However, throughout the summer of 2020, being essentially home bound, trying to do my best to not be one of the people spreading CoVid19, I have focused more on learning about race, systematic racism and have begun to think about what I can do to bring about change. I have been part of four different virtual discussion groups. One examining the Scene-on-Radio podcast Seeing White, another that is discussing So You Want to Talk About Race by Ijeoma Olue, the third started by my dear friend Damianne where we discuss Ruha Benjamin‘s Race After Technology and finally one I started to try to connect all of this with teaching math. I put out a call on Twitter and sent out an email to math colleagues around the world that I’d worked with and we ordered and started discussing High School Mathematics Lessons to Explore, Understand and Respond to Social Injustice.

First of all, I have to admit that I’m scared. I said as much to my group last night. I’m scared of push back from parents and students… “but you’re supposed to be teaching them math, you don’t have time to spend on anything else.” I’m about to start at a new school, so I don’t have a feel yet for the administration and how supportive they’ll be. Fear aside, I’m also excited. Reading chapter 3 where math and social justice standards were listed side by side got me thinking about starting the school year (digitally) and how I can best get to know my students. As I read through the Teaching Tolerance (2016) Social Justice Standards for 9-12 graders I was grading myself… (**E**xceeding, **M**eeting, **N**eeding **I**mprovement)

Having students perform their own self-assessment could be a good introduction to including social justice in the mathematics course. Continuing on the theme of getting to know students while also bringing in some of the work from this book, we discussed how the first example lesson could help with this. The lesson, titled The Mathematics of Transformational Resistance is built off a 2001 article by Solórzano and Delgado Bernal. Mathematically it gives students a new framework for the quadrants of a Cartesian plane. In terms of social justice, it guides students towards creativity in action as well as consideration of diverse experiences. I took the lesson and created a Desmos Activity for it (of course I did). We’ll be discussing it as group the next time we meet to tune it up some more. But, at least I’ve made a start.

]]>So, I began with locus of points leading into conic sections. Students had been briefly introduced to conic sections along side quadratic functions, but we don’t get into the development of conics as a locus of points. Teaching it from this perspective allowed us to develop equations for “tilted” conic sections, such as ellipses that have a major axis which has a non-zero/infinite slope. We also had the chance to do constructions and paper folding! They wrote instructions and taught the principal how to do it.

From this, I segued into polar graphs and finally parametric equations. Along the way I had students using Flip Grid to give me reflections on their learning. Mostly 2 minutes videos about how the were making connections between prior learning and new learning.

Last month, I started introducing them to the idea of writing math papers. Since we are not a full IB school, most students had never been exposed to the idea of writing a paper in math. So I started them out where we were all working on the same thing. First I had them answer the questions from Underground Mathematics Conic Sections in Real Life. From there, I asked them to write a maximum 4 page paper summing up their findings on how mathematics can be used to explain GPS location determination methods and gave them an outline for a math paper.

Here’s an excerpt from an introduction:

In our current math class, I have been learning the conic section for a few months. We defined the maths behind it not only by its functional equations, but also by the locus of points it satisfies. Moreover, by studying the concept of how certain locus of points form the shape of the conics, we were able to understand the characteristics behind it; such as, ellipse is a locus of points where the sum of distance between that point and other two fixed point is constant. Now, I am trying to imply my learning to real life situation and I found out that the satellites use the conics to identify the location of the individuals using the GPS.

Another student wrote and created diagrams:

While students were writing, I was providing comments via Google Classroom and Google Docs. The papers were good, but we all know, reading many of the essentially same paper can be boring. So next up, I had students choose their own topics to write about. We started with a brainstorm:

Next, students picked their topics. This class is small, only 8 students. I had them start by writing to me about what math the would be using to see if their ideas were feasible. To do this, I highlighted the key parts of the outline for a math paper. In the end, here are the eight topics I approved:

- Sundials
- Path of a Roller Coaster
- Path of a paper airplane
- Light refraction in telescopes
- Whisper Galleries
- Hyperbolic Navigation
- Planetary Orbits
- Trajectory of a Baseball

Way more fun to read. The student who wrote about the whisper galleries spent a full class up at the white board trying to figure out how to model his elliptical shape using the speed of sound. When he got it, well, it was magical.

