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Mathematics Workshop Mathematics

Workshop

- Planning Student-Centered
- Mathematics Around
- Big Ideas
- Susan Muir
- K-4 Math Coach

Planning Student-CenteredMathematics

Instruction

- Beginning with the end in mind

Agenda

- Handshake Activity( warm-up)
- My Role as a Math Coach
- Planning for Outcome-Based Curriculum
- Four Step Process for Backwards Design
- 1.Identify the outcomes to be learned- outcomes

indicators activity - 2.Determine how the learning will be observed-

assessment - 3.Plan the learning environment- creating a

mathematical classroom - 4.Assess student learning and follow up
- Three-Part Lesson Format for Problem Based

Lessons - Questions (wrap-up)

Handshake Activity

- If every person shakes hands with every other

person once, how many handshakes will take place? - If there are 5 people in your group, how many

handshakes would occur? - 10 people?
- 20 people?

Handshake Activity

- People of Handshakes
- 5 ___
- 10 ___
- 20 ___
- Strategies?

Strategies.

- 5 432110 handshakes
- n(n-1) of people ( of

people- yourself) - 2 repeated handshakes
- 5(5-1)
- 2

Mathematics

- Mathematics is the science of pattern and order.
- We look at the worlds patterns and generalize

so we can predict the rule to apply it to other

patterns.

Where Do I Begin???

Planning for Outcome-Based Curriculum

- What is it that the student needs to know,

understand and be able to do?

Step One Identify the outcomes to be learned

- What are my students interested in and what do

they want to learn? - What do my students need to know, understand and

be able to do based on the big ideas and outcomes

in the curriculum?

Outcomes

- Describe what students will know or be able to do

in a particular discipline by the end of the

grade or course. - Are unique from grade to grade, but may build on

or expand on outcomes from previous grades.

Indicators

- Are a representative sample of evidence that

students would be able to demonstrate or produce

if they have achieved the outcome. - Define the breadth and depth of the outcome.

Planning the Year

- Curriculum Documents http//central.gssd.ca/math/?

page_id760 - Strands
- -Patterns and Relations
- -Number
- -Shape and Space
- -Statistics and Probability (Gr.3-4)

Goals for Mathematics

- The four goals are broad statements that identify

the knowledge, understandings, skills and

attitudes in mathematics that the students are

expected to develop and demonstrate by the end of

grade twelve. - Within each grade level, outcomes are directly

related to the development of one or more of

these goals.

Logical Thinking

- Develop and be able to apply mathematical

reasoning processes , skills and strategies to

new situations and problems.

Number Sense

- Develop an understanding of the meaning of,

relationships between, properties of, roles of,

and representations(including symbolic) of

numbers and apply this understanding to new

situations and problems.

Spatial Sense

- Develop an understanding of 2-D shapes and 3-D

objects and the relation between geometrical

shapes and objects, and numbers and apply this

understanding to new situations and problems.

Mathematical Attitude

- Develop a positive attitude towards the ability

to understand mathematics and to use it to solve

problems.

Four Strands

- Number
- Patterns and Relations
- Shape and Space
- Statistics and Probability

Seven Processes

- Problem solving
- Reasoning
- Communicating
- Connections
- Representations
- Mental Math and Estimation
- Technology

Big Ideas in Mathematics

- The Mathematical Big Ideas are important topics

that provide a focus on the mathematical

experience for all students at each grade level.

They are related ideas, skills, concepts and

procedures that form the foundation of

understanding, permanent learning and success at

higher mathematics. - (Adapted from the NCTM Curriculum Focal

Points, 2006)

Essential Questions

- What makes a pattern?
- Why do we use Patterns?
- When do we use patterns?
- How do they help us in the real world?
- By answering these questions, we get the

Big Ideas

Big Ideas Patterns

- Mathematics is the science of patterns
- Patterning develops important critical and

creative skills needed for understanding other

mathematical concepts - Patterns can be represented in a variety of ways
- Patterns underlie mathematical concepts and can

be found in the real world.

