Two topics have been pulling at me recently.  Here’s a quick look at both:

Back to School. And Teachers.  Again.

Back-to-school talk is growing, and it seems almost everyone is on board.  Parents, for the most part, are anxious (and of course, one empathizes with many of the reasons).  Students themselves seem excited – also easy to understand.  School administrations seem to want it, though perhaps that’s not universal? Politicians, now on both sides of the aisle, are pushing to get in-person classes restored.  At least the current administration’s plan also includes considerable funding for both schools and states to make this easier and safer. 
Seemingly unstoppable inertia and better safety planning have caused me to retreat somewhat from my earlier health concerns.  But you can probably guess what still worries me.  Reread the previous paragraph. It may become readily apparent that an all-important constituency in the equation is not mentioned.  The teachers, of course.   A strong case can be made that teachers are not only heroes in every manifestation of the pandemic responses, but they’re also the ones who have been under-appreciated, under-valued, and constantly getting short-changed, not only in terms of working conditions, but also in terms of input.   Even if this movement were favored by everyone, it couldn’t happen for anyone without the teachers.
If the momentum is building, then shouldn’t states (and the CDC!) be more proactive in quickly moving teachers up the suggested priority lists for receiving vaccine shots?  I’m fully aware that moving one group up in priority can affect other groups, including mine.  But talk about ‘essential workers’!! 

Student Understanding – An Enigma?

So easy to understand and agree on, at least in general principle.  Yet there may be no harder concept to evaluate in all of education. 
These thoughts re-surface now, out of an e-mail exchange after my last column.  The column contained two quote/excerpts that I wanted to re-share.  One of them contained an inspiring vision for mathematics education, and – almost as an afterthought – I had dropped in the opinion that progress was indeed being made in exactly those directions.
A reader asked (politely, yet dubiously?) what empirical evidence I had to support that opinion.  He commented that as a parent and grandparent (with former graduate math classes in his background), “I can’t say that I’ve seen any improvement in math understanding over time, and in fact it appears worse!”
As to his question, it was a fair one, and I did not necessarily want to dodge it.   And further, I do not doubt his perception that he sees no evidence of improvement in math understanding, any more than I doubt my own perception that I do see such evidence. 
So, therein lies the (first) fly in the ointment.  What if both of our perceptions are ‘correct’, based on our own understanding of the tricky term ‘math understanding’?!  (And that, in turn, is likely based on what each of us believes ‘math’ itself is – and isn’t – a whole other topic!)
I said most of this in my reply, and, in order to begin to pin down our perceptions, I asked his question back to him.  I generally asked him, in his experience, what kind of evidence he ‘didn’t see’ to support the lack of ‘math understanding’.  This is, what evidence would he want to see?
I haven’t heard back yet – perhaps I’ve lost him.  But the age-old educational question remains:  Exactly what is ‘student understanding’ (in general, not just in math), and far more importantly, how do we determine when it exists for a student in a subject? Do ‘achievement tests’ do that?  Watch for more.