EDUC 4769 - Computational Thinking and Coding In Education - Final Project

Physics 20 Gravitational Acceleration Unit

Abstract

This unit focuses on teaching students about gravitational acceleration, a key part of the Physics 20 curriculum, and takes advantage of computational thinking concepts to enhance student learning and expertise in working with data and equations. The unit starts off looking at the background of Newton’s Law of Universal Gravitation, where students will determine how to calculate gravitational acceleration, and moves on to expand the students’ expertise using real world tools such as spread sheets. Students then will gain experience developing tools to help conduct real world measurements, and culminates in students proving for themselves that the acceleration due to gravity is indeed able to be considered constant around the world for most kinds of calculations via a small excursion around the school and surrounding environment.

One key skill students will use and build in the unit, especially as it culminates, will be abstraction. There are so many details and measurable parameters in real world physics and engineering problems, so much so that if we didn’t approximate and abstract out certain unnecessary details many problems would be incredibly difficult or impossible to solve, with an overwhelming amount of things to calculate. Having experience with abstraction and focusing on which variables matter will enable students to recognize situations like this in the future where some details can be left constant (such as the acceleration due to gravity on earth, as students will learn in this unit), since the change is so minor it doesn’t have a real world or measurable affect on the situation at hand. This memorable lab unit/experience/adventure will hopefully reinforce this critical physics and engineering concept for students so that they can add this use of abstraction to focus on the relevant details, and hold other minor variations constant, as a step to their algorithm they use to approach real world physics and engineering problems.

Something Professor Heidebrecht mentioned to me was the power and memorability of exciting activities for students, where he had students who remembered those activities years down the road and thus the learning contained within. One of my goals with this set of lessons, and the excursion taken at the end, was to make this learning about gravity, which we often take for granted, an exciting and memorable hands on experience with students proving to themselves, not just being told, that the acceleration due to gravity can be considered to be approximately constant anywhere on earth.

Also note that if your school’s schedule allowed for such, this unit could be integrated to collaborate with the mathematics 20 classes as well, since as noted in the Physics 20 program of studies there are many overlapping and related concepts from the mathematics 20 curriculum used within this unit, such as graphing, measurement and unit conversions, solving equations, and scale diagrams (Alberta Education, 2014). Being able to reinforce these mathematics, physics, and computational thinking concepts in different classes would hopefully benefit students in reinforcing the skills and knowledge through the use of repetition. For the case of this unit, I’ve written it only as a physics unit though, as those kinds of integrations with other classes would be specific to the school and other classroom teachers.

Lesson Plan 1

Lesson 1 introduces Newton’s law of universal gravitation, where students will learn to solve for g and calculate g at two specific locations on earth. Students will make use of, and practice, the computational thinking skills of decomposition and pattern recognition as they attempt to solve two equations for g, gravitational acceleration, looking for commonalities between the formulas, and simplifying them by breaking down the equations and reducing them to their simplest forms by canceling out equivalent variables on either side.

Please find below the embedded PDF for lesson plan 1.

Lesson Plan 2

Lesson 2 introduces students to spreadsheets and using them to do repetitive calculations on data. In this case the spreadsheet will allow students to quickly and accurately calculate many different values of g at different elevations in order to show them how we would expect there to be very little variation in g along the earth’s surface.

Pattern recognition skills are reinforced as students troubleshoot possible recurring errors when replicating their formula down cells, as well recognizing where certain variables need to be held constant in position and where others don’t. Pattern recognition skills are also engaged in a way as students come to realize how the value for g seems to almost be staying exactly the same, even under drastic changes in elevation. Abstraction skills are also engaged in that analysis of g remaining almost constant, in that students have to focus in solely on the minor variation of g regardless of the wide variation in elevation. Lastly, this activity is the embodiment of an algorithm, as students have taken the method they developed to find g in lesson 1 and can express it in a way (the spreadsheet formula) such that they can hand over that work to be done by a computer, very much in the spirit of computational thinking.

Please find below the embedded PDF for lesson plan 2.

Please find below the embedded PDF for the student exemplar after completing lesson 2.

