2021 Revision of the Mathematics Framework for California Public Schools
cde.ca.gov
cde.ca.gov
> Ms. Ross teaches fifth grade at the Jackie Robinson Academy. She has been focusing on developing her students’ sociopolitical consciousness through language arts and wants to bring mathematics into their thinking (SMP.1, 2). To begin the process, the class is led in an analysis of word problems from their fifth-grade mathematics textbook (NF.1, 2, 4, 5, 6). Ms. Ross selects three word problems to connect with the class’s current read-aloud of George, a novel by Alex Gino that shares the story of a 10-year-old transgender fourth grader and her struggles with acceptance among friends and family. In doing so, the teacher is reflecting the recommendations of California’s Health Framework, which suggests that sensitive discussions of gender are important for students
> The word problem analysis serves as a springboard for students to investigate their own questions. One student asks, “Are there word problems that have a male knitting a scarf, cooking, cleaning?”; and another ponders, “Does the textbook always use girl names for girl stuff and boy names for boy stuff?” Lastly, another student asks, “Are there word problems that challenge gender stereotypes?” When examining the entire textbook, the students noted that there were a few instances of gender-fluid problems (e.g., David’s dad baked a dozen cookies to share with him, his sister, and his mom); however, the problem continued to conflate gender with a heterosexual identity. The class could not find problems involving non-nuclear families (e.g., two moms, a single dad) or gender nonconforming characters (e.g., John cutting ribbon). Ms. Ross has students notice these patterns, but also asked students to question why certain items (e.g., toys, activities, careers) are perceived as being “for” only girls or boys, and the implications for these assumptions. She continues to engage her students by asking, “Why does this matter? Who does this privilege? Who is silenced?”
This lesson is highlighted as an exemplary instance of mathematics education. The students go on to "fix" the word problems (in one instance completely losing the sense of the original problem).
I think it's good to re-write mathematics textbook word problems to be more inclusive. I don't think it's good to have students play out that process in their math class. Math class is for learning... math. They can learn how to perform a social justice critique in social justice class. If this is representative of the direction the state wants to move in, then I don't have a lot of optimism for the future of public education in California.
Speaking for myself, I always paid more attention when my math teachers mentioned Newton, Gauss, ancient Greeks, Flatland, etc. But the fact that most historical examples were European could give students the impression that Europe was the only part of the world that thought math was important. I guess we heard that “Arabs invented the number 0,” but that’s it. I would love for classes to include mentions of ancient Indian ( https://en.wikipedia.org/wiki/Indian_mathematics ) or Chinese math development ( https://mathshistory.st-andrews.ac.uk/HistTopics/Ten_classic... ).
I would be really happy if classes mentioned important mathematicians that had suffered because of something not related to math. Such as math professors losing tenure for being Jewish, Chinese academics caught up in “struggle sessions,” Alan Turing, etc.
The above isn't an example of pure math education. It's an example of what math teachers should do if they want to incorporate for example elements from the Health or Social Sciences curriculum.
For the vast majority of students, the way they will use math most of the time is only after analyzing problems and translating them to mathematics, which for many students also really does help the math part work better. And ultimately before you start specializing your math classes (some may argue we should do it earlier than is done in the US, and I'd agree), it makes sense to train students to apply math a solid minority of the time in ways that aren't "just math".
Until the last two years of so of high school, the skills that are mainly being taught in math class aren't necessarily "just math", and the main reason they are being taught isn't to help people be better at pure math, but because they are foundational skills elsewhere.
These ideas aren't just there for fun. They're there because a significant amount of research has been done and replicated dozens of times around the world and found that for the educational objectives at that point in time it is the most efficient way to do so. If the hypothesis is that actually teaching math another way that completely gets rid of word problems and tie-ins to other subjects is more efficient, this is a testable hypothesis that is sure to be very interesting to the scientific community, and I'd love to see it put to the test.
The people involved generally are the kind of people who think that career would accomplish something.
Those people actually accomplished something. Their local education system became #4 in the world in mathematics without unreasonable hours or high levels of stress.
Given the kinds of communication I receive from the district (the majority are coordinating welfare programs rather than supporting some academic mission), recent news, and these sorts of standards cropping up, I'm becoming increasingly convinced that I should avoid the public school system here. The preschool is dealing with such basic things that it probably doesn't matter, but as time goes on the picture doesn't sound promising.
So to take this discussion off on a tangent... is private school the only real option? Are there home-schoolers here that can provide some insights? I did mention he's autistic, but very high functioning and we're already making progress without the aforementioned district autism services anyway. Anyway, not sure where to start in the Bay Area and this head-shaking document prompted the thought to ask.
If we're interested in the mathematical method and its power, a good start might be to, well, go with more exploration-based approaches, where students have to learn things in order to solve a "real"(-ish) problem. Of course, the training required and attention to students would rocket and is likely infeasible, but hey, if Euclid's elements in the original Greek are on the table, this doesn't look too bad !
> more exploration-based approaches
Do you know of any that you'd recommend?
