in formulas or parameter settings, leading to noticeable deviations from expected results.

Beginning
1 Points

The SIR model implementation contains significant errors in formulas or parameter settings, resulting in a model that does not accurately simulate disease spread.

Criterion 2

Report Quality

Thoroughness of the written report, including clear explanations of the methods, results, and limitations of the SIR model.

Exemplary
4 Points

The report provides a comprehensive and insightful analysis of the SIR model, including clear explanations of the methods, results, limitations, and potential improvements.

Proficient
3 Points

The report provides a thorough analysis of the SIR model, including clear explanations of the methods, results, and limitations.

Developing
2 Points

The report provides a basic overview of the SIR model, but may lack detail in the explanations of the methods, results, or limitations.

Beginning
1 Points

The report is incomplete or lacks clarity in the explanations of the methods, results, or limitations of the SIR model.

Criterion 3

Presentation Effectiveness

Clarity and effectiveness of the presentation, including clear communication of key insights and challenges encountered during the modeling process.

Exemplary
4 Points

The presentation is exceptionally clear and engaging, effectively communicating key insights and challenges encountered during the modeling process with compelling visuals and explanations.

Proficient
3 Points

The presentation is clear and effective, communicating key insights and challenges encountered during the modeling process.

Developing
2 Points

The presentation is understandable but may lack clarity or engagement in the communication of key insights and challenges.

Beginning
1 Points

The presentation is unclear or difficult to follow, with limited communication of key insights and challenges.

Category 2

Clinical Trial Data Analysis

Evaluates the student's ability to perform and interpret statistical analyses on clinical trial data.
Criterion 1

Statistical Test Selection and Validation

Appropriateness of statistical tests and the validity of assumptions

Exemplary
4 Points

Chooses the most appropriate statistical tests, with clear justification, and thoroughly validates all assumptions.

Proficient
3 Points

Chooses appropriate statistical tests and validates the assumptions.

Developing
2 Points

Chooses statistical tests with some inconsistencies and partially validates assumptions.

Beginning
1 Points

Chooses inappropriate statistical tests and doesn't validate assumptions.

Criterion 2

Data Interpretation and Conclusions

Accuracy of data interpretation and conclusions drawn from the statistical analysis.

Exemplary
4 Points

Draws insightful and nuanced conclusions fully supported by the statistical analysis, demonstrating a deep understanding of the data.

Proficient
3 Points

Draws accurate conclusions supported by the statistical analysis.

Developing
2 Points

Draws partially accurate conclusions, but the interpretations require further support from the statistical analysis.

Beginning
1 Points

Draws inaccurate conclusions based on the statistical analysis.

Criterion 3

Report Quality and Clarity

Quality and clarity of the statistical report, including appropriate use of tables, figures, and statistical notation.

Exemplary
4 Points

Produces a well-organized, clear, and concise statistical report with appropriate tables, figures, and statistical notation. Peer review feedback is thoughtfully addressed.

Proficient
3 Points

Produces a clear and concise statistical report with appropriate tables, figures, and statistical notation.

Developing
2 Points

Produces a statistical report with some inconsistencies in clarity, organization, tables, figures, or notation.

Beginning
1 Points

Produces a poorly organized and unclear statistical report.

Category 3

Drug Dosage Calculations

Assesses the student's ability to calculate and justify drug dosages based on patient-specific information.
Criterion 1

Dosage Calculation Accuracy

Accuracy of dosage calculations, considering patient-specific factors and drug properties.

Exemplary
4 Points

Calculates drug dosages with exceptional accuracy, comprehensively considering patient-specific factors and drug properties, including bioavailability and drug clearance.

Proficient
3 Points

Calculates drug dosages accurately, considering patient-specific factors and drug properties.

Developing
2 Points

Calculates drug dosages with some inaccuracies, overlooking some patient-specific factors or drug properties.

Beginning
1 Points

Calculates drug dosages with significant inaccuracies, demonstrating a poor understanding of patient-specific factors and drug properties.

