MAT133: Calculus and Linear Algebra for Commerce Project #6
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MAT133: Calculus and Linear Algebra for Commerce
Project #6
2022
Along with your solutions to the individual problems, you’ll need to include an academic integrity statement.
UofT upholds high standards of academic integrity. It is your responsibility to read and understand the Code of Behaviour on Academic Matters and to adhere to the list of “OK” resources below.
An important note on group chats: If you have administration privileges for any online chat that involves anyone not on your team and in which assignment content is shared, you must delete any non-authorized content from that group chat as soon as you see it (if this is technologically possible on that platform). Otherwise, you are considered to have helped someone cheat and therefore committed an academic offence.
As part of your individual project submission, you’ll include an abbreviated statement to Gradescope that implies the following.
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In submitting this assessment ... |
In short |
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... I confirm that my conduct during this take-home exam adheres to the Code of Behaviour on Academic Matters. |
I know the Code. |
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... I confirm that I have not acted in such a way that would consti- tute cheating, misrepresentation, or unfairness, including but not limited to, using unauthorized aids and assistance, impersonating another person, and committing plagiarism. |
I didn’t cheat. |
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... I confirm that the work I am submitting in my name is my own work. The work submitted for the pod project is the work of myself and my pod. |
This is my work. |
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... I confirm that I have only used the aids marked as approved in the “OK List”. |
I only used “OK” aids. |
The individual problems are to be completed by each student individually. You are allowed and encouraged to discuss these problems with other members of your hive, but you must write your own solution for submission.
The individual problems will be accessed and submitted on gradescope.ca.
2 Pod Project: Metaphors for Mathematical Ideas Through Art
“Metaphor is not a mere embellishment; it is the basic means by which abstract thought is made possible.”
– George Lakoff and Rafael Nu˜nez
In this pod project, you will create a mathematical art piece! Before digging further into the details, we’d like to be clear on the goals of this project:
● Reinforce your understanding of the concepts you’ve learned in MAT133.
● Help your classmates reinforce their understanding of the concepts.
● Have fun!
2.1 Introduction: How do abstract mathematical ideas exist in our brains?
In your journey through mathematics, from elementary school to MAT133, you have come into contact with a variety of abstract mathematical objects and ideas: numbers, matrices, vectors, functions, derivatives, integrals, and so on. You have drawn connections between these ideas and used them to investigate real-world problems. A person might look at the abstract symbols written across the pages in your notebook and wonder, what goes on in your head when you write this? How do you make sense of all this? This is a valid question!
As a mathematician, how do abstract ideas live in your head?
Where does your mathematical intuition come from?
According to some scholars in linguistics and cognitive science, our understanding of abstract ideas, in mathematics and elsewhere, is grounded in metaphor. 12 In your hive meetings on March 3-4, you’ll discuss examples of metaphors you use in everyday language, as well as examples of metaphors for numbers and arithmetic. This will help you to understand what metaphors are and why they are important for understanding mathematical concepts. From there, you’ll have some time to think about metaphors for concepts you’ve learned about in MAT133.
Your main tasks are as follows:
1. Construct a metaphor for a mathematical object or idea from MAT133.
2. Create a new piece of art to represent your metaphor. You may choose any medium! It can be a drawing, painting, skit, comedy act, song, poem, ... The important thing is that it is a new, original piece of art that you created specifically to communicate your metaphor.
3. Write a caption to explain how your art piece connects to an idea or concept from MAT133. In your caption, please include:
(a) your metaphor, with a description of how your art illustrates your metaphor, (b) an explanation of the concept from MAT133 that your metaphor refers to, (c) discussion of aspects of the mathematical concept that your metaphor captures well,
(d) discussion of aspects that your metaphor does not capture well.
In order to collaborate as a pod, we recommend that each pod member choose an idea from a different module in the course. For example, you might have one pod member focus on a mathematical object or idea from within one of the following segments of MAT133: linear algebra, differential calculus, integral calculus, multivariable calculus. This way, each pod member would create a piece related to an idea from a different segment of the course. In this case, each pod member should write their own caption.
However, if your pod has an idea for a different way to work together, then please consult your hive leader or a member of the teaching team on Ed or [email protected]. We want to encourage your creativity and be flexible, but we also want to make sure that you are supported and able to submit your piece!
If you wish for your art pieces to be marked individually, you may do so. If your art pieces fit together coherently in your pod, or if you are all working on the same piece, then you may submit as a pod. We will consider how many students are included in each submission as we grade using the rubric below. More examples of submissions are provided in Section 2.5.2.
Citations: Your art project should be original, made by you, from scratch. This means that you likely won’t need to cite any sources for this project. That said, if you draw any inspiration from an outside source (e.g. another art piece), then it is important to acknowledge this in your caption.
