Context
Our classroom setting, again, is in an afterschool program. Our students are eighth grade and the program is concentrated to help students within STEM. At the beginning of class, the students work on their homework with Trinity Mentors from 3:30 pm to 4:15 pm. The other half they work on “STEM-related projects or courses.” Yet, this is not the case.
When I and Rafael were setting up and talking to students, I noticed that when it was going to hit 4:10 pm, our placement teacher pulled out UNO cards and Jenga. Technically, that shows that the program is not doing what is supposed to, rather the real context of our classroom setting is more about having a place to get tutoring and then the rest is playing games and having fun. There is nothing wrong with having fun, but already knowing that after 4:15 pm you are going to play games is a struggle that I and my partner face while creating a curriculum.
That being said, based on our first lesson the students did not enjoy it. We asked the students to answer some questions for a reflection, to see their understanding of the lesson and if they enjoyed it. Many of them said that it was not fun because they felt like they were in class all over again. We took the students advice, which is why our second lesson was based more on art than in math since it is more creative and is more hands-on.
Objectives
-Students will create tessellations to demonstrate the use of rotations and translations
-Students will apply knowledge of sequencing rotations and translations
These objectives are pulled from portions of the 8th-grade mathematics Common core standards:
- Describe the effect of translations, rotations, and reflections on two-dimensional figures using coordinates.
- Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them
Activities
We began the workshop by rearranging the desks into a circle, instead of having them be spread out across the room. This forced the students to face each other and actually interact with our other. We sat within the circle and sat next to students, instead of teaching them up on the board. We decided to do this because we felt that h Next, students will be prompted to consider the connection between art and mathematics. We then open with the question “ Who here likes art or considers themselves artists?” Some of the students were like yes and others said no. I think they taught of being famous artists or being really good with the arts. That being said, this question may have brought a lot of anxiety amongst the students. After a couple of students answered we asked them “ Can you envision what you can do with math to make art?” and “Is it possible to use math to create artwork?” These questions really did turn off a lot of students as their smiles were wiped off of their faces, yet many were very intrigued and had many ideas as to how math and art can correlate with one another.
I then passed around printed copies of tessellations. However, when we passed them out, we let the students examine the images so that they can be engaged when we asked a couple more questions. The images below are the real-world patterns that students see in their daily lives. That way they can see how math, in this case, tesselations, are all around us.
After a while of them looking we asked them what do they noticed? Some students noticed that they were different shapes, colors, images, and size. We kept asking more questions that would lead them to mention that what they are seeing are patterns. That was our main cue to have a transition to defining tessellations.
We explained to the students with some detail that a tessellation is a repeating pattern with no gaps that infinitely covers a space. As we defined tessellations we then moved into asking the students what tessellations they see around them at that moment? and what tessellations to they see in their everyday lives? This got them really thinking that tessellations (math and art) are all around us. It is just a matter of looking closely.
Next, we passed around printed pictures of select artworks that are tessellations, these pieces of art reflected only translations so that the students can notice what happens to each side and noticed the pattern. The following image was the art piece that we decided to use.
After they saw the picture and noticed the patterns, I moved into explaining how to create a tessellation with translation. The following video demosntrate the way I went about showing the steps to do the translation tessellations.
After about 10 mins of letting the students work on their tessellations, we moved into rotations within tessellations. We moved their attention from creative work to analyzing again. We showed them an image of a tessellation that used rotations and asked the student what they noticed about the pattern. We asked if they noticed whether the tessellation was moved in any way, shape, or form. One student noticed that the tessellation was rotating to fit into the pieces, which was our key moment to move onto a new form.
We basically repeated the same steps as for the translation sections, yet the steps to making the tessellation is a bit tricky. Taught the same way as in the previous video.
- Create a tessellation template out of a square piece of construction paper
- Make the design on one side of the square
- Cut out the design
- Rotate it to the opposite side
- Trace it
- Cut out the design
- Rotate the previous piece to the top of the square
- Tape it
- Rotate the other piece to the bottom of the square
- Tape it
- Trace your tesselation over and over
Equity
During our lesson plan, we wanted to use different ways of teaching to show the kids how to perform and demonstrate their understanding of tessellations. So what we decided to do was have a visual reference for students to observe. Those were the images that we had passed around and me physically showing them how the tessellations worked. I also explained verbally to students when I would go one by one to explain the steps again.
