Today’s post will consider changes in math instruction over the past 10 years and what its future might look like...
‘The Next Chapter Doesn’t Include Tricks’
Alison J. Mello is an author and consultant who has been an educator for 30 years working as a classroom teacher, math specialist, curriculum director, assistant superintendent, and graduate instructor:
Ten years ago it was 2016. The Common Core State Standards were still relatively new, the Apple watch debuted, and COVID-19 was unheard of. To say a lot has changed since then would be a colossal understatement. What about math education? What has changed in the last 10 years, and what needs to change in the next 10?
As a curriculum director in 2016, I was struggling with the realization that we had focused so heavily on the changes to the content standards that we missed the critical importance of the Standards for Mathematical Practice. We focused on the “what” but not the “how.”
Thankfully, the National Council of Teachers of Mathematics published “Principles to Actions” which outlined eight teaching practices to support the “how,” and, as we discovered, these practices were the key to changing the hearts, minds, and experience of teaching and learning math.
- Establish mathematics goals to focus learning
- Implement tasks that promote reasoning and problem-solving
- Use and connect mathematical representations
- Facilitate meaningful mathematical discourse
- Pose purposeful questions
- Build procedural fluency from conceptual understanding
- Support productive struggle in learning mathematics
- Elicit and use evidence of student thinking
These shifts did not happen all at once, nor have they been actualized fully during the last 10 years, but some seem to be taking root. In my district, and in the many districts I now support, the most exciting changes I see center students in the learning process. Shifting from teachers as the purveyors of knowledge who show students “the one way to solve” to facilitators who set conditions and empower students to collaborate, discuss strategies, productively struggle, and make connections is extremely powerful.
In these learning environments, I see more visuals, more movement, and more tools and manipulatives to support conceptual understanding. I see more student independence and see a focus on sense-making, something I did not experience as a student. These shifts not only make math more interactive, creative, and hands-on but make instruction more engaging, effective, and enjoyable for both teachers and students. They also make learning accessible to more students, resulting in more equitable experiences.
Between 2016 and 2026, countless open educational resources have emerged, and in recent years, the push for high-quality instructional materials has grown. With AI gaining momentum, the next 10 years are hard to envision. While there will undoubtedly be more resources than we can even imagine, history tells us it all comes down to instruction.
The teaching practices above can, and should, inform the next 10 years so students are prepared for a world that will unquestionably be different from the one we know today.
Since Alexa, Suri, or Photomath can easily solve even complex calculations, we must shift from procedural fluency to truly understanding math. This will position students to have the depth of knowledge to know if the output from these tools makes sense. To develop this capacity in students, teachers need to be intentional about creating student-centered learning environments that value thinking, reasoning, debate, questioning, and relevance. Some ways to get started include:
- Engaging students in solving relevant problems that interest them (practice #2)
- Flipping the ratio of teacher versus student talk (practice #4)
- Posing intentional questions that support reasoning (practice #5)
- Creating conditions for collaboration that foster productive struggle (practice #7)
- Normalizing mistakes and valuing thinking versus answer-getting by having students share their strategies and defend their reasoning (practice #8)
In addition to these shifts, teachers must know their standards. To engage in practice #3, it is essential to understand how concepts are related and how they develop across grades. This is where teachers can leverage the power of AI to build their own capacity.
Leaning into technology is one way to empower teachers to prepare students for a world where memorization is obsolete. The next chapter doesn’t include tricks to get answers and step-by-step procedures. Instead, it elevates student voice through critical thinking, reasoning, technology, and problem solving. Will math education in 2036 look wildly different from what it did in 2016? If we want students to thrive beyond our classrooms, it must.
‘Change Will Be Slow’
Henri Picciotto is a consultant and curriculum developer who has led hundreds of in-service workshops in the course of his career. He retired from the classroom after 43 years teaching at all levels, K-12. He maintains a math education website:
Robin Pemantle, a member of the National Academy of Sciences, is a professor of mathematics at the University of Pennsylvania. He has developed math content courses for college freshmen and preservice teachers.
Together, Henri and Robin authored a recent book entitled There is No One Way to Teach Math: Actionable Ideas for Grades 6-12:
In the last 10 years, there was much discussion of the Common Core State Standards . It had some impact, as new textbooks are aligned with it. Many who in principle opposed it ended up adopting some of its features nonetheless. Unfortunately, the math wars continued, centered around false dichotomies such as skills versus understanding and teacher- versus student-driven pedagogy.
New controversies include the creation of a data-science track in high school and tracking in general. For a while, it appeared the temperature might be cooling and some syntheses of the two poles might be established, but this seems to have been thwarted by renewed politicization of math education.
The unrealistically large number of content standards in the common core was imposed on teachers through the persistence of high-stakes testing. The eight mathematical practices promoted by the standards most likely were only taken up by a minority of teachers—those who attend conferences and read journals. In the end, we suspect there was little net change in most classrooms.
To balance this underwhelming picture, there are a few things we can hope for in the next 10 years. We will mostly avoid discussing AI, which will surely have a noticeable effect on math education. It’s too early to make any predictions, but we hope that one result will be to offload some of the most routine teaching tasks so that math teachers at all levels can spend more time on habits of mind without compromising basic skills knowledge. That would be a win for all sides in the math wars.
A necessary component of positive change lies in teacher education. Degrees that certify teachers all require mathematics content. The extent and nature of this content varies tremendously across the 50 states and the thousands of individual degree-granting institutions. Once on the job, teachers are asked to implement ever-changing curricula, often attached to long lists of cognitive goals. Lesson planning and delivery in this context require insights and sophistication from teachers, which cannot be reached this way.
Standards-based reform can be ineffective. The words are all there, but no verbal description suffices to capture such standards as “understand this” and “be able to explain that.”
There is a tremendous opportunity for growth in teacher-development programs, both preservice and in-service. The instructional faculty in these programs, whatever their philosophies, do understand what is meant. Future and current teachers need to experience and reflect on strategies for deep learning in their own education. They need to tackle the material in a way that prefigures what their students will need to do: intellectual engagement beyond mere algorithm proficiency.
There is typically no shortage of time in math education content courses or professional development programs for teachers to engage in this kind of experiential learning because the actual math is material teachers are supposed to know already, at least at a naïve level. Teacher training can lead both to more depth of understanding and more pedagogical sophistication.
Decentralization means that this kind of change will be slow. While there is a de facto national math curriculum, there is no national teacher math curriculum. On the flip side, this means that change is possible in every locale and that individual teacher-preparation programs usually have the authority to implement courses that will better support their graduates.
Successful programs that produce above-average teachers will have a chance to influence the national discussion. This is admittedly a long game: It may take a generation (which, in terms of teacher turnover, is shorter than you think), before the effectiveness can be determined.
We see some encouraging signs in this direction. GeT: A Pencil is an online community of instructors of geometry courses for prospective teachers. They jointly developed a set of student learning objectives and continue to work together across institutions. In the in-service domain, mathematicians and math educators are working together, facilitating 65 tath teachers’ circles, in a program initiated and supported by the American Institute of Mathematics and carried out by hundreds of volunteers around the country.
Thanks to Alison, Henri, and Robin for contributing their thoughts.
Responses today answered this question:
How has math instruction changed in the last 10 years, and how should it change in the next 10?
Consider contributing a question to be answered in a future post. You can send one to me at lferlazzo@epe.org. When you send it in, let me know if I can use your real name if it’s selected or if you’d prefer remaining anonymous and have a pseudonym in mind.
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