[jburtkinderman]

Bill,

I guess the issue is that I am seeing such huge payoff within my district (I am a K-12 math coach for a rural district) in leading with the message that students should build on steps they can justify. We are avoiding cross-multiplying, FOILing, and all sorts of shortcuts that are previously accepted as if they were ideas unto themselves… I am a strong believer in keeping the arrows of this change all pointing in the same direction, as the change is just enormous and is so very important.

If we are to unpack the thinking of this particular repeating decimal to fraction process, and have students replicate it, as I see it, the following is what is going on:

x = 17.171717…

100x = 1717.1717…
(here student should be able to answer why we choose 100)
(student should also be able to answer why the second equation is true, assuming the first / why the equations say the same thing)

Now, to move forward, student needs a reason subtracting the first from the second results in an equally true equation. If we are to regularly say:
“well, then, why would it be really cool to know what 99x is? why would this be a better idea that 101 x?”

then I suppose we are teaching students to replicate a teacher seeing a cool structure and making use of it, but I don’t think we can reasonably call this the students looking for the structure. In the classrooms that I’m observing and coaching, this task as a standard does not build meaning, but rather a notion that math is magic…

If we teach this as a most simple application of systems, I don’t think you encounter the same disconnect.

As an underlying issue, I’m not even sure that I see the real relevance here… Perhaps you can illuminate the importance of the idea of changing repeating decimals (we would only see this with a calculator) to fractions? If this is truly just a nice mathematical problem, should it not be a resource for MP 7 or a specific suggested treatment of 7.EE.4? Can you give me another example of a nice mathematical problem that is important enough to be turned into a standard?

I so appreciate the feedback and debate, because the process is so clarifying and cleansing. Further, as someone doing my work without a peer group, This site is a gem. It is beyond wonderful to have this level of feedback. If I’m missing something here, I’d enjoy seeing it from a new angle.

So Many Thanks,

Joanna

[jburtkinderman]

All,

I’m a district math coach and coordinator in WV and have great interest in this topic. I have been a passionate advocate in the last few years for allowing middle school acceleration as we transition to common core standards. It matters SO much in states like mine what the folks at the top are recommending and I’d love to have comment on my rationale…
In a state with the one of the least well-educated populations in the nation, with over half of our students living in poverty, where better than 1/5 of 9th graders failed 2 or more subjects, with less than 40% even proficient in math, I am concerned that it’s more important than ever to give future leaders every possible opportunity for brain stretching.
I totally buy the argument that, with common core standards, content is deepening and that students do not need to ‘skip’ so much as they need to deepen. However, it really only resonates in a theoretical context. What I can’t wrap my mind around is that as the theory morphs down into practice, learners will continue to need different amounts of time to own and personalize ideas. Next year, we will begin to implement these new standards with the students that we have with a great mix of ability, need and desire. Even while working at elite Southern private schools, where 100% of the students finished Algebra by the end of 8th grade, the hungry, naturally gifted learners finished Geometry by the end of 8th.
I worry that changing curriculum can get confused with changing audience. In my (granted, limited in comparison!) experience, the most naturally gifted learners easily learn at both a pace and depth two times greater than the average. In addition, I find that these learners struggle mightily at the beginning of a truly rigorous course surrounded by their peers. But after a short adjustment period, as the sore muscles in their brains transform into stronger cerebral muscles, their potential for engagement and depth grow exponentially.
In short, there’s a difference between the local community college where I have taught and Haverford, where I went to school myself (and where my thesis advisor and lasting friend, Jeff Tecosky-Feldman, still speaks highly of you, Bill!). The institutions don’t serve the same audience, and thus don’t use the same strategies. In our most educationally disadvantaged areas, it’s so important to do the very best by the higher-level students. The ratio of need for highly qualified leaders to availability thereof in all fields is much higher here than in those states lacking our dismal stats.
As one teacher put it… “are we not just moving from no child left behind to no child pushed ahead?” We should continue to delve deeper into these standards, to strive to make our curriculum fertile ground for learning. As our classrooms improve and deepen, the hope is that the learning potential of ALL students will rise, leaving the group of mathematically gifted still with needs beyond the grade level.
My idea in regards to middle school advancement is not to leave out a middle school course, nor to identify kids as 5th or 6th graders. Instead, 8th graders who are ready, willing and able to go an extra mile could take an elective math class in 8th grade in addition to their regular class.
I appreciate feedback, insight, and the opportunity to join the conversation.

My Best,
Joanna

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