I saw today a Fox news coverage on the “ridiculousness” of the new CA Mathematics framework. “Great, now numbers are racist.” Instead of getting incensed by poor journalism I decided I’d respond to a few of the issues. I chose this article from Reason.com, “In the Name of Equity, California Will Discourage Students Who Are Gifted at Math” because it wrote specific objections (as opposed to other articles that just covered that there was controversy without going in-depth about what the objections were).
Just FYI, I am a secondary math teacher in California and have taught it before Common Core (when it was pre-algebra and algebra for 7th and 8th grade) and post-common core. I also took math in Palo Alto Unified School District that *does* track students and had an interesting run. Because I was homeschooled in sixth grade, I took a placement exam and ended up in “lower math” for 7th. Over the summer, I took a bridge course and ended up in “higher math” for eighth. 9th-11th grade, I stayed in the highest math track, and in 12th grade, I started BC calculus. I realized that the real tears I shed over math were not worth it and moved down to AB Calc where I coasted through the year, earned a 5 on my AP test and went to a UC, where my peers, who also took AP level maths (whether AB or BC) and most ended up doing pretty well. A lot of my college peers though, who took AP level math courses at their schools, ended up having to repeat the Calc 1 equivalent anyway in college. end FYI.
California’s Department of Education is working on a new framework for K-12 mathematics that discourages gifted students from enrolling in accelerated classes that study advanced concepts like calculus.
The draft of the framework is hundreds of pages long and covers a wide range of topics. But its overriding concern is inequity. The department is worried that too many students are sorted into different math tracks based on their natural abilities, which leads some to take calculus by their senior year of high school while others don’t make it past basic algebra. The department’s solution is to prohibit any sorting until high school, keeping gifted kids in the same classrooms as their less mathematically inclined peers until at least grade nine.
“The inequity of mathematics tracking in California can be undone through a coordinated approach in grades 6–12,” reads a January 2021 draft of the framework. “In summary, middle-school students are best served in heterogeneous classes.”
Okay. For me, this just seems like a no-brainer. In all brain science, it shows that homogenous groupings are not helpful for learning. I guess this starts with defining what learning is. If learning to you is all about memorization and reproduction of algorithms, then fine, we should group kids homogeneously. If learning math means being able to explain your thinking, knowing what place values actually stand for, understand why distributive property works, conceptually understand decimals as expressions of fractions within a base-ten numerical system, then heterogenous groupings is what matters. It is true that someone who has emerging understanding shouldn’t be paired with someone who is at mastery, but studies have shown that pairing students with emerging understandings with students who have progressed a bit more actually benefits both. It’s like pacing. It doesn’t serve someone who is just getting back into shape to pace themselves with a marathon runner, but asking someone who has been running for a while to exercise their mental faculties in maintaining a pace for someone getting started is helpful for both because it requires the person who has progressed further to become more metacognitive. If they both have a coach (aka a teacher), even better!
As a middle school teacher, I have had brilliant students who, as soon as they entered high school, were placed in lower courses (despite standardized test scores) because of the schools they came from or their last names. It’s just common.
I know I am getting anecdotal, but lastly, I want to say that although it is hard to differentiate, it is beautiful to be able to see how different people see numbers and work with numbers. It is helpful for kids who rely on memorization and rules to pause and listen to a more visual learner (who may feel “lower” in a traditional sense) explain the patterns they are catching and the spatial understanding of what a fraction could be.
Middle school math is not just algebra, it’s early stats, it’s exponents, it’s geometric concepts of congruence and dilation, distinguishing rational numbers, conceptualizing the difference between a negative and a fraction (or God-forbid, a negative fraction), and let’s not forget, the skill that even adults struggle with: rations and proportional reasoning. I definitely have students who are more precise, who work harder, who have better math fluency, than others… but have they sat in my class bored? No. Because, if you’re doing a good job, you’re pushing conceptual development along with providing rigor. You are also training young adults to become collaborative partners (vs faux-llaborators and lone wolves), coaches (vs “here I’ll just do it), and active listeners. AKA, actual skills for life.
Let’s just pause and think. The smartest kids in your middle school math class are not the most successful people in your alumni group, right?
In fact, the framework concludes that calculus is overvalued, even for gifted students.
“The push to calculus in grade twelve is itself misguided,” says the framework.
As evidence for this claim, the framework cites the fact that many students who take calculus end up having to retake it in college anyway. Of course, de-prioritizing instruction in high school calculus would not really solve this problem—and in fact would likely make it worse—but the department does not seem overly worried. The framework’s overriding perspective is that teaching the tough stuff is college’s problem: The K-12 system should concern itself with making every kid fall in love with math.
Why is this a debate? Calculus is overvalued. It’s stupid that it’s required for pre-med, business, etc. If anything we should be pushing Stats or Information Science or content-specific maths. I loved Calculus. I loved figuring out the area under a curve. I rocked differentials. Because, I just loved learning and my teacher (shout out to Deanna Chute) literally loved teaching it and loved us. Annnnnd, I have no idea how to do it now, and it has not served me when it comes to calculating the best house to buy, figuring out my finance strategies, etc. All AP Calculus taught me that still remains me with me now is the importance of being with a great teacher and work ethic. I’d posit that those two pieces can be taught through any subject.
Broadly speaking, this entails making math as easy and un-math-like as possible. Math is really about language and culture and social justice, and no one is naturally better at it than anyone else, according to the framework.
“All students deserve powerful mathematics; we reject ideas of natural gifts and talents,” reads a bulletpoint in chapter one of the framework. “The belief that ‘I treat everyone the same’ is insufficient: Active efforts in mathematics teaching are required in order to counter the cultural forces that have led to and continue to perpetuate current inequities.”
Duh. Folks who are “talented” probably had many hours that were devoted to that part (see Talent Code). Strengths are contextual (see Dark Horse). Have you heard of neuroplasticity? Believing that you’re naturally talented can actually prevent you from achieving more — because you rely on what you think is fixed versus understanding that your can develop neurons and concepts can be learned and mastered.
And of course it’s not enough to “treat everyone the same” because we don’t treat everyone the same. We have natural biases based on where we grew up and how we were raised (most recently read What Happened to You, which talks about this but Gladwell’s Talking to Strangers is a good resource too). We need to consciously bring it to the forefront whether we teacher social studies or PE. Math should be no different.
The entire second chapter of the framework is about connecting math to social justice concepts like bias and racism: “Teachers can support discussions that center mathematical reasoning rather than issues of status and bias by intentionally defining what it means to do and learn mathematics together in ways that include and highlight the languages, identities, and practices of historically marginalized communities.” Teachers should also think creatively about what math even entails: “To encourage truly equitable and engaging mathematics classrooms we need to broaden perceptions of mathematics beyond methods and answers so that students come to view mathematics as a connected, multi-dimensional subject that is about sense making and reasoning, to which they can contribute and belong.”
Again, this seems pretty obvious, and in practice, what you would see is NOT a 30-minute discussion about marginalized communities and math. What you would see in an inclusive classroom is the attribution of algebra to Arabian civilization, the discovery of zero to the Mayans, trig and triangulation to other ancient civilizations. You would see word problems that are connected to what kids understand (teaching systems of equations through word problems about sailboats doesn’t work when you teach in a CA urban city).
And yes, math would go beyond how-tos and answers, because how many times in your life do you do long division on paper (vs a calculator) whereas in a grocery store, do you KNOW all the cool different ways kids have taught me to compare deals and figure out the best unit rate without pen and paper? And in what world are you hired to just find answers as opposed to making sense of a problem and reasoning through why yours is the best approach?
All of the above naturally brings about contribution and belonging.. bc creating artificial environments to do so never actually achieves it. When do you feel most at home in a company? When you know that your ideas are valued and that you’re respected/seen.
This approach is very bad. Contrary to what this guidance seems to suggest, math is not the end-all and be-all—and it’s certainly not something that all kids are equally capable of learning and enjoying. Some young people clearly excel at math, even at very early ages. Many schools offer advanced mathematics to a select group of students well before the high school level so that they can take calculus by their junior or senior year. It’s done this way for a reason: The students who like math (usually a minority) should have the opportunity to move on as rapidly as possible.
For everyone else… well, advanced math just isn’t that important. It would be preferable for schools to offer students more choices, and offer them as early as possible. Teens who are eager readers should be able to study literature instead of math; young people who aren’t particularly adept at any academic discipline might pick up art, music, computers, or even trade skills. (Coding doesn’t need to be mandatory, but it could be an option.)
