I decided to make today the final day of thinking problems that are not
explicitly targeted at specific outcomes from the program of studies.
I gave my first class the probability and Sudoku problems I gave my
second class
yesterday,
and their progress was much the same.
I gave my afternoon class the following problem:
A heart is constructed by attaching two white semi-circles to the
hypotenuse of an isosceles right triangle whose equal sides measure
√ 8 cm. The new figure is then mounted onto a rectangular piece of red
construction paper as shown below. (The dashed line, the side
measurement and the right angle symbol will not actually be on the
finished card.)
You are going to write your valentine a message in red ink on the
white region of the card.
Determine the total amount of area available for your special
valentine greeting.
I was expecting this to be a quick problem, however it ended up taking
about ¾ of the class. As usual, it started off very slowly with a lot of
standing around with little engagement. Eventually one student student
asked about formulas (hypotenuse, I think). I responded that they could
google any formula they needed.
Eventually, with a little prompting from me, all groups were successful
in solving this problem.
Observations / Reflection
In my first class, students persisted on unsolved problems even
after a second one was put up. I take this as a good sign of
engagement.
I realized that in my zeal to not give answers, I was reducing my
engagement with students too much. Today I engaged more, asking
questions about their solutions.
Talking with students is important for relationship building, which
I've always thought to be important, but today was a reminder that
it's still important in this style of teaching
Even when students are doing correct math and using appropriate
problem solving approaches, they have a lot of difficulty
verbalizing their approaches. When I ask them to verbalize, it gives
them practice and helps them learn how to do it (with some prompting
and coaching from me, of course).
I was especially impressed by one student who googled the Pure Math
30 diploma formula sheet and correctly used the cosine law to solve
for the hypotenuse of the triangle
Tomorrow I will start the Linear Relations unit, leveraging questions
from the MathWorks 12 textbook and workbook.
