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In this semester I've realized that many of the problems (my) students have can be solved by reading better. The most recent example I've encountered was in the last exam; I asked them the following:

Given the following set $X=\{a,b,c,d,e\}$, find how many subsets with $r$ elements are in $X$.

What many of them did was to find how many subsets there are in $X$, regardless of the number of elements.

So I figured that maybe if I made some reading exercises, they could actually worry about the maths and not lose points because of things like this. Is this something accurate/doable? where can I find good books for this?

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    $\begingroup$ some other suggestions: bold the important words, have the students read through all of the directions outloud together before starting on the test, and most importantly a piece of advice my university Discrete Structures professor told me.."Slow Down!" :) hope this helps! $\endgroup$ – celeriko Dec 1 '14 at 19:35
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    $\begingroup$ I often find I trip students up with my own inconsistency, so I think a lot can be said for purposefully fixing your own language choices so that they recognise words and phrases when they see them. For example, there are no $r$-element subsets 'in' $X$ as far as we are aware (unless one of $a,b,c,d$ or $e$ is itself a set with $r$ elements), but there are 10 $r$-element subsets 'of' $X$. Encouraging this kind of linguistic pedantry in discussion, identifying flaws in their language, and even correcting yourself mid-speech, I find makes learners far keener to the importance of details. $\endgroup$ – Shai Dec 3 '14 at 0:37
  • $\begingroup$ At the time I wrote this, I was thinking of $r$ as 3... Case in point! $\endgroup$ – Shai Dec 3 '14 at 6:49
  • $\begingroup$ Adding to Shai's comment about the way in which your question is phrased, I would also suggest that you quantify $r$: For each nonnegative integer $r$ (or whatever you want), determine the number of subsets of .... $\endgroup$ – Santiago Canez Dec 3 '14 at 20:14
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I'd like to enthusiastically reinforce celeriko's comment above. It seems that students often don't pick up on the fact that really "juicing" something basic is what allows for fluent thought about later mathematics. We should build assignments that aim to teach students to slow down and read carefully to process what is being said. We should encourage them to work out simple examples and to modify hypotheses, to find easier questions and harder ones. I suggest that for assignments like these it should be made very clear that the point is not to get an answer but to build a solid mental picture that one can fluently think and talk about.

Here is a quote from Bill Thurston:

"I was really amazed by my first encounters with serious mathematics textbooks. I was very interested and impressed by the quality of the reasoning, but it was quite hard to stay alert and focused. After a few experiences of reading a few pages only to discover that I really had no idea what I’d just read, I learned to drink lots of coffee, slow way down, and accept that I needed to read these books at 1/10th or 1/50th standard reading speed, pay attention to every single word and backtrack to look up all the obscure numbers of equations and theorems in order to follow the arguments."

—Bill Thurston, from the foreword to Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

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