The essence of good schooling is choice. Individual kids benefit from a wide range of possible educational options. Permitting them to diversify, specialize, and chart their own paths—with helpful input from the adults in their lives—is the course of action that recognizes vast differences in interest and ability. Holding back kids who are gifted at math isn’t equitable: On the contrary, it’s extremely unfair to everyone.
… Um, there is an assumption that schools are able to offer aLL of the choices that a child could be good in? In economics, we call this limited resources. Given limited resources, at a public institution, we do our best to give all kids the best basic framework from which they can then pursue their endeavors. That includes being able to read, being able to write, being able to reason, and knowing the historical, cultural context within which we perform. And oh yes, running a mile in under 20 minutes.
And why does this article assume that having heterogenous classrooms assume that we are holding kids back? In fact, let’s go back to my personal experience in Palo Alto. When kids were split up from 6th grade, it was based off of a test and off of parents’ loud advocacy, and teacher choice. If we just did a test, there might be times when there are only 16 kids ready for “advanced” and 34 in the “lower”. Are we going to do that? No. So then 9 of the “lower” kids might get put into the “advanced” track based on all sorts of factors (teacher’s perception of behavior, hard work, etc). This introduces a lot of bias. The crazy thing is, kids internalize what they’re told. So even if you are a brilliant boy who’s antsy and mouthy, and whose parents are too busy to advocate for you, you might be told your whole life that you’re not smart based where you are tracked. That does affect your performance. Google it!
Yet the framework seems to reject the notion that some kids are more gifted than others. “An important goal of this framework is to replace ideas of innate mathematics ‘talent’ and ‘giftedness’ with the recognition that every student is on a growth pathway,” it states. “There is no cutoff determining when one child is ‘gifted’ and another is not.” But cutoffs are exactly what testing and grading systems produce, and it’s absurdly naive to think there’s nothing innate about such outcomes, given that intelligence is at least partly an inherited trait.
Is intelligence a partly inherited trait? What the actual Fork? I feel really sorry for your child. Because yes, here is where the worldviews split. Where one group believes there can be an artificial human-made cut off for “giftedness” and where a “growth pathway” is derided. I don’t want to live in that world, and guess what, I don’t. Most thriving people don’t. Because we understand that change can always be made and we understand that there are multiple ways to grow strong in an area and that a lot of what people choose is more based on passion than ability. You can hone ability if you are passionate.
If California adopts this framework, which is currently under public review, the state will end up sabotaging its brightest students. The government should let kids opt out of math if it’s not for them. Don’t let the false idea that there’s no such thing as a gifted student herald the end of advanced math entirely.
Um okay. The fact that I have middle schoolers deriving the pythagorean theorem from their knowledge of angle relationships and solving complex systems of equations, and finding multiple ways to demonstrate proofs through both inductive and deductive reasoning, and building machine learning algorithms to teach emotional intelligence… all within a heterogeneous classroom that believes in growth mindset, systemic oppression, and critical hope is but one example of why this wouldn’t be “the end of advanced math’ entirely.
What does suck though, is then watching these kids move on to high school where they are tracked and somehow end up in lower math classes with less experienced teachers, losing their interest and belief in themselves.
In Palo Alto, when I was in lower math, even in that rich district, I went through three teachers in one year. A white kid threw a chair out a window. When I took a random bridge course over the summer (which was a lot of worksheets and movies), I entered the higher math class in 8th grade not necessarily “prepared.” But that teacher was amazing. He had us writing, performing, explaining, art-ing all in math (wayyyy before Common Core). He led math workshops for other teachers, he published a book. I entered high school ready, and freshman year, my teacher sucked. Sophomore year, she was terrible too. Junior year was amazing and like I said, I enjoyed AB Calc (and did well) my senior year. It was interesting though, because I saw how in other classes that were also tracked, whenever I dropped a level, the classroom grew more diverse. It is a very very awkward thing when you think you’re tracking and creating gifted classes solely by merit, and somehow all the color gets concentrated in the lower classes. And somehow you don’t think bias has anything to do with it,what does that say about you and your reasoning capabilities?
Junia
forks and hope, smiles and soap 