Collaborative Inquiry for Learning MfT Math Study Group E ...three-dimensional figures. Many young children recognize three-dimensional figures, but name them by ... Let’s unpack

Collaborative Inquiry for Learning MfT

Math Study Group E St Cyril

Toronto Catholic District School Board

Session #3 – April 4th, 20143 D Geometry

Who’s Here?Our Lady of Peace, Our Lady of Wisdom, St Agatha, St Cecilia, St Cyril







Our Lady of PeaceSonia Correia (gr 2) late Kelly Micco ( gr 3) lateAnna Maria Mondano (gr 2) lateWarnes Keldi (Gr 2) John Prifti (3)Gerrard Bonello (VP)

Our Lady of WisdomTiffany Rego (gr.2)Suzan Haggar (gr.2)Mari-Berje Georgy (gr. 3)Renate Purr (gr. 3) absentFrancesca Polito (gr. 3)(P) Sandra Filicetti - retreat(VP) William Kwon – other school

St AgathaRick Saba (gr.2) - absentClarisse Tavares M (gr 2) - absentNicole Sicotte (3) - absentJonathan Remigio (3)(P) Bela Matayas (mtg – emailed)

St. CeciliaKathleen Walsh (gr. 2)Gabrielle Faion-Kralik (gr. 2)Melissa Guitard (gr. 3)Sandra Wilson (gr.3)Susan Balgavy (gr. 2)Diana Pamula (gr. ½)(P)Lorinda Mazza

St. CyrilWafaa Ghabour (gr. 3)Mukendi Dibula (gr. 3)Nicole Guegueirre (gr 2)Marie-Josee Duchesne (gr2)(P) Sylvie Talarico

Superintendents: Math Dept:Wilma SimmonsAICT: Liane Paixao

Tentative Flexible Agenda

Plan for the Public Research Lesson•Study and do the math•Review the main concepts and strategies from research•Anticipate the success criteria and descriptive feedback based on the lesson learning goal

Co-teach/observe the Public Research Lesson•Debrief the lesson •Discuss students’ communication skills – bansho board writingPedagogical Documentation•Sign in to our blogReflect on Collaborative Inquiry Question/s•Reflect on/review our action plan•Share ideas/strategies with grade partners

Preparation for Public Research LessonMarie-Josee’s Gr 2 Class – 3D Geometry

Preparation for Public Research LessonMarie-Josee’s Gr 2 Class – 3D Geometry

Marie-Josee’s Gr 2 ClassWhat’s the mathematical thinking?



●Draw a series of 5 triangles. After the first, each new one should be different in some way.

●Write down why you think each one is different.

●Share with others at your table.

STUDY - Let’s Do Math As A Teacher

STUDY - Let’s Do Math As A Teacher

17TCDSB Mathematics Dept, 2012

Use what you know about shapes to sort the objects in the basket.

What information are we going to useto solve this problem?

● sort shapes

●Put into groups

●Different shapes in basket

Nelson Chapter 11, Lesson 2

Break

STUDY - Let’s Do Math As A TeacherSolve this problem in 2 different ways

STUDY - Let’s Do Math As A TeacherSolve this problem in 2 different ways

What do teachers need to know . . . to teach 3 D geometry?

What are the critical concepts and skills regarding 2-D and 3-D shapes that students need to learn and be able to do?

●Properties – identify them in different shapes

●Difference between 2D and 3D

●Prisms and pyramids

●Names of the shapes

●Names of the polygon faces

●Relate 3 D shapes to real life objects

●Decomposing 3 D shapes into 2 D shapes

Geometry and Spatial Sense Trajectory

Young Children’s Experiences

●From infancy, children interact with objects in their environment, and develop some understanding about three-dimensional figures.

●Many young children recognize three-dimensional figures, but name them bytwo-dimensional shapes or by common objects.

Ball Circle

Sphere

Getting Beyond The Known!

●Some students leave the primary grades knowing little more about geometry than they already knew when they entered school.

●Many students retain the narrow, stereotypical understanding of shapes that they had at Kindergarten.

Stages Of Development

●At first students recognize shapes by their visual appearance only.

●Through experience in manipulating and talking about shapes, they begin to learn some of the properties of various shapes.

●The goal is to increase students’ ability to analyze and describe geometric properties, rather than simply learn definitions of shapes.

