Mixing Math & Art - Symmetry
Learning Module
- Creator(s):
Abstract
Teaching and learning reflectional symmetry through a STEAM curriculum that connects math and art.
Keywords
STEAM, symmetry, reflection, totem poles, student-centered, multimodal
Teaching and learning reflectional symmetry through a STEAM curriculum that connects math and art.
STEAM, symmetry, reflection, totem poles, student-centered, multimodal
Throughout this learning module, students will be engaged in a multimodal pedagogy relating to learning about the connections between mathematical reflections, symmetry, and how it relates to art, specifically totem poles. There will also be a focus on students making connections of the new learning to their prior lived experiences. John Locke supports this approach in "An Essay Concerning Human Understanding" when discussing how an individual's mind thinks the specific way it does because of the experiences it has been through in its life. Locke states specifically that within experiences "all our knowledge is founded; and from that it ultimately derives itself" (Locke, 1690). Since the students will be engaged in an overall project that involves creating an art picture relating to mathematical symmetry and totem poles, there is underlying pedagogy related to meaning-making of visual represenations. Throughout thier project, students are creating a unique totem pole that is connected to their lived experiences. Through the imagery the students create, they are explaining their understanding of what a totem pole represents. Additionally, since they will be incorporating mathematical symmetry into their artwork, the students will be communicating their mathematical understanding of reflection symmetry through their totem pole art. The pedagogical reasoning behind this instructional decision is related to the video below by Dr. Bill Cope from the University of Illinois College of Education:
Education at Illinois. (2016, Apr 19). 11.6 Image Making as Design. [Video]. YouTube. https://youtu.be/nw4RUnJXGuk?list=PLV_zfgB7n1yS3-Wk65IC7-Sd4_9lpiU2_
I have previously taught this lesson in my high school math classes as part of STEAM curriculum obtained from PBS Math + Arts. When I originally implemented this lesson, it was for in-person instruction. This learning module takes my original implementation and modifies it to fit a hybrid learning model. In a hybrid model, students alternate between in-person and virtual learning days. The learning module will have learning materials for both in-person and virtual days so that the entire lesson plan will flow for understanding. The virtual assignments have been modified to fit an instructional design where students create their own representations of their understanding of the lesson goals. For example, instead of having a mainly teacher-led discussion on totem poles, their relevance and historical background, and their relation to mathematical symmetry, the students will search through the learning module instructional materials to connect these ideas to their own prior knowledge for deeper conceptual understanding.
Who is this Learning Module for?
What should you know before starting this lesson?
What materials do I need for this learning module?
After this learning module I will be able to...
How long will it take to complete this learning module?
This learning module covers the following curriculum standards:
This learning module is designed for 8th grade mathematics students, but can also be used for Geometry level students. The goal of this learning module is to incorporate STEAM principles of learning, with a focus on the connection between mathematics and art. Prior to engaging in this learning module, students should be able to:
Section 1 of this learning module incorporates a pre-assessment to determine the students' current level of understandings. Use the results of the pre-assessment to decide if you need additional supports for gaps in learning.
Most importantly, students should be seeing the connection between math and art throughout the process of completing their art project.
This learning module is designed for a hybrid learning model. This means students alternate between in-person instruction and virtual days. It is designed to be suitable for both synchronous and asynchronous virtual learning days. How I personally would implement the structure of the lessons would be to have section 1 (Introduction & Prior Knowledge) be virtual, section 2 (Art & Math Vocabulary) be in person, and to alternate from there. This way, the gallery walk presentation at the end of class can be an in-person experience for students. However, this learning module could easily be transformed to fit a fully virtual model by creating a space online for shared assignments that enables peer feedback (like CGScholar). Overall, this learning module should take six instructional days to complete. Since this learning module fits a hybrid learning model, students will need access to the Internet and a device. Graph paper, rulers or straightedges, and colored pencils or fine tip markers are additional materials students can utilitze throghout this module.
The Common Core State Standards that are aligned with this learning module are stated on the student side.
What are totem poles? What do you know about totem poles?
Learning task: Learn at least 3 new facts about totem poles.
Using the QR code below, make a post on the padlet to share what you know about totem poles. Be sure to include at least one media element in your post. Upvote on posts that you agree with or find interesting.
Pre-Assessment
Complete the pre-assessment GoogleFrom CLICK HERE. The pre-assessment is just to see what you know and what you don't know before starting to learn this fun, new stuff! Don't sweat it if you don't know the answer to some of the questions.