Unfortunately I didn't have this experience until I was an undergraduate. For the prior 12 years of formal schooling, math mostly felt like repetitive drudgery with occasional flashes of excitement when I would learn a new technique.
Edit: I think that was the first class where we learned about proofs and we solved so many that I really get the hang of it.
The description is so full of contradictions that it can't be rationally understood- there are not allowed to be advanced students, but "high achievers" are helped by going "more in depth", while they "learn to appreciate the beauty of mathematics and the connections between mathematical areas". They sit there and complain about a "rush to calculus", but then in order to take Calculus in SFUSD you have to rush through the classes that immediately precede it.
"All students can take Common Core-aligned mathematics 6, 7, and 8 in middle school and still take calculus, data science, statistics, or other high-level courses in high school."
And how does that turn out?
"In SFUSD, students have many options for a fourth year of math, including Pre-Calculus, AP Calculus and AP Statistics. There are also many ways to reach a fourth year of math, including choosing to take a “compression” course that combines Algebra 2 and Precalculus in 11th grade; choosing to “double up” on math during 9th or 10th grade; or taking a summer Geometry course between 9th and 10th grades."[1]
Why the great opposition to 8th grade (or earlier) Algebra?
"In order to reach algebra in grade eight, students must cover all of middle grades math in just two years (or else skip some foundational material)."
Or, you need to cover the 9 years (K-8) in 8 years, which doesn't sound quite as daunting...not to mention the possibility of starting ahead. However, they are concerned that a student's path is set in 5th grade. Rather than look at this as a lack of imagination in the naming of courses, such that they all need to be one year endeavors...
I fully support getting rid of some closed notion of "tracking" where people have no ability to move at their own pace and speed up or slow down. However, all of their complaints against tracking (save one) apply to this solution, as it is locking all students into one, inadequate track.
[1] https://archive.sfusd.edu/en/assets/sfusd-staff/1.9.19%20Mat...
The most recent archive.org (Dec 17) doesn't have the "the draft chapters approved by the IQC".
Google cache has the page, and at least some of the chapters. Fwiw.
I think a lot of what people complain about with Common Core is bizarrely written school materials that were developed by some bureaucracy and don't make a whit of sense to an adult who already knows the skill, let alone to a kid. Khan Academy definitely does better on that count in my opinion, so it's a good supplement.
You should check out Khan Academy because it's well aligned to the Common Core. The general effect of the CA Common Core was advance the math curriculum by about 6 months.
I did however make a friend at that high school (in English class) whose dad worked at a big tech company and helped me get into the industry. The school's computer programming club was fun too.
Then again I'm almost 40; maybe it's different for younger people.
Presumably writers seldom end up writing about the texts they studied in high school, but they may pick up similar impressions of what they like, and what they are good at.
I am sad to see Jo Boaler/youcubed quoted and promoted in this Middle School Math framework. This person has persuaded school districts and admins throughout CA to believe that every mathematics lesson should be a student-led, creative, multi-disciplinary experience. School districts are shown hyper-curated math lessons where teacher input is minimal and students are allowed to creatively interact with a math topic that's several grade levels below them, and school districts then have their district-level math coaches repeat these lessons ad nauseum to teachers in order to push teachers to a more student-led instruction model. I once saw one of these district coaches in an 8th grade honors Algebra classroom present a lesson on counting dots -- how interesting it is how some students count one by one, some group count, some use symmetry, some start at the top, some at the bottom, etc. Don't get me wrong, these demonstrations are interesting, and allow students the ability to explore and discuss more than a standard teacher-led mathematics classroom. But my experience is that they are closer to one-off, interesting demonstrations rather than an appropriate model to handle an entire mathematics curriculum. When superintendents and administrators are presented these demonstrations, and they observe how much discussion there is, how students can be creative, how students are able to confidently interact with the material, they then believe that's what every math lesson should look like, and set their expectations accordingly.
There are a lot of fancy ideas of what modern day math lessons should look like. Student-led investigations, few teacher prompts, creative outlets for students, and for some unknown reason, an underlying belief that students who are deficient in math will be able to achieve higher with this model. These ideas, and the people that promote them, are then able to secure massive textbook and district consultation contracts, but the actual teachers in the district are left wanting. The thing is, for this type of lesson model, the amount of resources necessary for every lesson is incredible. Interactives, worksheets, the overall pedagogical arch of the lesson, the right teacher questions to ask -- for the types of lessons that is being promoted, it's just not something that can be done 5 times a week for multiple classes. The district/admin expectations are set by these companies/evangelists, the appropriate materials are not furnished to the teachers to actually do something as involved as what they're expecting, and there's no possible way that teachers could create the amount of content that's expected.
Ideologically, it was hard for me to square my love of math and what I fundamentally believe how math should be taught with what I saw at the admin/district level, and my Principal was more than happy to explain that I was in the wrong.