The student who was looking at the path of a roller coaster designed a series of parametric conic sections and then drove a roller coaster over them on Desmos!

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So, I went into the 2017-2018 school year wanting to connect. I also wanted them to know why I ran a flipped classroom. So, I started on Day 1 with a get to know you activity that I designed on Desmos. There’s a version for students who are new to me: Learning Math (New Students) and for this 2018-19 year, a version for students who now know me: Learning Math (HL2).

The activity asks students about themselves:

Then, they have to think about what I see as the steps to learning math and how easy or challenging they are for each student individually along with home much you need to understand the content in order to complete the step:

Student answers are all over the place…

But, most useful to me is reading this part.

Mostly based on the first two slides, I email each student individually. I take the chance to connect with them on a personal level:

I love guacamole too!

How I Met Your Mother was one of my favorite shows back in the day. I can’t believe you’re watching it now!

And I can also talk to them about how I think my flipped classroom style will help them with their individual learning needs:

It seems to me that you really like working with other people to learn your math. I hope that you’ll find doing the notes at home and practicing in class gives you lots of time to work with other people.

By taking notes at home, you’ll be able to have the time to write them out clearly for yourself. I know sometimes I can be confusing in the videos. So when there are things you don’t understand at first, please ask me (or someone else) to explain it again or a different way! I’m happy to help.

All told, it took me about 45 minutes to email a class of 20 students. I spent more time on them and wrote longer emails than I did last year because I’m not going to write to the ones I am teaching again in year two (for those, I am talking to them each individually in class). All in all, this is how I want to start every year because of this:

Hi, Ms,SlimanThank you for emailing me!I am so happy to be in your class.Best regards

As you might expect, TMC is full of a bunch of math nerds, my peeps, or Tweeps as I now know to call them. See, I’m pretty terrible at using Twitter. I find it to hard to keep up with. I still don’t know the best way to curate all the ideas that I come across. Plus, I just don’t feel as though I’m that interesting. I don’t think I even learned about TMC through Twitter, rather I think I heard about it through Henri Picciotto’s blog initially. In May, when I told my colleague @BeckyHall75 that TMC was in Atlanta this year and since I was going to be in Atlanta visiting the folks I would attend she said to me “have you already registered? If not, it’s already full.” What?! Twitter Math Camp is so popular it fills up? I had no idea, because again, not on Twitter enough.

But one of the biggest things at TMC is that everybody is “whatever enough” to participate. The themes of presentations in the 5 minute form of “Favorites” are often about building relationships with students and amongst the community of teachers…. which is why I found the backlash against Dan Myer’s move to switch from #MTBoS to #iteachmath so interesting. And by backlash, I mean, *what felt to me*, constant shaming of #iteachmath. It often made me feel like an outsider at TMC. I don’t have the background, but I understood quickly that there were strong feelings involved.

Remember me saying I’m terrible at Twitter, I had no idea what #MTBoS was (turns out it’s Math Twitter Blog o’Sphere) and early into TMC17 the newbies were encouraged to get themselves on the list. But it wasn’t (and still isn’t) clear to me what the list was/is… is it a list of math blogs? Is it a list of math enthusiasts? I haven’t used #MTBoS yet because I’m terrible at keeping up with this blog, along with Twitter. And I don’t know that I expect anyone to read it ever, so why put it out there to the Blog o’Sphere? And because I’m not well known on Twitter or for my blog, I don’t feel right using #MTBoS or somehow getting added to the list…

But then on the last day after everyone else had taken off, I stuck around and had lunch with David and Taylor and got a whole new perspective on #MTBoS. Back in the day, I think around 2011, many of the TMC folks got together through #MTBoS. For some, yes, it is a way to refer to blogs, but for many more it was a safe place to come and ask questions about teaching. Putting your insecurities out there to be supported, get new ideas. It formed a community that has become tight knit and led to the first TMC. Not intentionally exclusionary, but people excited to have found their Tweeps and now 6 years into TMCs people excited to see their friends.

