Joseph G. Rosenstein, a distinguished professor of mathematics at Rutgers University, is mightily disappointed in the Common Core math standards. Professor Rosenstein has spent the past 30 years focused on K-12 mathematics education. He helped to write state standards over the past 20 years. He believed that New Jersey had excellent math standards. But in the pursuit of Race to the Top funding, New Jersey adopted the Common Core standards and junked its own successful ones. He believes the CC math standards are deeply flawed.
He writes:
What are some of those inadequacies? One is the assumption that all students should learn the material that is typically in an Algebra II course. When that proposal was first raised by the commissioner of education in 2008, I wrote an article for the Star Ledger that was given the title “Algebra II + all high schoolers = overkill.”
I also testified on that issue to the Joint Education Committee of the New Jersey State Legislature and asked them if they were able to calculate 64 to the two-thirds power, a typical Algebra II question. It became clear to them that such topics are not for all students, and the proposal to require all students to take Algebra II was rejected.
Yet a number of political organizations continue to argue that Algebra II is necessary for career readiness for all students. It isn’t. For those students who hope to choose an education and career path that includes science and technology, it is essential, but for those not going in those directions, it is simply unnecessary.
Unfortunately, the Common Core mathematics standards is based on the false assumption that all students should learn much of what is found in an Algebra II course. And that assumption has implications all the way down to the early grades, where it is manifested in what one educator called “a fanatical focus on fractions” in the Common Core mathematics standards.
A second inadequacy of the Common Core mathematics standards is that they essentially banish statistics, probability, and discrete mathematics to the later grades; these are topics that should be woven throughout the curriculum and all grade levels
Students in elementary school should be drawing bar graphs based on their everyday experiences, should be conducting experiments involving coin-tossing, should be discovering and generating patterns, and should be following and writing directions for carrying out simple tasks (like walking from their classrooms to the school office). And students in middle school should be building their understanding of statistics, probability, and discrete mathematics based on their previous activities.
Activities like those are in the previous New Jersey mathematics standards, and the modeling and reasoning and problem solving they entail likely contributed to the success of New Jersey students on the NAEP. (Full disclosure: I have written a textbook entitled “Problem Solving and Reasoning with Discrete Mathematics.”)
Such activities were banished from the Common Core standards because of the mistaken belief that elementary school mathematics should be directed exclusively toward success in algebra and eventually calculus.
Diane Ravitch's blog 
The Math Common Core is developmentally inappropriate. There is no doubt. Ohio’s old Math curriculum was not broken and was very good. It has been frustrating going to a new curriculum which you know is inferior to the program that was abandoned. Years of following the common core will leave students way behind in Math achievement. Great article! 😊😊😊😊😊
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What we fail to understand is THEY do not care if these standards are bad. As a matter of fact bad is what they want. Failure is what they want. How can they shut down schools and fire teachers if our kids are doing well. We have presented so much proof that these standards are BAD and so far all of our efforts have fell on deaf ears. They don’t really care about our kids or education. They care about money, power and control. Until you threaten their money, power or control we will get nowhere. This is why I say it is time to STARVE THE BEAST. They cannot accomplish any of this without our kids. So get your kids out of the system. Make the sacrifice for 1 year. Your kids would be better off sitting on the sofa reading good books and doing good math problems for 1 year instead of sitting in the government indoctrination centers we call public schools. No kids the system implodes and they come begging to us instead of us begging to them. If you don’t have the courage to take your kids out then at minimum STOP taking AP, SAT, PSAT, GED, ACT. Take the College Board down. REFUSE HIGH STAKES TESTS. We have the power to ruin them but not if we continue to give them what they need to exist.
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AMEN!
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I wonder about this. Clearly most adults who are not educators or in STEM will never need to understand fractional exponents, but aren’t some high schoolers too young to know whether they will go into education or STEM? Also, regarding “a fanatical focus on fractions,” I’m in favor. I run into Algebra II and precalculus students all the time who don’t understand fractions, and I work in a high-performing, high SES school district. And all adults should understand fractions.
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“I also testified on that issue to the Joint Education Committee of the New Jersey State Legislature and asked them if they were able to calculate 64 to the two-thirds power, a typical Algebra II question.”
I seriously doubt most legislators, governors, Congress members, or presidents would even be able to “calculate” 64 to the three-thirds power.
For a good laugh, try to picture GW Bush puzzling over that question.
Or perhaps I just misunderestimate him?
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Money makes up for/overcomes brains in Georgie the Least’s world.
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He would just ask Cheney.
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The glass is always two to the negative one power full.
