Challenging students to work smart
I have been reading Dr Carol Dwecks’ book Mindset: the new psychology of success in
which she talks about fixed mindsets
and growth mindsets and the effects that these can have on people as learners.
It resonates with me on many levels but particularly in regard to students who
believe that they have innate talent, are the best at maths in the class and do
not stop to think before applying a long-winded strategy to a problem. They do
not stop to think:
“Could I use a save-brain-space
strategy that would be quicker and safer?”
They simply used a tried and tested method without
stretching themselves. This was brought home to me in a Year 4 classroom this week
when I posed a problem that can be solved in many ways and which easily
identifies the students who stop and think from those who apply an overused and
familiar strategy. Here is the version I used, but I’m
sure you could adapt it to suit your class.
Note: There is
usually a reason for a fundraiser so just adapt this a bit. Also, the amounts
can be changed to suit a range of learners but ensure that the numbers allow
for efficient strategies.
The students were asked to think smart and to record their
thinking. In this particular Year 4 class there were five students who came and
told me that the problem was too easy for them because they were the best in
the class at maths and had special work. I told them not to worry that when the
first part was finished I had two stings in the tail for them. Off they went
quite happily to do the first part in anticipation of the stings.
This is when the
fixed mindset became evident. They each sat and without conferring quickly made
a series of ‘sums’ that used methods that they were familiar with.
And then of course they had a long vertical addition to
finish it off.
Now they demanded where was the sting? I looked at their
work and said
“I am not overly impressed with
your strategies!”
One student began to protest and then stopped and demanded
to know why.
I told them that being a mathematician entailed always
looking for the most reliable and efficient strategy possible.
“Your strategy is not
particularly reliable, not very efficient and certainly not the elegant method
of solution I would expect of a good mathematician.”
I asked them to rethink, to work together and find a more
efficient strategy that saved brain space and could easily be carried out
without pencil and paper.
At first both the students and the teacher were shocked by the
feedback but it wasn’t long before the students were deeply engaged in a
conversation about ‘what she meant’ and began to think in more interesting
ways. It took nearly 5 minutes before they decided to count the dozens, also
adding the ¼ and the ¾ together and arriving at 20 dozen. It is not a big step
from there to find that 10 dozen is 120 and doubling 120 gives 20 dozen, then
adding 6 for the remaining half dozen.
They of course got to work on both stings in the tail.
Sting 1
The local baker said that
he would give them cake trays so that they could sell the cakes in trays of 6.
How many trays were
needed?
Needless to say
traditional division came to the rescue. But again why divide when you could
apply a more efficient strategy without the aid of pencil and paper algorithms.
Think about it, the students had also identified that 20 dozen plus a half
dozen was the answer to the first part so why not us the relationship of double
6 makes a dozen and multiply 20 dozen is 40 by two. Again I challenged the
students’ thinking and
they stopped and thought and spotted the easier
strategy.
Sting 2
They sold each tray for
$3.45. How much money did they raise?
The lesson ended too soon but not before I heard the group
say ‘She must have a good strategy for working out how much money was made.
Let’s see if we can find it.’
It is interesting to note that there was one student who was
not of a fixed mindset. In fact he knew that he needed to think hard to solve
the problem and actually tried to ‘save brain space’ .He quickly spotted that
it would be easier to count the dozens and work from there. Students really
like the term ‘save brain space’. Once introduced to it, they begin to look for
a wider range of strategies to see if they can actually find a method of
solution that is easier to carry out, more reliable in finding the correct
result and which can be seen to ‘save brain space’.
So the point of this is
let’s stop praising and rewarding raw talent and start prompting for real
thinking and response to challenge. Let’s insist on a growth mindset not a fixed
mindset. In the end I think we will have more resilient and more self-regulating
learners who actually enjoy maths.
