Aug 20, 2010

Critical Conversations/Problem Solving

I've just finished a very intense week of learning in mathematics and teaching. I first attended a session called What's a Problem...That's the Problem. This was nothing new to me because I've taken a problem solving approach to teaching math for quite some time. My students are engaged and constantly expected to solve problems. I think it's important to remember, and it was expressed several times, that problem solving doesn't just have to mean students solve word problems. Sometimes, not having a pencil can become a huge problem in grade two. I would imagine in any grade. Here are some examples of very simple problems we worked on:

Problem #1. 
Tell me about 1. Students write what they know about 1. To create more of a problem ask them to build their representations using what ever they want and have others guess what they think their 1 represents.

Problem #2.
Find and write two numbers with a difference of two. Once students have selected their two numbers, have them say them to you and you write them on the board or have them. Once a list has been generated, get the students to sort or order the numbers and see what they come up with. Discussions around why and their reasoning behind their choices are amazing.

A problem must be obtainable for all to complete. If it's too difficult it can shut some students down but if it's too easy then it's not a problem. Finding the balance is the tricky part.

Critical Conversations were on Thursday and Friday. This is where the real learning took place. It was so refreshing to meet with like minded teachers who've been on the same journey, as myself,  with my mentor, Geri Lorway. She is an amazing woman who works tirelessly to improve teachers understanding of their craft, not just mathematics. Her specialty is math but she is really trying to get teachers to understand the curriculum and what it means to engage students and listen to them.

The conversations focused on the Alberta Math Curriculum but it was about so much more. We spoke about assessment at great length. The tasks or activities you create need to provoke curiosity in students. They need to allow students to take risks and persevere. They must also allow students to work together in a group and think.  When tasks or activities have all of these learning skills, then it's important to build rubrics with your students to assess them on these learning skills. These are the skills that we really value in students. We want them to be curious, to take risks and to work together. We say it all the time. Therefore, we should be helping students obtain such skills.  I'm sure there are more that could be added to the list but these 3 or 4 were what our grade two's focused on.

What I learned about math and assessments:

- it takes at least 6 tasks or activities before you can assess students on the learning skills of curiosity, risk-taking, thinking and group work.
- rubrics should be created with students - we all know that
- they should be short - students and teachers will not use them if they are too long
- rubric should help guide students in their learning journey, not hinder them
- they should contain no numbers but instead think about having an arrow at the top with a mark on the arrow. This allows students to move along the continium of the rubric at which ever place they feel their learning is.
- a rubric should only have three columns not the traditional four - what's the difference between mostly and somewhat?
- start by building a t-chart with students eg. not curious and curious - what do each of these look like, sound like, feel like
- middle column should be wider than the other two - that way the student and/or teacher can move the mark/line along the arrow, based on how they feel about their performance or a teachers observation
- we should not be ranking students, that's why we don't need the numbers on the rubrics

I found the discussions with like minded colleagues to be so reflective and refreshing. It was amazing to be in an environment with teachers who "got it" and who were "passionate" about  teaching kids. I look forward to keeping in touch with the other grade two teachers and see how developing rubrics with students that reflect learning skills of curiosity, risk-taking and group work have worked in their classrooms the first month of school.

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