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De-emphasizing Content for Processes?
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What does it mean to de-emphasize content in favor of processes? How does it help students to reach their potential as thinkers and problem solvers in school mathematics?
“Mathematics is no more computation than typing is literature.”
—John Allen Paulos, Mathematician
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High School Reimagined, Revitalized, and Relevant was released at the end of September as a joint publication from NCTM, NCSM, and ASSM.
It includes a section that suggests de-emphasizing content in favor of processes. As a person who loves mathematics, I have to admit that language makes me a little nervous! What does this book from these three national mathematics education organizations really mean when it suggests de-emphasizing content?
Where Is Your Focus?
This question reminds me of a session I saw at a conference more than a decade ago. The speaker was a linguist from Australia who had been studying the language, words, and speech in classrooms across many countries. The teachers in the American classrooms that he studied told him that they hoped students would pick up on patterns as they worked problems, and that students would use generalizations to make solving easier and make sense of what they were doing.
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However, he also noticed that teachers almost never included these words in the assignments. Teachers didn’t instruct students to look for patterns, to use patterns to find shortcuts for solving, or to describe those patterns in generalizations. Students weren’t looking for patterns, because they weren’t asked to do so, even though the teachers had identified that as the purpose of the problem set. Even during the debrief of these assignments, teachers often focused conversations on correcting answers and adjusting mechanics to ensure right answers moving forward, without engaging in discussion about the patterns students might have noticed, or about making sense of bigger ideas that might have been emphasized by these assignments.
The linguist suggested small but nuanced shifts to make big differences in what students got out of these lessons. He suggested that when giving students problem sets, teachers shift the focus to the patterns and generalizations, perhaps by saying “there is a pattern I am hoping you will notice as you complete this problem set.” The teacher could ask students to do as many problems in the set as they needed to find and describe a meaningful pattern about the problems. Then, the debrief could be about the patterns each student saw. The students could listen to each other’s reasoning, find similarities and differences in their ideas, and get to more meaningful discussions about the big ideas of the content they are studying. I believe this nuanced shift is an example of the suggestion of “de-emphasizing content” in favor of processes in High School Reimagined, Revitalized, and Relevant.
Much of what we have traditionally taught, particularly in high school mathematics, is procedural, computational, or about manipulating symbols. But deeper learning and understanding can happen! Students can engage in computation and symbol manipulation and leverage those skills in service of the greater goals of thinking and reasoning about the world using mathematics. By shifting our focus to the processes, symbolic manipulation and computation become a foundation that allows students to engage with, reason about, and make sense of important mathematical concepts.
The processes in High School Mathematics Reimagined, Revitalized, and Relevant are derived from decades of research about productive mathematical and statistical habits of mind of professionals who use and apply mathematics every day.
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Shifting Emphasis
The book presents a mathematics example of this shift in emphasis of factoring a trinomial. There are several methods of factoring a trinomial, all of which involve manipulating the mathematical symbols to rewrite a polynomial as a product of its factors. Factoring is often used to solve quadratic and other polynomial equations.
However, rather than focusing on the methods of manipulating the symbols we could shift our focus to emphasize what factoring helps us to see and understand about polynomial expressions and equations. Factoring helps to connect a symbolic representation of an equation to its graph, to see patterns in the number of linear factors as related to the degree of the polynomial, and to find the roots of a polynomial equation. Students can then discuss what roots, zeros, and factors mean, both in context and mathematically.
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Though this idea of shifting emphasis to processes is presented in a book about high school mathematics, it is equally applicable in other grades! For instance, in elementary grades, we might shift the focus from the procedures of long division and subtraction of multi-digit numbers to having students’ reason about what is happening in these operations, ensuring they are making sense of the traditional and alternate algorithms.
As we think about how we best prepare our students for today’s context, with new technologies arising that help with the procedural and computational aspects of mathematics more and more, we do students well to hone in on the mathematics and statistical thinking that will always be needed in day to day life as described in the processes.
How might you discuss this idea with the educators in your system? What mindset and belief shifts would need to happen to move more emphasis to processes? How can you start, with small adjustments in your practice, to move toward focusing on processes with both educators and students?
— Katey Arrington, NCSM President
“We will always have STEM with us. Some things will drop out of the public eye and go away, but there will always be science, engineering, and technology. And there will always, always be mathematics.”
— Katherine Johnson, Mathematician
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Virtual Coaching Labs
2024-2025
NCSM is excited to announce the return of Virtual Coaching Labs!
Virtual Coaching Labs are 90-minute virtual sessions in which leaders and coaches learn about mathematics coaching, hear from featured speakers, and have the opportunity to practice coaching skills.
- November 19: Amy Lucenta and Grace Kelemanik
- December 10: Courtney K. Baker and Melinda Knapp
- January 7: Mona Toncheff
- January 28: Barbara Dougherty and Nicora Placa
- February 18: Dionne Aminata and Deborah Peart Crayton
- March 4: Abel Maestas
Each session will highlight a specific aspect of coaching. During each session, participants will have the opportunity to practice coaching skills in real time through role play experiences in small groups.
Registration open, with spots filling quickly!
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Proposal Submissions Open
We're accepting proposal submissions for our 57th Annual Conference happening October 2025 in Atlanta, GA.
At our Annual Conference, we invite you to share your learnings, change strategies, and leadership efforts in fostering and motivating high-quality mathematics teaching and learning daily for all students.
We invite proposals that focus on the following conference strands.
- Accelerating Student Learning
- Elevating Mathematics Instruction Through Bold Leadership
- Equity Rising: Transformative Practices in Mathematics Education
- Lifting Teacher Practice Through Coaching
Learn more and submit your proposal here.
Submission Deadline is Dec 2.
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NCSM Board Nominations Close 11/15
Capitalize on your NCSM Membership and Leadership. Consider running for an open Board position or nominating someone for a position.
All nominations are due by November 15. We encourage and welcome a diverse pool of nominees.
Open positions:
- Second Vice President
- Regional Director, Central 1 (Illinois, Indiana, Kentucky, Michigan, Ohio)
- Regional Director, Eastern 1 (Connecticut, Maine, Massachusetts, Military AE: APO/FPO, New Hampshire, New York, Rhode Island, Vermont)
- Regional Director, Southern 2 (Alabama, Arkansas, Louisiana, Mississippi, Oklahoma, Tennessee, Texas)
Learn more and nominate someone today.
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Leading with Technology: Enhancing Mathematics for ALL Students
We believe that in order to develop all students’ mathematics proficiency, mathematics leaders must purposefully integrate appropriate technologies in the classroom to strengthen teaching practices, enhance the curriculum, attend to students’ diverse learning needs and better assess student learning.
This new position paper, Leading with Technology, offers a refreshed take on the use of technology in mathematics education.
Read the full statement.
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Save the Date!
NCSM Book Study 2025
Join us in a book study opportunity in the new year.
We'll be reading and discussing Rethinking Disability and Mathematics: A UDL Math Classroom Guide for Grades K–8 by Dr. Rachel Lambert.
Discussions will take place January 13 and February 10, 2025, at 8pm EST. Dr. Lambert will be in attendance to lead the discussion and answer your questions.
Save the dates now and feel free to start reading! More information, including registration info and Zoom links, will come soon.
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Journal of Mathematics Education Leadership
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Essential Actions Book Series
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Thank you to our Conference sponsors!
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Of Interest to Our Members
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