Delaware Math Coalition New Normal Cohort 2 – How do I get my groups to work? 13 jan 2015

Delaware Math CoalitionNew Normal

Cohort 2 – How do I get my groups to work?

13 jan 2015

Agenda Summarize content and share reactions to Strength

in Numbers

Share out data collected during & experiences with your Team-based homework – implement a lesson

More transformational geometry

Strategy to teach talking & listening - Talking Points

lunch – then split into grade-based groups

More mathematics

Next round: team-based lesson planning

Homework & Exit reflection

Cohort 2 – Workshop Goals

Utilize rich tasks in order to promote more robust problem solving endeavors;

Support students in productively grappling with important mathematics;

Promote a classroom climate where students build upon each other’s ideas and respectfully question and debate one another;

Position students in ways that support richer, more mathematically productive small-group and whole-class discussions;

Increase students’ capacity to more routinely engage in the Standards for Mathematical Practice; and

Successfully promote generalization, justification and proof particularly in relation to the study of geometric thinking.

Goals – short version

What can I do to draw out more focused and more purposeful interactions from more of my students?

How can I further the geometric thinking and mathematical reasoning of more of my students?

What we Know1. Children (re-)invent (mathematical)

knowledge

2. Students learn mathematics by thinking (hard).

3. Students learn through interaction.

4. Tracking does little if anything to improve the achievement of high scoring students, and has demonstrably reduced achievement of other students.

Strength in Numbers

Discuss Horn’s chs. 1-4Current (Expert) Group: Summarize assigned

chapter, preparing to report to other colleagues

Mixed Groups: report on own chapter & prepare for whole class

Whole Group comments


chapter, preparing to report to other colleaguesDiscuss / react to chapterCreate a summary of chapter contentNote particular passages that led to a-ha’s,

reactions or questions within group






Reports by chapter, allowing for brief discussionPause to talk about noticings & wonderings from

chs. 1-4Prepare: (A.) 3 central ideas/take-aways from chs. 1-

4; (B.) 2 a-ha’s, insights, concerns, or questions for author; and (C.) 1 wondering for discussion





Whole Group commentsGroup report A, B, CSome conversation about Crepeat

Team Homework Share Out

Team Homework – 11/18/14

What are you thinking you want to try out in your class?

What is your reason for trying this? i.e. What is your Personal Teaching Goal?

What data will you collect that will give you information about what you tried?

Please plan to continue to practice the Multiple Ability treatment, which begins with identifying a group-worthy task. Maybe the thing you try is done with your team members, on the same task.

Team Homework Review1. Remind each other what you agreed to do

collectively, or each individually

2. Give each team member 5 min. to sharea. Overview of your intentions and what actually

occurredb. What data did you want to collect and why?c. Share your datad. What did you notice, what do you wonder?

3. Last 5 minutes consider what next stepsa. What have you already done to follow-up?b. What are you interested to do next (this year, next

year)?c. …

Transformational Geometry


Are all parabolas similar?

What transformations retain similarity? “scaling” – i.e. dilation, contraction, expansion, ...

What translations retain congruence? translation rotation reflection


Last session we took on the task to locate a point (m’, n’) that described the coordinates of any point (m, n) reflected about any line y = ax + b.

Take a few minutes to review your notes and chat with current group about (A.) what you’ve learned so far with this task, and (B.) what questions you currently have.


Next step of investigation: Your group will be assigned one of the two following tasks to investigate next.

A.Slide (Translation): A slide transformation can be broken down by analyzing its horizontal and vertical components.

B.Spin (Rotation): A rotation is the result of “spinning” an object around a fixed point—called the center of rotation. The rotation will be some number of degrees θ, usually measured counterclockwise.



A.Slide (Translation): A slide transformation can be broken down by analyzing its horizontal and vertical components.

For example a slide diagonally up and left might be precisely 3 units to the left and 5 units up. This slide transformation (a translation) could be defined by the vector <-3, 5>. Such a transformation would shift any point (x, y) to the new point (x–3, y+5).

