Part 1: Sustaining

So your school has done the huge lift of creating a cultural shift around mathematics in your building? You’ve redesigned your curriculum, improved student achievement, and see evidence of teacher and student confidence in their own problem solving skills around mathematics? Great! That’s done - time to tackle a new school challenge!

Wrong! Of course mathematics does not always have to be the key focus of your work plan, however if you want to sustain the hard work you’ve begun, it is crucial to ensure there is a plan for maintaining this transformation going forwards.

The biggest component of this struggle will be staff turn-over. In no other discipline is hiring so precarious. Not only is there a shortage of teachers looking to be middle and high school math teachers, but additionally, those who do apply will not come into your school community having done the lifting on vision, mindset, content, and curriculum that the rest of your staff has done. It is key to have a plan to onboard and support these new staff.

Additionally, returning staff will have differing needs for support to sustain their mathematics development. It is imperative that schools maintain a Math Culture Lead (Recommendation #1) who can continue to lead the school’s culture and curriculum around math education and, if they are an in-house staff member, is supported to continue to grow their understanding of the mathematics field.

Part 2: Deepening

“Why do I need to learn this? When will I ever use it?”

Too frequently math teachers hear these common pushback phrases when introducing or assessing math concepts. Unfortunately for all, the easiest and most common response is to point to a necessary exam, college admissions or passing to the next grade level. The further students advance, too frequently, math becomes a means to an end.

But what if topics of study clearly mapped to the important and quite complex uses they do have in society: self driven cars, oceanography, Pixar’s animation studios, our capitalist economy, architecture, nursing, carpentry and so many more parts of our world rely on the structures of mathematics. Unfortunately, students and teachers alike don’t make these connections. Due to the way the majority of us have learned mathematics, it is not easy to envision the ways in which much of the math taught in schools is applicable into daily life and the complex careers we hope our students will someday have.

What if it were possible to support these connections more?

The answer is not simply to pop some math into social studies or science expeditions (as we frequently do with literacy standards). At no fault to anyone, math additions often end up as fast additions to a final product -- statistics is always a favorite, or a quick ratio table. While not a poor idea, this is rarely well planned, mapped with standards, and assessed. True integration of the mathematics would mean planning for the math as a part of the design for the final product and the work within the expedition (including appropriate grade level or related standards that are assessed as a portion of the product). Math centered expeditions are also a possibility, but must truly center around a mathematical idea.

Although EL Education has paired back mathematics integration as a central piece of Core Practice 15, it has not been removed as an eventual explorative goal. How we go about it, however is crucial. It must be achieved in a way meant to support students in seeing the mathematics in the world around us and its daily use or career specific use.

Finally, it must be noted that in EL Education schools -- and many schools across the United States -- literacy integrate is supported and mandated across every subject area (math included). Numeracy, however does not have the same requirements; it is not required to be integrated across subject areas. Schools looking to deepen their thoughtful support of student growth should require all subject teachers to focus on both literacy and numeracy. Regardless of final product integration, ownership over students’ numeracy should be shared across middle and high school faculties.

Part 1: Sustaining

Ongoing professional development for old staff

• • Reflect on the vision yearly. Set goals around editing, unpacking and further defining the vision each year.

  • Continue the successful practices from years past

  • Hire outside support to come in and do professional development to push practices that are not yet meeting your school vision (see some that have worked with EL Education or Deeper Learning Schools before):

    • DMTI (Developing Mathematical Thinking Institute) - Jonathan Brendefur (PreK - 12) (Works with Anser Charter School and Odyssey in Denver)

    • Stephanie Smith - (K - 5) - CGI math coach/consultant (Works with High Tech High Elementary in San Diego, CA and Success Academy Charters in NYC)

    • EduQuate LLC (PreK - 8) (works with Polaris Charter Academy, WHEELS, and supports EL Education National)

  • Shift leadership from being the primary responsibility of the Math Culture Lead to being shared throughout the school. Offer leadership opportunities for staff to mentor new staff or lead some professional development within the school

  • Allow staff to attend (or even present at!) national and international math conferences (see examples below)

    • NCTM (national conferences) (PreK - 12)

    • Metamorphosis (PreK - 12)

    • YouCubed - Jo Boaler (PreK - 12)

    • See a longer list compiled by Michigan State’s School of Education here

    • And of course EL Education’s annual National Conference

Create structures that allow new staff onboarding: ideally in the summer or before school lets out the prior year. Include the following sessions as mandatory:

• • Math Culture onboarding: Sharing their Math Story and unpacking the current national story of mathematics in the United States

  • Unpacking of the school’s already constructed vision. Ensure new staff unpacks the school vision, can see it in action, and agrees that this is the best method of instruction (even if they are not yet able to teach this way).

