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?

• 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! – celeriko Dec 1 '14 at 19:35
• 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. – Shai Dec 3 '14 at 0:37
• At the time I wrote this, I was thinking of $r$ as 3... Case in point! – Shai Dec 3 '14 at 6:49
• 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 .... – Santiago Canez Dec 3 '14 at 20:14