Assessment
As I mentioned earlier, we were going to have a worksheet that held questions:
- How is this activity connected to mathematics?
- Does this activity change what you thought about mathematics?
- What did you most enjoy about this exercise?
- What did you not enjoy about this exercise?
Yet, we forgot to print them out. So, what we did was go around and ask the students individually to see what they learned, what they liked, and just honestly heard them out. That was more of our verbal assessment, yet we had a physical one as well.
Throughout our whole lesson, we had students create their own tessellation. I would show the process of how to properly create it and then they would replicate the process, but with their own design. In the video, you notice how we go around and help students. That is our second assessment. We observe as to whether or not they are understanding the process and if their tessellations even work. By them just being able to properly translate and trace the tessellations perfectly to create the pattern, that would show their learning and understanding of how tessellations work.
Reflection
I am going to start with the very positive things from the lesson plan. I loved to see the expression and energy that the students had that day. They were all on task, well most, and they all had a good grasp on the concept. The students were conversing with one another and looked more lively than the previous lesson that we held. Now, in the previous lesson there were certain students that did not participate and that were just acting very smart with us. During this lesson it was a whole different story. The students participated when we asked questions and really took the activity serious. In terms of how I felt, I felt pretty prepared and very excited. Me and Rafael took a huge leap when it came to our lessons. It was fun, artsy, and the students were just so different. I learned a lot from my first lesson and really felt that I grew with our second lesson. There are very minor things that I would change, but in all I loved every second of it.
There were also things that I felt could be improved. The first thing would be the environment in which our lesson is being held. Since we did not have a reflection sheet for the students, me and Rafael decided to go around and ask students the questions. The question that got to me was “What would you want us to imrpove on?” One of the students told me how they still felt like they were in class. They physically are in a classroom, but what they meant was that they were bored. They just signed and said they were bored. This made me really sad because Rafael and I are in a very tricky situation, when it comes to our placement. As I mentioned earlier, the students are already accustomed to have free time, which to them is fun. So, having that in mind, I would love to have something where students can be outside and not feel like they are still in class. I do not want to have an activity that is not math related, but like I want it to be really fun to the point that the students don’t feel like they are in class.
The second thing that I would change from the activity would be the use of math vocabulary. Rafael and I were focused a lot in the questions, which in my opinion were really good, but could have been improved. The second question into the lesson had the word ‘math,’ and I noticed that the student’s face automatically changed. They at first seemed very excited about the art making, but the math part just changed their smiles. The changes would just be the wording of words, to not trigger the students to think they are in class. I know this program is for STEM related topics, but they are not accustomed to that, so it is more about trying to get to them in a way that they don’t know we are doing math.
Lastly, my last revision would be conducting the lesson. At some points me and Rafael were just not on the same page and that really threw me off completly. I understand that teaching can be a little nerve recking, but we did have a lay out and we should have sticken to it. I felt like I was not taken seriously at some points and that got me really frustrated. Yet, it falls more with the communication aspect at the end of the day. We both realized that things did not go to plan and noticed how we could support and validate one another through our teaching segments. This way we can be more comfortable when teaching and actually focus on making the lesson plan engaging and useful, for the students.
Sources
http://www.exploratorium.edu/files/geometryplayground/Activities/GP_Activities_6-8/ExploringTessellations_%206-8_v4.pdf
https://www.google.com/search?q=mathematical+connections+to+tesilations&rlz=1C1CHBF_enUS832US832&oq=mathematical+connections+to+tesilations&aqs=chrome..69i57.13729j0j7&sourceid=chrome&ie=UTF-8#kpvalbx=1
http://www.corestandards.org/wp-content/uploads/Math_Standards1.pdf
http://www.magnatiles.fr/wp-content/uploads/valtech-magna-tiles-tessellation-stone.jpg
https://www.mathsisfun.com/geometry/tessellation.html
https://www.mathsisfun.com/geometry/congruent.html