Mathematics in Healthcare: A Rich Context for the Common Core Standards on Modeling Lindsay Good Dan Ozimek Mary Phillips.

Mathematics in Healthcare: A Rich Context for the Common

Core Standards on ModelingLindsay GoodDan OzimekMary Phillips

To download this PowerPoint presentation and to access additional resources for your classroom, please visit:

http://www.danozimek.com/pctm

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

Mathematics Offerings

• Introduction to Statistical Thinking

• Clinical Mathematics for the Health Sciences

• College Algebra

• Statistics

Clinical Mathematics for the Health Sciences

• A required course for many of the associate level programs.• Course Outcomes

1. Solve linear, fractional and decimal equations.2. Simplify algebraic and numerical expressions.3. Model real life applications using algebraic techniques.4. Translate data among graph, table and list formats.5. Calculate measures of central tendency and variation for sets of data.6. Convert measurements within and between the metric, apothecary and

household systems.7. Perform calculations requiring conversions within/between metric,

apothecary and household systems. 8. Calculate oral, parenteral and intravenous medication dosages correctly.9. Determine adult and pediatric dosages based on body weight or body

surface area.

• A wide range of mathematics with a focus on application.

“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, 2007. Adapted from Lesh & Doerr, 2003, P.17.

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

Mathematics in Healthcare: A Rich Context for the Common

Core Standards on Modeling

Delivering Correct Medications

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

The doctor orders 800 mg of

Amoxicillin every 8 hours for 10 days.

• How many mL should the nurse administer?

The doctor orders 7 mg of diazepam

twice a day.

• How many mL should the nurse administer?

Identifying the variables

What information is needed?

Formulating a model

Create a formula to calculate the amount to administer

Validating the conclusions

Put your formula to the test

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?

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?

The doctor orders 18 mg of lidocaine HCl prior to stitching a

wound

• How many mL should the nurse inject?

Mathematics in Healthcare: A Rich Context for the Common

Core Standards on Modeling

Titration Application

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.

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 8 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 10 mcg/kg/min.

• Your patient is a 5’11” male who weighs 97.7 kg.

Titration Example – Identifying the Information

• Starting Rate: • Incremental Adjustment: • Maximum Dose: • Strength of Medication:• Desired physiological effect: • Patient info:

Patient’s ChartTime 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

Identifying the variables

What information is needed?What are the variables? What are the constants?

Formulating a model

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

Validating the conclusions

Put your formula to the test

Patient’s ChartTime 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

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

References• Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for

Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp-content/uploads/Math_Standards.pdf

• 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, 763-804.

• Meyer, D. (2015). Missing the promise of mathematical modeling. Mathematics Teacher, 108(8), 578-583.

To download this PowerPoint presentation and to access additional resources for your classroom, please visit:

http://www.danozimek.com/pctm