Post on 27-Mar-2015
transcript
SVMI Network Meeting
October 31, 2012
A Look at Module 5 and Collaborative
Tasks
Network Meeting, October 31, 2012Silicon Valley Mathematics Initiative
www.svmimac.org
Collaboration
Welcome
Please sign in, help yourselves to refreshments,
find a seat, and introduce yourself to your tablemates.
Agenda
Welcome
Announcements, Norms and Introductions
Collaborative Task: Build Its
An in depth look at a different MAP Module
Doing Collaborative Mathematics: A Problem Solving Task
Announcements
Norms
The Social Culture of our Network
Seek to Understand
Respectfully Speak your Truth
Monitor your Airtime
Getting Acquainted or Re-Acquainted
Goals and Outcomes
Goals and Outcomes
Exploring Social Norms and Socio/Mathematical Norms
Enhance participants’ ability to use high-quality mathematics problem solving tasks and professional development modules to support teachers in their classrooms
Strengthen participants’ content and pedagogical content knowledge and leadership abilities
Deepen participants’ understanding of the Common Core State Standards in Mathematics and the Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the
reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated
reasoning.
Mathematical Practice
Information
Jordan School District, Utah There are different “posters”
for different grade level spans Google Jordan School District
posters One website for CCSSMP: LiveBinderwww.livebinders.co
m/play/play?id=99717
Lenses to Consider During Professional Development
Sessions
Learner Lens Coach/Admin Lens
Collaborative Activity
Collaborative Task
Build Its
Get it Together Collaborative Tasks
Developed by EQUALS Math is accessible to every student Changing the standing of teachers in the classroom
Opportunity for each student to learn at his/her maximum potential
Encourage students to work cooperatively Promote use of mathematical language and
discourse Encourage students to persist Meaningful resource to use if beginning group
work or good problems to use for experienced group workers
Behavioral Norms
Follow the directions Everybody is to participate Listen to what others say Help others without telling them what to
do or by giving answers Ask others for their opinions Ask for help when you need it Try to give mathematical reasons for
what you say
Collaborative Task Rules
Pass out the clue cards. You will be working in groups of four.
When you get your clue, you may only look at your own clue. You may not look at anyone else’s.
You may share your clue by telling others what is on it, but you may not show it to anyone else.
Then, everyone reads their clue out loud with no comments or questions.
Discourse follows: paper/pencil may NOT be used.
Collaborative Task Discussion
When finished with each Build It [there are 5 of them ], discuss in your group…
When did we know that we were right?
Could any clue be eliminated? Why or Why not?
Which clue, if any, seemed most important?
Record each of your solutions on the isometric dot paper provided to you.
Collaborative Task
Build Its
Collaborative Task Debrief
Share your findings, drawings, and thinking so far with another group[s].
Are you in agreement? If so, did you take a common path?
Are you in disagreement? If so, can you reach agreement?
Whole group popcorn share: What were your “take aways” from this experience?
MAP Mathematics Assessment
Project
Professional Development Module #5
Students Working Collaboratively
Research on Collaborative Work
Research has shown that cooperative small group work has positive effects on learning
However, productivity is dependent on the existence of shared goals for the group and individual accountability for the attainment of these goals.
Cooperative small group work has a positive effect on social skills and self-esteem.
Activity A
Experiencing a Discussion We begin with another experience of
collaborative work on mathematics. First, on your own, write a response to your
small group’s agreed upon problem from Handout #1.
With your small table group, compare your responses and try to refine your answers until you feel you have reached consensus.
You may not totally complete the problem or come to consensus. What is important is that you have had time to discuss and explore ideas together.
Activity A
Reflecting upon Activity AConsider these questions:
Did you find it helpful to have a chance to think about the question yourself before it was discussed in your group?
Did someone “take over”? Was someone a “passenger”?
Did you build on each others’ ideas to construct chains of coherent reasoning?
Did you feel able to share your ideas without fear of embarrassment of being wrong? Did anyone feel uncomfortable or threatened? If so, why?
Activity A
Debrief of Activity A
Jot down your thoughts to the following question: What are the implications of this activity in a classroom?
Take a few minutes to share your thoughts with your table group.
Whole group sharing using Round Robin Protocol – one sharing per table group.
Activity B
Analyzing a Discussion There is a clear difference between working in
a group and working as a group. Often times students work independently
though seated with others. Often times students disagree with group
members and make individual decisions. Often times students do listen to group
members but build uncritically on what each other has said.
For true collaborative work, students need to have critical and constructive exchanges where challenges are justified and alternative ideas are offered.
Activity B
Analyzing a DiscussionFollow these steps:
Role play the three transcripts on Handout #2.
Talk about how these discussion transcripts either help or hinder learning for students.
Look at the characteristics of helpful and unhelpful talk shown in Handout #3. Would you describe the discussion transcripts as Disputational, Cumulative or Exploratory Talk? Discuss with your table group.
