I thought
Saturday’s class went very well. My greatest challenge is trying to move your
thinking away from doing calculations to representing problem situations using
models. How many times did you want to get the answer then try to fit the
diagram to the computations? Think about the last problem we worked on. The
amount of cards was 4/3 and we added 48 cards to one child which is a nice even
number so we can divide that nicely into 2, 4, 6, 8, 12, 16, or 24 smaller
sections…the drawing is easy. But!!!! The other child collected 13 so the model
has to show 13 not 12 so will be a different length than the 12 most of you
were playing with…and I admire those who persevered with the model. But, how
many of you sat back and said the answer is 11 but I don’t know how to show it?
Now fast forward to your own students. How many times do you show them
something that makes sense to you but your students say “I don’t get it?” I
would hazard to say, “Very often!” I know that phrase is frustrating to hear
but most often our students do not know how to articulate what they don’t get.
They do know that what you are saying makes no sense to them.
Now, back
to the model for the problem you are working on. How can you show one child
adds 13 cards to what he already has even if the other child is adding a
multiple of 12?
The whole
purpose behind both the mathematical practices and the new content standards is
to engage students in sense-making, reasoning, and modeling mathematics. This
translates into our, every one of us who teaches mathematics, to change how we
approach the mathematics, and to recognize how uncomfortable it is going to be
for us on this journey to help a generation of adults who embrace mathematics
rather than dreading it or worse avoiding it at all costs. So, I will be
pushing you past your comfort zone or as Vygotsky says, The Zone of
Proximal Development, to enable you to
visualize and model some of the mathematics that we all can do algebraically or
arithmetically.
Think about
the next few months as a journey of learning and understanding.
Anne
4/1/14
ReplyDeleteI had more diificulty with the homework assignment then I thought I would come across. I did fine with the first three graph problems but the ratio problems got me. Even though they seem like the same style of question, I can only assume that there is less given information. I do not want to solve anymore problems using guess and check which makes the assignments that more harder. I am trying many learned strategies from this class, but I'm not seeing any daylight. I also tried to solve an easier problem but still I'm not getting the answers I seek. I feel as though I can solve them but that I am simply using the wrong approach. (Which is normally the case in situations like these)