Criterion 2

Dosage Justification

Justification of chosen dosages, including clear explanations of the rationale and any adjustments made based on patient characteristics.

Exemplary
4 Points

Provides exceptionally clear and comprehensive justifications for the chosen dosages, thoroughly explaining the rationale and any adjustments made based on patient characteristics, with detailed supporting evidence.

Proficient
3 Points

Provides clear justifications for the chosen dosages, explaining the rationale and any adjustments made based on patient characteristics.

Developing
2 Points

Provides justifications for the chosen dosages, but the explanations may lack clarity or detail regarding the rationale or adjustments.

Beginning
1 Points

Provides inadequate or unclear justifications for the chosen dosages.

Criterion 3

Patient Profile Quality

Completeness and organization of patient profiles, including relevant medical history, current medications, and dosage recommendations.

Exemplary
4 Points

Develops comprehensive and exceptionally well-organized patient profiles that include all relevant medical history, current medications, and dosage recommendations, presented in a clear and logical manner.

Proficient
3 Points

Develops complete and well-organized patient profiles that include relevant medical history, current medications, and dosage recommendations.

Developing
2 Points

Develops patient profiles that may be incomplete or lack organization, with some relevant medical history, current medications, or dosage recommendations missing.

Beginning
1 Points

Develops incomplete and poorly organized patient profiles.

Category 4

Medical Graph Interpretation

Evaluates the student's ability to interpret medical graphs to diagnose and monitor patient conditions.
Criterion 1

Feature Identification and Measurement

Ability to accurately identify and measure key features in medical graphs (e.g., heart rate, rhythm, amplitude, frequency).

Exemplary
4 Points

Demonstrates an exceptional ability to accurately identify and measure all key features in medical graphs with precision and attention to detail.

Proficient
3 Points

Demonstrates a strong ability to accurately identify and measure key features in medical graphs.

Developing
2 Points

Demonstrates some ability to identify and measure key features in medical graphs, but may struggle with certain features or measurements.

Beginning
1 Points

Struggles to identify and measure key features in medical graphs accurately.

Criterion 2

Presentation Quality

Quality of the presentation, including clarity, organization, and use of visual aids to explain medical graph interpretation.

Exemplary
4 Points

The presentation is exceptionally clear, well-organized, and engaging, with compelling visual aids that enhance understanding of medical graph interpretation.

Proficient
3 Points

The presentation is clear, well-organized, and informative, with effective use of visual aids to explain medical graph interpretation.

Developing
2 Points

The presentation is understandable but may lack clarity, organization, or effective use of visual aids.

Beginning
1 Points

The presentation is unclear, disorganized, and lacks effective visual aids.

Criterion 3

Case Study Analysis

Accuracy and depth of the analysis of case studies involving medical graphs and patient data.

Exemplary
4 Points

Provides insightful and comprehensive analyses of case studies, demonstrating a deep understanding of the relationship between medical graphs and patient conditions, leading to accurate diagnoses and treatment recommendations.

Proficient
3 Points

Provides accurate and thorough analyses of case studies, demonstrating a strong understanding of the relationship between medical graphs and patient conditions.

Developing
2 Points

Provides basic analyses of case studies, but may lack depth or accuracy in the interpretation of medical graphs and patient data.

Beginning
1 Points

Struggles to analyze case studies effectively, demonstrating a limited understanding of medical graphs and patient data.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

How has your understanding of the applications of mathematics in medicine evolved throughout this project?

Text
Required
Question 2

What was the most challenging aspect of applying mathematical concepts to medical scenarios, and how did you overcome it?

Text
Required
Question 3

To what extent do you agree that mathematical modeling and statistical analysis are essential tools for advancing medical knowledge and improving patient outcomes?

Scale
Required
Question 4

Which specific activity (SIR model, clinical trial analysis, dosage calculations, or graph interpretation) was the most impactful for you, and why?

Multiple choice
Required
Options
SIR model
Clinical trial analysis
Dosage calculations
Graph interpretation