Newtonian Mechanics In Sport

 

Description

A learning task that we envisage to be completed with our digital product is an open-ended investigation, in which students are expected to develop their own experiments. This is possible because the form of data delivered by our product is not specific to any particular investigation: it is simply motion data including speed, acceleration and trajectory. One example, which we will describe in some detail for illustrative purposes, is an investigation of projectile motion, in which students investigate the problem of finding the projection angle that maximises the range of a projectile.

 

Rationale

From the Physics and Science Syllabi

 

Investigations are suggested throughout the Physics and Science syllabuses, including computer-aided ones. Projectile motion, for example, is a topic in the Physics (Board of Studies NSW, 2009), which mandates the study of projectile motion. In particular, the syllabus suggests a first-hand investigation, followed by the use of data loggers and computer analysis. This is a recommendation that we are explicitly addressing with our learning task and product, because students are required to record data graphically and analyse this data computationally.

 

Moreover, the task reinforces work that the students have previously done on motion in year 10 Science, in which they became acquainted with the physical concepts of force, acceleration and speed. To complete the learning task that we envisage, students will be reminded of these concepts and their significance. For example, our digital product confronts students with both acceleration and speed data, which they will need to distinguish and interpret correctly.

 

Cross-Disciplinary Scope

 

Motion is not of interest to students of Science and Physics alone. It is also a topic studied in Mathematics. In these courses, students derive the equations of motion for a projectile and describe the motion with calculus. These students who also study Physics would benefit from the reinforcement that our learning activity provides, especially since they would be approaching the problem from a different angle to what they may be used to.

 

Our learning activity also enables the opportunity for students to analyse the performance of physical actions, kicking and throwing. This context is of interest to students who also study Physical Education and enables a cross-disciplinary approach to sports science.  The Personal Development, Health and Physical Education Stage 6 Syllabus (Board of Studies NSW, 2009) calls for the performance and analysis of movements such as throws and kicks. Our learning activity exposes Physics students to  a real-world situation in which an object moves, and shows PE students a new way to analyse throws and kicks.

 

As an example of how the learning experience is redefined (as according to the SAMR model; e.g. Puentedura, 2010) by our approach, we revisit the case of projectile motion. If this physical circumstance is considered from a purely analytical perspective, as is usually done, the projection angle that maximises the range of the projectile is 45°. However, students investigating this problem in the real world, in the manner enabled by our digital product, may find that this is not the case for practical reasons: because a student can launch a projectile farthest by kicking it, and the strongest kick may not be at this angle. With our digital product, students could investigate this most efficiently, by recording many kicks and using the analysis tools we have provided to process the data quickly. This is a valuable and redefining change to the learning experience because it highlights a physical nuance that is often overlooked in the classroom, but is significant in the real world.

 

Underlying Learning Model

 

The goal of our digital product is to provide an engaging technological platform that enables meaningful learning. It implements the Experiment Design Pattern, by providing the student with a scaffolded platform from which they can carry out an investigation. Students are able to use the digital product we provide to carry out an investigation of their choice. Projectile motion is one possibility among many.

 

Jonassen et al. (2008) emphasise the importance of the nature of the learning task in motivating students to learn, and the necessity of this motivation in meaningful learning. In particular, the students need to be wilfully engaged, and the learning activity can encourage this engagement by entailing cooperation and non-linear problem solving with clear real-world relevance. This is achieved by the learning activity we suggest, with its potential for cooperative problem solving and engagement that takes students both outside the classroom and outside their specific key learning area.

 

Technology as a Means to Provide a Scaffolded Platform

 

As discussed by, for example, Chen (2014), the scaffolding required to produce a meaningful learning experience varies according to the student. Accordingly, we have provided scaffolding in a manner that allows the teacher to vary the level of technological assistance. We have provided instructional videos that explain how the motion data can be obtained and analysed, and a program that produces plots of data derived from what is directly provided by the proprietary software.

 

We stress, however, that the technology does not serve as a teacher, and nor should it (Jonassen et al., 2008). The teacher should vary the level of technological scaffolding to optimise the value of the learning activity, and this will depend upon the student. For example, the program that we have written plots data automatically. The teacher may decide, however, that processing the data and plotting it for themselves would be a worthwhile exercise for the students, and not allow them to use the program. On the other hand, the teacher may prefer to allow use of the program where students have already mastered the low-level skills and would gain most from completing the high-level investigation that the derived data enable. This is the utility of technology suggested by, for example, Noura (2005).

 

A Redefinition of the Learning Experience

 

There is a great difference between the learning experience that we suggest, enabled by our digital product, and students’ usual study of topics in motion. Students do not normally have the opportunity to analyse the motion of objects with the precision that is enabled by our digital product, and rarely are they able to analyse the motion data with the ease afforded by the tools that we provide.

 

We provide a digital product that records of the position of an object in flight every one third of one tenth of a second. This is impossible without technology of the kind that we have described. Moreover, our digital product enables students to analyse and visualise this data quickly, and in a manner that can be repeated many times, to facilitate experimentation, which is the goal of the learning activity that we envisage. This is because we have written a program that automatically calculates and plots the derived quantities as many times as the student desires as part of their investigation. This is simply not possible without a program like what we have written. We have redefined the learning experience (as according to the SAMR model; e.g. Puentedura, 2010).

 

As an example of how the learning experience is redefined (as according to the SAMR model; e.g. Puentedura, 2010) by our approach, we revisit the case of projectile motion. If this physical circumstance is considered from a purely analytical perspective, as is usually done, the projection angle that maximises the range of the projectile is 45°. However, students investigating this problem in the real world, in the manner enabled by our digital product, may find that this is not the case for practical reasons: because a student can launch a projectile farthest by kicking it, and the strongest kick may not be at this angle. With our digital product, students could investigate this most efficiently, by recording many kicks and using the analysis tools we have provided to process the data quickly. This is a valuable and redefining change to the learning experience because it highlights a physical nuance that is often overlooked in the classroom, but is significant in the real world.