David and Taylor both made me feel comfortable with how to move forward with #MTBoS. It doesn’t have to be about the blog at all, it can just be about mathematical best practices, which I am all for. So #MTBoS, I’ll be looking at you and hopefully to you for help in the coming year(s), because there is always room for me to become a better teacher/learner/community member.

]]>Dear Miss Sliman,

I recently came across your Further Mathematics videos on YouTube, Discrete Mathematics particularly, and the videos help me a lot. Is there a link where I could download the notes from your videos?

It inspired me to post my notes documents and link to my videos here on this site. I’ve put a lot of work into this course this year. And have been blessed to have students who enjoy the math and the hard work.

]]>The one thing that I’ve started this year is to be better at tagging my videos with the content and putting more details into the titles as well. I’ve also opened another Google account just to have a YouTube channel for my math videos only. This keeps students off my personal page, but also keeps my videos in a way that when I move to another school (not something I plan on doing anytime soon!) I’ll have them. So if you’re interested in seeing any videos, check out the MsSlimanMath YouTube channel!

]]>So then we get to IB Further Math. This course is all those optional topics plus two others, Linear Algebra and Geometry. To emphasize, all of these are at the college level, but an introduction to each. One of the options will be taught by their higher level teacher (as all these students will also take the IB HL class) and the remaining options come in the IB Further Class. The course is typically taught in over two years. We’re doing it in one by having students complete one of the topics after school the year before (my students did the Statistics option last year with another teacher) and if necessary, I’ll also do one after school this year.

As I mentioned earlier, I was an applied math major. So while I had a few pure math classes, I did not study all of these topics. Group theory is definitely new to me and so that’s the one I’m starting with, knowing that at the start of the year is generally when I’m at my freshest. Of course this year is an anomaly as I’m also going through chemo to combat my Hodgkin’s Lymphoma, but because of that I’m off work for the start of the semester, so I can focus on writing stellar lesson plans. For the first time ever, I’m writing blank notes and typing out their answers so that I’m well prepared when I make the videos. I’ve also met the students (all 4 of them) and they are super into math. They are going to be the perfect audience for a flipped class, already preferring to work at their own pace.

But I’d be lying if I said I wasn’t intimidated by this course. Intimidated and super excited.

]]>For my math studies courses which are smaller and mostly grade 11 students, I tried to learn everyone’s names and got them straight into the math. I made use of the 4Es document and basically combined all the suggestions into one document. For each “E” there were 3 problems and I told them to choose one to solve. They had the option to be up and writing on the white board and they took advantage of it. For 2 of the 3 classes, I had time to end with the #mathis exercise and that was awesome. It went as expected with the words “hard,” “frustrating,” and “worst” appearing a lot. But there were some good ones. I think my favorite is “I like money, money is numbers, numbers is math. #mathis money.” I’ve posted them up on a padlet for your viewing pleasure. I think that students walked away from the class feeling good about having solved problems and expressing themselves.

We’re 4 days in and I still haven’t discussed the syllabus. It’s online, they’ve found it if they care about it. They know that this is a place we spend 85 minutes a lesson doing math and that’s what I care about.

]]>To that end, I’ve been sourcing first day challenges. I’m teaching 2 sections of a grade 10 integrated class at the higher level, another teacher has 1 section. We’ve got our first warm-up set and I will use that. Meanwhile, I’ve got 3 sections of year 1 IB Mathematical Studies. I’m the only teacher with this class this year, so I’ve got loads of flexibility.

For both classes I’ll be using this problem solving heuristic throughout the year. For both classes I’ll also end the day with this #MathIs tweet idea for the first day. For the day 1 problems for the Math Studies class, I will make some sort of combination of the ideas presented in this opening day quiz. I’m going to be sure to not call it a “quiz” though because I definitely don’t want to emphasize grades on the first day!

