This latest from Greenwich CT:
“A parent entering a second-grade math classroom in September will see students designing their own lessons. The children will be moving around, working at different tasks that they have chosen to explore the idea of, say, subtraction. They will be discussing math with each other, not just the teacher. The teacher will hop from student to student, making sure they are on the right track and answering questions, but only as a guide, not the autocrat telling the students how to learn. This is the vision Irene Parisi, assistant superintendent for curriculum, instruction and professional learning for Greenwich Public Schools and her team of teacher and administrators have for the widely anticipated “elementary math pilot.” “
It isn’t as if this hasn’t been tried before. And when it has been tried before with dubious results, the general fallback excuse is “Teachers aren’t doing it right” or other forms of “Teachers are traditionalists in reform clothing”. When scores do rise, there have been (to my knowledge anyway) no studies adjusting for help at home via tutoring, or help from a learning center such as Sylvan, Huntington or Kumon.
But they’ve hired consultants to give workshops to make sure this goes off without a hitch.
“[The} workshops focused on how to teach students to reason their way through math problems instead of memorizing math algorithms and trying to apply them without understanding. “All I’m trying to do for kids is make sense of things,” Tang [the consultant] told the math pilot teachers. “Solve through reasoning versus grinding: that is truly what nobody is teaching students to do.” “
OK, let’s examine this statement. Nobody is teaching students how to reason apparently. The popular mythology about the math teaching that apparently never worked and failed thousands of students is that students solved problems without knowing why the procedure worked and were unable to apply those procedures to other problems in new settings–thus becoming part of a growing body of “math zombies”, guilty of “doing” but not “knowing” math.
I have just finished a year of teaching my students how to solve problems using concepts and skills developed in class. I taught the underlying concepts of how specific procedures and algorithms worked so it wasn’t as if they were devoid of the “understanding”. But as often happens, the students were more interested in the algorithm or procedure than in understanding how or why it worked–so there weren’t many who remembered the derivations. Nevertheless, their capability of working with the algorithm/procedures ultimately helped them solve problems.–even new ones in different settings.
What does it mean to “apply without understanding”? If you know what fractional division represents, and that to find how many 2/3 oz servings of yogurt are in a 3/4 oz container one divides 3/4 by 2/3, does understanding the derivation of the invert and multiply rule help you to solve the problem? Or is it the understanding of what fractional division, and division in general, represents? There are times when the underlying concepts are part and parcel to applying a procedure or strategy. But just as importantly there are times when the concepts are not.
But such questions and issues remain in the province of the marginalized traditionalists, while people like Parisi hold sway with the oohs and ahhs of others who are subscribed to this particular groupthink. And they continue on, unabashed and unhindered:
“The teachers are also working on developing a “flexible curriculum,” including resources that will allow children to go deeper than the current math lessons if they desire, and designing lessons that will allow students to choose how they learn, Parisi said. They also must create new ways of assessing how students demonstrate what they learn — whether an oral presentation, illustration, video, written statement or another way. ‘A lot of it is going to be the mindset, the student ownership, the student voice in all of this. That’s going to be significant because we’ve already seen the power of that,’ ” said Parisi. ‘So the question is, how do we do more of that.’ “
The question also is how do we get away from this magical thinking?
traditional math 
In Ontario, a long-serving grade 2 teacher has had 15 plus years of this type of P.D. and has long since independently worked out the best methods to teach grade math. At least should be able to work them out, but given the pressures to teach a certain way, may not have.
And they still don’t get it. At least that is the refrain in Ontario, which is spending millions to force this ideology on the teaching staff.
Who can believe this? For grade 2 math?
LikeLike
I found myself nodding along for this entire piece, Barry. Especially this section:
In terms of how to get away from this “magical thinking”… I have no solutions, but it’s an important question. Nice piece.
LikeLike
Well put. It’s so tedious hearing about deeper understanding when no one can really explain what they mean by that. Isn’t understanding how and when to apply an algorithm/procedure/rule deeper understanding? The underlying mechanics are often very complex and really serve to confuse kids if too much focus is put on that part of maths early on. As you say, often the deeper understanding comes from a Eureka moment after a student has executed many, many maths problems using standard, traditional procedures. Then they often “see” what it is that they are doing. That’s my experience anyway.
LikeLike
Greg Tang – “He earned his B.A. and M.A. degrees in economics from Harvard, and he also holds an M.A. degree in Math Education from New York University.”
He is NOT a mathematician. He knows how to identify a demand (educator) and fill it.
“Speaker, Educator, Writer and Online Game Developer. My goal is simple. Help kids become smart, well-rounded individuals who love to learn!”
… who are not able to actually DO the math that leads to the algebra in 8th grade track.
… and, of course, to sell his products and services.
I’ve NEVER seen any of these consultants and educators start from their own 7th grade math tracking requirements and work backwards, curriculum and test-wise, to give students and parents specific skill feedback on a test-by-test basis, when the information can be acted on. They only concern themselves with testing that’s a year late and many tutoring dollars short.
“Hess’s competencies are different from Greenwich Public School’s current math curriculum because they group what students should know into grade bands — for example K-2 — instead of individual grades. That means under Hess’s math pilot model, students might spend three years mastering the same broad math concepts — counting, adding and subtracting — as opposed to spending one year on more limited math strategies — like dividing whole numbers.”
“We’re moving beyond the idea of just grade placement,” said Parisi.
Not only does CCSS define a NO-STEM K-6 math education, but these people set even lower expectations – three year “bands.” They do not separate the teaching and curriculum variables from individual student effort. So, if kids do not make the 7th grade math track split, it’s their own fault, or IQ, or something other than what the school is doing. Just look at all of the kids who did make the upper math track – but don’t ask us parents what we had to do at home.
Maybe that is what’s in Tang’s “Family Math Night Kit” – how to get parents to feel like it’s their responsibility to do the teacher’s job – practice math facts. Been there – done that.
That’s educational incompetence and it increases the academic gap. Achieving one’s potential is not a natural process that allows for 3 year target bands. In math, it’s all over by 7th grade. High school, college, career, and life are anything but natural. I thought they wanted kids to learn “grit.” That never happens naturally with 3-year bands. It would be one thing if this was some sort of separate opt-in choice, but it isn’t. They should allow for some opt-out choice where students get an extension of the current (pushy) traditional high school math track back into K-6. Then compare the results. They would complain that the process was not natural. Hello? Reality check. Low expectations do not help students achieve their potentials. Full inclusion with leveled in-class groups only hides the home help with skills. It’s not even an IQ sort because the skills are really dumb-ass simple. Even Andy Isaacs of Everyday Math conceded that learning the traditional arithmetic skills are really not that difficult, and perhaps necessary to keep parents happy. Whatever, just do it at a level that gives all kids an equal opportunity to get on the algebra in 8th grade track. Education is not just some sort of natural process where all you have to do is lead students to the math trough.
LikeLike