  • Allow for grade level partnerships (when possible) and structures and time for common planning. For example, a new 3rd grade teacher has a returning third grade teacher as a partner teacher and has sacred common math planning time each week.

  • Allow for math mentorships - Allow teachers who are looking for leadership opportunities and have proven successful at implementing the schools math vision to get support from Math Culture Lead to mentor or formally coach new teachers.

Reflect on Math Academic Data: Look deeply into your schools academic data around math (State Test, Benchmark Data (internal tools, NWEA Map test, etc)

• • As Leadership

    • Reflect on next steps to achieve full implementation of your math vision

    • Place into your work plan if a part of the next years big moves, or ensure the Math culture guide has vision for moves within their daily work (separate from a big school shift)

    • Make adjustments if needed to scope and sequence or curricular documents.

  • Whole Staff

    • Allow all staff to reflect on benchmark math data at least three times a year to adjust, reflect on implementation.

    • Hold end of year vertical conversations to allow for consistency and feedback of programming between grade level teams. See example agenda of such a meeting here.

Part 2: Deepening

Mathematics in other subject areas:

• • Start simple:

    • Focus on the crossover ideas between subject areas: Plan for meaningful integration of core mathematics concepts that will need the most focus for students. See the work of Tina Chunk out of Stanford for key ideas and crossovers for ELA, Math, and Science standards.

      • One step further: Choose a schoolwide goal that can be touched by all teachers (see diagram in the link above) such as proving an argument with evidence. Unpack as a teaching team or school to create consistent language and structures.

    • Give some math to science and history: Be thoughtful about where some easier to integrate concepts live - for example, statistics and linear timelines standards in history or analyzing data in science. Be sure to fully “share” or “give” those standards to those teachers, such that the standards are fully unpacked and assessed (at the right grade level appropriate rigor level) along with the science and history learning.

Mathematics in expeditions. Math does deserve a place in well planned expeditions and final products, but consider the following options when planning:

• • Math as a component in an expedition

    • Many social studies, history, and science expeditions can naturally add a component or two of mathematics: a graph or a table or some statistics are the norm. What is often missed is the intentionality of the math rather than as a “bonus” add-on. Be deliberate about which standards are being chosen at the beginning of the planning process for the expedition. Much as the “Four T’s” planning process encourages choosing topics that support the targets and grade level goals of an expedition, so too should the topic be in service to the mathematics. This is a difficult puzzle fitting process that sometimes works beautifully to match core grade level math targets with an already tricky to plan expedition. However it can be done. We will continue to work to find and share examples of success in this regard.

  • Math-led expedition

    • There is possibility for an expedition to be centered around a key mathematical guiding question. This expedition would engage history, art, literature, etc as components in answering that mathematics-centered guiding question.

    • Our culture of teaching and learning math in schools does not currently understand the true definition of mathematics. As a result, we have not planned true math-led expeditions, nor in many cases thought it possible.

    • A Mathematician’s Lament, by Paul Lockhart unpacks these complex reasons why our culture doesn’t feel comfortable with the Math-led expedition. See below for an unpacking of some ideas and next steps around attempting this work.

Except from the Mathematician’s Lament

Why don’t we want our children to learn to do mathematics? Is it that we don’t trust them, that we think it’s too hard? We seem to feel that they are capable of making arguments and coming to their own conclusions about Napoleon, why not about triangles? I think it’s simply that we as a culture don’t know what mathematics is. The impression we are given is of something very cold and highly technical, that no one could possibly understand— a self fulfilling prophecy if there ever was one. Mathematics is about problems, and problems must be made the focus of a students mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process— having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other’s work. Specific techniques and methods will arise naturally out of this process, as they did historically: not isolated from, but organically connected to, and as an outgrowth of, their problem-background.

Thoughts for Math-led expeditions

• We as a culture do not understand what mathematics is, and focus instead on the skills our students will be assessed on.

• We therefore don’t understand the great problems and questions of mathematics (those that were historically questioned to produce the theorems and equations we take for granted today).

• Essential questions and ideas of mathematics can and should be discovered as a part of a math-led expedition.

Except from the Mathematician’s Lament

A problem, a genuine honest-to-goodness natural human question— that’s another thing. How long is the diagonal of a cube? Do prime numbers keep going on forever? Is infinity a number? How many ways can I symmetrically tile a surface? The history of mathematics is the history of mankind’s engagement with questions like these, not the mindless regurgitation of formulas and algorithms (together with contrived exercises designed to make use of them).

Thoughts for Math-led expeditions

• It is challenging, however, to identify and create these plans as culturally, we view mathematics as a developing of skills to use in the real world (adding so we can balance a checkbook) rather than a set of interesting questions about the world around us.

• Our teachers and our schools are not prepared to tackle the planning and implementation of such work in most cases.

• Where could this happen? When? While still working in the confines of our current education systems treatment of mathematics.