Forced Awareness: Speeding things Up

It isn’t as violent as it sounds.  I thought it would be important to provide an infographic to make it clear what forcing awareness is and isn’t per Dave Hewitt’s article.

This technique interests me most, and I realize it will take some skill.  The objective is to create a series of questions that would lead the student to awareness.  The questions needed begin as very straightforward and I would say familiar.   As an educator, you have to really know your students, and you also have to know how to choose questions that will advance a student’s learning without providing any explanation to the student. You have to contemplate how does one come to a particular understanding, and what sorts of questions could cultivate awareness.

I took time out this past weekend to prepare myself with the line of questioning that Hewitt prepared as an example in his article.  I was fairly confident that the kids could easily answer the questions in the beginning, and if Hewitt was right with his questioning, I could bring them to the same arrival that the line of questioning is supposed to bring the kids.

I tested the idea out Sunday evening at dinner.  I realized it would be better suited for my children if I provided a picture for them in my line of questioning so I modified the question to include apples.   I began with the questioning:

How many halves are there in one apple? -2

How many quarters are there in one apple? -4

How many tenths are there in one apple? -10

How many thirds are there in one apple? -3

This questioning continued as outlined in Hewitt’s article until I felt certain that they understood the rhythmic pattern.  The kids were responding with ease.  There was nothing foreign to them.  They have been playing with fractions for a while between Saxon and a couple of iPad apps. Hewitt then leads the questioning to words instead of numbers.

How many flinkerty flooths are there in one apple? 

My kids laughed at this question and I was prepared for them to say they didn’t know, but to my surprise, they answered Flinkerty flooths. Ahh, they were aware of the pattern. So I continued.

How many nths are there in one apple? -n

So here it seemed we had arrived at the first generalization.  Josiah explained it as “how you divided the apple told you how many parts there were of the apple.”  It seemed obvious and straightforward so I moved forward to the next series of questions.

How many halves are in one apple? –“Duh, we did this already. 2”

“Okay kids, I am just following the script and there is a reason.  We are going somewhere.” -Me

How many halves are in two apples? -4

How many halves are in three apples? -6

How many halves are in four apples? -8

How many halves are in six apples? -12

How many halves are in ten apples? -20

Ah, I skipped some but it didn’t phase them.  They had caught onto the pattern.

How many halves are in nine hundred fifty two? -double nine hundred fifty two

I thought that they would have tried to do the math in their head, but instead they provided the equation instead.  This was certainly ideal.

How many halves are there in x?  x times 2

Now I knew they were aware enough to move on to the next line of questioning.  I decided at that point to provide the arbitrary equation that they just explained to me.

 x divided by ½ = x times 2

I decided that this was sufficient for the evening, and I would continue the line of questioning during our math play time the next day.

As I sit back and assess what just happen, I am amazed at how through the line of questioning, the kids were able to conclude for themselves how to easily find the answer.  Without teaching them an algorithm, they were aware in some fashion that the denominator influenced their answer.  To be honest, I wasn’t sure where the questions were leading to, but now I am beginning to see.

The kids are going to discover for themselves why they multiply the reciprocal to get the answer when dividing fractions. Without giving them any received knowledge, they would become aware of it themselves.

Now we have taken quite a break from Saxon, and Josiah has learned to divide fractions.  However, I know that he never understood why he used the reciprocal to find the answer, and now this line of questioning is about to draw him to that very conclusion.

I would say that I quite enjoyed this line of questioning, and it felt a lot like what Arthur Powell (the lead teacher) was doing during the Gattegno Conference.  In fact, I pretty sure it is.  He was always asking questions and never providing the answers, but he always managed to help individuals find the answers by asking more questions.

Now I am pondering how can I come up with my own.  I will share where the rest of the questions from Hewitt’s article lead us on another post, so stay tuned.  I am a little nervous because it feels like it gets tricky, but only the experience will tell.

Can you come up with a line of questioning?  Where would you take this? Comment below.  I would love to hear, and if you decide to make a post on your own blog on this technique, please put a link in the comments section.  We would all love to see!