Mathematical Design • Project

Mathematical Design, Spring 2024

Course Projects

Skip to: Project 1 • Project 2 • Project 3 • Portfolio

Overview

This class involves being creative with mathematics and realizing your creativity by creating pen plotter art. There will be three main projects throughout the semester and a final portfolio for you to assemble, discuss, and display your artwork in a group setting.

The work that you submit for each project will be only one piece of art. However, as you work on your submission, you will be creating other pieces which serve as practice pieces or which explore other possible avenues that could have led to a submission. It is important to keep these unsubmitted works too. They will help you explain your process and your intentionality in the essay that is part of each project.

As a rule of thumb, make sure that you keep 3–5 additional pieces of art from each project. You will include these artworks in the final portfolio you create at the end of the semester. Furthermore, looking at all your artwork together will help you discuss your artistic evolution throughout the semester.

Project 1

The first project is to create a drawing based on a family of related functions.

Specifications

The final product of this project will consist of:

A Desmos notebook, and
A pen plotter drawing,
A one-to-two-page lab report.

The art that you create must:

Be developed through an intentional Double Diamond Design Process.
Be designed in Desmos and realized on the AxiDraw pen plotter.
Be constructed from snippets of one or more parent functions. These snippets shall be derived by introducing parameters and adjusting the values of these parameters intentionally through Desmos's sliders.
Have an aesthetic that can be described using precise artistic language.
Not include grid lines or coordinate axes.
Be revised multiple times through a thoughtful feedback cycle.

The one-to-two-page lab report must:

Provide key details about your artwork. Discuss the process you went through from conception to final result, including challenges and successes. Provide clarity about the mathematical and artistic choices you made using appropriately technical language. Discuss challenges and successes with the AxiDraw machine. Discuss the revision process and reflect on how you might want to push this work further if you had more time. See below for more details about the evaluation rubric.
Be written in a clear and organized manner, using full sentences and proper English.
Use 1 inch margins, 1.5x spacing, and 11-point Times New Roman font. (Your report will be approximately 500-800 words.)
Include a separate cover page with an image of your artwork, the title of your artwork, your name, and the date.
(This page does not count toward your one-to-two pages.)

Timeline

Gain Expertise by Tuesday, February 13:
By this day, you should have gained expertise with all the skills necessary to complete the project. This includes understanding function transformations, using Desmos to graph functions, incorporating function parameters and sliders into your Desmos graph, creating lists in Desmos, and incorporating lists into your parameters to create multiple transformed copies of your function.
Explore Possibilities by Tuesday, February 20:
By this day you should be exploring different properties that your artwork might have. Smooth? Angular? Linear? Periodic? Regular? Irregular? Intersecting? Asymptotic? Will you focus on the Negative space? Positive space? Save at least three different compositions and bring them to class to discuss.
Project Due on Thursday, February 29:
By this date, you are expected to have completed your project including the lab report. You will complete a peer review activity with classmates on this day.
Project Revision Submitted on Tuesday, March 4:
By this day, turn in your project before class through the links provided on our Course Content page. Make sure to save and keep track of three to five other pieces to add to your final portfolio later in the semester. (Put them in a location that you can find easily later.)

Grading

Grading details coming soon.

This project represents 15% of your semester grade. You will be graded on each of the following standards.

Engagement: (10%)

Did you make steady progress on your project from start to finish, respecting project deadlines?
Did you regularly attend the in-class work days, discuss your progress with classmates, and check in with the professor?
Did you turn in your final project by the deadline?

Intentionality: (20%)

Did you follow the Double Diamond Design Framework?
In the Discovery Phase, did you create three different types of artwork?
In the Define Phase, did you choose one of those types of artwork?
In the Develop Phase, did you create three different artworks of that same type but with different aesthetics?
In the Deliver Phase, did you hone your final piece of art using internal and external feedback?
It is clear that the final piece of art has been honed over multiple iterations?

Desmos Notebook: (10%)

Did you use the techniques from class involving sliders and curly braces to create one or more snippets of functions?
Did you use the techniques from class to create multiple copies of the snippets (possibly modified further)?
Did you remove the grid lines and coordinate axes from your Desmos notebook?

