September 29, 2011

We're making this collaborative

Because two minds are better than one. Especially two inspired ones with uniquely creative ideas on how to revolutionize education 100 kids at a time... Introducing Amy Park!


Amy Park

Wow, we have had two days of powerful math happening in our classes. As per our last discussion, we gave each student a 100s chart. We began by asking students to colour in all of the multiples of one. To our surprise…most kids had no idea what we were talking about. In fact, many confused looks were exchanged among the students - and us, as we realized that few kids knew where to start. Then the magic began…students started making conjectures, they began supporting and refuting others' conjectures, they were talking about abstract concepts and began developing an in-depth understanding of the concept being discussed. The light bulbs were going off. Misconceptions were discussed and partial truths were reworded to become complete truths. We discovered new definitions and new ways of thinking. It was powerful. We captured a great deal on video and we took several photos.

The discussion today was based on the question "what is a multiple of 2?". The first picture is the kids initial ideas, the second picture is their refined/reworded conjectures. The last 2 pictures are of students individual journals, where we asked them to define "even" and "odd".  This is evidence of powerful mathematical learning happening in grade 4 :) It was powerful for teachers, admin (who popped by) and for our students. Although it seems rudimentary, we believe we are setting the foundation for solid mathematical reasoning, establishing conjectures, working through the conjectures to find truths, and discovering that their is not just one way of "doing" math.

September 26, 2011

Grade 4 Math turns abstract...

Deirdre Bailey

I spent Sunday trying to combine the best of Mighton's mathematical understanding with Fosnot's teaching style in order to develop a way of reinforcing times tables in way that would be engaging, meaningful and memorable. I re-wrote the whole lesson about 8 times. I started with the idea of trying to teach number patterns but a conversation with my husband reinforced that these should arise as personal strategies. We all have different ways thinking through multiples of nine in our head...

I learned more about math yesterday than I think I might have in all of Elementary. It was fascinating. I was particularly intrigued by a series of "Rightbrainmath" videos by Mr. Numbers which visually demonstrated the patterns which result from multiples. I felt pretty excited about Math Conference today. We started by handing out number sheets and asking the kids to color in multiples of one. It became apparent immediately that none knew where to start, so rather than instruct we introduced the idea of "mathematical conjectures", ideas about what something might mean which might prove to be incorrect, partially true or completely correct. The kids volunteered conjectures on definitions for multiples of one. Initially, we had suggestions which included "any number with a one in it" and "every second number from one to nine". Eventually, we visually demonstrated that a multiple of one is any original number that can be split into groups of one and then asked the kids to support or refute the conjectures on the board based on our explanation. Partial agreements about some conjectures lead to conversation about whole numbers. Could one student and one half of a second student be split into groups of one? Why not?

The kids, on their own, debated whether zero and negative numbers should be included in a definition of multiples of one. We looked at whether two non-identical conjectures could mean the same thing and both be completely correct. We modified conjectures to make them true. 

I thought we'd breeze through multiples of one. We'd planned on coloring in multiples of one, then multiples of two, then moving on to defining odds and evens before the end of class. We didn't even get past multiples of one. There is so much material that is so often neglected in "simple" math. What a waste to present kids with a definition and miss the magic of abstract mathematical discussion and debate among nine year olds. 

How will we know what they understand, how will they know that they do, unless we allow them to debate, to defend and to support their ideas?

We can't. They won't.

I have three things to think about for next time:

  • How can I guide a discussion without directing it?
  • How do I end a conversation without eliminating further possibilities for exploration within the topic?
  • How do I know whether everyone "gets" the conversation? How do I continue to provide opportunity for everyone to contribute?

September 6, 2011

Second verse, same as the first...??

Not even remotely.

Last year caught up with me. I muddled through, effected some changes, kept my head above water but failed to document and the absence of valid reflection has left me sincerely sorry to myself. I feel robbed of the learning process. The U of C MT program would be so proud to see that 2 years too late I can finally acknowledge that there is value in metacognition.

The brief overview:  New teaching position this year - Grade 4 Math/Sci with a homeroom. Phenomenal, innovative and decorated team teaching partner, somewhat traditional and less enthusiastic pod partner. So many more lessons to be learned, and this time, to be documented.

I'm not sure how this will look in the long run, whether the reflective process should be general and vague or focused, lesson-specific, it might be moments, it might be units, revelations.

  • Construct meaningful, valuable, innovative lessons
  • Manage the classroom, papers, information, students diverse learning needs
  • Master the art of dealing with people
  • Reflect daily on what went well, what I achieve, what I will make sure to do forever and must remember at all costs
  • Reflect daily on what I would do differently in the future
Today was a PD day. It was productive, SO busy, lots of good ideas but they don't feel totally organized. I have written everything down but it is not all in one place which worries me a little. My biggest effort today was to start every reply with positivity (yes, definitely, lots of nodding). I think it went great distances in helping our team to build cohesiveness. We have big ideas. I hope we can make them feasible in the classroom. I also hope I don't get so excited that our my explanations are confusing or that tasks are not clear. In the last few weeks I have learned that children cannot see inside my brain and that my explanations, when I am excited, can become fairly muddled.

Tomorrow it is my goal to slow down. To allow them time for transitions, to settle, to ask questions at the start or end of each period and to make sure that I always wait until I have all of their attention to speak.

It is also my goal to consistently give indication of the amazing things I believe them to be capable of. I'll keep you "posted". HA!