California Passes its New K-12 Mathematics Framework
by Keith Devlin @KeithDevlin@fediscience.org
On July 12, the California State Board of Education passed the new California Mathematics Framework to guide the state’s K-12 mathematics education program. The vote was unanimous, in my experience a rare occurrence in the mathematics education world.
Good summaries of the new framework and its approval were provided by John Fensterwald in EdSource and Sarah Schwartz in Education Week.
I wrote about the sometimes contentious four-year process to develop the California framework in my April 2022 Devlin’s Angle post, where I observed that it was very similar to the new PISA 2022 Framework I had written about the previous month.
[DISCLOSURE: I know two of the educators who were involved in the CMF development (one on the university mathematics side, one on the university mathematics education side) and two on the Board of Education (a K-12 education professor and the former mathematics education professor who chaired the board); but I myself was not involved. I played a minor consulting role in the PISA 2022 project.]
The comments to the Fensterwald article provide a glimpse of some of that contentiousness regarding the proposals, but those comments are a tiny sample from people who read EdSource. Social media exploded with furious responses, none of which I’m linking to, though the majority appeared to be written by people without any experience in K-12 mathematics education (including, sadly, some professionally-trained mathematicians and STEM folks) and often gave every indication the commentator had not actually read even the brief summary of the framework (a mere 750 words) provided by the California Department of Education on its website. (The framework itself stretches to around 1,000 pages.)
Given the current irrational furor about education across the US, with textbooks being banned and curricula re-written not by educators but politicians, and school-board meetings full to overflowing with angry parents (and non-parents), this reaction was to be expected.
There are, to be sure, some debatable issue in the proposal, and much debate about them has already taken place. Both PISA and the CMF reflect major changes in the way mathematics is done in today’s world, where we have ubiquitous, powerful tools to perform more or less all the procedural calculations that arise in mathematical problem solving.
Moreover, both frameworks also reflect the different world that awaits today’s mathematics learners than students of earlier generations met. In an era where mathematics plays a major role in many daily activities—in particular pretty well anything that involves the Internet—connecting mathematics to other parts of people’s lives has becomes an important goal. The days when mathematics could be taught “in isolation” are gone.
That doesn’t mean individual classes, or some courses, cannot continue to be taught that way; indeed, that is often the best way to teach large parts of mathematics. But today we need to adjust the mathematics we teach and how we teach and assess it. The goal of school education is, after all, to prepare tomorrow’s citizens for life (including work, but not only that) in tomorrow’s world.
A case in point with regards to assessment, I wrote in my June post two months ago about a freely available AI package that scored 98% in the mathematic assessment in the UK that’s the equivalent of the US math SAT, for entry to university. Not only do we need to design education and assessment so that a software system cannot ace the test, we should also ask ourselves, if a task can be performed by a computer, why are we asking students to master it? (There may be a good reason, but the onus is on us to provide that reason.)
Top page of the National Science Foundation Act, passed by Congress in 1950. Note items 1 through 4, right at the top of the bill.
The current mathematic education package followed in the US was shaped during the early days of the Cold War, when the nation faced an existential threat, which required that we produce many thousands of citizens skilled in mathematics, science, engineering. A key step in setting that educational juggernaut in motion was the establishment in 1950 of the U.S. National Science Foundation as a federal agency, when President Harry S. Truman signed Public Law 81-507, the “National Science Foundation Act of 1950.”
The UK took similar steps, which meant that when I was growing up, I was fed a high octane package of STEM subjects that propelled me onto a mathematically-rich (and highly rewarding) life journey totally different from that of my working class parents.
The US’s single-minded educational program was hugely successful in meeting its goal; particularly high profile, global successes were the Apollo Moon landing in 1969 and the world domination in digital technologies coming in large part from Massachusetts and (to a greater extent) California in the 1970s and 80s. But it came at a cost. With the focus on producing the STEM whizzes the nation needed, the far greater segment of the nation’s students who did not make the grade were left with their educational needs not being so well met. For far too many, if algebra didn’t turn them off, calculus did. Defending ourselves against nuclear fallout led to massive human fallout in our educational system.
Looking back, I was the only student in my UK elementary school who passed the exam for entry into a newly established, academically-focused secondary school. And, as a high school senior, while I was working on college-calculus material, taken out of the math class and guided one-on-one by my two math teachers, the rest of my cohort were struggling to survive their obligatory calculus class, waiting only for the misery to end.
Almost all my fellow students at university (Kings College London) had similar stories to tell, since Kings’ Mathematics Department took 25 UK students each year who excelled at high school but had not been to elite schools providing the college preparatory courses required to get into Oxbridge.
The same had happened in the US, as I learned after I had moved here in 1987 and became part of the American mathematical community.
Given the circumstances of the Cold War era, that strategy was, to my mind, defensible. But not today. The very fact that so many in our society today feel left out, and are now angry at, and frustrated with, the education system, shows the cost as a society that we paid for that single-minded focus on STEM, which endured long after the Cold War had ended.
A slide from an actual NSF presentation deck. Note in particular the last item.
The Common Core, introduced in 2010, was one major national initiative to adjust the direction education should take to meet the needs of today’s world, but it went only so far.
California (my home state) had a particularly vexing problem to address. Its hugely successful economy (large parts of which are based on STEM, including, these days, our vast agricultural industry) was a result of that Cold War educational push. But just as I experienced back in the UK, the mathematics education being provided had from the start failed a large proportion of our highly diverse student population, many of whom did not feel their classes were relevant to them. Enter the CMF.
The state took on the challenge of developing a new framework with characteristic Californian zeal. We’ve always been a change-agent state. (We became a state only in 1850, driven largely by civil rights issues.) CMF undoubtedly has contentious elements.
Unfortunately (though not unexpectedly, given the current social unrest in the nation), the measures proposed in the CMF to address specifically its crucial educational inequity problem, being novel (and to some observors radical), were the ones that came in for the most opposition, and in many cases dismissive ridicule.
The following CMF proposals in particular (taken from the CDE’s summary I cited above) were all met with ire or derision for being, “too touchy-feely”, “not rigorous”, or “DEI-oriented” (which a broad swath of contemporary American society dismayingly views as a bad thing to be avoided):
Allow students to “see themselves” in curriculum and in math-related careers by making math instruction culturally relevant and empowering.
Instill confidence in learners by dispelling myths about who can and cannot learn math.
Stimulate deep learning by sparking student curiosity through lessons that encourage inquiry and problem-solving.
Structure the teaching of the state’s math standards around “big ideas” that integrate rather than isolate math concepts.
Develop in students a “growth mindset” about mathematics.
Develop instruction and curriculum that is “multi-dimensional” and employs the use of visuals, graphics, and words in addition to numbers and equations.
These are all in line with PISA 2022, by the way, as is the entire CMF.
The CMF’s suggestions for more data science in K-12 education were seen by some critics as a bad thing, though to my mind highly valuable (indeed essential) in today’s world. Here they are:
Connect learning to the “real world” through authentic examples and use of data, prompting students to ask and answer meaningful questions. Adding authenticity to lessons helps teachers answer students’ questions around “why do I need to learn this?”
Encourage students across age spans to become proficient at understanding and using data—a key skill in the 21st century job market.
Help students to identify misleading uses of data and use data to make decisions in their roles as global citizens.
These points would, I suggest, be better described as data literacy, though my own experience teaching at high school and first-year university level is that diving into a problem involving data can rapidly take you into industrial strength data science.
There are, to be sure, debates to be had about data science, one being what goes into the courses, another how do higher education institutions view it in terms of entry qualifications? Indeed, should it even be handled as part of mathematics at school level? But given the role played by data science in today’s world, it cannot be left out.
Since I’ve pulled out some of the key proposals listed in the CDE’s summary press release, I’ll list the remainder. If the angry CMF critics on social media had taken time to read the list, they would have discovered that the doomsday scenarios they claimed the framework would result in (dumbing down math, holding students back, not teaching topic X, etc.) could only happen if schools were to ignore the Framework; to whit:
Increase focus on developing student mathematical expertise as described in the Common Core Standards for Mathematical Practice, which include the ability to make sense of problems and persevere to solve them; to reason abstractly and quantitively; to attend to precision; and to apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
Ensure that students develop both appreciation of math concepts and fluency in using math efficiently through the productive use of algorithms and mastery of math facts they have come to understand.
Ensure that all high school math pathways are open to all students.
Support multiple ways to get more students to higher level mathematics—ranging from successful acceleration to differentiated instruction, personalized supports, extra lab sections, and additional coursework offered at multiple junctures—augmenting more effective core instruction.
Expand high school math course options to encourage more students to go beyond minimum course requirements.
Yes, the CMF advocates a major change in both the emphases and the delivery in mathematics education. The state’s responsibility, after all, is to provide an adequate (at least) education for all its young people. Making the core accessible and useful to all, while allowing the flexibility for each individual student to maximize their own potential, seems to me the way to go.
That inevitably means accepting that the State can no longer socially-afford a system that centers on, and is driven by, the relatively small segment of students who can go on to pursue a career in STEM. Rather, we have to cater for them with the kind of measures in that final list above.
True, the STEM-oriented students will no longer be in a system that revolves around them. (Truth be told, in a state system, we never were, because we were in the minority. My teachers had to make special accommodations for me. But forcing my fellow students to engage in mathematics that was beyond them at that age simply resulted in their being turned off math, in many cases perhaps for ever.) Society is surely better served by designing education to benefit all, and allowing teachers the freedom to make special arrangements to meet the needs of the relative few. The CMF does that, and teachers will always find a way to cater to students who want to, and are able to, move ahead.
Of course, there are specialized schools that focus on STEM. In our society, parents always have the right to opt out of the state system, and no one is suggesting that right will be curtailed.
Incidentally, the CMF is not a curriculum, nor are school districts obligated to follow it. Many of the social media complaints I read were arguing about curriculum. It is, however, an important and influential document that will shape California’s mathematics education system (and hence its society) for many decades.