A New IPLS Course: From Design to Dissemination

A New IPLS Course: From Design to Dissemination

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David P. Smith Duane L. DeardorffAlice D. Churukian Colin S. Wallace Laurie E. McNeil

University of North Carolina at Chapel Hill

SESAPS Meeting – November 2016

Physics & Astronomy Education Research Group

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2Motivation and Design

¡ National reports supporting change in undergraduate biology education¡ BIO 2010¡ Vision and Change¡ Scientific Foundations for Future

Physicians

¡ Can the quantitative skills being used at the research/graduate level in biology begin to permeate through to undergraduate education?


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¡ Learn from leaders in the community¡ Joe Redish and the Physics Education

Group at the University of Maryland, College Park.

¡ Dawn Meredith and Jessica Bolker, University of New Hampshire

¡ Catherine Crouch, Swarthmore College¡ Ken Heller and the Physics Education

Group at the University of Minnesota


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¡ Challenges raised in sustainability of a new IPLS course transformation

C. H. Crouch, K. Heller, AJP 82, 2014


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¡ Local Level

¡ What are the needs of our student population?

¡ Does our course meet these needs?


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6Design Process

¡ Begin with a blank slate

¡ Multiple discussions with faculty in all three scientific disciplines.¡ Outcome was on focus on skills

rather than concepts¡ Many desired an emphasis on

logical and critical thinking


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7Evaluation of TopicsTopic

1-D Motion2-D MotionForcesPlanetary MotionRotational MotionTorque and EquilibriumMomentumWork and EnergyThermal PhysicsFluidsGeometrical Optics

TopicWave OpticsElectric Fields and ForcesElectric PotentialDC CircuitsMagnetic Fields and ForcesInductionAC CircuitsRelativityQuantum PhysicsNuclear Physics


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8Evaluation of TopicsTopic

1-D Motion2-D MotionForcesPlanetary MotionRotational MotionTorque and EquilibriumMomentumWork and EnergyThermal PhysicsFluidsGeometrical Optics

TopicWave OpticsElectric Fields and ForcesElectric PotentialDC CircuitsMagnetic Fields and ForcesInductionAC CircuitsRelativityQuantum PhysicsNuclear Physics


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9Evaluation

New Topics Revised Topics Removed Topics

Biological Scaling

Stress and Strain

Diffusion

Forces and Kinematics combined. Non-linear accelerations

Torque and its role in biomechanics

Planetary Motion

Rotational Kinematics

Allometry –Biological Scaling

Stress and Strain

Diffusion

Forces and kinematics

Torque and its role in biomechanics

Thermodynamics

Fluids

Planetary Motion

Rotational Kinematics

AC Circuits


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10Examples

¡ Newtonian Mechanics¡ Jumping Grasshoppers

¡ Impulse and Momentum¡ Collisions and concussion

¡ Chemical Energy¡ Potential energy of chemical bonds

¡ Fluids¡ Viscous Fluids and Poiseuille’s

Equation


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11Examples

¡ Electric Potential and Circuits¡ Electrocardiogram¡ Nerve signal propagation

¡ Magnetism¡ MRI

¡ Optics¡ Eye


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12Course Structure

¡ Research-based and research-validated teaching methods.

¡ Fit within the administrative constraints of the department.

¡ Adopted New Studio model developed at Kansas State University and Colorado School of Mines.


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13New Studio Model

¡ Increased time with hands-on activities and tutorial exercises.

¡ Significant improvement in coherency between lecture and lab material.

Mon Tues Wed Thurs Fri

Morning Lecture

Afternoon Studios

Morning Studios

AfternoonStudios

MorningLecture

AfternoonStudios

Morning Studios

AfternoonStudios

Review session


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14Surface Area to Volume Ratio

¡ Considering that heat loss is related to surface area and metabolism is related to volume/mass, surface area to volume ratios can be critical for survival.

Area∝ l2

Volume∝ l3

Volume∝ Area32

Area∝Volume23

Area∝Volume23

AreaVolume

∝Volume−13

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Physics Activities for the Life Sciences (PALS) © Physics and Astronomy Education Research Group The University of North Carolina at Chapel Hill

Scaling: Mathematical Models

Introduction

In the previous two lectures, and in the Breathing Worms studio activity,

we addressed a number of ideas related to biological scaling. In the Breathing Worms activity, we identified particular limits on the growth of an earthworm due to its ability to absorb and use oxygen. In lectures, we introduced a number of mathematical tools that allow us to investigate these particular scaling laws.