Process Discussion in the Writeup: (25%)

Did you reflect on the Discovery Phase? How did you come up with the ideas from your artwork? What did you experience? What was difficult? What choices did you make?
Did you reflect on the Define Phase? How did you finalize your artwork type? Are there parts of the other pieces you created that inspired your final piece?
Did you reflect on the Develop Phase? How did you explore the possibilities that came from your definition of the type of functions you would include?
Did you reflect on the Deliver Phase? How did you arrive at the final piece of art? What choices did you make? How did the peer review process impact the final piece?

Technical Discussion in the Writeup: (20%)

Have you explained the programming methods you applied in Desmos?
Do you use mathematical terms (like translation, domain restriction) to explain the process / artwork? Are you using these technical terms correctly?
Do you use the artistic and design terms (for example: negative/positive space, symmetry/asymmetry, light/heavy) to explain the process / artwork? Are you using these technical terms correctly?
Did you share how your experience with the AxiDraw machine impacted the final piece?

Writing style and format: (15%)

Did you use full sentences, use proper English, and do your paragraphs flow well?
Does your artwork have a title?
Did you include a separate cover page with with an image of your artwork, the title of your artwork, your name, and the date?
Did you follow the writing format requirements?

You will be assigned a score for each criterion on an E-M-R-N scale as follows.

First I ask myself:

Does this work meet the expectations outlined in the criterion?

If it does, then depending on how complete and clearly communicated your work is, you will receive one of the following scores:

E	Exemplary	The work meets or exceeds the expectations of the assignment. Communication is clear and complete. Mastery of the concepts is evident. There are no non-trivial errors in understanding.
M	Meets Expectations	Understanding of the concepts is evident through correct work and clear, audience-appropriate explanations. Some revision or expansion is needed, but no significant gaps or errors are present.

If it does not, then you have not demonstrated understanding of the concept. In this case, I will determine if you show partial understanding, and you will receive one of the following scores:

R	Revision Needed	Partial understanding of the material is evident, but there are significant gaps that remain. Needs further work, more review, and/or improved explanations.
N	Not Assessable	Not enough information is present in the work to determine if there is understanding of the concepts. Work is fragmentary or contains significant omissions. Or, there are too many issues to justify correcting each one.

Your final project grade will be based on the number of scores at each level as follows.

Every E grade corresponds to 100%, every M grade corresponds to 90%, every R grade corresponds to 50%, and every N grade corresponds to 0%. These scores are then combined using a weighted average corresponding to the percentages listed above.

Project 2

The second project is to create a drawing that uses advanced mathematical and AxiDraw techniques.

Specifications

The final product of this project will consist of:

A Desmos notebook, and
A pen plotter drawing,
A 1½-to-2½-page lab report.

The Desmos notebook must:

Include the graphs of one or more functions.
Intentionally apply advanced mathematical techniques. Use at least one of the following:

Apply multiple transformations to the same function
Combine multiple functions into one function
★ Customize Polar Functions
★ Apply transformations to Polar Functions
★ Incorporate randomness into the placement of the curves

Note 1:

Note 2:

★

Be organized into folders.
Include text cells that explain the intentionality behind each function cell.

The pen plotter drawing must:

Be generated from your Desmos notebook and drawn using an AxiDraw plotter.
Intentionally use advanced AxiDraw techniques. This can be one or more of the following:

Use a more advanced type of pen.
Use multiple colors of pen on the same drawing.
Use multiple line thicknesses on the same drawing.
Use multiple types of pen on the same drawing.
Use a special type of paper.
Assemble multiple pieces of paper into a collage.
Draw on a surface that is not a piece of paper.

Note 1:

Note 2:

Be generated multiple times. Submit two (2) copies of the same artwork.

The 1½-to-2½-page lab report must:

Provide key details about your artwork, the choices you made during its conception, the process from idea to final result, the mathematics behind the drawing, a reflection about how you stretched your knowledge, and the revision process. See below for more details about what will be evaluated.
Be written in a clear and organized manner, using full sentences and proper English.
Use 1 inch margins, 1.5x spacing, and 11-point Times New Roman font. There should be no extra space between paragraphs. (Your report will be approximately 900-1200 words.)
Include a separate cover page with the title of your artwork, your name, and the date.
(This page does not count toward your 1½-to-2½ pages. This information should not be repeated on the other pages of the report.)

Timeline

Gain Expertise by Thursday, March 14:
By this day, you should have gained expertise with all the skills necessary to complete the project. This includes understanding dilations, combining multiple functions, polar functions, and polar transformations.
Explore Possibilities by Thursday, March 21:
By this day you should have a conceptual goal for your artwork. How will you be pushing yourself mathematically? How will you be pushing yourself artistically? How will you be pushing yourself on the AxiDraw? Bring your ideas to class to discuss.
Project Due on Thursday, March 28:
By this date, you are expected to have completed your project including the lab report. You will complete a peer review activity with classmates on this day.
Project Revision Submitted on Tuesday, April 2:
By this day, turn in your project before class through the links provided. Make sure to save and keep track of three to five other pieces to add to your final portfolio later in the semester. (Put them in a location that you can find easily later.)

Grading

This project represents 25% of your semester grade. You will be graded on each of the following standards.

Engagement: (10%)

Did you make steady progress on your project from start to finish, respecting project deadlines?
Did you regularly attend the in-class work days, discuss your progress with classmates, and check in with the professor?
Did you turn in your final project by the deadline?

Intentionality: (15%)

Did you follow the Double Diamond Design Framework?
Did your process explore mathematical possibilities intentionally?
Did your process explore artistic possibilities intentionally?
Did your process explore AxiDraw possibilities intentionally?
Did you choose your materials thoughtfully?
It is clear that the final piece of art has been honed over multiple iterations?

Growth: (15%)

Did you push yourself mathematically?
Did you use more advanced mathematical techniques than in Project 1?
Did you push yourself artistically?
Is there a discernible aesthetic in the final piece?
Did you push yourself with your AxiDraw skills?
Did you use more advanced AxiDraw techniques than in Project 1?

Context Discussion (10%)

Did you discuss your inspiration and goals for the piece?
Did you convey how your piece changed over time?
Did you share difficulties or successes you had along the way?
Have you explained how the peer review process impacted your final piece?
Did you explain what you would want to explore further if you had the time?

Mathematical Discussion (10%)

Did you discuss the mathematics that you involved in your piece?
Have you explained how you arrived at the function(s) that forms the basis for your work?
Do you use mathematical terms (for example: translation, domain restriction) to explain the artwork? Are you using these technical terms correctly?
Did you explain how you have pushed yourself mathematically above and beyond your work in Project 1?

Artistic Discussion (10%)

Have you explained the artistic qualities you were going for in this piece?
Do you use the artistic terms (for example: negative/positive space, symmetry/asymmetry, light/heavy) to explain the artwork? Are you using these technical terms correctly?
Have you explained how you arrived at the artistic qualities in the piece by applying mathematical and programming ideas?
Did you explain how you have pushed yourself artistically above and beyond your work in Project 1?

AxiDraw Discussion (10%)

Did you share your experience in using the AxiDraw machine and the Makerspace?
Did you discuss the choices you made about the pens and paper in the piece?
Did you discuss the pros and cons of the choices you made?
Did you explain how the choice of materials impacted how you worked with the AxiDraw machine?

Desmos Notebook: (10%)

Is the Desmos notebook well organized, with related parts grouped together into folders?
Are the functions and folders presented in a logical order?
Did you preface every function cell with a text cell to explain what its role is?

Writing style and format: (10%)

Did you use full sentences, use proper English, and do your paragraphs flow well?
Does your artwork have a title?
Did you include a separate cover page with with an image of your artwork, the title of your artwork, your name, and the date?
Did you follow the writing format requirements?

You will be assigned a score for each criterion on an E-M-R-N scale as follows.

First I ask myself:

Does this work meet the expectations outlined in the criterion?

If it does, then depending on how complete and clearly communicated your work is, you will receive one of the following scores:

E	Exemplary	The work meets or exceeds the expectations of the assignment. Communication is clear and complete. Mastery of the concepts is evident. There are no non-trivial errors in understanding.
M	Meets Expectations	Understanding of the concepts is evident through correct work and clear, audience-appropriate explanations. Some revision or expansion is needed, but no significant gaps or errors are present.

If it does not, then you have not demonstrated understanding of the concept. In this case, I will determine if you show partial understanding, and you will receive one of the following scores:

R	Revision Needed	Partial understanding of the material is evident, but there are significant gaps that remain. Needs further work, more review, and/or improved explanations.
N	Not Assessable	Not enough information is present in the work to determine if there is understanding of the concepts. Work is fragmentary or contains significant omissions. Or, there are too many issues to justify correcting each one.

Your final project grade will be based on the number of scores at each level as follows.

Project 3

The third project is to design and create a physical object based on parametric curves. You will use a machine in the Makerspace to realize your creation.

Specifications

The final product of this project will consist of:

A Desmos notebook, and
A physical object, and
A 1½-to-2½-page lab report.

The Desmos notebook must:

Intentionally apply advanced mathematical techniques involving parametric functions.

Note 1:

Be organized into folders.
Include text cells that explain the intentionality behind each function cell.

The physical object must:

Be generated from your Desmos notebook and rendered on a machine in the Queens College Makerspace. (Students using an AxiDraw machine are expected to level up their skills considerably.)
Be generated multiple times. Submit two (2) copies of the same artwork.

The 1½-to-2½-page lab report must:

Provide key details about your artwork, the choices you made during its conception, the process from idea to final result, the mathematics behind the drawing, and a reflection about how you stretched your knowledge, and the revision process. See below for more details about what will be evaluated.
Be written in a clear and organized manner, using full sentences and proper English.
Use 1 inch margins, 1.5x spacing, and 11-point Times New Roman font. There should be no extra space between paragraphs. (Your report will be approximately 900-1100 words.)
Include a separate cover page with the title of your artwork, your name, and the date.
(This page does not count toward your 1½-to-2½ pages. This information should not be repeated on the other pages of the report.)

Timeline

Choose a medium by Thursday, April 11:
By this day, you should know which machine you want to use to create your final artwork. You will practice using this machine multiple times before creating your final artwork.
Gain Expertise by Tuesday, April 16:
By this day, you should have gained expertise with all the mathematical skills necessary to complete the project including parametric equations, parametric transformations, and linear interpolations. You will also learn how to use the appropriate software.
Explore Possibilities by Thursday, April 18:
By this day you should have a conceptual goal for your artwork. How will you be pushing yourself mathematically? How will you be pushing yourself artistically? Bring your ideas to class to discuss.
Prototype Due on Thursday, May 2:
By this date, you should have created a physical prototype of your artwork. We will critique everyone's art together on this day.
Final Project Due on Tuesday, May 7:
Bring your final piece of art to class on Tuesday, May 7. Submit your Writing and Desmos files using the links on Teams.

Grading

This project represents 25% of your semester grade. You will be graded on each of the following standards.

Engagement: (10%)

Did you make steady progress on your project from start to finish, respecting project deadlines?
Did you regularly attend the in-class work days, discuss your progress with classmates, and check in with the professor?
Did you turn in your final project by the deadline?

Intentionality: (15%)

Did your process explore mathematical possibilities intentionally?
Do you show various drafts of the functions/parameters that you explored before deciding on this final version?
Did your process explore artistic possibilities intentionally?
Did your process explore Makerspace machines intentionally?
Can you convey what you were trying to do and how your piece was able to achieve it?
It is clear that the final piece of art has been honed over multiple iterations?
Did you submit two (as) identical (as possible) copies of the final piece of work?

Growth: (15%)

Did you use push yourself mathematically and use more advanced mathematical techniques than in Project 2?
Did you push yourself artistically and acheive an aesthetic that involves more reflection than in Project 2?
Did you master a new machine in the Makerspace? (Or find a way to reach new levels of sophistication with the AxiDraw?)

Context Discussion (10%)

Did you discuss your inspiration and goals for the piece?
Did you convey how your piece changed over time?
Did you share difficulties or successes you had along the way?
Did you explain what you would want to explore further if you had the time?

Mathematical Discussion (10%)

Did you discuss the mathematics that you involved in your piece?
Have you explained how you arrived at the function(s) that forms the basis for your work?
Do you use mathematical terms (for example: translation, domain restriction) to explain the artwork? Are you using these technical terms correctly?
Did you explain how you have pushed yourself mathematically above and beyond your work in Project 2?

Artistic Discussion (10%)

Have you explained the artistic qualities you were going for in this piece?
Do you use the artistic terms (for example: negative/positive space, symmetry/asymmetry, light/heavy) to explain the artwork? Are you using these technical terms correctly?
Have you explained how you arrived at the artistic qualities in the piece by applying mathematical and programming ideas?
Did you explain how you have pushed yourself artistically above and beyond your work in Project 1?

Machine Discussion (10%)

Did you discuss how you gained experience with the software and workflow related to the machine you used?
Did you share your experience in using the machine the Makerspace?
Did you discuss the choices you made about the materials in the piece?
Did you discuss the pros and cons of the choices you made?
Did you explain how the choice of materials impacted how you worked with machine?
Did you compare your work with this machine with how you used the AxiDraw in Projects 1 and 2?

