Msjwright2's List: Math: Classroom Culture & Mathematical Practices

• 75% of 8th graders presented with the nonsensical problem, “There are 125 sheep and 5 dogs in the flock. How old is the shepherd?” answered with a number.
• many students admitted they didn’t understand the problem, and still gave a numeric answer anyway.

• problematic beliefs our students have about doing math:

   
   
  1. All math problems have to be answered with numbers.
   
  2. All math problems can be answered.
   
  3. It’s normal for math not to make sense.
• force students to slow down and make sense, first.
• Notice and Wonder
• Brian Stockus wrote a great blog called “Numberless Word Problems,”
• “Fermi questions'” (66). Fermi Questions are mathematical questions where answers seem impossible, but we can get close by making some assumptions and then approximating

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• Talking Points are simply a list of thoughts. They are statements which can be factually accurate, contentious, or downright wrong.
• The activity stimulates speaking, listening, thinking, and learning. It offers ways in to thinking more deeply about the subject under discussion. It gives everyone a chance to say what is on their mind, so that others can decide whether they agree or disagree.

• skill and drill warm-up.  You know the process, you give the kids the five questions, they pretend to do them, you go over the answers, they write the answers down and pretend they got them all correct.  Great learning going on there right?
• Each day we do Estimation 180.
• Besides just the reasoning and number sense provided by the activity I love the focus that we have been able to place on finding the percent of error.
• Math Talk Monday
• Counting Circle Tuesday
• Would You Rather Wednesday
• Tough Pattern Thursday
• Find the Flub Friday
• I love the focus this has allowed us to place on mathematical reasoning and processing and not skill and drill. 
• I can see the effort

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• system for math free choice developed by Justin Lanier (@j_lanier) and Paul Salomon (@lostinrecursion)
• list of potential tasks
• every one of them sought to challenge themselves. I also noticed that the students were motivated by their peers.

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• why students might be reluctant to participate

• two concepts that I found to help teachers address these challenges and successfully establish rich classroom discourse with their students.

   

  The first one is classroom norms. The second is addressing social status
• ways of developing norms that help alleviate status problems

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• group work norms/ground rules from four sources
• Strength in Numbers
• Thinking Together (University of Cambridge)
• The Value of Exploratory Talk
• Shell Centre PD

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• prior to engaging students with a problem (which could be a scenario, a graph, an image, a video, etc.), first ask what they notice about it, and faithfully record everything they say
• Math Forum's notice-and-wonder
• Then, ask what they wonder, and faithfully record every question they ask
• lowers the barrier to entry
• directs students' attention to the things that are mathematically important
• when is it appropriate to use a notice-and-wonder, and when is it not?

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• participation in their class discussions
• Asking students for their "ideas" or "hypotheses" or "predictions" or to "share their thinking" rather than asking "what do you think the answer is" or "what did you get" or "who knows how to do this?" minimizes the risk
• Asking direct questions, rather than "who can tell me" or "does anyone want to share" or "someone tell us" or "can anybody explain" reduces the temptation for students opt out
• Providing clear instructions for how others should engage when their peers are talking, beyond simply "tracking" or "listening" or "following along,"

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