The rubric will be flexible enough to accommodate any type of art piece. We want to encourage you to have fun and be creative!
Your mark will be broadly based on the following:
● Artistic Effort: To what extent did you put forth effort to artistically depict your metaphor? We do not expect you to be a professional artist! However, we can see the difference between a drawing that was sketched in a few minutes and a piece created with more effort. The number of students included on the submission will be considered when we assign you a mark for artistic effort.
● Discussion of your metaphor: You will be graded on the clarity of your statement of your metaphor, your explanation of the underlying mathematical concept, as well as your discussion of aspects of the mathematical concept that your metaphor captures and aspects that it does not capture.
● Mathematical Language: We will also assess the overall clarity and accuracy of the mathematical language in your caption. It should be written clearly enough that any of your classmates should be easily able to understand it.
Please note that your mark will NOT be based on any of the following:
● Artistic technique: We do not expect you to be a professional artist!
● Importance or scope of the mathematical concept you chose: You do not need to have a metaphor for all of calculus, nor do you need to focus on the most important ideas from the course. You may focus on any idea of the course, no matter the scope.
These tips are from past student reflections.
● Start early – you might struggle for a few days to come up with a nice metaphor.
● Pick a topic you’re genuinely unsure or unclear about, because creatively working through it will definitely reinforce the core concepts!
● Share your ideas with someone instead of being alone.
Each individual student must upload a single-page draft to Gradescope by 3pm on Mar 9, 2022. For this project, the first draft may consist of a few sentences to describe your metaphor idea(s), or a picture of the art piece you’ve done so far.
Please upload your Project 6 in the form of a pdf, as usual. You must include access to your art piece and your caption in your submission. Below are a few examples of submissions.
Example #1: Sarah submits a painting. Sarah and her podmates decide to submit individually, rather than as a pod. Sarah created a painting for this project, so she will submit a photo of the painting, followed by her caption, which includes (1) her metaphor, (2) an explanation of the concept from MAT133 that her metaphor refers to, and (3) a discussion of the aspects of the mathematical concept that her metaphor captures well and doesn’t capture well.
Example #2: The pod “Tide Pod” creates a video and submits as a pod. All four podmates shared the creative work of imagining their metaphor and creating a video that represents it. In this case, they will post their video on YouTube, myMedia, or any other platform, ensuring that their video is viewable by anyone with the link. In their submission to Gradescope, they will include a link to their video and then their caption. When they wrote their caption, they also divvied up the writing amongst pod members, so both their art piece and their caption reflects significant efforts put forth by all four pod members.
Example #3: The pod “Integral Whales” creates four separate pieces, but submits as a pod. This pod decided to focus on four different ideas in the course, with every student creating a metaphor and art piece for a different idea. However, they all came up with metaphors that relate to each other, with an “under-the-sea” theme, so they want to submit their pieces as a pod. In this case, each student will create their own art piece and caption, but they will merge all four art pieces (or links with access to the pieces) into a single pdf and submit to gradescope as a pod. The order of their submission is:
1. Art Piece 1 and Caption 1
2. Art Piece 2 and Caption 2
3. Art Piece 3 and Caption 3
4. Art Piece 4 and Caption 4
With this style of submission, the Integral Whales understand that they will be marked as a pod, not individually. They should be sure to complete their project at least 2 days before the deadline, so that they can give each other feedback on their pieces and captions, then have time to make improvements accordingly!
Are you still not sure how to submit your art piece? If you have an idea for an art piece in mind that doesn’t seem to fit the above instructions, then please reach out to us in Ed or at [email protected] to discuss ways of submitting and presenting.
IMPORTANT: If you submit your art piece by sharing a link to a shared folder or video, then please be sure that the permissions are set to be viewable by the public so that the grader can open it!
Your art pieces will be presented in the form of a gallery in your tutorial room. However, if you have a performance piece (such as a video, song, or play), then your TA will set aside time for you to present to your hive. All students will be asked to explain their art piece and their metaphor to their TA for marks. You’ll also share your art pieces with your peers.
Your grade will be based on your efforts to thoughtfully reflect on each question, according to the instructions provided. While we do ask that you write in full English sentences, we will not judge your grammar or syntax. Please don’t worry too much about writing perfectly! Think of it as a journal entry.
The estimated time to complete these questions is approximately 45 minutes. Quercus will save your work as you go. For example, if you wish to complete one question and come back later for the rest, you may do this. Just
be sure to push submit if and only if you are finished writing your responses. (You are only able to push submit once.) The reflection questions will become available after your art gallery.
2022-03-16