## Imagine IT Update 11/25/16

We just finished our quarter/unit on number theory and proof techniques. I find myself at a point where I am already thinking about what I might do differently next year. I think about how to make things a bit more student-centered. At the moment, I find myself doing a bit too much of the mathematical lifting in class, although it's a long sometimes slow process for students to keep stabbing in the dark with proofs.

I posed a vote to students about our next content: graph theory, advanced non-euclidean geometry, abstract algebra. I think I sold them on the advanced geometry by asking them to consider if all the things they know about parallel lines, angle sum of a triangle becomes warped. They especially liked the ideas with spherical geometry, so I'm looking forward to this. I think because there is a more visual element to this, it can really be something that students can "show off". I am going to be using this book as a start: www.maa.org/press/books/exploring-advanced-euclidean-geometry-with-geogebra , which really emphasizes proof as a construction (Draw the picture!), and there's also an emphasis on an inquiry-based progression of learning.

For my goals of culturally relevancy and active engagement, I'm thinking about how students can create videos and show what they are doing to the school (Make Math Cool Again! #toosoon ). Some students are also part of math team, so they have been exposed to the video contest style: ccmlmath.org/files/vid21617.pdf so I hope to incorporate that in as well. Also, I really want to set up a project where students research their own mathematical topic and create a mini-lesson around this topic to the class, along with exercises, etc. I need to think about how to scaffold this somewhat, but something in the same style as: mathcirclesofchicago.org/ for their peers.

That's all for now! I will update as we continue working with Geometry and Technology.

I posed a vote to students about our next content: graph theory, advanced non-euclidean geometry, abstract algebra. I think I sold them on the advanced geometry by asking them to consider if all the things they know about parallel lines, angle sum of a triangle becomes warped. They especially liked the ideas with spherical geometry, so I'm looking forward to this. I think because there is a more visual element to this, it can really be something that students can "show off". I am going to be using this book as a start: www.maa.org/press/books/exploring-advanced-euclidean-geometry-with-geogebra , which really emphasizes proof as a construction (Draw the picture!), and there's also an emphasis on an inquiry-based progression of learning.

For my goals of culturally relevancy and active engagement, I'm thinking about how students can create videos and show what they are doing to the school (Make Math Cool Again! #toosoon ). Some students are also part of math team, so they have been exposed to the video contest style: ccmlmath.org/files/vid21617.pdf so I hope to incorporate that in as well. Also, I really want to set up a project where students research their own mathematical topic and create a mini-lesson around this topic to the class, along with exercises, etc. I need to think about how to scaffold this somewhat, but something in the same style as: mathcirclesofchicago.org/ for their peers.

That's all for now! I will update as we continue working with Geometry and Technology.

## Phase 5: Confer with Colleagues and Students

In my phase 4 of the ImagineIT project, I asked: How can I make the classical proof-based mathematics culturally relevant to my students, students of the Southside of Chicago.

First, I asked my colleagues this question. Several of them started by wondering just how much of their own teaching was culturally relevant, and several admitted that it can be a struggle with mathematics. Our AP Statistics teacher told me that he really appreciates listening to his students as they analyze the biased and racist origins of modern statistics. Another teacher suggested that I look into the history of number theory (our current topic of study) to see what connections I could make.

Then, I asked my students about this. I didn’t ask them exactly, “How can I make this math more culturally relevant to you?” But I asked them what they thought of the class so far, and if there is anything they could change about how it’s run. I also asked them how they think this class fits in with their own culture. Several students thought the class was really challenging, but not necessarily in a way they expected. This comment made me laugh and really opened the atmosphere: “Compared to other classes, it takes forever to solve one problem; I have to write an essay!” However, like me, they weren’t really quite sure how to answer about cultural relevancy. They talked about how the school views mathematics. “There’s a lot of focus towards doing many different calculations in other classes, but this class is all about explaining your thoughts, one step at a time, and it’s more like a big puzzle to figure out in the end.” I asked if they could imagine what the math culture would be like if they had proofs, and they thought that it would be different, but not necessarily so bad. Wise beyond her years, a student pointed out that you probably would not be able to teach as many topics, but you could really study a few topics closely. I finished my discussion with students by thanking them for their thoughts and encouraging to think about how what we do in class could translate to other math classes.

After discussing with my students, I think I see a way forward. I can show my students many proof techniques and they can create several proofs on their own, but I think what we do only becomes culturally relevant when we show our work and our creations to the broader school community, contributing to the culture of the school. I don’t think it’s necessarily about finding historical culture within the annals of mathematics, but taking what we do in the small group setting of upperclassmen to the whole 7-12 school. Again, I don’t want to dictate exactly what that looks like, because I think my students can generate something that shows how math can be creative, fun and social. I think this is a better approach, because I can give students more autonomy to think about how to create a more mathematical community for the school.

First, I asked my colleagues this question. Several of them started by wondering just how much of their own teaching was culturally relevant, and several admitted that it can be a struggle with mathematics. Our AP Statistics teacher told me that he really appreciates listening to his students as they analyze the biased and racist origins of modern statistics. Another teacher suggested that I look into the history of number theory (our current topic of study) to see what connections I could make.

Then, I asked my students about this. I didn’t ask them exactly, “How can I make this math more culturally relevant to you?” But I asked them what they thought of the class so far, and if there is anything they could change about how it’s run. I also asked them how they think this class fits in with their own culture. Several students thought the class was really challenging, but not necessarily in a way they expected. This comment made me laugh and really opened the atmosphere: “Compared to other classes, it takes forever to solve one problem; I have to write an essay!” However, like me, they weren’t really quite sure how to answer about cultural relevancy. They talked about how the school views mathematics. “There’s a lot of focus towards doing many different calculations in other classes, but this class is all about explaining your thoughts, one step at a time, and it’s more like a big puzzle to figure out in the end.” I asked if they could imagine what the math culture would be like if they had proofs, and they thought that it would be different, but not necessarily so bad. Wise beyond her years, a student pointed out that you probably would not be able to teach as many topics, but you could really study a few topics closely. I finished my discussion with students by thanking them for their thoughts and encouraging to think about how what we do in class could translate to other math classes.

After discussing with my students, I think I see a way forward. I can show my students many proof techniques and they can create several proofs on their own, but I think what we do only becomes culturally relevant when we show our work and our creations to the broader school community, contributing to the culture of the school. I don’t think it’s necessarily about finding historical culture within the annals of mathematics, but taking what we do in the small group setting of upperclassmen to the whole 7-12 school. Again, I don’t want to dictate exactly what that looks like, because I think my students can generate something that shows how math can be creative, fun and social. I think this is a better approach, because I can give students more autonomy to think about how to create a more mathematical community for the school.