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Or empty! Good one TC
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What is even more insane is that the goal is for students to be proficient in Algebra II. In other words, they should all be B-students. How many of those directing these standards were B or above students in Algebra II? Or like many, did they squeak by in their higher math courses, including College Algebra?
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He is right. Math teaches a WAY of thinking, not WHAT to think about. A concept the Common Core authors missed completely. The goal is to help students learn to solve problems using logic, axiomatic systems, and transference. Math III is now required in our area which includes Fundamental Theorem of Algebra and Trigonometry. Way too much. Students should NOT be penalized on some flawed VAM test because they can learn problem solving through other means!
Statistics is always the afterthought in a curriculum. The professor is correct. It should be interwoven and integrated. Voters need to be able to see through the garbage politicians use to get elected. For example, when Kasich says Ohio ranks 10th in jobs, that is subpar because Ohio is 7th in population. He just doesn’t mention the last part. And his unemployment “facts” leave out that many Ohioans are dropping out of the workforce, making the unemployment rate look better than it is. But voters continue to believe the Ohio miracle. Maybe that is the miracle.
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People also need to be taught how to understand graphs and basic correlations so that they are not so readily VAMboozled.
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The good news is that the CC$$ math standards are significantly better than the NG$$ standards. I did not think that was possible until I spent some time reviewing these awful science standards.
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NG$$ ???
You lost me on that one tultican! Please explain. TIA!
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Next Generation Science Standards: the Louis Gerstner inspired standards that are truly awful.
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Any idea when that “next generation” starts?????
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It has already started in many states.
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I presume NG$$ is this:
http://www.nextgenscience.org/next-generation-science-standards
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Reblogged this on The Grey Enigma.
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“What are some of those inadequacies?”
How about the fact that those standards are COMPLETELY INVALID. To understand why read and comprehend Noel Wilson’s never refuted nor rebutted 1997 treatise “Educational Standards and the Problem of Error” found at: http://epaa.asu.edu/ojs/article/view/577/700
Brief outline of Wilson’s “Educational Standards and the Problem of Error” and some comments of mine.
1. A description of a quality can only be partially quantified. Quantity is almost always a very small aspect of quality. It is illogical to judge/assess a whole category only by a part of the whole. The assessment is, by definition, lacking in the sense that “assessments are always of multidimensional qualities. To quantify them as unidimensional quantities (numbers or grades) is to perpetuate a fundamental logical error” (per Wilson). The teaching and learning process falls in the logical realm of aesthetics/qualities of human interactions. In attempting to quantify educational standards and standardized testing the descriptive information about said interactions is inadequate, insufficient and inferior to the point of invalidity and unacceptability.
2. A major epistemological mistake is that we attach, with great importance, the “score” of the student, not only onto the student but also, by extension, the teacher, school and district. Any description of a testing event is only a description of an interaction, that of the student and the testing device at a given time and place. The only correct logical thing that we can attempt to do is to describe that interaction (how accurately or not is a whole other story). That description cannot, by logical thought, be “assigned/attached” to the student as it cannot be a description of the student but the interaction. And this error is probably one of the most egregious “errors” that occur with standardized testing (and even the “grading” of students by a teacher).
3. Wilson identifies four “frames of reference” each with distinct assumptions (epistemological basis) about the assessment process from which the “assessor” views the interactions of the teaching and learning process: the Judge (think college professor who “knows” the students capabilities and grades them accordingly), the General Frame-think standardized testing that claims to have a “scientific” basis, the Specific Frame-think of learning by objective like computer based learning, getting a correct answer before moving on to the next screen, and the Responsive Frame-think of an apprenticeship in a trade or a medical residency program where the learner interacts with the “teacher” with constant feedback. Each category has its own sources of error and more error in the process is caused when the assessor confuses and conflates the categories.
4. Wilson elucidates the notion of “error”: “Error is predicated on a notion of perfection; to allocate error is to imply what is without error; to know error it is necessary to determine what is true. And what is true is determined by what we define as true, theoretically by the assumptions of our epistemology, practically by the events and non-events, the discourses and silences, the world of surfaces and their interactions and interpretations; in short, the practices that permeate the field. . . Error is the uncertainty dimension of the statement; error is the band within which chaos reigns, in which anything can happen. Error comprises all of those eventful circumstances which make the assessment statement less than perfectly precise, the measure less than perfectly accurate, the rank order less than perfectly stable, the standard and its measurement less than absolute, and the communication of its truth less than impeccable.”
In other word all the logical errors involved in the process render any conclusions invalid.
