## Wednesday, October 4, 2017

### The Apple Question

Lately I've been experimenting with small questions that pack a punch.

To qualify, a question has to have a small number of words (obviously) but the question should require the child to step out of their comfort zone and include some words that seem harmless or innocent but are in fact very demanding.  The question has to challenge the core skills with the exception of working memory which may not be possible under the circumstances.  The question can't be like a brain teaser that requires some outside trivia to answer.

Test Prep Math throws quite a few punches, especially in bonus questions.   The effect I'm looking for is "You can't expect me to answer that question.  My boring math book at school doesn't expect me to answer questions that require thinking.  This is not fair."  But small question that packs a punch would stand on it's own in terms of time requirements, and frankly 12 words on a page would look stupid, especially if some lucky kid takes 60 seconds to answer it.  Maybe I'll do some more experimentation for the 4th edition.

Here is the apple question.  I think this is suitable for ages 6 to 9 or 10.   I'll answer it below.

Describe in detail the third best way to eat an apple.

Some Background First

This line of research came from this question:  "Name the 4 arithmetic operators".

When teaching math, quantitative reasoning, or quantitative test prep to children under the age of prealgebra, it's pretty much all adding, subtracting, multiplying and dividing.  For younger kids, it's halving and doubling instead of multiplying and dividing.  Countless times a child has been totally baffled by a question, and if they just took a step back and asked 'which of the 4 operators is this unusual diagram doing or word problem asking for?' then they could eliminate 3 of them and do the work.

When I first pointed out to my own child "It's got to be one of the arithmetic operators, just try them all and see which one works" he responded "what's an arithmetic and what's an operator?"   If this were reading, I would just explain away (of course the bear has an ulterior motive, let me explain greek tragedies...) but this is thinking practice, and a parent is not allowed to answer questions.   This question came up recently and it was a fun for me not to answer it with someone else's kids.  When you can get a child to tell you what 'arithmetic' and 'operator' mean and answer the question, you've got real learning going on.  This question packs a punch for the parent.

Back To The Question
The first response I get to the apple question is total bafflement that I would ask them a question like this so out of nowhere.   I've only asked this question only to kids who have at least started working with Test Prep Math so they all know they can't get out of it and I'm not going to help.   The older ones ask me to repeat the question and the younger ones just stare at me so I repeat it anyway.

That covers the first skill which is to be baffled without tears or frustration.

The range of answers I get is breath taking.   The best answers are kids who are thinking "Well, I eat it.  That's the normal way.  Sometimes mom cuts it up."  Then they are totally out of ideas and have to invent a convoluted apple eating machine or something.  Ideally I'll watch them attempting and discarding ideas before they announce the answer.  Other kids go a completely different route and think of apple recipes.  By the way, did you ever wonder why apple sauce was invented?  You'd know the answer if you were a German in 1870 and you were staring at a bountiful apple harvest rotting in the barn.

The answer is always wrong.  (Core skill #3, get it wrong).

Sometimes the kid names the method so we'll start reading the question again in more detail.  (Core skill #2).  It says 'describe in detail'.  I'll get a correction with more detail.

But in analyzing the question, there are the words 'third' and 'best', and these require a much more complete answer.  "Are you correct?  Prove it to me." I'll ask.  Because there is no solution manual for this problem, this requires naming the other 2 (which is the most fun when the child has already forgotten what they are) and then explaining why the third one is not as good as the first 2.

There are 2 more even punchier punches behind this question.

Years from now, if you can see into the future as far as 3rd or 4th grade, you might see your child turn in a project or paper that is almost complete.  You might even see a limited effort.  This is unlikely because in 3rd or 4th grade the rubric is usually very detailed.  By middle school detailed rubrics don't help.  You'll see a range of work from 'good job' to 'way over the top extraordinary' and the kids who hit 'way over the top'  impute all of the extra demands from a limited number of words in the rubric.  That's what I'm going for.

But the most punchy punch of The Apple Question is that for the kids at a certain level of skills, it only takes this single question for them to totally get it.   Children usually respond to follow-up punchy questions by demonstrating that they won't get fooled again.

An evaluation of long term results are under way.