Development Follows Experience

●Students understand these properties through experience in identifying, comparing, sorting and classifying shapes.

●The more varied the configurations and orientations, the broader student’s understanding will become.

Children Learn What They See And Experience.

If children always see shapes presented like these,

their understanding of these shapes will be limited to these configurations.

Limitations Of Materials

●Some of the problem lies with traditional classroom materials (e.g., pattern blocks, attribute blocks).

●We also tend to model our visual displays, geometric games, etc. to these traditional shapes. Traditional shapes

Some Solutions!

●Locate or make creative materials that present shapes in a variety of formats.

●Encourage students to identify, sort and classify shapes in various configurations and orientations.

Triangles

Get Students Talking!

●Encourage students to describe what they see or feel.

●Focus on the properties (rather than the names),

e.g., ●Length of sides●Size of angles●Parallel lines●Number of sides

4 sidesOpposite sides equal4 right anglesOpposite sides parallel

Table Talk

Take a few minutes to discuss the significant ideas that students need to understand in each of these properties: ●Number of sides ●Length of sides●Size of angles●Parallel lines

Properties of Three-Dimensional Figures

It’s a 3-D World After All!It’s a 3-D World After All!

Properties of 3-D Figures

The properties of a polyhedron can be described according to:

● the number and shapes of its faces;

● the number of edges;

● the number of vertices. vertexedge

face

Properties of Prisms

●Two congruent, parallel polygons form the bases.(The shape of the base usually determines the name of the prism: rectangular prism, triangular prism.)

●Other faces are parallelograms.

Rectangular prism

Triangular prism

Oblique prism

Properties of Pyramids

●The base is a polygon. (The shape of the base determines the name of the pyramid: triangular basedpyramid, rectangular based pyramid, square-basedpyramid.)

● Other faces are triangles.

What does Marian Small say?





PREPARATION FOR PUBLIC RESEARCH LESSONNelson Mathematics Chapter 11.1,2 Gr 2

STUDYING MATHEMATICS FOR TEACHINGEQAO Analysis

What mathematics in grades 2 and 3 do students need to learn to solve these questions at a level 3 and level 4?


KKZ, 2011


48TCDSB Mathematics Dept, 2012

Questions– what shapes should we give them?

DURING (Working On It)

Use what you know about shapes to sort the objects in the basket.

KKZ, 2011

Grade 2What’s our Lesson Learning Goal?

Expectation: Identify 2D shapes and 3D figures and sort and classify them by their geometric properties Lesson Learning Goal/Success Criteria: Let’s unpack the expectation

PREPARATION FOR PUBLIC RESEARCH LESSONToday’s Public Research Lesson

●What’s the relationship between the curriculum expectations, lesson learning goal and success criteria?

● What are the important concepts and strategies for this lesson?

KKZ, 2011

This is what we decided a group . . .Success Criteria: To sort 3D shapes we:-group them by what’s the same and what’s differentEgs by different facesBy what they do – roll or slide or stack

What’s our Lesson Learning Goal?What’s Our Success Criteria?

KKZ, 2011

Ontario 3-Part Problem Solving Lesson Structure

●1- Before (Getting Started) - 5 to 10 minutes – revisiting mathematical ideas and strategies from a previous lesson that relates to the learning goal of the lesson

●2- During (Working On It) - 15 to 20 minutes - solving the lesson problem in pairs, small groups, or individually

●3a- After (Consolidation) - 20 to 25 minutes -> coordination of whole class discussion/analysis of student solutions; co-construction of success criteria

●3b- After (Highlights/Summary) - 5 minutes -> recounting key mathematical ideas and strategies related to the learning goal of the lesson (summary of co-constructed success criteria

●3c -After (Practice) - 5 to 10 minutes – solving a problem that is similar to the lesson problem in order to practise applying new ideas and strategies.Pa

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KKZ, 2011

BEFORE (Getting Started)

●5 to 10 minutes only

●Activating students’mathematical knowledge and experience that directly relates to the mathematics in the lesson problem

●Includes student responses to a prompt/problem that is similar to previous work to highlight a few key ideas and/or strategies

Grade 2 Public Research Lesson

• Have them compare 2 shapesRecord everything they say on the board. Our goal is to list all of the attributes/properties of 3 D shapesWhy is this task useful?