Daily Assignment:
The introduction activity about what students know about totem poles is a formative assessment of their prior knowledge entering this learning module. I have used Padlet to gain insight on my students' prior knowledge on new topics. From my experience, the students are more honest about what they do know and don't know about a new topic when the task to assess such knowledge is posed in a way that doesn't come across as a traditional test. With Padlet, students are able to utilize different media elements like images, videos, audio, and written text. The image below shows an example of what a completed Padlet wall could look like:
When implementing the pre-assessment GoogleForm, this again is just to gauge the students' current level of comprehension related to the concepts of this learning module. It is not to be graded and impact the students' grades for the course. I have used the results of the pre-assessment to help determine if students are ready for the content or to determine if I need to add in supplementary lessons to bridge any gaps in learning they may have prior to starting the new learning of this module.
Learning task: Connect the new vocabulary terms to my prior knowledge.
Listed below are the key terms for this learning module:
Art:
Math:
Today's task is straightforward: learn the new vocabulary terms for this learning module. However, instead of just looking up the written definition of the terms, find a way to represent these new terms. You will create a slideshow of the new terms that includes a written definition and a media element to further explain the term. For example, if the vocabulary term was "multiply" your slide could look something like the extremely short video below:
As you can see, this example has a gif, written definition, and a hyperlink to a website. For your vocabulary slide show you must have:
Assignment:
From my experience, students generally struggle to create deeper conceptual connections to new information when they don't have a full understanding of the new related vocabulary for the lesson. Because of this, I added in this section to focus on solidifying those terms before applying them to larger, contextual situations. By having the students create their own connections with images, gifs, or videos related to each vocabulary term, they will retain the meaning of that term but also be able to better apply it throughout this module and in their lives in and outside of school.
This lesson is great for a virtual asynchronous assignment because it does not require a lot of teacher input since the students are creating their own connections. However, if you plan on implementing this in person or synchronously, I would suggest giving students time to brainstorm individually before encouraging group work. Depending on the students, this may take less than an entire class period. I have often combined this lesson with the introduction lesson. The pacing of this module is all dependent on your students' current level of understanding (which should be assessed and known from the pre-assessment in section 1).
Use the students' slideshows as a form of assessment for this section. You can check that students are gaining the correct knowledge, definitions, and representations for their vocabulary terms through their work completed in their slideshows. Use this as a formative assessment to ensure students are on the right track. If you notice students have some incorrect information, send them direct feedback to correct this before moving forward in the module.
Learning task: Explain the historical background of totem poles.
Totem poles are carved pieces of wood, typically cedar, that "represent and commemorate ancestry, histories, people, or events" created by indigenous people of the Pacific Northwest. (Stewart, 1993). They are each designed uniquely by the person/people who make them. Use the resources below to learn more about the history of totem poles and what they represent.
Read this article by Colleen Messina about Native American Totem Poles, and answer the questions at the bottom of the article.
Assignment:
This section is centered around student-led instruction. If you are in person for this lesson, I would suggest starting with a short warm up activity to get a discussion started about the students' current perspecives on the history of totem poles. Some solid starting questions are "What do you think the history of a totem pole is? How do you think the tradition of a totem pole started? What do you think totem poles represent to the people that create them?" I have implemented this warm up discussion virtually through Padlet (similar to section 1) and have also held traditional in-person discussions. From my experience, it is more effective to have small groups of 3-4 students discuss these ideas before discussing them as a whole class. Once the warm up discussion has come to a general concensus, instruct students to watch the videos on their own and take notes on what they find interesting, things that were shocking to them, things they learned, and their new perspective on the history of totem poles.
For the article by Colleen Messina, "Native American Totem Poles," I have found that students working in partners creates richer discourse compared to doing so individually. For a virtual platform, students could go into breakout rooms on Zoom to do this. I have also assigned the article to partners of students through a shared document online like GoogleDocs so students can still share ideas when completing this task. Similar to the previous section, use the updates and work students complete as formative assessments to ensure they are gaining correct knowledge on the topic.
Learning tasks:
Watch the videos below, and take notes on reflectional symmetry.
Khan Academy. (2013, Aug 14). Axis of symmetry | Transformations | Geometry | Khan Academy. [Video]. Retrieved from: https://youtu.be/LrTn4cvsewk
Khan Academy. (2017, Oct 12). Reflecting points across horizontal and vertical lines. [Video]. YouTube. Retrieved from: https://youtu.be/F77xiSlCehI
Khan Academy. (2017, Oct 12). Line of reflection example. [Video]. YouTube. Retrieved from: https://youtu.be/435Ipnmp7bA
Khan Academy. (2017, Oct 12). Example reflecting quadrilateral over x axis. [Video]. YouTube. Retrieved from: https://youtu.be/lfBDOQddTD0
Khan Academy. (2015, Jul 16). Reflecting segments over line | Transformations | Geometry | Khan Academy. [Video]. YouTube. Retrieved from: https://youtu.be/kj3ZfOQGKdE
Once you're done watching the videos, complete the following IXLs to practice these new skills. Get up to a score of 90 on each:
Assignment:
For this lesson, encourage students to work individually or in small groups on the video notes. I generally allow students to choose if they prefer to take notes alone or collaboratively because they know how they learn best. If you are in-person for this lesson, your role shifts to more of a guide as opposed to a lecturer. If you notice students are disengaged or confused, step in and pose probing questions or provide clarifying examples.