5. The test makers/psychometricians, through all sorts of mathematical machinations attempt to “prove” that these tests (based on standards) are valid-errorless or supposedly at least with minimal error [they aren’t]. Wilson turns the concept of validity on its head and focuses on just how invalid the machinations and the test and results are. He is an advocate for the test taker not the test maker. In doing so he identifies thirteen sources of “error”, any one of which renders the test making/giving/disseminating of results invalid. And a basic logical premise is that once something is shown to be invalid it is just that, invalid, and no amount of “fudging” by the psychometricians/test makers can alleviate that invalidity.
6. Having shown the invalidity, and therefore the unreliability, of the whole process Wilson concludes, rightly so, that any result/information gleaned from the process is “vain and illusory”. In other words start with an invalidity, end with an invalidity (except by sheer chance every once in a while, like a blind and anosmic squirrel who finds the occasional acorn, a result may be “true”) or to put in more mundane terms crap in-crap out.
7. And so what does this all mean? I’ll let Wilson have the second to last word: “So what does a test measure in our world? It measures what the person with the power to pay for the test says it measures. And the person who sets the test will name the test what the person who pays for the test wants the test to be named.”
In other words it attempts to measure “’something’ and we can specify some of the ‘errors’ in that ‘something’ but still don’t know [precisely] what the ‘something’ is.” The whole process harms many students as the social rewards for some are not available to others who “don’t make the grade (sic)” Should American public education have the function of sorting and separating students so that some may receive greater benefits than others, especially considering that the sorting and separating devices, educational standards and standardized testing, are so flawed not only in concept but in execution?
My answer is NO!!!!!
One final note with Wilson channeling Foucault and his concept of subjectivization:
“So the mark [grade/test score] becomes part of the story about yourself and with sufficient repetitions becomes true: true because those who know, those in authority, say it is true; true because the society in which you live legitimates this authority; true because your cultural habitus makes it difficult for you to perceive, conceive and integrate those aspects of your experience that contradict the story; true because in acting out your story, which now includes the mark and its meaning, the social truth that created it is confirmed; true because if your mark is high you are consistently rewarded, so that your voice becomes a voice of authority in the power-knowledge discourses that reproduce the structure that helped to produce you; true because if your mark is low your voice becomes muted and confirms your lower position in the social hierarchy; true finally because that success or failure confirms that mark that implicitly predicted the now self-evident consequences. And so the circle is complete.”
In other words students “internalize” what those “marks” (grades/test scores) mean, and since the vast majority of the students have not developed the mental skills to counteract what the “authorities” say, they accept as “natural and normal” that “story/description” of them. Although paradoxical in a sense, the “I’m an “A” student” is almost as harmful as “I’m an ‘F’ student” in hindering students becoming independent, critical and free thinkers. And having independent, critical and free thinkers is a threat to the current socio-economic structure of society.
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He is correct that many topics that used to be covered in Algebra 2 and AP stats and also some pre-calc have now been moved down to Algebra 1. But he is mistaken about statistics and probability. Sixth grade covers measures of central tendency, histograms, dot plots and box plots, which are picked up again in 7th along with population sampling, mean absolute deviation and probability (although dependent events are left out). The statistics are covered again in more depth in Algebra 1, including standard deviation and probabilities under a normal curve.
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Abby, I’m not going to get into an argument with you, but Joe Rosenstein is intimately familiar with the previous NJ math standards, having been the principal author of them. Further, he said “essentially banished” until later grades. That’s not the same as “entirely removed.” And, yes, some descriptive statistics things remain, for reasons I could suggest but will leave alone at present. What’s missing is the meat, the inferential aspects.
More important to Joe, I suspect strongly, is the removal of discrete mathematics. He fought hard to get a meaningful discrete math strand included in the state standards, and as a result of his efforts, New Jersey was one of the few states that had them. Discrete math, which includes a range of topics – graph theory, Boolean logic, combinatorics/discrete probability, recursion, algorithms, set theory, and much more – is vital for computer science, among other things. You really don’t want to have a K-12 math curriculum that is essentially (that word again) void of these things, but most states have had just that for . . . well, almost forever. There was a movement in the ’80s to make discrete mathematics a reasonable and – ahem – rigorous path (gotta get that word in, of course) for secondary mathematics. Not every kid needs or wants to climb Mt. Calculus. There are many, many intriguing fields that require discrete mathematics and the subjects are accessible without every skill that goes into conquering analysis (calculus). I’ve had low-achieving, at-risk students do really well in areas like graph theory despite their shortcomings in other areas of the traditional path.