As explained in lesson plan 2, the students would be informed that this section's work would need to have at least 10 rows of data, including sea level (0 meters), the town's elevation, and 10 meters above the town’s elevation for the height of the school’s second floor. Students would be informed that they can choose the other data point locations at random, perhaps increasing by a certain amount each step up from sea level to our location, or including some of their favourite locations around the world. In the lesson students are informed that the table will be marked out of 5 marks, 3 for having enough data points and properly entering and replicating your formula down the cells, and 2 for properly formatting your chart as explained in the lesson.

Lesson Plan 3

Lesson 3 focuses on programming the micro:bit so that students can take actual experimental measurements of the acceleration due to gravity, not just look at theoretical expectations.

While there were other options, such as the smart phone based app phyphox, which enables students to take acceleration measurements using smartphone sensors, I ended up deciding upon the micro:bit as I found that both had the same sensitivity with somewhat sizable uncertainty in the measurement due to the variations in recorded values due to vibrations of the earth and surrounding environment. While both options would fulfill the same need, rather than using a premade solution like the phyphox app, the use of the micro:bit enables students to do the real work that would be needed to setup and use sensors in a real lab environment. Not only this, but it provides students with a similar visual programming environment to what they might see in some physics research labs where some researchers use the LabVIEW software, a visual based programming language, to control instrumentation used in conducting real research.

This lesson lets students use decomposition skills to break down the problem into it’s simplest form, since there are big concepts like forces, acceleration, mass, laws of gravitation, and g all flying about. Students have to break the problem down into its simplest terms of just measuring one variable, and utilize their abstraction skills to ignore the large amount of other information available. Finally students have to develop an algorithm, their code, that will allow them to consistently measure the acceleration due to gravity while not being dependent on the orientation of the micro:bit.

Please find below the embedded PDF for lesson plan 3.

At the end of this lesson students would have their micro:bit displaying accelerometer data using code similar to the example shown below.

Example code similar to what students would create to accomplish the task of lesson 3.

Shown below is a GIF of my micro:bit running this example code, demonstrating how the orientation does not affect the measurement of g, within uncertainty, since the strength parameter was used rather than a specific direction for the accelerometer data.

Animated GIF showing the micro:bit running the example code.

The only criteria for this lesson for students is that their program needs to display the current value of the gravitational acceleration, regardless of the orientation of the micro:bit. Students are informed in the lesson to ensure they take a screenshot of their code for submission at the end of the unit.

Lesson Plan 4

In lesson 4, students get to determine for themselves whether or not g truly remains nearly constant over the surface of the earth by taking their own measurements using the micro:bits they prepared in lesson 3. Students will be taken around to a variety of locations and elevations in the local area to measure the value of the gravitational acceleration there and will be engaged in discussion after each measured result.

This section will give students the experience and confidence as to why they can make the abstraction that g is a constant for most typical problems they would use it in on earth, leaving them able to focus on the other details relevant in that problem. Students will be able to use this abstraction skill for variables that remain close enough to constant to be considered a constant in the algorithm they use to approach and solve real world problems in normal life and in fields like physics and engineering.

Please find below the embedded PDF for lesson plan 4.

After this section, students will have recorded their values measured for g, and will be able to write a conclusion that states something similar to the following: “In this investigation we were able to calculate the theoretical values of g as well as measure the values of g in our area using the micro:bit we programmed. Within the uncertainty of our sensors, the theoretical and measured values for the gravitational acceleration (g) agree, and thus with the variations being so small as we’ve both calculated and measured, g can be considered a constant for most calculations”. Students will be informed as part of lesson 4 that they’ll need to include their recorded values of g and the location at which each was measured in a table, and that their conclusion needs to explain whether their expected (theoretical) values of g agree with their measured values within uncertainty, and why you can consider g to be constant on the surface of the earth for most calculations. Students will be told that the work for this section will be out of three, one mark for each part.



The work from these lessons would be compiled into a report, based upon the standards that would have been previously set for the content of a report at the start of the Physics 20 class. Along with the standard requirements from the report, included would also be the table created in lesson 2, the code created in lesson 3, the table of values recorded for g in lesson 4, and their conclusion. Each section would be marked based upon the criteria described within and after the lessons above, which would be given to students as part of each lesson.

References