 

Innovation

The technical innovation in our product lies in our use of a range of technologies as ingredients in the learning activity – video-recording, graphical annotation and computer-aided analysis. We have written our own code to assist the students’ analysis of motion data, and used technology (in the form of instructional videos) to show how our digital product may be used. Moreover, we have created a webpage that students can visit to access all resources associated with our digital product in one convenient location. Students could visit this webpage and view the videos before the learning activity to realise a “flipped classroom” approach.

 

We exhibit pedagogical innovation by devising a learning experience that is simultaneously cross-disciplinary, differentially-scaffolded and technologically-engaging. This novel experience should also be memorable and allow many follow-up discussions in lessons that follow. Students can receive feedback from teachers while performing their investigations, and when their completed work is assessed.

 

Task Evaluation

 

This task was trialled in the classroom as part of the year eleven physics unit ‘moving about’.  Projectile motion is an important part of the physics syllabus, so it seemed to be an ideal lesson for a trial.  In its original form, the intention of this task was to provide a more exciting and engaging method for introducing mechanics to students.  Projectile guns were used to fire aluminium balls at a known angle.  The technology was used to measure the initial speed of the projectile, and from this we developed a model that would predict the entire trajectory of the ball, including a prediction of where the ball should land.

 

This did engage the students, and the results were acceptably accurate.  There were problems however with ball size, and ball speed.  If you pause the video below, you will see that the ball appears as a faint white streak, so to plot a point it is necessary to find the centre of the white streak.  This introduces a level of error.  The mottled background of a classroom can also make identification of the ball problematic.

 

Another problem with this particular trial is that it is only at the Augmentation level on the SAMR scale. We would have liked to test an implementation of our approach in which its potential for Redefinition (as we have discussed earlier in this report) was realised.  The task would work much better with a bigger, more colourful ball, preferably further from the camera.  The feedback we received from the students, and the observations I made have contributed to the product that has been submitted. Moreover, this trial was only partial: it did not include student use of the program that we wrote. Our final product, which we now have and with all of its elements included, is what we argue would form a Redefinition of learning activities in the topic of motion.

 

Video of the trial of this product is available for viewing on

http://www.prictor.com.au/wp-content/uploads/2014/09/IMG_01281.mov

 

To improve this product in future, we would consider a greater variety of options to include with the script that we wrote. For example, we have noted that part of the pedagogical thought in our approach is in the ability of the teacher to adjust the level of technological scaffolding that is available to the students. Some Physics students may have a higher level of computer literacy than their fellows, and we could use this script as a basis for extended activities.

 

Another possibility that could be explored is an online collaboration tool that students could upload their results to and compare results. For example, if a teacher had set the same task to several groups of students with the aim of later comparing their results (one investigation like this would be the empirical determination of the acceleration due to gravity), students could upload their results and compare them. A web interface could be designed to accept data and perform statistical comparison as desired by the teacher.

 

Appendix A: Additional Resources

 

The instructional videos that guide students in their use of our digital product, and the code for the python program that we wrote, may be found at this webpage:

• Digital Learning: Introduction to Sports Science

Further detail can also be found at this page.

Appendix B: Plots of Data Produced by Our “extraplots” Program

We wrote a program to process and visualise experimental data. Our script (the code for which we have made available online) can also write these data as comma-separated values (.csv) files.

 
Figure 1: Acceleration in the x- and y-directions is plotted against time, and against one another. These data are derived using the formula a = (v-u)/t applied to the x- and y- velocity data and the time between consecutive frames in the original videos. Acceleration is related to force by Newton’s second law of motion, and thus to impulse and work, which describe the time profile of an applied force and the energy expended by a force, respectively.
Figure 2: The total speed of an object is calculated by applying Pythagoras’ theorem applied the x- and y-components of the velocity. Note that while the horizontal and vertical components of the motion are related to the forces that act in these directions, the total speed is more closely related to the total kinetic energy of the moving object. The angle of elevation is the angle between the path of the object and the (horizontal) ground. A positive angle of elevation indicates that an object is rising, while a negative angle of elevation indicates that an object is falling. Note that it is highly sensitive to small variations in position, as evidenced by the data at about 3 seconds.
Figure 3: The same data as in Figure 2, including the flight of the projectile while it is subject to no forces (almost) other than gravity. These are the data pertinent to studies of projectile motion. Our program deduces the relevant portion of data from the maximum height (y), the beginning of projectile motion from when acceleration becomes negative and the end from when the object bounces (the object begins to rise). This is the task that is most easily accomplished by a program of the kind that we have written and not a less-sophisticated tool.

Reference List

Board of Studies NSW (2009). Physics Stage 6 Syllabus. Sydney NSW 2001: Board of Studies NSW.

 

Chen, C. (2014). An adaptive scaffolding e-learning system for middle school students’ physics learning. Australasian Journal of Educational Technology, 30(3), 342-355.

 

Jonassen, D., et al. (2008). Meaningful Learning with Technology (3rd edition; pp.1-12). Upper Saddle River, New Jersey :Pearson Education.

 

Noura, K. (2005). Technology enhanced mathematics education. Presented at the Proceedings of the Twentieth Biennial Conference of The Australian Association of Mathematics Teachers.

 

Puentedura, R. R. (2010). SAMR and TPCK: Intro to Advanced Practice. Retrieved September 30th 2014, from Hippasus.

http://hippasus.com/resources/sweden2010/SAMR_TPCK_IntroToAdvancedPractice.pdf