NCTM recently released the document Catalyzing Change in High School Mathematics for public review and feedback. The purpose of the document is “to identify and address some of the challenges to making high school mathematics and statistics work for each and every student”. You can find the document and give feedback on the NCTM site here. This post is adapted from my feedback.
I just finished reading Catalyzing Change in High School Mathematics, and I’d like to offer feedback.
I love the content of the document. Your choice of what to include — the purpose of school mathematics, tracking, equitable instruction, essential concepts for focus, and pathways through high school math — paints a broad and compelling vision of what an effective high school mathematics program should look like.
A chapter devoted specifically to tracking is an incredibly important message. Eliminating tracking, both of students and teachers, is the most important change that could happen in high school math. Dodging this question in such a document would be a shame, and Catalyzing Change takes it on admirably, presenting a research-informed argument for eliminating tracking while also distinguishing tracking from acceleration.
The essential concepts for focus are both deliberately chosen and framed effectively. The content is framed through the lens of proof and modeling, two big ideas that should be present throughout all topics. The topics in Algebra, Functions, Statistics, Probability, and Geometry will form a practical and manageable curriculum that will set students up for future success while avoiding the bloat of many current high school curricula. Based on my read, the curriculum would be similar to a year of Algebra I, significant portions of typical Geometry courses, and a semester or more of statistics and probability, though with a focus on essential ideas that would allow significantly more flexibility than many current curricula and standards. For those who don’t want to explore the document in detail, the specific essential concepts are:
- Connecting Algebra to Functions
- Data Analysis
- Statistical Inference
- Making Decisions and Quantitative Literacy
- Geometric Arguments, Reasoning, and Proof
- Modeling in Geometry
I love that Catalyzing Change is not trying to be a standards document. Each essential concept for focus begins with a narrative explaining its place in the broader curriculum, the relevance of those topics to students’ mathematics experiences, and the habits of mind students should exercise through those concepts, including the intersections with proof and modeling. Where the list of topics above would be insufficient to guide a high school math program and a standards document is likely to get lost in the weeds, this paper balances the two. It offers a manageable number of topics, names 2-6 big ideas that should guide each topic, and makes clear how the topics are connected to students’ broader mathematics progression. Any math educator who reads the essential concepts will come away with a deeper understanding of the essential ideas in high school mathematics.
I think the increased flexibility of 2 1/2 years of common experiences before the possibility of multiple pathways will be great for students. Whether they go on to calculus, statistics, discrete math, modeling, or other courses, this plan will create a trajectory that minimizes the race to calculus and creates opportunities for more students to feel engaged and connected to their math courses, while also ensuring every student engages with essential core content.
Finally, I love the focus on equity. A chapter on creating equitable structures and a chapter on implementing equitable instruction zoom in specifically on what equity looks like in high school mathematics. At the same time, equity is not sidelined to its own chapter; it is also evident throughout the document in language that constantly asks how the guidance in Catalyzing Change supports positive experiences and outcomes for all students.
While I think the core content of this document is important and necessary for high school math programs, I worry that it will not have the intended impact. The front matter is vague and avoids making the goals of the document explicit, with statements of purpose like, “Creating equitable structures in mathematics–confronting the impact of student and teacher tracking and support systems”. The end tries to appeal to too many different groups, with separate recommendations for teachers, district and building leaders, K-8 teachers and leaders, policymakers, curriculum developers, and mathematics educators. There are four key recommendations at the end of the document, but it is easy to lose the forest for the trees and miss essential ideas in Catalyzing Change because there is no single place where it makes a compelling case for what high school mathematics should look like. The document as a whole feels a bit like it is trying to appease too many groups at once, like there are competing ideas vying for attention instead of a coherent message. I don’t get this sense on a page-by-page level; instead, I get this sense because after reading I wasn’t sure how I would capture the essence of Catalyzing Change in an elevator speech. Compare this with Principles to Actions — a similarly detailed, research-based document — which derived much of its success from the concise guiding principles and eight mathematical teaching practices. Catalyzing Change will be read by many, but more of the audience will learn about it by word of mouth, summaries, and excerpts. What is the positive, ambitious vision that NCTM has for high school mathematics? What is it that mathematics educations should do to realize this vision? And how can this be communicated clearly and effectively to the broadest audience possible?
One might add to the front matter and the recommendations at the end of Catalyzing Change a clear and affirming statement of what effective high school mathematics programs must do. For instance:
An effective and equitable high school mathematics program must:
- Emphasize the multiple purposes of school mathematics: expanding professional opportunities for all students, using math as a lens to understand and critique the world, and experiencing the wonder, joy, and beauty of the discipline of mathematics.
- Eliminate student and teacher tracking systems that perpetuate inequitable experiences for students in qualitatively different, dead-end pathways, and work to provide common experiences and necessary supports so that all students engage with essential mathematical concepts.
- Implement equitable instruction that promotes effective mathematics teaching practices with attention to how those practices foster positive mathematics identity and create opportunity for all students.
- Focus on essential concepts in algebra, functions, statistics, probability, and geometry that will best prepare students for higher education and the workforce while engaging with big ideas of high school mathematics.
- Develop an equitable and common 2 1/2 year pathway for all students that includes the five essential concepts and allows for student choice in a final 1 1/2 years of study that best suits their individual goals.
These are welcome suggestions for many in math education, but they are also radical in the sense that they recommend a serious departure from math programs in the vast majority of high schools. A radical set of recommendations deserves a prominent place in the document that is easily shared and easy to remember.
I am an early career teacher, and I hope to be in this profession for several decades to come. I know that change will not happen quickly, but I hope that this is the start of a transition that I will get to see through in my time in the classroom. I hope that this document is able to catalyze that change. Thank you for your hard work, and I look forward to reading the final version.