Consider defining the translation of a line by saying every point on that line is translated by the same distance, in the same direction (i.e. a vector). So, if line y = ax + b were translated by some vector <m, n>, what is the equation of the new line?

How about a quadratic y = ax2 + bx + c translated by <m, n> ?



B.Spin (Rotation): A rotation is the result of “spinning” an object around a fixed point—called the center of rotation. The rotation will be some number of degrees θ, usually measured counterclockwise.

Rotate a series of easy points some easy number of degrees around the origin. Generalize: determine the new coordinates after rotating any point (m, n) some θ degrees about the origin.

Generalize to rotation about any point (h, k).

A. Slide (Translation): A slide transformation can be broken down by analyzing its horizontal and vertical components.

For example a slide diagonally up and left might be precisely 3 units to the left and 5 units up. This slide transformation (a translation) could be defined by the vector <-3, 5>. Such a transformation would shift any point (x, y) to the new point (x–3, y+5).

Consider defining the translation of a line by saying every point on that line is translated by the same distance, in the same direction (i.e. a vector). So, if line y = ax + b were translated by some vector <m, n>, what is the equation of the new line?

How about a quadratic y = ax2 + bx + c translated by <m, n> ?

� Spin (Rotation): A rotation is the result of “spinning” an object around a fixed point—called the center of rotation. The rotation will be some number of degrees θ, usually measured counterclockwise.

Rotate a series of easy points some easy number of degrees (tip: start with 20°) around the origin. Generalize: determine the new coordinates after rotating any point (m, n) some θ degrees about the origin.

Generalize to rotation about any point (h, k).

Talking Points

Talking PointsLyn Dawes:

Exploratory talk is the greatest singlepredictor of whether group work iseffective or not, yet most symmetrical classroom talk (peer talk) is either cumulative (positive but uncritical) or disputational (merely trading uncritical disagreements back and forth)

Talking PointsTalking Points offer a strategy for stimulating speaking, listening, thinking and learning. Talking Points are basically a list of thoughts - statements which may be factually accurate, contentious or downright wrong. They provide a focus for speaking and listening and a chance to find out what others think. They can be thought-provoking, interesting, irritating, amusing, smart, simple, brief or wordy. Talking Points are easy to make up, read and understand, but offer ways in to thinking more deeply about the subject under discussion. They enable everyone to say what is in their minds, so that others can decide whether they agree or disagree.

Talking PointsPURPOSE

to support students’ exploratory talk skills by pushing them out of cumulative and disputational modes and into a more exploratory talk mode (i.e., speaking, listening, justifying with NO COMMENT)

to reveal student thinking about speaking, listening, justifying and about having a growth mindset

to cultivate a growth mindset community

–from Elizabeth Statmore @cheesemonkeysf

Talking PointsHave someone read the first talking point with NO COMMENT.

Round 1: Go around the group, with each person saying in turn whether they AGREE, DISAGREE, or are UNSURE about the statement AND WHY. Even if you are unsure, you must state a reason WHY you are unsure. NO COMMENT. You’ll be free to change your mind during your turn in the next round.

Round 2: Go around the group, with each person saying whether they AGREE, DISAGREE, or are UNSURE about their own original statement OR about someone else’s statement they just heard AND WHY. NO COMMENT. You are free to change your mind during your turn in the next round.

Round 3: Take a tally of AGREE/DISAGREE/UNSURE and make notes on your sheet. NO COMMENT.

Move on to the next talking point and complete the same steps.

Lunch

Rainbow Logic

Rainbow Logic

The Grid Designer prepares a secret 3 x 3 color grid, using 3 squares of each color.

All squares of the same color must be connected by at least one full side.

Example of a Secret Grid

Patterns Not Allowed

Rainbow Logic

Your team’s goal:

To be able to give the location of all colors on the grid after as few questions as possible.

