“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?