As a 6th grade math teacher, I was told by my Principal that every student (and their parent) entering my classroom had been taught math under this "Jo Boaler" model, and had never seen a math fact quiz. So when a student needs to multiply 7 by 8? I actually had students that were making an 8 x 7 grid of dots and then counting to 56. Even though the Common Core framework has comments about the need for fluency, this model of instruction where students should both investigate a topic and then use that same investigative approach (e.g., setting up m rows of n dots to multiply m * n rather than memorizing the result for 0 <= m,n <= 12) just didn't jive with me. A common kneejerk argument for not prompting students to memorize math facts is because students can "just use a calculator." There's even calculators on their phones nowadays! However, I believe basic math facts are closer to language than math, especially with how often such basic math facts are expected to be known as students progress. A 7th grade teacher adding two fractions together with unlike denominators isn't going to stop mid-example and do a counting exercise for 6 * 7, so wouldn't it be a minor detriment each time a student that doesn't have 6 * 7 memorized see that unknown math fact in class? Saying that the student could simply use a calculator each time they encounter an unknown math fact is, in my opinion, like saying that there's no need to memorize words when learning a foreign language, because if you don't know the definition of "el", "es", "esta", or "un" when in a Spanish class, you can just use Google Translate to figure it out!
What I found out from veteran teachers -- I was told too late for me to be saved, unfortunately -- is that the expectation for new teachers is to drink all the admin Kool-Aid with reckless abandon until you have tenure, and then you see admin maybe once every five years after that. Instead, when I had issues with the textbook we were provided, or saw struggling students left in the dust during student-led investigations, it was in my error as a new teacher to question these approaches and provide other instructional materials for students. Too bad for me, as I really loved teaching that middle school age group and interacting with my students. The money, freedom, and severely reduced working hours in software engineering, though, are a welcome change :P
Equity is at odds with equality; they cannot exist together.
This is why CA fought (and lost) to revoke Prop 209 which guaranteed a certain racial equality. As seen in the recent SF school admission, the board would have prefered a neoracist admission standard, but couldn't do that overtly because Prop 209 still stands, so they changed it from test to lottery.
In this context (Math), everything is political, including (especially) math and the sciences. Everything is political because equity theorists say that everything, including math, is socially constructed. So the structural racism (axiom) that is present everywhere must be deconstructed in every classroom and every workplace.
It is all neoracist. It is the new, hip, way to achieve segregation and discrimination based on race.
"But one man is superior to another physically, or mentally, and supplies more labor in the same time, or can labor for a longer time; and labor, to serve as a measure, must be defined by its duration or intensity, otherwise it ceases to be a standard of measurement. This equal right is an unequal right for unequal labor. It recognizes no class differences, because everyone is only a worker like everyone else; but it tacitly recognizes unequal individual endowment, and thus productive capacity, as a natural privilege. It is, therefore, a right of inequality, in its content, like every right. "
Marx, Critique of the Gotha Programme, Chapter 1.
In this sense it is true that in modern social science, the ideas of equity do come from Marx, as do many things, as Marx along with Durkheim and Weber are the fathers of social science, in the same was as Rahmanujan, Cantor, Galois, etc... are the fathers of modern mathematics. What is meant by equity is explicitly not equality, and even Marx argued against those who tought so.
The ideas of racial equality come from a very simple argument that you would have to refute to make your case. The argument is that there is no racial superiority, and thus given equal opportunity, on average, racial groups will come out more or less equal in practice (which they often do).
When you get politics and ideologies to be taught in school, you're doomed. It's sad to see the US turning into this.
You're conflating historical bias with a STEM field that is arguably as important as reading in modern civilization.
This is an attempt to change the political landscape in the future through indoctrination. And it will not stop here.
And let me tell you that I've been kind of indoctrinated by hardcore left wing history teachers. They wouldn't stop at teaching, they actively tried to make us think that the left was inherently good and the right bad. Sometimes it even backfired when they were exposed by someone who knew about the topic.
Hell, one of my teachers even whitewashed a terrorist group that was still active killing people back then.
This may be an extreme example but that doesn't change anything. Bad history teaching is not an excuse to bring more ideologies into school.
- Columbus was a smart guy that was the only one at the time that thought the Earth is round. He was laughed out of royal court because everyone knew the Earth was flat. (Laughed out because he calculated the size incorrectly, turns out.)
- Poor ol' United States was just sitting there minding its own business when out of nowhere the Japanese attacked Pearl Harbor w/o provocation. I didn't find out about any embargoes until years later.
- Colonialism: those natives aren't going to civilize themselves.
I could go on, but the ideology I was taught last century is easily summarized as, "America: Fuck Yeah!" I think a bit of self-examination is warranted on whether or not the fecal output of the U. S. actually does stink. Like whether or not we overly fetishize the nuclear family, for example.
That's not an ideology, it's bad teaching. And while not knowing your history is bad and can affect the way you see the world and hence your ideology, it is not nearly as bad as directly indoctrinating kids to make them think exactly what you want. I mean, we're talking about identity politics in math, not a history lesson that missed some points.
There were certainly teacher who would say the last one not even that long ago. It's unacceptable practically nowadays because of wokeness.
And yes, that is ideology. Actually, thats almost exactly the essence of ideology. Worldview!=Ideology.