Have them play with Feely bags• They feel the shapes and

describe the properties to a partner who tries to guess what shape it is.

KKZ, 2011






Why is this task useful?

KKZ, 2011






Why is this task useful?

KKZ, 2011



● 15 to 20 minutes ● Understand the problem, Make a Plan,

Carry Out the Plan● Understand the problem - Ask, “What

information from the problem will we use to make a plan to solve it? Explain.”

● Teacher records below the problem the information the students identify in a list.

● Students solve the problem in pairs or in small groups

● Teacher circulates to notice the range of mathematics used by the students in their solutions and to discern the sequence of student sharing of solutions (one solution should relate to and elaborate from the previous solution)




















KKZ, 2011

1. What mathematics (i.e., concept, algorithm, strategy, model of representation) are the students using in their solution? - How does this mathematics in the solution relate to the

mathematics lesson learning goal?2. Which solutions are conceptually-based?

- Which solutions have an efficient method or algorithm? Which solutions include or have the potential for a mathematical generalization?

3. How are the solutions related to each other, mathematically?

Understanding Students’ Mathematical Thinking – Work Analysis

AFTER (Consolidation)

• 5 minutes• Summary of co-constructed

success criteria• Teacher revisits in the

different solutions the key ideas, strategies, and models of representation that are related to the lesson learning goal

• Teacher records key ideas, strategies, and models of representation separately, so the students see the explicit focus of learning from the lesson


AFTER (Highlights/Summary)






We sort objects by:-their attributes-their properties

AFTER (Highlights/Summary)






AFTER (Practice)● 5 to 10 minutes● Teachers chooses 2 or 3

problems, similar to the lesson problem for students to solve individually (or in pairs as a scaffold).

● Problems are different by number (choice, size), problem contexts, or variation of unknown that needs to be solved

● Students are asked to use a strategy different from the one they used in the lesson to solve the practice problems


AFTER (Practice)● 5 to 10 minutes● Teachers chooses 2 or 3

problems, similar to the lesson problem for students to solve individually (or in pairs as a scaffold).

● Problems are different by number (choice, size), problem contexts, or variation of unknown that needs to be solved

● Students are asked to use a strategy different from the one they used in the lesson to solve the practice problems


Today’s Co-Teaching Public Research LessonCo-Teachers, Insider and Outsider Researchers

Co-Teaching and Public Research Teams:● Lead Voice – Marie - Josee

● Co-teachers – Nicole (board writer) Wilma (banshowhisperer)

● Knowledge Mobilizer –

● Inside Researchers – ½ the group

● Outside Researchers – ½ the group

PUBLIC RESEARCH LESSON POST DISCUSSION

●Students were shy – did not participate as much●When they didn’t know the word in French – they don’t speak in English – they ask Marie-Josee how to say it in French●Loved the lesson – forced them to talk in French ●Students could prepare the feely bags●Fabric bags as the paper bags were too noisy●Only put fewer objects to sort so you force them to sort in certain ways

Lunch Grace Before Meals

Bless us,O Lord,

and these thy gifts,which we are about to receive

from thy bounty.Through Christ our Lord.

Amen.

Reflect on our Collaborative Inquiry Question/s

●What impact will letting students collaborate, make mistakes and try to solve problems by themselves, have on students’ ability to solve multi-step problems?

●How will analyzing students’ solutions and giving them immediate descriptive feedback, impact their ability to independently solve multi- step problems?

●How will building students’ vocabulary impact their ability to communicate their mathematical thinking in French?

What Do WE Want to Study?SUMMARY of OUR Study Group Learning Goals

•Help students solve multi-step problems even in multiple choice type questions

-Let students problem solve by themselves – make mistakes – analyze it and give them immediate descriptive feedback – allow students to give each other feedback – collaboration

•Build vocabulary – bring back artefacts

Reflect on our Collaborative Inquiry Question/s

What have you been practising? What is the impact on Student learning?-Word walls, sentence stems helping-if you wait students will not speak in English-students enjoy problem solving and working on chart paper

Pedagogical Documentation

●What is it?

●How do we do it?

●Our Blog

Documents

Collaborative Inquiry for Learning MfT Math Study Group E ...three-dimensional figures. Many young children recognize three-dimensional figures, but name them by ... Let’s unpack