Overcorrecting

Overcorrecting is something I do on a regular basis, so I get it.  And I’ve always had students who do it, but not so many in the same exact way as now.

One common misconception that students seem to arrive with is that “=” means “and here’s the next step”.  So you get bizarre false statements like

5x-2=13=5x=15=x=3 ,

and the worst part of it is that students don’t realize that what they have written claims that 13=15=5 .

And so we have conversations in my class about the meaning of symbols, and how it is acceptable to write = as a random connector symbol in your history notes, but in math class = is used to mean actual equality and nothing else.  I stress the importance of clear communication, and give examples of basic mathematical communication standards — like how

\displaystyle \lim_{h \to 0} = 2x-5

might be fine as a note to yourself, but would be poor communication.

All this I did the same as always.  It usually results in an ongoing conversation, but at the end of the semester, they have improved a lot.  And the result this semester?  I had fourteen students (out of 88) that did not write a single = sign on the last test.  Equality is problematic, so it’s best to avoid it altogether?  Yeesh.  Overcorrection.

So I think I need to write some explicit standards of mathematical communication.  I think there will need to be separate standards for explanations in words, sequences of statements, and possibly graphs/visual stuff (yeah, my own communication might need some work here).

Brainstorming here:

  • When writing a sequence of mathematical statements, each statement must have a “verb”, which will usually be an =.
  • A line can start with an =, which means it is equal to the line above it.
  • Someone with a strong mathematical background who does not attend our class must be able to follow your work
  • Use standard mathematical notation

I know there needs to be more.  Thoughts?

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Standards Based Blogging

It’s an idea that just popped into my head… also Siobhan Curious wrote about how she plans to give her (English) students monthly blog grades.  And in the comments, someone suggested having a separate grade for comments.

So maybe I have some list of blogging standards.  Maybe they include things like content standards, as well technology-mastery standards.  Maybe positive community participation is a standard that can be met by commenting on other students blogs, or by writing response posts (and then you’d get the pingback, so it shows up with the comments).

I don’t think I actually want to call them standards.  This is something different.  Maybe.  Don’t know yet.

I had been thinking about having a midterm blog grade, but I like the idea of splitting the semester into thirds, and having a meeting each time for feedback.

On making changes…

I’ve decided that I just need to start using this blog to get thoughts down quickly, and expand on them as I have time.  For some reason, it’s nerve-wracking to hit publish on a rough idea, but with the crazy state that my life has entered, I’m never going to write anything if I wait till I have time to polish it.

So… I will definitely be doing the blog project again.  I will only be able to do it for one class a semester, because there is no way I can keep up with more than 40 student blogs.  But there are definitely some changes that I will make.  (And, in the spirit of the way I’m changing my blogging style, I’m not going to try to list all the changes I want to make at once!)

First, I will make the blogging project worth 50% of the grade.  It’s a lot of work, and that work should be valued.  And I’ll abandon the weird double-table approach I had last time.  It just confused the students. When I was asking them to do something so far out of their comfort zone as writing about math, I should have recognized that keeping as much as possible familiar would make the students happier.

Stay tuned for other changes!  And here’s a gratuitous picture of my baby:

malcolm