About the Project

About the project:

I ran this project with some students at a summer camp last year. I would be very interested in working with anyone who wished to implement part of this project, particularly if we could then study its effectiveness and then present at an appropriate meeting. (Contact me, Richard Lahti, 218-477-2149, [email protected])

Ways to use it: In a regular class, I would use this as a final authentic assessment project for a unit on mechanics. If I was really crazy and knew I had a class that could handle it, I might go full blown discovery learning and try to teach all of mechanics “just in time” to the students as they needed it throughout the unit.

This project covers both math and science standards, and I see it working best as a team endeavor (unfortunately the standards do not line up as well across grade levels as one would hope, with 6th grade, 9th grade physical science, and 12th grade physics containing most of the science content standards and 6-8 math containing most of the math standards).

Activities in this unit aligned with 15 Nature of Science and Engineering standards (grades 6-12), 9 physical science standards (grades 6-12) and 17 mathematics standards (grades 6-8), including all of the new middle school emphasis on algebra!

As typical, I have used the 5E learning cycle (loosely at times) throughout most of the lessons.

ENGAGE: Each year before the NFL draft, athletes go to the NFL Combine, where their physical statistics (height, weight, etc.), performance (40 yard dash, bench press, etc.), and other factors (Wunderlick IQ test, etc.) are measured. From these numbers, some draft analysts think they can predict who will be a better professional ball player than by comparing the player's actual game statistics!

Show a some video clip of vertical jump:  http://www.youtube.com/watch?v=T8C3lJBcXxE&feature=related (basketball) . http://www.youtube.com/watch? v=NvohSII2C9o&feature=PlayList&p=8099867A75B3E8A2&playnext=1&playnext_from= PL&index=25 (high jump) . http://www.youtube.com/watch?v=7vL19q8yL54 (weight room, mute, because of swearing) . http://www.youtube.com/watch?v=QoKhEiAHfYs&NR=1 (Volleyball, 50 inch vertical)

ELICIT: Next, brainstorm what factors (variables) might contribute to these people being able to jump so high? As they come up with ideas, try to build consensus as to whether the relationship should be a positive correlation or a negative correlation (use of the terms is not critical) and whether the correlation should be weak or strong. An example brainstorm chart might look like this. Strong Positive Strong negative Weak Positive Should not Might be correlation correlation correlation matter interesting to look at Strong Glutes Mass Strong upper Height Foot length body Strong quads Flexibility Gender (does it matter if everything else is equal)? Strong calves Age? Long Jump 40 yard dash

At this point, we talk about a few Nature of Science ideas. I ask whether the above are hypotheses or not? (I argue, NO, since these are not EDUCATED guesses. For our purposes, an EDUCATED guess will mean based off of an existing scientific law, theory, model, etc.) Thus, while it is common sense that people who have strong legs should be able to jump higher, before I let them call it a scientific hypothesis, they had to be able to find some piece of scientific evidence (like Newton’s 2nd law, etc.) that would support this idea.

EXPLORE: While in true 5E the next step would be to “Go forth and measure,” In my case I was dealing with students who I knew next to nothing about. If students are adequately prepared from the physics standpoint so that they are already thinking in terms of force, mass, acceleration, etc. then turn them loose. In my case, I was more interested in having them apply these ideas to the real world, and cheated – giving them some basic physics relationships to help them think about which of the above possible relationships they might want to measure.

Mini-physics lesson. The goal was not to teach full lessons on these, just enough to get them to the next phase, some equations to more exactly quantify their “common sense” above.

a. Newton’s 2nd law, F=ma. Greater acceleration from more force or less mass… b. Conservation of energy, work = KE = PE. A person who can do more “work” whatever that is, can go/throw faster (kinetic energy) or jump/throw higher (potential energy). c. Work = Fd. This relates back to (b.), because we now define work as depending on force (stronger muscles should make a difference) and distance (perhaps a longer foot, deeper knee bend…?). Give example with barrel length and guns (longer barrels tend to produce higher velocities in the exact same bullet). d. In a physics class, I would perhaps derive: Final velocity for object under acceleration Vf = √(2ad) (again, the distance over which the force (and thus the acceleration) is applied matters?) e. In a physics class, I would perhaps derive: Equation of motion for object 2 launched vertically h = vi /2g. Thus height depends on initial launch speed. f. It is possible we might end with a final equation like height α Fd/mg

After hitting each of these nuggets, I then asked students to turn some of their brainstorming relationships into hypotheses. Vertical jump height should increase as [variable x] increases/decreases BECAUSE (cite equation, law, theory, etc.).

Now that they have hypotheses (divide into groups at this point depending on #variables to test and #of students in class) it is time to design the experiment.

Experimental design. If we were going to try and figure out which of these variables actually DO correlate with vertical jump, how would we design a fair test? It turns out that we really can’t. Apart from jumping on one leg vs. two, or jumping with increasing weights in each hand (dumbbells) or weights in a backpack, it is hard to keep the most important variable, the jumper, the same. Thus, for most variables, a series of different jumper’s jump and 1 other measurement (length of leg, leg press, etc.) will be measured.

Within these constraints, it is still possible to talk about appropriate experimental design.

Collect data in a weight room on various measurements. While a 1 rep max is the best measure of maximal force, this is unsafe. For safety, use http://www.xplosivespeed.com/transfer/strengthmaxconversion.htm to convert their “multiple rep max” to a “1 rep max”. Have them shoot for the lower weight/high rep.

