Re-Imagining High School Math

First, I need to start with how much I love the school where I teach. We have amazing autonomy, a truly learner-centered program, where the needs of our students are our highest priority. That said, there are certain things I would change if I could – and to a certain degree, I have earned the trust of my administration to research and explore different ways we can work with our kids to vastly improve their experience and success in mathematics. The school has not had any significant overhaul in the math program, probably since its inception. It is a very traditional curriculum for the most part, with a sequence of Algebra 1 – Geometry – Algebra 2 – Pre-Calculus – Calculus. We also offer an Intro to Algebra class and a Consumer Math (now Financial Literacy) class, for students who wanted or were perceived to need an alternative to the traditional sequencing in order to fulfill their requirement of 3 years of math. As a result, we have students who enter our school at a large variety of math background, and leave with almost as much variety in the math they have seen over their four years in high school. There is no real change in equity – most Black and Latinx students do not take calculus, most students with learning disabilities do not take calculus, and the calculus class is usually mostly white or Asian students. Furthermore, students who do well only have the option of calculus, even if they do not plan to pursue studies in fields that will actively use calculus techniques and would benefit from other class options.

I’ve been thinking about how to better serve our students for a while now, and this past April at NCTM Annual Meeting in Washington, D.C., I picked up a copy of the highly promoted book Catalyzing Change in High School Mathematics, which gave me a lot of the framework and research that I was looking for, all compiled in one place. Between that and the “Re-Imagining High School Mathematics” morning session at this summer’s Twitter Math Camp, led by Carl Oliver and Sadie Estrella, I was able to work through a long term plan outline. There are a lot of details to work out, but here is the general framework of what I want our students to have for their classes:

  • Move from a traditional Algebra 1 – Geometry – Algebra 2 -Pre-Calculus sequence to an integrated Math 1 – Math 2 – Math 3 sequence that incorporates the most essential mathematical skills that students will need.
  • Work with the other math teacher(s) and administrators to determine what those essential mathematical skills are. These are the skills that we expect all high school graduates to have in order to be well prepared for any further math class, as well as to participate fully and successfully in society.
    • Algebraic reasoning skills
    • Financial literacy
    • Understanding of plane and solid geometry, measurement, etc.
    • Ability to read, interpret, and evaluate data, graphs, and basic statistics
    • Preparation for calculus, statistics,  discrete math, or computer science classes
  • Develop a support class, preferably a zero period class that can be required for some students and a drop-in class for others.
    • Give students a just-in-time support for reviewing essential skills before they come up in the core Math 1/2/3 classes
    • Extra help, support, and practice for the content of the core classes
    • Opportunity for peer tutors to receive credit as well as review and build leadership skills
  • Create multiple options for a fourth year class, including Calculus and Statistics.

There are going to be (very valid) concerns about moving to this model. Firstly, many of our students with various learning disabilities may feel overwhelmed by facing math that may be familiar to their peers. Secondly, many students who took Algebra 1 in 8th grade may feel that they will not get much out of a class with so much review (in their eyes). Thirdly, many students who need that support class may have a hard time arriving on time if it’s a zero period class that starts 45 or 50 minutes before their first class. (This is especially true of students with anxiety who may avoid attending school when overwhelmed).  Fourthly, will we be able to handle such significant changes in terms of staffing and scheduling, and will we be able to hire a third teacher? It is going to be up to us to see what we can do to address or alleviate these concerns, and will take some good research and planning to do so.

Despite the challenges we have ahead, and the many questions we have to put forth and then answer, I’m looking forward to bringing this proposal formally to my department and administration this fall. A change like this won’t happen immediately, and I don’t foresee any change at all this year. I’d like to put the plans into place over the coming year to start rolling out a new set of classes, starting with an integrated Math 1 and Support Class in the 2019-2020 to replace our Intro to Algebra and Algebra 1 classes. By the 2022-2023 school year, my hope is to have a math program where (except in extraordinary circumstances) all students are taking Math 1-3 in 9th-11th grades, and taking a fourth year math elective in 12th grade. My goal is to see Calculus and Statistics classes that are full and reflect the ethnic, racial, LD, gender, and other diversities that make our school so great.

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Late #TMC18 Recap

I got back from Cleveland nine days ago. After my wife’s quick business trip to Chicago, my older daughter’s 7th birthday party, and my mother-in-law arriving for a visit, I am finally getting an opportunity to reflect on my second time at Twitter Math Camp. There is something amazing to me about getting together with passionate math education professionals, many of whom pay their own way to this informal, grassroots conference. The NCTM Annual Meeting has its benefits, with enormous vendor areas, nationally known keynote speakers, and exciting new locations. My local state conference, CMC-North at Asilomar, is much more intimate, in a beautiful oceanside resort setting, with outstanding presenters and attendees. TMC is a mix of both worlds, with a new location each year, an international crowd, and small groups working on interesting things.

