1. Lindsay Good Dan Ozimek Mary Phillips
Mathematics in Healthcare:  A Rich Context for the Common Core Standards on Modeling
Lindsay Good
Dan Ozimek
Mary Phillips
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2. Our College Located in Lancaster, Pennsylvania
Affiliated with Lancaster General Health
Brief Timeline
1903: Established
2001: Associate Degrees
Cardiac Electrophysiology, Cardiovascular Invasive Specialty, Diagnostic Medical Sonography, Nuclear Medicine Technology, Nursing, Radiography, Respiratory Care, Surgical Technology
2009: Bachelor’s Degrees
Health Sciences, Healthcare Administration, Nursing
2015: Master’s Degrees
Healthcare Administration, Health Sciences Education, Nursing Administration, Nursing Education
Students
86% female
59% 25 years of age or older
52% live in Lancaster County

3. Mathematics Offerings
Introduction to Statistical Thinking
Clinical Mathematics for the Health Sciences
College Algebra
Statistics

4. Clinical Mathematics for the Health Sciences
A required course for many of the associate level programs.
Course Outcomes
Solve linear, fractional and decimal equations.
Simplify algebraic and numerical expressions.
Model real life applications using algebraic techniques.
Translate data among graph, table and list formats.
Calculate measures of central tendency and variation for sets of data.
Convert measurements within and between the metric, apothecary and household systems.
Perform calculations requiring conversions within/between metric, apothecary and household systems.
Calculate oral, parenteral and intravenous medication dosages correctly.
Determine adult and pediatric dosages based on body weight or body surface area.
A wide range of mathematics with a focus on application.

5. “Model real life applications using algebraic techniques.”
Modeling vs. Problem Solving (Lesh & Zawojewski, 2007)
Students create complex artifacts (mathematical models) that are useful, sharable, and reusable in other situations
Solutions to modeling tasks evolve over multiple cycles
Modeling cycle from Lesh & Zawojewski, Adapted from Lesh & Doerr, 2003, P.17.

6. CCSSM Modeling
Identify, Formulate, Analyze/Perform, Interpret, Validate, Report
Textbook analysis (Meyer, 2015)
Recommendation: Provide students with
more diverse opportunities to model.
“Fill the gaps” in the textbooks by
focusing on the actions, Identify,
Formulate, and Validate.
(CCSSI, 2010, p. 72)
Actions
# of Occurrences
(out of 83 problems) %
Identify 7
8.4
Formulate 20
24.1
Perform 71
85.5
Interpret 67
80.7
Validate 4
4.8

7. Delivering Correct Medications
Mathematics in Healthcare:  A Rich Context for the Common Core Standards on Modeling
Delivering Correct Medications

8. The doctor prescribes the medication in mg, but the nurse administers pills or mL.
Doctor’s order: acetaminophen 500 mg every four hours as needed for pain

9. The doctor orders 800 mg of Amoxicillin every 8 hours for 10 days.
How many mL should the nurse administer?

10. The doctor orders 7 mg of diazepam twice a day.
How many mL should the nurse administer?

11. Identifying the variables
What information is needed?

12. Create a formula to calculate the amount to administer
Formulating a model
Create a formula to calculate the amount to administer

13. Validating the conclusions
Put your formula to the test

14. The doctor orders 500 mg of azithromycin twice a day for 21 days for a 10 year old child who had a tick bite.
How many mL should the nurse instruct the parents to administer?

15. The doctor orders 440 mg of naproxen sodium twice a day as needed for pain
How many pills should the nurse instruct the patient to take?

16. The doctor orders 18 mg of lidocaine HCl prior to stitching a wound
How many mL should the nurse inject?

17. Titration Application
Mathematics in Healthcare:  A Rich Context for the Common Core Standards on Modeling
Titration Application

18. Titration of IV Medications
Titration is the process of adjusting a medication based on the patient’s response while keeping the dose within the doctor’s order.
The nurse will frequently need to convert the order, in mL/hr, to reflect the correct dose, in mcg/kg/min, in the patient’s chart.

19. Titration Example
400 mg of Dopamine (Intropin®) in 250 mL D5W is ordered to maintain systolic blood pressure between 100 to 120 mm Hg.
The doctor ordered the titration to begin at mL/hr and increase by 5 mL/hr every 5 to 10 minutes until the desired blood pressure is reached. The dose should not exceed mcg/kg/min.
Your patient is a 5’11” male who weighs 97.7 kg.

20. Titration Example – Identifying the Information
Starting Rate:
Incremental Adjustment:
Maximum Dose:
Strength of Medication:
Desired physiological effect:
Patient info:

21. Systolic Blood Pressure
Patient’s Chart
Time
Systolic Blood Pressure
IV Flow Rate (mL/hr)
Dose (mcg/kg/min)
0800
80 mm Hg
8 mL/hr
0805
84 mmHg
13 mL/hr
0815
87 mmHg
18 mL/hr
0825
90 mm Hg
23 mL/hr
0835
95 mm Hg
0840
98 mm Hg

22. Identifying the variables
What information is needed? What are the variables? What are the constants?

23. Formulating a model
Create a formula to convert between the rate (mL/hr) and the dose (mcg/kg/min)

24. Validating the conclusions
Put your formula to the test

25. Systolic Blood Pressure
Patient’s Chart
Time
Systolic Blood Pressure
IV Flow Rate (mL/hr)
Dose (mcg/kg/min)
0800
80 mm Hg
8 mL/hr
0805
84 mmHg
13 mL/hr
0815
87 mmHg
18 mL/hr
0825
90 mm Hg
23 mL/hr
0835
95 mm Hg
0840
98 mm Hg

26. Additional Concepts to Explore
Intravenous (IV) Dosage
Convert between mL/hr and gtt/min
Model the remaining volume as a function of time
Elimination Problems
Formulate exponential models to describe the amount of medication remaining in a patient’s body

27. References To download this PowerPoint presentation and to
Common Core State Standards Initiative (CCSSI) Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
Lesh, R., & Doerr, H. (2003). Foundation of a models and modeling perspective on mathematics teaching and learning. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspective on mathematics teaching, learning, and problem solving, (pp. 9-34). Mahwah, NJ: Erlbaum.
Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. Second handbook of research on mathematics teaching and learning, 2,
Meyer, D. (2015). Missing the promise of mathematical modeling. Mathematics Teacher, 108(8),
You can access this PowerPoint presentation and additional resources at
To download this PowerPoint presentation and to
access additional resources for your classroom, please visit: