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.
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.
- Include the graphs of one or more functions.
- Apply mathematical transformations to each function, involving one or more parameters.
- Use lists to specify the values of each parameter.
- Be generated from your Desmos notebook.
- Not include grid lines or coordinate axes.
- Be drawn using an AxiDraw plotter.
- 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. (Your report will be approximately 700-1000 words.)
- Include a separate cover page with 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 Thursday, February 9:
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 Thursday, February 16:
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 Tuesday, February 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 Thursday, March 2:
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
This project represents 15% of your semester grade. You will be graded on each of the following standards.
- Engagement:
- 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:
- Were the graph(s) in the artwork chosen intentionally?
- Are the translations placed in a deliberate way?
- Does the final piece have a consistent feel that matches with the artistic terms cited in the lab report?
- It is clear that the final piece of art has been honed over multiple iterations?
- Desmos Notebook Content:
- Did you use the techniques from class to create one or more graphs of functions or pieces of graphs of functions?
- Did you use translations to move the graphs functions up, down, right or left?
- Did you use a list to generate multiple translates of graphs?
- Desmos Notebook Style:
- Is the Desmos notebook well organized, with related parts grouped together into folders, with text cells to explain what each part is, and presented in a logical order?
- Process Discussion
- Have you explained your artistic process?
- Have you conveyed how your piece changed over time?
- Did you share your experience in using the AxiDraw machine and the Makerspace?
- Did you share difficulties or successes you had along the way?
- Have you explained how the peer review process impacted your final piece?
- Technical Discussion
- Have you explained how you arrived at the function(s) that forms the basis for your work?
- Have you explained how you determined which transformations you applied to your functions?
- Have you explained the programming methods (using sliders, lists, colors) in Desmos that you applied?
- Do you use mathematical terms (like translation) to explain the artwork? Are you using these technical terms correctly?
- Artistic Discussion
- Have you explained the artistic qualities you were going for in this piece?
- Do you use the artistic terms (like negative space) 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?
- Writing style and format:
- Does your artwork have a title?
- Did you use full sentences, use proper English, and do your paragraphs flow well?
- Did you follow the writing format requirements?
- Did you include a separate cover page with the title of your artwork, your name, and the date?
You will be assigned a score for each criterion on an E-M-R-N scale as follows.
First I ask myself:
If it does, then depending on how complete and clearly communicated your work is, you will receive one of the following scores:
| 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. | |
| 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:
| 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. | |
| 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.
A (95+) Earn a score of M or higher on all standards and a score of E on at least five standards. B (85) Earn a score of M or higher on all standards and a score of E on at least three standards. C (75) Earn a score of M or higher on six standards and no N scores. D (65) Earn a score of M or higher on five standards and at most one N score. F (50–) Have fewer than five E or M scores OR earn two or more N scores.
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 1.5-to-2-page lab report.
- 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
- Be organized into folders.
- Include text cells that explain the intentionality behind each function cell.
(Note 2: Students who have taken Math 200 or above are expected to use a starred ★ technique.)
(Exceptions will be considered; discuss directly with Prof. Hanusa.)
- 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.
- Be generated multiple times. Submit two (2) copies of the same artwork.
(Note 2: If you have an artistic background, aim higher.)
- 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 900-1100 words.)
- Include a separate cover page with the title of your artwork, your name, and the date.
(This page does not count toward your 1.5-to-two pages. This information should not be repeated on the other pages of the report.)
Timeline
- Gain Expertise by Tuesday, 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 Tuesday, 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 Tuesday, 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 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
This project represents 20% of your semester grade. You will be graded on each of the following standards.
- Engagement:
- 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?
- Mathematics Intentionality:
- Did you push yourself mathematically?
- Did you use more advanced mathematical techniques than in Project 1?
- Did you acheive your mathematical goals in an intentional way?
- Artistic Intentionality:
- Did you push yourself artistically?
- Is there a discernible aesthetic in the final piece?
- Does the aesthetic match the technical artistic language used in the lab report?
- It is clear that the final piece of art has been honed over multiple iterations?
- AxiDraw Intentionality:
- Did you push yourself with your AxiDraw skills?
- Did you use more advanced AxiDraw techniques than in Project 1?
- Did you choose your materials thoughtfully?
- Desmos Notebook:
- 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?
- Context Discussion
- 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
- 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 (like translation) 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
- Have you explained the artistic qualities you were going for in this piece?
- Do you use the artistic terms (like negative space) 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
- 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?
- Writing style and format:
- Does your artwork have a title?
- Did you use full sentences, use proper English, and do your paragraphs flow well?
- Did you follow the writing format requirements?
- Did you include a separate cover page with the title of your artwork, your name, and the date and not include this information any other page?
You will be assigned a score for each criterion on an E-M-R-N scale as follows.
First I ask myself:
If it does, then depending on how complete and clearly communicated your work is, you will receive one of the following scores:
| 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. | |
| 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:
| 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. | |
| 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.
A (95+) Earn a score of M or higher on all standards and a score of E on at least eight standards. B (85) Earn a score of M or higher on all standards and a score of E on at least five standards. C (75) Earn a score of M or higher on eight standards and no N scores. D (65) Earn a score of M or higher on seven standards and at most one N score. F (50–) Have fewer than seven E or M scores OR earn two or more N scores.
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 1.5-to-2-page lab report.
- Intentionally apply advanced mathematical techniques involving parametric functions. (Note 1: Everyone is expected to push themselves further mathematically in Project 3 than in Project 2.)
- Be organized into folders.
- Include text cells that explain the intentionality behind each function cell.
(Note 2: Students who have taken Math 200 or above should be using more advanced techniques.)
- Be generated from your Desmos notebook and rendered on a machine in the Queens College Makerspace. (If you use the AxiDraw machine, you are expected to push yourself further in Project 3 than in Project 2.)
- Be generated multiple times. Submit two (2) copies of the same artwork.
Timeline
- Choose a medium by Tuesday, April 18:
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 25:
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 27:
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 Tuesday, May 2:
By this date, you are expected to have completed a physical prototype of your artwork. We will critique everyone's art together on this day.
- Final Project Due on Thursday, May 4:
By this day, we will install the final pieces of art on display in the library. 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
Details about grading will be posted in the future.
This project represents 25% 20% of your semester grade. You will be graded on each of the following standards.
- Engagement:
- 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?
- Overall Intentionality:
- Are you excited about your piece?
- Can you convey what you were trying to do and how your piece was able to achieve it?
- Did you submit two (as) identical (as possible) copies of the final piece of work?
- Mathematics Intentionality:
- Did you push yourself mathematically?
- Did you use more advanced mathematical techniques than in Project 2?
- Did you acheive your mathematical goals in an intentional way?
- Do you show various drafts of the functions/parameters that you explored before deciding on this final version?
- Artistic Intentionality:
- Did you push yourself artistically?
- Is there a discernible aesthetic in the final piece?
- Is it clear that the aesthetics and feel of this final piece of art have been honed over multiple iterations?
- Makerspace Intentionality:
- Did you use a new machine in the Makerspace? (Or find a way to further explore the AxiDraw)?
- Did you master the workflow associated with your new machine?
- Did you choose your materials thoughtfully?
- Do you have drafts of your work that show your learning process?
- Desmos Notebook:
- 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?
You will be assigned a score for each criterion on an E-M-R-N scale as follows.
First I ask myself:
If it does, then depending on how complete and clearly communicated your work is, you will receive one of the following scores:
| 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. | |
| 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:
| 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. | |
| 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.
A (95+) Earn a score of M or higher on all standards and a score of E on at least four standards. B (85) Earn a score of M or higher on all standards and a score of E on at least two standards. C (75) Earn a score of M or higher on five standards and no N scores. D (65) Earn a score of M or higher on four standards and at most one N score. F (50–) Have fewer than four E or M scores OR earn two or more N scores.
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 portfolio.
- A two-to-three page semester reflection.
- A three-to-five minute presentation of your portfolio and its story with the class.
- 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.
- Pass through a critiquing and peer review process.
- Be able to be shared in class on Presentation Day.
- 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 the title of your artwork, your name, and the date.
- 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!
Timeline
- Create artwork: Throughout the semester.
- Assemble artwork and start developing the narrative: by Thursday, May 11.
- Create a final draft of your Portfolio: by Friday, May 19.
- Complete a peer review of your portfolio: by Sunday, May 21.
- Bring your portfolio to class and be prepared to present: on Tuesday, May 23.
Grading
This project represents 20% of your semester grade. You will be graded on each of the following standards.
- Engagement:
- Did you make steady progress on your portfolio from start to finish, respecting project deadlines?
- Did you turn in your final project by the deadline?
- Coherence of images:
- 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.)
- Development of context:
- Has each image been put into context by adding text?
- Does the text flow well from image to image?
- Did you use full sentences, use proper English, and do your paragraphs flow well?
- Your Progress as a Mathematician:
- 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.
- Your Progress as an Artist:
- 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.
- Your Progress as a Maker:
- 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.
- Additional Reflections:
- Did you discuss other themes that have occurred to you throughout the semester in your reflection?
- Did you discuss how this semester made you feel in your reflection?.
- Portfolio Appearance and Structure:
- Does the portfolio have a coherent visual theme?
- Is the organization of the portfolio easy to follow?
- Presentation Content:
- 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?
- Presentation Style:
- Did you put time and effort into crafting your presentation?
- Did you explain your work in a clear and engaging way?
- Did you respect the time constraints?
- Did you give video feedback to your assigned classmates' presentations?
You will be assigned a score for each standard on an E-M-R-N scale as above.
Your final project grade will be based on the number of scores at each level as follows.
A (95+) Earn a score of M or higher on all standards and a score of E on at least five standards. B (85) Earn a score of M or higher on all standards and a score of E on at least two standards. C (75) Earn a score of M or higher on five standards and no N scores. D (65) Earn a score of M or higher on three standards and at most two N scores. F (50–) Have fewer than three E or M scores OR earn three or more N scores.