EXPLAIN: Again, I felt like it was appropriate to interrupt and do a little instruction on how to use Excel to generate a scatter plot, and then find a trendline, and finally to interpret the slope and intercept of that line.

While in the weight room, I demonstrated the leg press, using a Vernier force plate to measure the actual force needed to push the leg press as additional weight was added.

weight added force measured Weight added (pounds) (N) (N) 0 0 430 90 400.9090909 700 180 801.8181818 970 270 1202.727273 1230 360 1603.636364 1480 Students entered this data into Excel, and then were taken step by step through the process of generating an XY scatter plot, and finally adding a trend line, and displaying the equation and the R2 on the chart. The chart looked like:

This ends up being an instructive place to start, because this graph has a very easy to interpret, real-world slope and intercept.

The intercept of 436N at 0N of additional weight added corresponds to the apparent weight of the apparatus that slides back and forth and which holds the additional weights. A student sitting under the leg press can feel that even though no weight has been added, there is a definite force needed.

The slope of 0.656 actually comes out close to what one would expect from an inclined plane of the dimensions measured. The slope should be relatively close to the tangent of the angle of incline (vertical distance travelled/total distance travelled). Because of the inclined plane present in the system, the lifter only lifts 66% of every Newton added.

R2 was also discussed in terms of “goodness of fit”. While I did not go into great detail, the idea that the square root of this number (R) is the fraction of the variation in the dependent variable that the independent variable explains could be discussed. Therefore, an R= 0.7 would mean that the variations in the independent variable in that case explained 70% of the variation seen the dependent variable, a very important variable indeed. After completing this intro to graphing, students completed Excel graphs of their own individual hypotheses about jump height.

EXPLAIN: Students can share their results with the class and see what conclusions they come to.

1. Which variables seem to be most strongly related to vertical jump? Use a linear equation to make a prediction – “if I wanted to increase my vertical leap by 2 inches, I would need to increase my leg press by X pounds…” Try to get students to do it graphically (by looking at the graph) and algebraically (by plugging into the equation) both. 2. Discuss correlation and causation. It may turn out that upper body strength is as strongly related to vertical jump as lower body strength is. Does that mean doing more curls (or bench) would help you jump higher? Or possibly, is it because people who tend to exercise tend to exercise all body parts, and thus have stronger arms too, in addition to stronger legs, and that effect leads to this correlation between arm strength and jumping (important idea, but not explicitly in standards?) 3. Assuming that there are a roughly equal number of boys and girls. What happens if these data points are graphed separately (Jump height vs. leg press boys only, Jump height vs. leg press girls only)? Are any parts of the equations pretty close (slope? Intercept?) should they be? Why or why not? (the intercepts perhaps might be different, but the slopes should probably be similar, because the relationship between force and mass and acceleration is dictated by Newton’s Law. The variables not explicitly being studied ends up lumped together in the intercept. Thus, if it was leg press and jump being studied, then the intercept would be different because boys (at least at older ages) tend to have more mass than girls. But in both cases (boy and girl) a student with stronger legs should, all things being equal, jump higher. 4. Explain that a more sophisticated program than Excel can factor out a variable (if all other factors are equal, would a girl with the same leg press and mass as a boy have the same vertical or not?). It can also say what variables are most important. I intended to run Minitab on our data set and show it the results but 9 data points was not sufficient).

EXTEND/ELABORATE. At this point students were set free to select a different trait to research on their own (again, I had the advantage of 4 teachers to 9 students; obviously you would probably have students work in groups and might wish to restrict topics to preserve sanity). It took some careful planning to make sure all the traits were measured safely, accurately, and with as little wasted time as possible. Those of you at small schools might be able to tag team with PE and see if some of these measurements could be taken in PE class.

If students needed more ideas: 1. Watch some more videos. a. http://www.youtube.com/watch?v=9DgK_qiSut8 (discus throw, a safer alternative is a basketball throw from knees) b. http://www.youtube.com/watch?v=bCugqNjPemU slow motion pitching … length of motion actually should be important in pitching speed. c. http://www.nfl.com/combine/videos/features#page:2/video:09000d5d80ee 0a12 (broad jump) d. http://www.nfl.com/combine/videos/features#page:2/video:09000d5d80ed c4c7 (shuttle run) e. http://www.nfl.com/combine/videos/topperformers#page:1/video:09000d5 d80edffeb (top 40 yard dash) f. Certainly other topics than these could be studied. (Students chose to investigate such relationships as punch force, sprinting time, shuttle run, long jump, throwing speed, and volleyball serve speed.)

2. Brainstorm important variables that might lead to big results in the chosen event.

3. Mini-physics lecture on angular momentum – longer objects are harder to accelerate, but achieve a greater linear speed at the same rotational speed. Several demos (this should give students ideas to measure arm length for basketball throw).

4. Repeat basic ideas from above: a. Form hypotheses based off of physics principles. b. Decide on what data needs to be collected, what variables matter. c. Decide on procedures. d. Collect data. I would expect, in addition to the data already collected, additional upper body measurements (military press, bench, curl, arm length) might be needed. e. Determining speed of a pitch/serve is where video analysis became useful. Without video analysis, distance makes a good surrogate, since the faster the initial speed, the further a particular object will go, assuming that the angle is the same. f. Analyze data g. Form conclusions

5. Look at correlations between some of the measures – are they redundant? For instance, if 40 yard dash, shuttle run, broad jump and/or vertical jump all seem to depend on the same things, is it necessary to measure all? In part, this is why a combine only uses about 5 measurements to make multimillion dollar decisions.