In this activity we will extend on those ideas by exploring how linear, power law, and exponential functions can model biological observations. We will begin by investigating the mass growth rate of baboons and finish with exploring the relationship between lifetime expectancy and resting heart rates.

Learning Goals

After completing this studio, you should be able to…

• List at least one example of a scaling law used in a biological context.

• Make plots in Microsoft Excel®.

• Determine the best fit trendline from a scatter plot.

• Describe the physical meaning of a slope and intercept from the plot of a set of data.

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A. How does a baboon’s body mass change with time?

In their paper “Body mass and growth rates in a wild primate population,”1 J. Altmann and S. Alberts present the results of an experiment in which they measured the growth rate of body mass in wild baboons (Papio cynocephalus) in Amoseli National Park, Kenya. The data were obtained without trapping the animals. Instead, the authors of the study placed a dialtype platform scale under the tree where the baboons were sleeping, and in the morning the baby baboons climbed on it to play. The observers stood a few meters away from the scale and read it using binoculars. Some uncertainty in the mass values arose from the animal’s tail hanging off the scale and resting on the ground.

The scientists (Alto and Hook) gathered data on two social groups of the same species of yellow baboons. The data for each group is shown below.

Alto Female Alto Male Hook Female Hook Male

Age (mos.)

Mass (kg)

Age (mos.)

Mass (kg)

Age (mos.)

Mass (kg)

Age (mos.)

Mass (kg)

7.00 1.60 12.0 2.50 5.50 1.80 7.50 1.9014.0 2.75 18.5 3.40 7.00 1.30 17.5 3.9014.5 2.90 18.5 3.70 9.50 2.75 19.5 3.9015.5 2.80 22.0 3.70 11.5 2.75 21.0 4.5016.0 3.00 23.0 3.60 12.0 2.30 30.0 5.2017.5 3.30 23.0 4.30 17.0 3.50 35.0 6.0019.5 3.20 31.0 4.90 19.0 3.3020.0 2.75 32.5 5.00 19.5 3.7037.0 5.60 37.5 5.50 24.5 4.20

25.0 4.0035.0 7.0036.0 6.30

1. Download the Excel template from Sakai and make a single plot to include these data for the female and male baboons of the Alto group. Decide which function best describes how the baboon’s mass changes with time, and add an appropriate trendline for each set of data.

2. Write down the equation of both trendlines and the R2 values.

3. Another group of students has carried out the same exercise. Their discussion went as follows.

1. J. Altmann and S. Alberts, Body mass and growth rates in a wild primate population, Oecologia 72, 15-20 (1987).


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Jennifer: “Well, the data looks pretty linear. Maybe we should add a linear trendline and find the R2 value.”

Isaiah: “That’s a good place to start. But maybe we should also find the R2 value for other functions.”

Julia: “Oh look, the power function has a better R2 value for the male baboon. I think we should go with that function.”

Suppose that you were to take Julia’s advice and model the growth rate as a power function. Are there any flaws in this model? What would the model predict as the time goes to zero? Does it make sense to have two different models for the growth rate of the male and female baboons? Explain.

✓Check your answers with a TA before proceeding.

4. The equation for each trendline should contain two numbers. For a single trendline, explain the meaning of each number in the context of these data, and determine the units using dimensional analysis.

5. How do the numbers for the male baboons compare to those of the female baboons? Explain.

6. We define growth rate as the amount a specific variable changes by per unit time. In this context, the researchers are interested in how the mass of the baboon changes with time. Which of the numbers in the equation of the trendline represents the growth rate?

7. For Hook’s group, make a similar plot including data for both the female and male baboons, and determine the corresponding growth rates.

8. How does the growth rate of the male and female baboons in Hook’s group compare to those in Alto’s group? Explain.

9. Suppose that another researcher has gathered data on the mass of the same species of baboon but is unsure of the age. Determine an approximate age of each baboon. Explain your method clearly.

Number Sex Mass (kg)

1 Male 3.502 Male 4.603 Female 3.204 Female 4.40


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B. Measuring the growth rate of E. coli

As part of a microbiology lab, students are investigating the growth rate of Escherichia coli (E. coli). Beginning with the original E. coli culture, 1 ml is transferred to another test tube containing 9 ml of broth, thus creating a 1:10 dilution. This method is continued until they have created a 1:100,000-dilution factor and this sample to transferred to the petri dish. The students counted eight cells on the plate and continue to monitor the growth at regular intervals over a period of two hours. The data is shown at right.

