## Teaching the strange phrasing of technical mathematics

I’ve given my first geometry test this year (yes, I’m back on geometry, high five to all my geo-buds) and this is the first test I’ve given with the PARCC in mind.

Specifically, I made the phrasing match the technical language of PARCC questions, and I had my first experience with what happens when the students encounter something truly alien to them, like:

The point R is at (0, 3) and the point S is at (16, 7). Draw the line segment $\overline{RS}$.

Find a point L on the line $\overline{RS}$ such that $\overline{RS}$ is four times as long as $\overline{RL}$.

The first line didn’t go so bad. In a way students can plow through without reading it (draw a line segment? ok there must be points …. there they are!) but the second line had lots of bafflement.

It is a circumstance where vocabulary isn’t the issue, but phrasing is.

The issues seemed to be
a.) Not being clear where the question was; in this case it was directive to “find L”
b.) Students who got past the first hurdle were unclear in juggling the phrasing after; essentially the student brain seemed to go — first I find L, but to do that I need to worry about RS and RL, and somehow RS is — wait what?
c.) That rather than being told what to do (find the midpoint between X and Y) they had to hold a conditional in their head and fuss with a bit before they even understood they wanted a quarter-point to answer the problem.

This sort of conditional indirection seems to be common in PARCC questions: rather than being told what needs to be accomplished, be given some geometric object to assign THEN be told what will happen once that geometric object is in place THEN try to start unpiling what needs to be accomplished for those conditions to hold.

This sort of thing is routine in formal math texts but does not seem to be in the high school experience at all.

(From the PARCC sample Geometry test.)

Does anyone have experience teaching this sort of thing? How does one get students — both fluent and English language learners included — to read statements like the one above without blanking out?

### 5 Responses

1. It’s such a relief for me to read your analyses of the PARCC sample tests! I find the exam design flawed at best, and so many prompts seem to test reading comprehension more than math skills. Don’t even get me started on how difficult it is for many students to read a complex question on a computer screen and then accurately transfer information from screen to paper to work out the answer.

I’ve been reading your blog for a few weeks, but your “Telling left from right” post spurred me to make a comment. I will always remember the day that my students couldn’t write simple inequality statements from a number line graph because I was relying on the words “left” and “right” too heavily.🙂

2. Practice “technical reading”. Most of your students have never had to read anything technical, having been spoonfed interpretations by teachers for everything. Look at

• This is the sort of thing I’m hunting for, thanks.

3. Great analysis Jason, but one small correction: although AIR designed the platform for Smarter Balanced, it did not produce the item bank. Smarter Balanced item bank comes from many sources, including participating states and professional vendors, and has a pretty extensive review process (including by Illustrative Mathematics).

• Did you mean to leave this on my SAGE post? As far as I know (but please chime in if you know more) Arizona is drawing its questions from the AIR test bank.

Utah is also signed up to AIR independently so they’re the closest equivalent. Florida doesn’t have any samples up yet.

It’s of interest to Smarter Balanced folks because critiques of the interface still apply.

I’m still going to be posting about Smarter Balanced sample questions specifically, though. Obviously there’s interest!