Think about what strategies could be used to help students discuss more profitably. Share and discuss with your table group.
Activity B Analyzing a Discussion
Opportunity for table groups to share with the whole group:
Would you describe the role play discussions as Disputational, Cumulative or Exploratory? Why?
What strategies did your table group talk about to help students discuss more profitably?
Activity C
Recognizing the Concerns of Teachers
Handout #4
Common Obstacles to Classroom Discussion that need to be taken seriously and
addressed.
Which of these have you heard from teachers?
In pairs, choose one of these comments and imagine that it was expressed by a teacher in your district/school. Take a few minutes to prepare a response.
Using Round Robin Protocol, share your choice together with your response to the whole group.
Things to Remember It is important to recognize that group
work may not always be appropriate.
When the purpose of a lesson is to develop fluency in a particular skill, then individual practice may be more suitable.
Collaborative group work is necessary when the purpose is to develop conceptual understanding or strategies for solving more challenging problems.
Students need to share alternative views, interpretations, or approaches.
Activity D Creating & Establishing ‘Ground
Rules’ As we have seen, students do not always discuss in helpful ways.
Some are reluctant to talk and others take over and dominate. Therefore, there is a need to be taught how to discuss. Establishing ground rules in appropriate language to give explicit guidance on how to talk together profitably is helpful. Work individually; pair/share; popcorn share out with whole group.
Imagine that you are starting a new class or working with a teacher on how to begin to have students work collaboratively. What classroom ‘rules’ would you seek to establish?
Compare your ideas with those offered in Handout #5.
How would you encourage a class of students to develop such a list?
How would you encourage students to follow such a list?
Activity E Managing Collaborative
DiscussionA well-organized discussion lesson often has a number of
phases: individual think time, small group discussion and whole group discussion. How would you, as the teacher, manage a discussion lesson?
What are the purposes of ‘think time’? What is the teacher’s role?
What are the purposes of the small group discussion? What is the teacher’s role?
What are the purposes of the final whole group discussion? What is the teacher’s role?
Compare your thoughts with those given on Handouts 6 & 7
Solo time; pair/share; popcorn sharing with whole group.
Why Activity E is Important for Teachers
Many teachers are used to transmission methods in the classroom and thus, are unsure of their role during discussion lessons.
Some teachers will quickly intervene and try to ‘ease the path’ by giving strong hints and explanations.
Other teachers withdraw and offer little help, as though they now expect students to discover everything by themselves.
The most effective teachers take neither of these positions; they challenge students to think deeply, explain, and justify.
Activity F Observe and Analyze a Discussion Lesson
There is a video clip on the MAP website with this problem, Estimate how many teachers there are in the UK. The UK
has a population of 60 million people. Viewers are asked to consider the following issues:
How does the teacher introduce the problem?
Which ‘ground rules’ does she emphasize?
What different approaches are being used by students?
How does the teacher help students to discuss productively?
Can you characterize the types of talk students are using?
Activity G
Plan a lesson, teach it and reflect on the outcomes.
Select a problem to do with a class. Use the prompts on Handout #5, Planning for
Effective Questioning
If possible, audio record some whole class questioning
After the lesson, discuss the following issues: Which questions appeared to promote the most
thoughtful and reasoned responses from students? Why was this?
Which questions didn’t work well? Why was this?
Which of the 5 principles for effective questioning did you use?
What will you do differently next time?
Break
A Different Collaborative Activity
CONCEPT LESSONS
PROBLEM SOLVING LESSONS
LET’S DO SOME MATHEMATICS
Estimating: Counting Trees
Pre-Assessment Task: Solo
Pre-Assessment Task
Collaborative Activity: Improving the Solution
Sharing Work and Learning From Each Other
Collaborative Work: Joint Solution
1. Share your method with your partner(s) and your ideas for improving your individual solution.
2. Together in your group, agree on the best method for completing the problem.
3. Produce a poster, showing a joint solution to the problem.
4. Make sure that everyone in the group can explain the reasons for your chosen method, and describe any assumptions you have made.
P-62
Collaborative Analysis of Sample Responses
Analyzing Sample Responses to Discuss
P-64
1. Does the approach make mathematical sense?
2. What assumptions has the student made?
3. How could the solution be improved?
4. What questions could you ask the student, to help you understand their work?
Sample Responses to Discuss: Laura
P-65
Sample Responses to Discuss: Wayne
P-66
Sample Responses to Discuss: Amber
P-67
Whole Class Discussion
Whole Class Discussion
Ask students to comment on the strengths and weaknesses of each of the student samples.
Ask which groups used a similar method to Laura, Wayne, or Amber.
What was the same/different about your work compared to the student sample?
In what ways did analyzing the responses help you to identify errors in your own work?
Individual Reflection: How Did You Work?
Lunch