Rainbow Logic

1. Recall: all squares of the same color must be connected by at least one full side.

2. Players ask for the colors in a specific row or column.

3. Grid Designer gives the colors, but not necessarily in order.

Rainbow LogicTasks for the grid designer as an observer:

1. Keep track of how often people gave reasons for their suggestions.

2. Watch the character of the discussion to see if people really discussed before they came to a decision.

Rainbow LogicGroup Debrief

What do you think this exercise was all about?

How do you feel about what happened in your group today?

What things did you do in your group that helped you to be successful in solving the problem?

What things did you do that made it harder?

What could the groups do better in the future?

Rainbow LogicNew Behaviors:

DISCUSS AND DECIDE

GIVE REASONS FOR YOUR SUGGESTIONS

Small Groups

These expectations for mathematical interactions are called for in CCSS-M Practice Standard 3, Construct viable arguments and critique the reasoning of others.

We’ll consider an activity that can help you to develop these socio-mathematical norms: Rainbow Logic.

This is an exercise developed by the Family Math program at EQUALS in the UC Berkeley Lawrence Hall of Science to give the students practice in communicating their deductive thinking and spatial reasoning.

Team Lesson Development

A Multidimensional Classroom

What are among the countless variety of

mathematical abilities?

Your group will be successful today

if you have someone who is good at …

Your group will be successful today if you have someone who is good at …

Recognizing and describing patterns Justifying thinking using multiple representations Making connections between different approaches and

representations Using words, arrows, numbers, and color coding to communicate

ideas clearly Explaining ideas clearly to team members and the teacher Asking questions to understand the thinking of other team

members Asking questions that push the group to go deeper SKEPTIC: a person inclined to question or doubt all accepted

opinions Organizing a presentation so that people outside the group can

understand your group’s thinkingNo one is good at all of these things, but everyone is good at something. You will need all of your group members to be successful at today’s task.

Planning for a Talk-Worthy Task

We will work with teachers in a similar position to ours to plan for implementing (practicing) the Multiple Ability Treatment.

1.Select a task you will do in the near future.

2.Do the mathematics (as yourself). Challenge yourself to solve the task in at least one more way.

3.Consider the mathematical tools your students may bring to the task. Create at least one more approach that students might pursue toward solving.

4.List a variety of mathematical abilities that might be involved in solving the task.

Some Characters

Spy: Eavesdrop on another team to gather information and seek clarification of direction.

Ambassador: Report strategies or insights from your team to another.

Audience Expectations during Presentations

We are asking the presenter to share what they are thinking so far in their exploration. This is not intended to be a presentation of the right way of doing the problem. Rather it is an opportunity to consider another person’s ideas.

What does this create for the definitions of the audiences’ role and expectations for behavior?

HelpStudent behaviors in the classroom must be taught. The expectation to help and how to help both must be explicitly developed by the mathematics teacher in conjunction with his or her students.

Some possible expectations: Help other group members without doing their work

for them You have the duty to assist anyone who asks for help You have the right to ask anyone in your group for

help Everybody helps!!!

Penultimate Task1. Quickly review key structures for planning a lesson

recommended by Peg Smith et al. in Thinking Through a Lesson

2. Among the teaching techniques discussed today or previously to help improve student-student interaction, identify what your team members may want to try out in each of their classes? Identify the reason for trying this; i.e. What is your Personal Teaching Goal?

3. Collectively begin to craft a lesson using Peg Smith’s structures to achieve step 2.

4. Determine the data will you collect in your classroom to provide information about your Personal Teaching Goal.

Homework

HomeworkRead Strength in Numbers (chs. 5-6). Bring the

book, and be ready to share reactions and ideas at next month’s New Normal session.

Utilize the following teaching strategy at least once: Talking Points – use some of the listening points,

others found online, or make up your own TEACH a specific mathematical behavior, such as

“discuss and decide” or “give a reason why.”

Implement the lesson your team designed, collecting the data agreed to, & reflect in your journal (composition book). Bring back the data.

Documents

Delaware Math Coalition New Normal Cohort 2 – How do I get my groups to work? 13 jan 2015