The IXL assignments serve as a formative assessment to check for student understanding. Through IXL's teacher dashboard, you can monitor student progress and even see which questions the students are answering correctly and incorrectly. If you are implementing this section virtually, IXL has a feature that allows you to direct message your students if they are "live" and working on IXL. Or you can always just email them to help out if they are struggling. Starting at time 0:58, the video below provides an overview of what this feature looks like on IXL's webiste:
IXL. (2016, Feb 23). IXL Analytics: Classroom insights and delights. [Video]. YouTube. https://www.youtube.com/watch?v=5y-ymj1C9Jc
Learning tasks:
Design your own totem pole!
Your project should include:
Your artwork project will be peer reviewed by two of your classmates, and you will peer edit two of your classmate's artwork projects. Read through the resources below on how to critique a work of art. The rubric for your peer review feedback is also posted below:
Assignment:
This section of the learning module focuses on the students' art project and peer feedback process. I have often broken this section into two day's worth of instructional time: day one focusing on brainstorming and making a rough draft of the project, day two focusing on how to provide effective feedback and giving students time to provide such feedback. Whether you are implementing this in-person or virtually, it is important to go over the rubric with students prior to the start of the peer feedback process. Doing so will help students understand what is expected of them when providing feedback. The peer feedback process is helpful because it allows students to revise and improve their work. Additionally, as students work through revising others' works, they will notice where their own work may be lacking. From my experience implementing peer feedback activities, it's typically better to allow for time during class for students to complete this. Students will have questions as they read through and assess the projects, especially if they are new to the peer feedback process. It is immensely helpful for the students to have someone to bounce their own ideas related to giving feedback ("Is this too harsh? Am I being too easy going when grading this?"), and that is the role the teacher should have during this section.
Learning tasks:
Post your revised artwork project to our class Padlet by using the QR code posted below. Feel free to 'like' others' projects as they are posted.
Complete the post-assessment for this learning module: CLICK HERE!
This section is called "Gallery Walk & Post Lesson Survey" because it was initially designed for an in-person classroom model where students could physically display their artwork through the class. I have adapted this to fit a virtual model by using Padlet again. Even if students have created a physical artwork, they can upload images of their work to the Padlet page to still have a virtual gallery walk of their final projects. From my previous experience doing gallery walks, students feel much more confident in their work and the knowledge they have gained from the project being displayed.
The post-lesson survey/assessment mirrors the pre-assessment students took at the beginning of this learning module. This should be used as a summative assessment of learning in conjunction with the finalized art project.
Locke, John. 1690. An Essay Concerning Human Understanding. Book II, Chapter 1: 1. Book I, Chapter 1: 1. Book II, Chapter 1: 2, 3, 4, 6, 22, 24.
Education at Illinois. (2016, Apr 19). 11.6 Image Making as Design. [Video]. YouTube. https://youtu.be/nw4RUnJXGuk?list=PLV_zfgB7n1yS3-Wk65IC7-Sd4_9lpiU2_
PBS LearningMedia. (2021). Math + Arts | Symmetry, Reflective Drawing, and Totem Poles. https://illinois.pbslearningmedia.org/resource/b25d1df3-44fb-44ae-b12d-f80cb7d2ba68/symmetry-reflective-drawing-and-totem-poles/
Messina, C. (n.d.). Native American Totem Poles. Retrieved from: https://www.nesd.k12.pa.us/cms/lib/PA01001139/Centricity/Domain/409/Totem%20pole%20history.pdf
IXL. (2016, Feb 23). IXL Analytics: Classroom insights and delights. [Video]. YouTube. https://www.youtube.com/watch?v=5y-ymj1C9Jc
Khan Academy. (2013, Aug 14). Axis of symmetry | Transformations | Geometry | Khan Academy. [Video]. YouTube. Retrieved from: https://youtu.be/LrTn4cvsewk
Khan Academy. (2017, Oct 12). Reflecting points across horizontal and vertical lines. [Video]. YouTube. Retrieved from: https://youtu.be/F77xiSlCehI
Khan Academy. (2017, Oct 12). Line of reflection example. [Video]. YouTube. Retrieved from: https://youtu.be/435Ipnmp7bA
Khan Academy. (2017, Oct 12). Example reflecting quadrilateral over x axis. [Video]. YouTube. Retrieved from: https://youtu.be/lfBDOQddTD0
Khan Academy. (2015, Jul 16). Reflecting segments over line | Transformations | Geometry | Khan Academy. [Video]. YouTube. Retrieved from: https://youtu.be/kj3ZfOQGKdE