And that’s what galls the traditionalists. It’s what fuels the rage of R. James Milgram, the “big name” mathematician from Stanford whose name, along with that of Sandy Stotsky, comes up in every article about how “inadequate” the Common Core Standards are, when the media wants academic, rather than glaringly political names to use.
Problem is, Milgram and Stotsky ARE glaringly political, as anyone who has followed them since the ’90s can tell you. And they don’t like no “fuzzy math.” Which means that if something isn’t 100% about getting the top kids to be able to take calculus as soon as humanly possible and get Ph.Ds in mathematics or some math-intensive field, Jim Milgram isn’t interested. His attacks on the CCSS-M is all about calculus and international competitiveness.
That’s not where Joe Rosenstein is coming from, bless him. And that’s not because he isn’t a research mathematician since in fact he is. He just has a broader, more inclusive perspective on mathematics and on the realities of American K-12 students, their interests, and their needs.
The “Calculus Uber Alles” crowd led by Milgram are elitists of the worst sort. They are the kind of folks who have always dominated American and English perspective on math education and made it horrible for so many. Let me offer a very recent anecdote in closing:
http://www.makinggameofthrones.com/production-diary/2015-san-diego-comic-con-maisie-williams-gwendoline-christie-panels
“When a fan asked Williams about her kill list, she had an answer that brought the house down:
“At school I really enjoyed maths; it’s something I enjoyed in primary school when I was 12. It was my leading subject and then when I went into secondary school, I started to hate maths because of my teachers,” she explained. “I feel like that’s how it is for a lot of people: When you don’t like your teachers, you start to hate the subject… So I’d kill all three of my math teachers.”
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I like the thought of a discrete math strand. Logic and proofs shouldn’t be a college level course either. My one regret is I am not better at proofs as many math grads. It is a hindrance in understanding high math. Even in college, proofs were skipped over. I remember our Calculus prof blowing by the delta-epsilon proof. So I keep at it trudging through on my own.
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We could be doing proofs in elementary grades. Of course, what comprises a proof in 1st grade is very different in many particulars from what comprises a proof for an undergraduate, graduate student, or working mathematician. But at heart, it’s the same: giving reasons that communicate to peers and those more expert (in this content, one hopes that is the classroom teacher) why something is true (which for a first grader equates to why something appears to be true).
An example: ask students at various grade levels to prove why the sum of two odd numbers is an even number. I guarantee that 1st graders can give reasonable, meaningful explanatiIS ons for this fact that communicate well to peers. A diagram or concrete illustration with physical objects could suffice here. But if we don’t ask children to explain their thinking and to begin to see that an example isn’t a proof (whereas a counter example IS a refutation) early on, then when they are finally expected to do so, first in high school geometry, and then possibly not until a rigorous course in analysis or an elementary course in number theory, abstract algebra, topology, or the like) they will be, as you have experienced, quite possibly overwhelmed and/or overmatched.
Please, if anyone is tempted to interpret the above to be a call for overburdening young children with “rigor” or inappropriate abstraction, that’s not what I’m talking about. Moving from concrete to abstract thinking in mathematics is much more of a continuum than most people realize, however, and it’s a mistake to think that Piaget and his followers believed that young children absolutely could not or should not go near abstraction. It’s a matter of levels and keeping in mind what works for most kids at a given point in their development. I’ve no interested in creating little automatons, but neither am I interested in delaying all abstraction so long that most kids think it’s impossible and/or pointless. After a typical K-12 math miseducation in the US, most kids have been ruined for the sort of abstraction that actually links mathematics and science with much of the beauty of art, music, literature, etc.
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This is the first convincing argument I have heard against the details of CC math. (However, I bet the majority of the people who hate CC math would not embrace the improvements Joe Rosenstein is suggesting). So far, I feel the math my third grader has been taught is an vast improvement over how I was taught and I am disappointed to see the math in the upper graders is flawed.
Calculus is not needed in HS even for a student majoring in a STEM field. I don’t understand the push for so many students to take calculus. I fear we are going to lose some potential great “STEM” professionals by scaring them off before they graduate HS :(.
Rather than a push for calculus, I think an in-depth Geometry class would serve students better.
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I know Joe Rosenstein from having done some summer work for high school math teachers at the DIMACS program at Rutgers. Joe ran the program for elementary teachers but also came to many of the meetings that were going on for us and the conference on applied graph theory that was running concurrently during the first half of our four-week institute. He is a remarkable guy in all sorts of ways. I really like him a lot.
