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Allied Health Applications Integrated into Developmental Mathematics Using Problem Based Learning

Shore, Mark; Shore, JoAnna; Boggs, Stacey. Mathematics and Computer Education38. 2 (Spring 2004): 183-189.

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For this FIPSE funded project, mathematics faculty attended allied health classes and allied health faculty attended developmental mathematics courses to incorporate health examples into the developmental mathematics curriculum. Through the course of this grant a 450-page developmental mathematics book was written with many problems from a variety of allied health fields (Shore, 2003). A pre-test, post-test, and questionnaire were developed and found to be reliable. Results consistently showed the experimental sections of developmental mathematics that incorporated allied health examples and problem-based learning scored significantly higher than the control sections. In fact, the scores for students in sections taught using PBL and allied health examples during the first year of the grant were significantly greater than the scores for students the preceding semester of the grant, taught by the same teachers. [PUBLICATION ABSTRACT]

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Abstract

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

Project Overview

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

Example Problem

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

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

Use the graph on the previous page to answer the following questions:

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 are above upper-normal?

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

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

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

6. Approximate the BUN level when the glomerular level is at 50%, and 75%.

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

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

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

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

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

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

13. Do you believe a linear function models this situation well? Why or why not?

Purpose and Results

This project addressed the high percentage of students that fail Developmental Mathematics courses. To try to make more students in these courses successful, this project developed a curriculum, a Developmental Mathematics book, and new assessments that would link the Developmental Mathematics curriculum to the allied health fields. It was hoped that through this integrated approach, students would find the Developmental Mathematics courses more meaningful and therefore would more likely succeed in the course. The results showed that this integrative approach did work, and hundreds of students benefited from the work from this project. Comparison of post-test scores for experimental sections and control sections of Developmental Mathematics consistently showed that the experimental sections that used problem-based learning and allied health examples performed significantly better than students in the control sections. Also from questionnaire results, experimental sections of Developmental Mathematics rated what they learned to be more useful in their science and allied health courses. This project could be used to link any mathematics course (developmental or general education) to any major field at any college. For example, a project could be developed similar to this one that links the mathematics courses that elementary teacher education majors need to take with computer literacy skills (such as using spreadsheets).

After completing this project we now understand that there are some Developmental Mathematics students that will not succeed no matter what the teacher does. The lack of success of these students often has little to do with ability, but rather their motivation and/or inappropriate reasons for attending college (e.g., to qualify for their parent(s) health insurance coverage). While the project consistently showed significantly higher scores for the experimental sections compared to the control sections, there were always students in both the experimental and control sections that did not bother to attend most of the classes and therefore did not succeed. It was also found during the course of this project that many mathematics faculty are entrenched in the belief that the topics that are currently taught in Developmental Mathematics should not change and are unwilling to make a change in the curriculum for fear that it would hurt the students' future mathematics courses. Therefore, any project that wishes to make a significant curriculum change must address the fact that some faculty members are unwilling to change. For example, while many Developmental Mathematics educators have changed their teaching and the curriculum to incorporate graphing calculators, the collaboration project found that allied health faculty did not want Developmental Mathematics students using graphing calculators, since allied health majors must do calculations without a calculator on state board tests.

As part of the grant, the percentage of test problems that related to allied health were to be at 30% the first year, 50% the second year, and 70% 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. A lesson here is that the project directors should not try to meet the goals of the grant as they were stated in the original write up, but adjust them based on the new knowledge gained during the project. Also, any future project that integrates two different curricula, must realize that faculty that are not teaching in the major area of the grant will have a very difficult time developing example problems.

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

Background and Origins

This project started as a workshop between nursing and mathematics faculty to illustrate to the rest of the college faculty the use of problembased learning and how to integrate topics from other fields (such as allied health) into other fields (such as Developmental Mathematics). Prior to this project the success rates (the percentage of students that obtained a grade of "C" or higher) in Developmental Mathematics was at 50%. The first year of the grant involved three mathematics instructors and two nursing faculty and affected 110 students. The second year of the grant added a respiratory therapy instructor, a radiology instructor, and a physical therapy instructor and affected 350 students. The third year of the grant involved everyone from the second year of the grant and added an occupational therapy instructor, two medical laboratory instructors, an additional mathematics instructor, as well as a helping fields instructor, and affected 512 students. During the course of the grant we received funding for equipment from Allegheny Energy, and two Eisenhower grants. These three additional grants allowed us to digitally record these problem-based learning lessons and to put them onto CD's and onto the college's web site. After the first year of the grant we bundled the Developmental Mathematics textbook we wrote with the current textbook so that neither the college nor FIPSE would have to pay for the cost of duplication. It is hoped that next year the textbook 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 to be reliable. Each semester the questionnaire and the test instruments were given 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 allied health), and "experimental sections" (sections that used problem-based learning and examples from allied health). Each year of the grant the experimental sections' scores were significantly higher than the control sections. In fact, the scores for students in sections taught using PBL and allied health examples during the first year of the grant were significantly greater than the scores for students the preceding semester of the grant, taught by the same teachers. The grant also satisfied the goal in constantly increasing the percentage of problems on tests in developmental mathematics that related to the health fields. The success percentage of students enrolled in Developmental Mathematics also went up for two of the three years of the grant. In the third year of the grant, the success percentage fell. This drop was due to two reasons; 1) the college had a sharp increase in enrollment and the majority of students that made up the increase tested (on placement tests) at a very low level, 2) the percentage of questions on tests that related to allied health for the third year of the grant was to be at least at 70%. The actual percentage was nearly 80% and I believe that this percentage of applied allied health mathematics problems, which are more difficult than procedural problems, also affected the success percentage.

Summary and Conclusions

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

References

References

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