1. Plot of the number of bacteria as a function of time in Excel, and compare to the plot for the baboon’s mass. Do these growth rates follow the same function? Explain.

2. You may be thinking that the cell growth is determined by either a power or exponential function. Power functions take the form y = nxk. Notice here that the variable x is raised to a fixed power k. Taking the log of both sides gives us log(y) = klog(x) + log(n), which takes the form of a linear equation, y = mx + c. Make a plot of log(no. of bacteria) versus log(time) to determine whether this is a power function. (This plot is called a log vs. log plot.)

3. Exponential functions take the form y = nakx. Notice the difference here; the variable x is now part of the exponent, with some base value a raised to the power of the variable kx. Taking the log to the base a of both sides results in the equation: log(y) = kx + log(n), which also takes the form of a linear equation. Make a plot of log(no. of bacteria) versus time to determine whether this function is exponential. (This plot is called a semi-log plot.)

4. After you have completed your analysis, write down the equation of the function that best describes the growth rate of the bacteria. Express the equation in both log and exponent form.

Time (min)

No. of bacteria

0 830 1760 3390 66120 120150 255180 505210 970240 1920


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C. Heart rates and life expectancy2

In this section we will explore how the lifetime and resting heart rate of a mammal varies with the mammal’s mass. We will then combine these relationships to investigate whether there is a given longevity for all mammals.

1. The data for several different mammals is provided at right. What trends do you notice in the data?

2. Make a plot of the heart-rate of each mammal as a function of its mass. What type of function (e.g., linear, power law, exponential) do you think best suits the data? (Hint: Try making a linear plot, a log vs. log plot, and a semi-log plot and compare.)

3. Make a similar plot for the lifespan as a function of the mammal’s mass and determine the most appropriate function that links these two quantities.

There has been much research on mammal longevity in regard to whether each mammal has a certain amount of heartbeats in a lifetime.

4. Calculate the total number of heartbeats for each mammal. Are the differences in the total number of heartbeats for each mammal greater than an order of magnitude?

5. Compute the average number of total heartbeats for the mammals given above. Assuming that humans had the same average number of heartbeats, what would be the average expected lifespan giving a resting heart rate of 75 bpm?

6. What did you notice in the previous question? Does the average heart rate and lifespan of humans fit with the data above? If not, hypothesize some reasons for any inconsistencies.

7. Please upload your Excel file that includes completed work for all sections using the Assignments tab in the Studio Sakai site.

8. Please record the total time in minutes that you have spent on this entire studio.

2. Herbert J. Levine, Rest Heart Rate and Life Expectancy, JACC Vol. 30, No. 4, October 1997 (1104-6)

Mammal Mass (g)Heart Rate

(bpm)Lifespan (years)

Mouse 20 650 2Hamster 80 400 3Rabbit 1100 130 8Cow 6.0 × 105 60 20Horse 5.0 × 105 35 25Elephant 5.5 ×106 30 60Whale 7.0 × 107 10 85



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15Scaling Post-test Questions

¡ The early equid Eohippus (Hyracotherium) lived about 52 million years ago. Skeletal evidence indicates that it stood approximately 35 cm at the shoulder. A modern thoroughbred horse stands 160 cm at the shoulder and has a mass of 450 kg. Based on the evidence of its descendent, what would you estimate the mass of Eohippus to have been?

A) 1 kg B) 5 kg C) 20 kg D) 50 kg E) 100 kg


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16Scaling Post-test Questions

¡ Our post-test show that many students still have difficulty with the scaling relationships between mass, volume, and length.

Answer % (N = 302)5 kg (Correct) 41%100 kg 48%


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17Force Concept Inventory

¡ How are our students doing on the FCI?


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18Concept Survey in E&M

¡ How are our students doing on the CSEM?


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19Conclusion

¡ All course materials are currently being prepared for widespread dissemination.

¡ Studio Materials¡ PALS – Physics Activities for Life Sciences

¡ paer.unc.edu

¡ Continue to improve current material, and explore additional topics and concepts.

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A New IPLS Course: From Design to Dissemination

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