Learning from Teaching Cases Summary

Monday - Friday, July 14 - 18, 2008

Monday
The focus for today was using group tasks in lessons. We began by discussing the article Group Worthy Tasks. After briefly analyzing a lesson on graphical interpretations, we watched and evaluated a video of the lesson being taught to a small group of high school students. We also began discussing potential projects for our group.

Discussion of article:
Group Worthy Tasks by Rachel A Lotan
(Educational Leadership, March 2003)

  • article gave good examples of differences between group & individual tasks
  • stressed key points for how to form tasks for best learning in groups
  • article was connected to Gail's powerpoint on designing lessons for group tasks and also to our groups brainstormed list of "Math Smartnesses"
  • it would be nice if article gave more specific examp[les related to math lessons
  • group tasks are a good way to help ALL students
  • teachers shouldn't try to do all of the planning individually - it works best done collaboratively with other teachers
  • planning group lessons takes considerable time and energy ont he part of the teacher
  • not all tasks are group worthy - there is still need for individual work also
  • not all group tasks need to take the full class period
  • planning for group lessons involves considering lesson goals, types of smartness needed, and assessment criteria
  • group tasks can narrow the achievement gap in classes & increase passage rates
  • making tasks "group worthy" involves tweaking existing curriculum lesson to make it more funcitonal for group

Graphical Interpretation Lesson
Video Analysis
Math Concepts Involved:

  • analyze a graph
  • understand relationshop between a story/situation and how to graph it
  • ability to explain reasoning (why... because...)

Comments on Video:

  • students did a good job justifying their choice
    • you don't start running at your full speed so it needs to come up in the beginning
    • they didn't start the clock until she reached full speed
    • it needs to drop straigh off when she hits the wall
  • would like to have seen her ask them if they could ahve rewritten the statement to
  • eliminate their confusion or draw a different graph that they though better represented situation and justify it
  • teacher did a good job of pulling out justification on why they eliminated 2 graphs right away

Teacher Stragies Observed in Video:

  • allowed everyone to take turns
  • allows students to speak out without being called on
  • didn't try to over control volume
  • teahcer movement through classroom/proximity to all students
  • kept focus on topic not on teacher
  • getting students to support one another
  • focus on "why" and "because"
  • using laser pointer as talking stick
    • allowed students who were not comfortable walking to front of room to still point out what they were explaining
    • helped keep it to one person at a time talking

Why/How Task was "Group Worthy":

  • it drew on real life experiences
  • in incorporated different types of reasoning and smartnesses
  • it was open ended

Questions/Comments About Group Work & Analyzing Videos

  • It is easier to analyze video when we have more information about leasson goals/context/etc
  • When should you move discussion along? When some kids get it? When everyone gets it? When students start losing interest/focus?
  • How do you keep from losing attention span of faster kids whiling bringing slower students to understanding?
  • How do you deal with multiple ability levels/speeds in one class?
  • It's difficult for inexperienced teachers to differentiate

Tuesday

Task Sorting Activity

Sort the activity cards in a way that each group agrees with justification and presents with a poster

Look at the posters and discuss about each otherÁs task order

4 categories suggested:
Procedure; procedure without connections; procedure with connections and doing mathematics

Tasks as they appear in books ------- Tasks as set up by teachers ------- tasks as how they are implemented by students Students Learning

Conversation Tracker ÁV shared by Kelly
Make it public in class, but record away from the groups

Nicole visits our group

The class in the video was her first successful whole class discussion with this group of students.

Questions for Nicole ÁV

Why did you decide to make the transition from first scenario 1 to scenario 2? They had experience with graphing in 8th grade but like to know what needed further development, IMP ÁK Trail? What do they know about the x and y relationship? Needed a topic that is ambiguous and listen to relationship; transit as soon as hear the relationship from a lot of people then transit to scenario 2. Teacher move - when asked Ray to call on Jonathan to support him. Ray is high status but low status academically but rely on his popularity.

Do you see status a more an issue in a small class than a big class? See it everywhere; pattern of behavior in group of 3 more than in group of 4; track class has different kind of status;
Expect every student learning from each other

Did you make connection or summarize? Not really but at the end they had talked about the relationship between x and y in class but did not talked about which one is the right or wrong answer. Convince yourself, convince someone else then convince someone who disagree with you.

Use of laser pointer ÁV control who is speaking with monitoring rather than with rules

Group work is the norms ÁV believe they can be better at their roles

If kids cannot sit together has to be behavior but not about academic

Work for Nicole that they change group once a month

Due to lot of truancy, group work helped a lot, depend on students to explain what is going on

Help teacher to interview all the students to see where they are

Watch last yearÁs video presentation ÁV focus on questioning and status and how to have video discussion (with positive questions rather than criticism, not judgmental). The goal is to talk about how to use video as a learning tool with colleagues that focus on student learning.

Our project product ÁV the goal is that we can take it back to our schools and it will make it public to everybody after a year with modification and improvement

Thursday

In today's case study we discussed chapter 1 pages 1-4 and chapter 3 on group work. Chapter 1 dealt with group work and we discussed that when teachers have working groups and they let the students work by themselves within their group, in essence, the teacher is delegating authority. Delegating authority we all agreed that it is what happens because the teacher is putting the responsibility of learning to the students by letting them struggle with each other and letting them come up with discoveries on their own. Another thing discussed is that group work should be done with very little teacher involvement and also that group work is a learned skill, that not everybody and even adults have struggles and it deal with working with groups. Also, that the teachers main job is to be the mediator by asking questions that will get the mathematical goal across and to make sure that every one is involved and participating within their groups. When groups are assigned, there will be a lot of intimidation and usually the dominance of status will take over with subtle personalities that the group members show during the first minutes of interacting with each other. One final thing that was discussed was that it was best to assigned groups randomly to avoid chaos and to avoid hurting the feelings of those students who are not very social or those who donÁt have any friends in the classroom.

Friday

Today the Mid-school and High-school groups came together to decide on a combined project. This actually happened in the second section.

During the first session we watched a video on Status Problems and had a group discussion thereafter. We each gave our opinion on what we observed. Attention was drawn to the last example when an African- American student was completely excluded from group discussions.

Solution
The role of the facilitator and team captain must always be to make sure that everyone in the group participates in discussions. Smartness must at every oppertunity be addressed to ensure full class participation. The teacher should always be alert to possible mind wandering and outsiders, a small movement of a paper could involve everyone.
Groups should be divided into sub-groups at random for best results.

Second session
During this session we firstly decided on a project. Each person gave their opinion but this was minuted.
Ideas were listed and every participant jotted their name opposite a topic. Topics without a name were eliminated.

The final product was:

  • video guidelines plus techniques - Ian
  • class Observations protocol and studdent work evaluation, protocol - Melanie, Stacey
  • ABC - book - Sergio, Katie, Lisa, Tracy
  • Status Brochure - Karen, Remy, Sandra, Raul

Everyone was happy and satisfied with the results of our discussions. Monday we will get together and continue where we left off.

Back to Journal Index

_____________________________________
PCMI@MathForum Home || IAS/PCMI Home
_____________________________________

© 2001 - 2014 Park City Mathematics Institute
IAS/Park City Mathematics Institute is an outreach program of the Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540
Send questions or comments to: Suzanne Alejandre and Jim King

With program support provided by Math for America

This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.