allied health applications integrated into developmental

- MATHEMATICS AND COMPUTER EDUCATION-

Allied Health Applications Integrated into

Developmental Mathematics Using Problem Based

Learning

Mark ShoreDivision Chair of MathematicsAUegany College of Maryland

12401 Willowbrook RoadCumberland, Maryland 21502

Mshore@allegany. edu

JoAnna ShoreDepartment of Business Management

Frostburg State University101 Braddock Road

Frostburg, Maryland 21532jbshorecgfrostburg. edu

Stacey BoggsMathematics Department

Allegany College of Maryland12401 Willowbrook Road

Cumberland Maryland 21502Sboggs@allegany. edu

Abstract

For this FIPSE funded project, mathematics faculty attended alliedhealth classes and allied health faculty attended developmental mathematicscourses to incorporate health examples into the developmental mathematicscurriculum. Through the course of this grant a 450-page developmentalmathematics book was written with many problems from a variety of alliedhealth fields (Shore, 2003). A pre-test, post-test, and questionnaire weredeveloped and found to be reliable. Results consistently showed theexperimental sections of developmental mathematics that incorporated alliedhealth examples and problem-based learning scored significantly higher thanthe control sections. In fact, the scores for students in sections taught usingPBL and allied health examples during the first year of the grant weresignificantly greater than the scores for students the preceding semester ofthe grant, taught by the same teachers.

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- MA THEMA TICS AND COMPUTER EDUCA TION -

Project Overview

This project started from a workshop that was made involvingmembers of the mathematics and nursing faculty which put together aprototype lesson that used problem-based learning and integrated a topicfrom nursing (kidney function). Through the collaborative work of thisworkshop, the mathematics and nursing faculty decided to write a FIPSE(Fund for the Improvement of Post-Secondary Education) proposal, whichwas accepted.

Example Problem

Blood Urea Nitrogen (BUN) and creatinine: Keys to kidney function.Although serum creatinine levels indicate renal damage more reliably thanBUN levels, a nurse needs both values for a complete view of kidneyfunction. Their simultaneous rise is the focus. As nephrons lose the ability toremove waste products from the blood, BUN and creatinine accumulate. Thechange is subtle at first because nephrons that can still function willcompensate for a while. But as more and more nephrons stop functioning,BUN and creatinine levels rise significantly. Although serum creatinine levelsindicate renal damage more reliable than BUN levels, you need both valuesfor a complete view of kidney function. Their simultaneous rise is the key todiagnosing kidney disease.

The graph below shows the relationship between glomerular filtration(in percent of normal as measured by creatinine clearance), BUN, and serumcreatinine. The broken horizontal line represents the upper normal BUN andserum creatinine levels. The curve shows changes in BUN and serumcreatinine levels as the glomerular filtration rate decreases. As much as 75% ofrenal function must be lost before BUN and serum creatinine levels rise abovenormal. However, further small losses of renal function cause large increasesin BUN and creatinine levels.

BUN <ino/ill)

225

200

175

150

125

100

Serum crestinine (mo^)

: 20

50 75 100

Gtomerular filtralion (% of normal)

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Use the graph on the previous page to answer the followingquestions:1. What are the approximate upper-normal BUN and serum creatinine levels?2. Approximately, what does a person's glomerular filtration (% of normal)

need to drop to before a person's BUN and serum creatinine levels areabove upper-normal?

3. Does your answer to question #2 agree with what is stated in theparagraphs next to the graph? Explain why or why not.

4. As a person's glomerular filtration (% of normal) increases, what ishappening to their BUN and serum creatinine levels?

5. Does a person's BUN and serum creatinine levels increase more when theglomerular filtration (% of normal) goes from 100 to 25 or when theglomerular filtration goes from 25 to 0?

6. Approximate the BUN level when the glomerular level is at 50%, and75%.

7. Find the slope of the line that goes through the points you got fromproblem #6.

8. What does the slope of the line tell us about the BUN and glomerularfiltration level?

9. Find the equation of the line (model) that goes through the points fromproblem #6.

10. What is the ;;-intercept and what does it tell us about the BUN andglomerular filtration level?

11. Use your linear model from problem #9 to predict the BUN level if aperson's glomerular level is at 90% of normal.

12. Use your linear model from problem #9 to predict the BUN level if aperson lost 90% of renul function.

13. Do you believe a linear function models this situation well? Why or whynot?

Purpose and Results

This project addressed the high percentage of students that failDevelopmental Mathematics courses. To try to make more students in thesecourses successful, this project developed a curriculum, a DevelopmentalMathematics book, and new assessments that would link the DevelopmentalMathematics curriculum to the allied health fields. It was hoped that throughthis integrated approach, students would find the DevelopmentalMathematics courses more meaningful and therefore would more likelysucceed in the course. The results showed that this integrative approach didwork, and hundreds of students benefited from the work from this project.Comparison of post-test scores for experimental sections and control

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sections of Developmental Mathematics consistently showed that theexperimental sections that used problem-based learning and allied healthexamples performed significantly better than students in the control sections.Also from questionnaire results, experimental sections of DevelopmentalMathematics rated what they learned to be more useful in their science andallied health courses. This project could be used to link any mathematicscourse (developmental or general education) to any major field at anycollege. For example, a project could be developed similar to this one thatlinks the mathematics courses that elementary teacher education majors needto take with computer literacy skills (such as using spreadsheets).