If you followed the Math Wars closely, as I did, you might know that Joe personally came under enormous attack from certain educationally conservative/reactionary groups in the previous decade because of his role in creating the NJ State Math Framework. Too creative, too off-the-beaten-track, too “not just like the way they taught math when I was hating math as a student,” etc. I was miseducated in northern NJ public schools and learned to despise mathematics by the time I hit high school. It’s an enormous fluke that I now have a masters in math education from U of Michigan and having been teaching mathematics at various levels for over a quarter century. Believe me when I say that if Joe and people like him had been running the show and had major input into teacher preparation and professional development in the ’50s – ’70s, things likely would have been vastly better.
So when he says that the CCSS-M standards have serious flaws, I listen. Because he’s coming from a progressive and deeply knowledgeable perspective on mathematics. He’s not a traditionalist, but he’s also not a “fuzzy math” person (which is to say that the Mathematically Correct/NYC-HOLD people would love to dismiss him as fuzzy, but he knows way too much math for them to do that honestly. There are others out there like him, notably Hyman Bass at University of Michigan via Columbia University, Alan and Tom Tucker of SUNY@Stony Brook and Colgate University, respectively, and Alan Schoenfeld of UC-Berkeley. They’re all Ph.Ds in mathematics who have been involved in mathematics education as well and don’t push a “back-to-basics” for the masses, high-stakes testing philosophy. Neither does Joe Rosenstein, regardless of what some angry people in Ridgewood, NJ (the town next to where I went to K-12) and other places would love everyone to believe.
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Thanks for all this info Michael. I’m sitting in C2.0 Algebra II training this week, so it couldn’t be more relevant.
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Great info. Math education has become disappointing. No wonder kids hate it with all the testing and rigidity. Heck, with CCSS, even the teachers ask themselves “are we going to do anything FUN today?”.
Once, for fun, I put the infinite hotel rooms, infinite guest problem to Algebra II students. They loved it.
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Did they forget that elementary students minds work in concrete operations? Not abstract?
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I saw him interviewed on PBS. He was right.
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This is a helpful post with an excellent series of comments for understanding the nuance behind the critiques of CCSS-M. I noticed that most of the critiques come from states where the existing state standards are high quality (e.g. Ohio and New Jersey) and should never have been replaced by CCSS. This was a major flaw in the waiver-exchange-for-CCSS-adoption model). What about states – I can think of at least 10 – for which the standards are a vast improvement? Is there any chance that the standards will be amended? I imagine that any policy or series of standards need to be in place for a short amount of time before they can be meaningfully amended.
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Ah but who knows more about math… a lifelong math professor or someone like David Coleman? “Ed Reformers” bet on David Coleman and why not… that thar them hills contain gold!
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Jason Zimba, the fellow who headed up the CC math standard project actually knows math quite well. He’s a PhD physicist.
But developing an appropriate set of math standards for k-12 is much more involved than simply “knowing the necessary math” (Lots of people actually know the latter.)
The real problem here is the very same one that is at the root of all issues related to “reform”.
The “directors” and “developers” are not experts on child development, learning, teaching and standards development and all the other relevant things but nonetheless believe they are more qualified than the people who are.*
It is very telling that the two people on the original CC validation committee who do have relevant expertise — Dr. James Milgram and Dr. Sandra Stotsky — had serious reservations with the adequacy of the CC standards and as a result, would not sign off on them.
You can not reason with the people directing and selling Common Core and the tests and VAMS and all the other baggage that go along with it because their entire stance is irrational and unscientific.
The best that one can hope for is to have folks like Rosenstein expose “reform” as the house of cards that it is.
*School “reform” is a textbook example of the Dunning-Kruger Effect (and on a fairly massive scale). Someone should do a study…
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SDP wrote: “It is very telling that the two people on the original CC validation committee who do have relevant expertise — Dr. James Milgram and Dr. Sandra Stotsky — had serious reservations with the adequacy of the CC standards and as a result, would not sign off on them.”
No, it’s actually not very telling for reasons I suggested in a previous comment. These are two people whose professional credentials are almost coincidental to their views on the Common Core. The real issue for them is a philosophy of education and a bunch of political assumptions that I suspect would be anathema to many followers of this blog. Do a little more digging and don’t be overly impressed by their “credentials.” After all, you don’t really accept Zimba’s Ph.D in mathematical physics as adequate for developing a K-12 mathematics curriculum and neither do I. There’s far more to figuring out good ways to do K-12 math than JUST knowing the math. It’s necessary, but far from sufficient.
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Thanks,
I’ll do some digging on Milgram and Stotsky.
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