]]>- What academic standards do you use, and what do I need to know about them?Here I am reading “academic standards” as “content standards.” For grades 11 and 12, these are those of the IB DP. For grades 9 and 10, these are set by the ISB math department, but closely aligned to many other international standards. These can all be found through the parent portal.
- How will you respond if or when my child struggles in class?I will do my best to figure out why your child is struggling. Is it because of the content? Is it because they have not yet had a chance to access the lesson? Do they need more practice? Then I will work with your child individually to help figure out how to remedy the struggle.
- What are the most important and complex (content-related) ideas my child needs to understand by the end of the year?The concept of functions regarding input and output and how the algebraic representations connect to the graphical representations.
- Do you focus on strengths or weaknesses?This depends very much on the student. For weaker students, I focus on the strengths – finding ways for the student to feel good about themselves in math so that they want to continue working on it. For students who are strong in math, I focus on what they do not yet know and try to challenge them.
- How are creativity and innovative thinking used on a daily basis in your classroom?Students will routinely be asked “what makes you say that?” and “what’s another way you can explain this?”
- How is critical thinking used on a daily basis in your classroom?I will never tell your student whether their answer is correct. Instead, I will ask them to justify to me why they believe their answer is correct. If the answer is, in fact, incorrect, I will continue the discussion until the child understands for themselves that their is a flaw in their logic.
- How are assessments designed to promote learning rather than simple measurement?All assessments will include questions that require putting together multiple ideas and solving problems in unfamiliar contexts. In order to access this type of problem, students must understand the content, not just regurgitate facts.
- What can I do to meaningfully support literacy in my home?Ask your child to explain how to solve a problem from class to you. As this is high school math, you should be able to understand it and your child should be able to explain it.
- What kinds of questions do you suggest that I ask my children on a daily basis about your class?What did you learn from the video? What did you struggle with today?
- How exactly is learning personalized in your classroom? In the school?As you will read about in questions 12 and 13, I used a flipped classroom approach. This means that your student will be watching videos that I have made at home to help them acquire knowledge before class. In class, time is spent solving problems related to the concepts. Each student will choose the problems that are best suited for him/her regarding their level of comfort with the concepts – from very basic problems to very challenging ones.
- How do you measure academic progress, and what are the strengths and weaknesses of that approach?Through daily warm-ups, I will have an overview of how well your student understood the content from the night before. Are they able to start the warm up? Are they able to solve the warm up? Are they able to help someone else? Also, through quizzes, both the students and I will better understand their areas of weakness. Cumulative assessments (tests and written tasks) will form the basis of the measurements.
- What are the most common instructional or literacy strategies you will use this year, and why?
- What learning models do you use (e.g., project-based learning, mobile learning, game-based learning, etc.), and what do you see as the primary benefits of that approach?I am answering 12 and 13 together. I used the “flipped classroom” method. As described above, students have “home learning” that they are to complete before they come into class. This will include actively watching a 20 minute (maximum) video made by me and completing the notes that go with the video. On the following night, students should attempt 3 – 5 problems related to this video. Students should come to class with the video watched and either the practice problems completed or specific questions related to the problems. For example, “I knew how to start this problem, but then I didn’t know what the second step should be.”
Then, in class, students will work together on a warm up related to the content. After the warm up, students will work either independently or in groups on further practicing the concepts and relating them to past materials.

Class time may also be used for mathematical investigations where we explore the content more deeply.

- What are the best school or district resources that we should consider using as a family to support our child in the classroom?Coming to see the teacher for help!
- Is there technology you’d recommend that can help support my child in self-directed learning at home?khanacademy.com and YouTube!
- What are the most common barriers you see to academic progress in your classroom?Being told “it’s ok if you don’t like math, math is hard.”
- How is education changing?Understanding is much more emphasized now rather than rote memorization.
- How do you see the role of the teacher in the learning process?I see myself as a facilitator and ultimately the student as responsible for learning the content.
- What would the ideal learning environment, free of any constraints, look like?Students working at their own pace through the material, asking questions as needed and taking the assessments when they feel like they are ready.
- What am I not asking but should be?