After completing this project we now understand that there are someDevelopmental Mathematics students that will not succeed no matter whatthe teacher does. The lack of success of these students often has little to dowith ability, but rather their motivation and/or inappropriate reasons forattending college (e.g., to qualify for their parent(s) health insurancecoverage). While the project consistently showed significantly higher scoresfor the experimental sections compared to the control sections, there werealways students in both the experimental and control sections that did notbother to attend most of the classes and therefore did not succeed. It wasalso found during the course of this project that many mathematics facultyare entrenched in the belief that the topics that are currently taught inDevelopmental Mathematics should not change and are unwilling to make achange in the curriculum for fear that it would hurt the students' futuremathematics courses. Therefore, any project that wishes to make asignificant curriculum change must address the fact that some facultymembers are unwilling to change. For example, while many DevelopmentalMathematics educators have changed their teaching and the curriculum toincorporate graphing calculators, the collaboration project found that alliedhealth faculty did not want Developmental Mathematics students usinggraphing calculators, since allied health majors must do calculations withouta calculator on state board tests.

As part of the grant, the percentage of test problems that related toallied health were to be at 30% the first year, 50% the second year, and70% the third year. While we met all of these goals, we found that the 70%level was too high and lowered the success level during the third year. Alesson here is that the project directors should not try to meet the goals ofthe grant as they were stated in the original write up, but adjust them basedon the new knowledge gained during the project. Also, any futtire projectthat integrates two different curricula, must realize that faculty that are notteaching in the major area of the grant will have a very difficult timedeveloping example problems.

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In designing a project, the project director should check backgroundreferences with department heads for the faculty members that want to be apart of the grant. The project director should also get in writing a memo ofunderstanding with the faculty team members of the grant to make sure theyunderstand what tasks they will need to complete and the time schedule forthe completion of each topic.

Background and Origins

This project started as a workshop between nursing and mathematicsfaculty to illustrate to the rest of the college faculty the use of problem-based learning and how to integrate topics from other fields (such as alliedhealth) into other fields (such as Developmental Mathematics). Prior to thisproject the success rates (the percentage of students that obtained a grade of"C" or higher) in Developmental Mathematics was at 50%. The first yearof the grant involved three mathematics instructors and two nursing facultyand affected 110 students. The second year of the grant added a respiratorytherapy instructor, a radiology instructor, and a physical therapy instructorand affected 350 students. The third year of the grant involved everyonefrom the second year of the grant and added an occupational therapyinstructor, two medical laboratory instructors, an additional mathematicsinstructor, as well as a helping fields instructor, and affected 512 students.During the course of the grant we received funding for equipment fromAllegheny Energy, and two Eisenhower grants. These three additionalgrants allowed us to digitally record these problem-based learning lessonsand to put them onto CD's and onto the college's web site. After the firstyear of the grant we bundled the Developmental Mathematics textbook wewrote with the current textbook so that neither the college nor FIPSE wouldhave to pay for the cost of duplication. It is hoped that next year thetextbook that we wrote will be able to be used as a stand alone text.

Evaluation/Project Results

A questionnaire and a pretest/posttest were developed and found tobe reliable. Each semester the questionnaire and the test instruments weregiven to all Developmental Mathematics students at the college.Developmental Mathematics sections were divided into "control sections"(sections that did not use problem-based learning and examples from alliedhealth), and "experimental sections" (sections that used problem-basedlearning and examples from allied health). Each year of the grant theexperimental sections' scores were significantly higher than the controlsections. In fact, the scores for students in sections taught using PBL and

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allied health examples during the first year of the grant were significantlygreater than the scores for students the preceding semester of the grant,taught by the same teachers. The grant also satisfied the goal in constantlyincreasing the percentage of problems on tests in developmentalmathematics that related to the health fields. The success percentage ofstudents enrolled in Developmental Mathematics also went up for two ofthe three years of the grant. In the third year of the grant, the successpercentage fell. This drop was due to two reasons; 1) the college had asharp increase in enrollment and the majority of students that made up theincrease tested (on placement tests) at a very low level, 2) the percentageof questions on tests that related to allied health for the third year of thegrant was to be at least at 70%. The actual percentage was nearly 80%and I believe that this percentage of applied allied health mathematicsproblems, which are more difficult than procedural problems, alsoaffected the success percentage.

m % of problems thatrelated to AlliedHealth

• Success rate

Year 3

Summary and Conclusions

There are many variables that affect student success inDevelopmental Mathematics such as; student and teacher motivation, properplacement, use of technology, and the use of real-life examples (such asallied health). This grant only focused on the use of real-life examples.More work needs to be done to incorporate the other variables, such asusing technology (e.g., spreadsheets), into the Developmental Mathematicscurriculum.

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References

1. Introductory and Intennediate Algebra: Applications and models related to the HealthFields, (2003), Pearson Education, ISBN 0-536-704821

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allied health applications integrated into developmental

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