Desmos Notebook: (10%)

Is the Desmos notebook well organized, with related parts grouped together into folders?
Are the functions and folders presented in a logical order?
Did you preface every function cell with a text cell to explain what its role is?

Writing style and format: (10%)

Did you use full sentences, use proper English, and do your paragraphs flow well?
Does your artwork have a title?
Did you include a separate cover page with with an image of your artwork, the title of your artwork, your name, and the date?
Did you follow the writing format requirements?

As before, you will be assigned a score for each criterion on an E-M-R-N scale. Every E grade corresponds to 100%, every M grade corresponds to 90%, every R grade corresponds to 50%, and every N grade corresponds to 0%. These scores are then combined using a weighted average corresponding to the percentages listed above.

Portfolio

The culmination of the semester is a portfolio that details your journey this semester becoming a mathematical artist. You have learned about transformations of functions, polar functions, parametric functions, elements of art and design, gained skills with Desmos, Inkscape, AxiDraw, the Makerspace, and a completely different machine! It is time to assemble the story of this journey into a writeup and presentation and share it with us.

Specifications

The final product of this portfolio will consist of:

A physical or digital portfolio.
A two-to-three page semester reflection.
A three-to-five minute presentation of your portfolio and its story with the class.

The portfolio must:

Be assembled physically or digitally.

A physical portfolio is a collection of images and text assembled in a physical format. There are official "studio art portolios", but this can be also achieved using a binder and sheet protectors that a viewer can flip through.
A digital portfolio is hosted on a website, such as Padlet, Wordpress, Cargo, Squarespace, or Adobe Portfolio

Include images that form a coherent story, including your submitted artwork from Projects 1, 2, and 3, images that inspired your submitted artwork, images that you developed for your projects but did not lead to the submitted artwork, images that show your progress as an artist, images that show your progress as a mathematician, and images that convey the feelings you experienced during this class. (If you are creating a physical portfolio, you will need to print out these images to include in the portfolio.)
Include text that explains how each of the included images figures into this semester's journey.
Be able to be shared in class on Presentation Day.

The two-to-three page semester reflection must:

Discuss Your Progress as a Mathematician, Artist, and Maker.

Think back to where you started this semester and think about where you are now. What has changed, and what about this semester's journey has led to this transformation?

Include additional reflections about this semester and this course.
Supplement the portfolio.
Feel free to refer to images and other parts of your physical or digital portfolio.
Use 1 inch margins, 1.5x spacing, and 11-point Times New Roman font.
Include a cover page with title, your name, and the date.
(This page does not count toward your 2-to-3 pages. This information should not be repeated on the other pages of the report.)

The presentation must:

Introduce yourself.
Share some of the images that you included in your portfolio.
Put the learning you did this semester into context.
Be organized and rehearsed.
You need to make sure that you have practiced what you are going to say a couple of times.
Respect the time limit.
Three to five minutes is a very short amount of time! This means you really need to have practiced multiple times so that you use your time efficiently.
Be prepared and ready to go on our presentation day!

Grading

This project represents 15% of your semester grade. You will be graded on each of the following standards.

Coherence of images: (15%)

Did you include images of the types described above?
Did you present the images in a logical order?
Did the images tell a complete story? (The opposite would be leaving holes in the story of your development this semester.)
Has each image been put into context by adding text?

Portfolio Appearance and Structure: (10%)

Does the portfolio have a coherent visual theme?
Is the organization of the portfolio easy to follow?

Sharing your Portfolio On Presentation Day: (15%)

Did you introduce yourself?
Did you share and talk about your images
Did you tell the story of your (mathematical, artistic, and maker) development throughout the semester?
Did you explain your work in a clear and engaging way?

Writing: Your Progress as a Mathematician: (15%)

Think back to where you started this semester as a mathematician and think about where you are now. What has changed, and what about this semester's journey has led to this transformation? Give some detailed examples.

Writing: Your Progress as an Artist: (15%)

Think back to where you started this semester as an artist and think about where you are now. What has changed, and what about this semester's journey has led to this transformation? Give some detailed examples.

Writing: Your Progress as a Maker: (15%)

Think back to where you started this semester as a maker and think about where you are now. What has changed, and what about this semester's journey has led to this transformation? Give some detailed examples.

Writing: Additional Reflections: (15%)

Did you discuss other themes that have occurred to you throughout the semester in your reflection?
Did you discuss how you experienced this semester or how the class made you feel in your reflection?