Monday, September 1, 2014

Tackling Group Work - Part 2

Types of Task

I believe that not all activities are suited to the type of group work that I described in my previous entry on group work.  For example, doing problems to practice a particular procedure does not lend itself to collaborative group work. While students benefit from asking each other for help, this type of discussion is usually asymmetric—a student who understands the procedure is helping a student who does not yet understand a procedure. The group work that I particularly want to foster in my classroom is more symmetric and involves all students sharing possible ideas and then together trying at least one of them out.

In Strength in Numbers (in case you can’t tell, I am pretty obsessed with this book), Horn suggests the following about “groupworthy tasks”
  • task focuses on central mathematical concepts or ideas
  • task require some interpretation
  • task provides multiple ways of being competent in problem solving
  • task is done in a group, which bolsters students’ interdependence
  • task is designed in a way that provides individual and group accountability
  • during collaborative learning time, only group questions
  • have clear evaluation criteria
These criteria overlap with the QUASAR description of “doing mathematics.” These tasks...
  • require complex and non-algorithmic thinking
  • explore the nature of math concepts, processes, and/or relationships
  • require analysis of constraints and connections
  • may involve some level anxiety due to unpredictability

I would like to commit to doing this type of task at least once a week. Some weeks this task will be intimately related to the content we are focusing on. Some weeks it will not be related at all, but will build other mathematical problem-solving skills (ex: diagramming, working backwards, developing a strategy when there are no hints for what the strategy should be).

Problem-Solving Days: Groupworthy Tasks

In general, I imagine that we will usually do some sort of problem launch for the whole class.  Students would then have a couple of minutes of PTT to start the problem on their own. This should not be enough time for any student to solve the problem or feel like they’ve solved the problem. Instead, it would be enough time to start thinking about a strategy for solving the problem. Once PTT is up, then the group work begins.

Here’s how I envision students starting a problem together after private think time:
  • each person explains their ideas(s) so far
  • each person makes sense of partner’s idea: what did they do and why did they do it
  • partners compare their ideas: similarities and differences      
  • partners evaluate their own and each other’s ideas
  • partners choose some next steps to try together

As they continue to work together, I imagine that there is a lot of exploratory talk. Here is a description that I think is important, again from The Value of Exploratory Talk.
“In exploratory talk, listeners gain the benefit of hearing a speaker’s tentative thoughts. Feedback from listeners may require a speaker to elaborate their point of view, to perhaps cast it in a clearer, more persuasive form—or even to change their mind. Talk of an exploratory kind is thus not only useful for an individual to sort out their thoughts, it can also help two or more people to solve problems because they are sharing ideas (some of which may only be partly developed) in a genuinely collaborative interaction.” (66)
Students may find that they would again take PTT at points during the work time. But they would continue to check back in with each other and follow the steps from above.

Supporting Students in Successful Groupwork

In looking and thinking about CI group work roles (see Strength in Numbers and here), two things were important to me. First that everyone pulls their weight, and second that responsibilities were not artificially divided when shared accountability would be more appropriate. Therefore, pulling from the different CI roles, I came up with the following for partners:

Partner Work Norms and Responsibilities
- read instructions aloud
- get the work off to a fast start
- watch progress and time
Resource Manager:
- call the teacher over if there is a question
- get and return needed materials
Both students will enforce partner work norms:
- Everyone gets a turn to talk and everyone listens
- Explain your reasons so that everyone understands
- Respectfully challenge and build on each other’s ideas
- Make decisions together after everyone has shared
- Everyone contributes to documenting and/or presenting

I also wanted to offer students some guidance in how to talk together once they have taken some PTT.
Partner Work Protocol
Sentence Stems
1. Each person explains their idea(s) so far
“What were you thinking?”
“What did you do?” “I started by…”
“I tried… because…”
2. Each person makes sense of partner’s idea: what did they do and why did they do it
“Can you explain that to me in another way?”
“What did you mean when you said…?”
 “Why did you…?”
 “How do you know…?”
“I don’t understand…”
“I have a question about…”
3. Partners compare their ideas: similarities and differences
“My strategy is like yours because…”
“This part is different because…”
“Our ideas connect if…”
4. Partners evaluate their own and each other’s ideas
“I agree/disagree with… because…”
“This makes sense/does not make sense because…”
“I got a different answer because…”
5. Partners choose some next steps to try together

“What are you thinking now?”
“I think…. is a good start because…”
“I think we should try… together because…”

I will also have various class structures/teaching moves to support students in working collaboratively while having individual accountability.

Most of these ideas are from Strength in Numbers. Here are explanations of ones that I had not heard of before:
Task card: Students share the problem/directions would also have evaluation criteria, students do not write on it or turn it in
Participation quizzes: Teacher calls attention to particular groupwork norm(s) and then publically tracks all groups on the norm.
Check points: Before the group can continue, someone randomly selected by teacher answers a few key questions.
Group quiz: Group has 4 questions to answer and everyone records on their own paper. Teacher chooses one randomly to grade and all group members earn that grade.
Shuffle quizzes: Teacher takes every group member’s paper, shuffles, and then chooses one. That person has to explain for the group.

Other Days: Non-groupworthy Tasks

When we’re not doing “groupworthy tasks,” my students will still sit in partners. They will be allowed/encouraged to work with each other, but it will be less structured than groupworthy task days. The following will always be my expectations and will be taped to all sets of desks.

Table Work Norms
Help! I don’t know what to do!
Before asking a teacher…
- look back at your notes (ex: first page of packet(s), similar problems, reference sheets)
- ask someone at  your table
- try something even if you’re not sure it will work
When you ask a teacher…
- all people at your table must be able to say the question
- you should have evidence of something you’ve tried
- all people at the table must be involved in conversation with the teacher
- you have the right to ask anybody at your table for help
- you have a duty to give help to anybody who asks
- helping is not the same as telling
- stay focused on your table’s work

 The most important thing to me in the above is that there is a protocol for asking me questions that makes the students think and use each other as resources first. The norms that make this possible are that everyone has the right to ask for help and a duty to give help when asked.

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