This year, my speaking proposal (on matrices and matrix applications for beginners) wasn’t accepted, but I was able to get in through the lottery. In some ways, I started to feel a bit of impostor syndrome sinking in, since the whole point of TMC is really to encourage everyone to share and collaborate. That feeling didn’t really leave until partway through the conference, when Julie Ruelbach gave a great lunchtime keynote on how prevalent impostor syndrome actually is, and reminded us all that we do belong. At that point, I thought about submitting a #MyFavorites short presentation, but wasn’t convinced I’d be able to put something together in time.  Next time I go, though, I’ll be sure to stand up and speak. On what? A debate format perhaps? Rethinking homework? How I do honors classes? Maybe something about 3D printing? Maybe a bit of linear algebra after all? How about the role of white teachers as allies for students of color, and how we can press forward with the hard questions surrounding equity? There are plenty of things I can speak about, many topics in math and education that interest me, and surely I have something to offer after 17 years in the classroom!

On to the sessions, with a brief description. I’ll be writing some follow-up posts about a couple of the big ones.

Morning session: Reimagining High School Math with Carl Oliver and Sadie Estrella. This session took place over three consecutive mornings for two hours each morning, and was an opportunity for teachers and teacher leaders to think about a way to change their own classroom, school, or district math program. I am fortunate to teach in a school with amazing support, and have received encouragement to work on my plan to revise the math program at our school. We have an interesting and diverse population: many students with diagnosed learning disabilities; many students with high anxiety around school in general and especially with math; several students who come from schools in lower-income areas with fewer resources, where their transcript that shows high grades and Algebra 1 in 8th grade may not match with a mathematical background that has not exposed them to deep and rich mathematical thinking. The question I have had for a long time is how to ensure that all students are given an opportunity to thrive in mathematics to the absolute best of their ability, regardless of their previous experiences. Other teachers in the session had a variety of goals and plans, but all related to improving the experience of math learners in their mathematical appreciation and ability. (Even Chris Nho‘s plan to improve the community feel of math educators in his district has potential long term benefits of building camaraderie and then collaboration among teachers in his district.) Check the #rehsmath hashtag on twitter to see more!

Afternoon sessions:

Promoting Equity through Math Talks, with Anne Agostinelli. Thinking about how math talks can be designed to progress throughout the week, with intentional structure, in order to address the SMP‘s consistently.

Interactive Notebooks for All, with Farica Erwin. (I’ve submitted to speak with Farica at the NCTM Annual Meeting in San Diego on rethinking homework, and this was the first time we met in person!) I’m not big into doing lots of crafty things, but I know that lots of people, teachers and learners alike, love interactive notebooks. What did I take away? The importance of being intentional about the interactivity, of not overdoing it, and most importantly, of page numbers and a table of contents. In fact, that’s the biggest takeaway, as I think about how I may try out digital notebooks this year in my classes – organizing by a table of contents and shared/common vocabulary so that all students can have a structure in place.

Living Proof: Enjoying Teaching 2-Column Proofs, with Elissa Miller. I may not be crafty, and Elissa is incredibly crafty, but I took away some great ideas and resources in this session. Lots of the proofs presented reminded me of the fun and creative ones found in Harold Jacobs’ Geometry (now out of print, unfortunately).

Sausages Without The Skin, with Nik Doran and Max Ray-Riek. I’ve been following the work of Illustrative Mathematics for a little while now, and have watched as they have snatched up so many great teachers to work with them on their new curriculum. Now they are getting ready to release new high school resources, and this was a chance to take a sneak peek at what they are creating. Although I’m hoping to move towards an integrated curriculum, which isn’t what they are currently working on, I do expect to be able to incorporate a lot of their lessons into our curriculum as we move forward over the next several years.

Anxiety, Mindset and Motivation: Bridging from research to practical classroom
structures, with Lisa Bejarano and Dylan Kane. I was really excited to see what Lisa and Dylan are doing to bring the research based ideas of Jo Boaler, Carol Dweck, and Ilani Horn directly to the classroom. We came away with some great ideas, including a new routine for my next year, Sara Van der Werf’s Stand and Talks.

Flex Session: Equity at TMC, with Tina Cardone and Sam Shah. This was a continuation of a session from last year, and one that has been on my mind for a while now – not just at TMC. Math education is a place where so many teachers are white, and so many visible leaders are white, and conferences tend to skew even whiter than the population of math teachers. If we want students of color to thrive, we need to ensure that they have teachers of color. Furthermore, if we want white students to buy into the capabilities of their black and brown classmates, they need to have teachers of color as examples and role models. (That’s not all we need, clearly – we have many math teachers who are women, but there are still fewer girls than boys going into math as college majors. Still, increasing the number of women who are teachers is an important step.)

Besides those great sessions, there were so many impromptu conversations, great socializing with new and old friends (including a vegan contingent), and a chance to see Cleveland, a place I’d never have intentionally sought out but which turned out to be a wonderful and welcoming city.

Next year it’ll be in Berkeley, and I hope to be there again, seeing friends and sharing in this great profession that we have chosen.