Think

- What are the prerequisites for each grade level?
- -look at the outcomes across the grade levels
- (See K-4 document Outcomes at a Glance)

Patterns And Relations

- Outcomes
- P2.1 Demonstrate understanding of repeating

patterns (three to five elements) by - describing
- representing patterns in alternate modes
- extending
- comparing
- creating patterns using manipulatives, pictures,

sounds and actions.

Patterns And Relations cont.

- Outcomes
- P2.2
- Demonstrate understanding of increasing patterns

by - describing
- reproducing
- extending
- creating patterns using manipulatives, pictures,

sounds and actions (numbers to 100).

Patterns And Relations cont.

- Outcomes
- P2.3 Demonstrate understanding of equality and

inequality concretely and pictorially (0 to 100)

by - relating equality and inequality to balance
- comparing sets
- recording equalities with an equal sign
- recording inequalities with a not equal sign
- solving problems involving equality and

inequality.

Step Two Determine how the learning will be

observed

- What will the students do to know that the

learning has occurred? - What should students do to demonstrate their

understanding of the mathematical concepts ,

skills and big ideas? - What assessment tools will be the most suitable

to provide evidence of student understanding? - How can I document the students learning?

Assessment

- Assessment should
- reflect the mathematics that all children need to

know and be able to do - enhance mathematics learning
- promote equity
- be an open process
- promote valid inferences about mathematical

learning - be a coherent process.

Assessment

- Assessment for Learning
- Assessment of Learning
- Assessment as Learning
- http//www.wncp.ca/media/40539/rethink.pdf

Effective Questions for Understanding

- . . . Questions stimulate thought, provoke

inquiry, and spark more questionsnot just pat

answers . . . The best questions point to and

highlight the big ideas. (Wiggins McTighe,

2005) - The curriculum has placed an emphasis on and

provides examples of questions that engage

students in a higher level of thinking.

What are Good Questions?

- They require more than remembering a fact or

reproduce a skill. - Students can learn by answering the questions,

and the teacher learns about each student from

the attempt. - There may be several acceptable answers.
- Good Questions for Math Teaching by Peter

Sullivan and Pat Lilburn

Rubrics and Checklists

Math Journals

Portfolios

- Each item in a collection of work should

illustrate something important about a students

development or progress, attitude, understanding,

conceptual understanding, use of strategies,

application of procedures (procedural fluency).

Math Tubs for Centers

Math Invitation Tables

Carefully select your items based on the

curriculum outcome.

Math at Home

Step Three Plan the learning environment and

instruction

- What learning opportunities and experiences

should I provide to promote the learning

outcomes? - What will the learning environment look like?
- What strategies do students use to access prior

knowledge and continually communicate and

represent understanding? - What teaching strategies and resources will I use?

Creating a Mathematical Community in the Classroom

- Teacher as facilitator/inclusive classroom
- Children feel safe, valued and supported in their

learning - As a facilitator of learning we are responsible

for creating a classroom environment that will

allow each student to experience success

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Inquiry

- A philosophical approach to teaching and learning
- Builds on students inherent sense of curiosity

and wonder - Draws on students diverse background and

experiences - Provides opportunities for students to become

active participants in a search for meaning

Climate and EnvironmentCreating a Mathematical

Community in the Classroom

Creating the Physical Environment

- Desk Arrangement
- When students desks are arranged in a group,

the students become members of a unit and develop

a sense of belonging.

Floor Plan

Group Meeting Area

- Central to the life of any community is a group

meeting area. - This is a place where every member gets together

to learn what it means to be part of a community.

Using the Meeting Area

- What do you think an effective meeting area
- LOOKS LIKE?
- SOUNDS LIKE?

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Using the Meeting Area

- To introduce a new mathematical concept with a

guiding question - To brainstorm what students already know about a

mathematical topic - To share a new manipulative and explore possible

uses - To revisit a mathematical concept to reinforce a

specific skill - Introduce a math centre
- Discuss difficulties arising from a previous

lesson - The show and share stage of the three part lesson

model

Storage of Materials

Math Word Wall

Math Word Wall

Using a Variety of Manipulativesfrom the

Environment

Math Mini Offices

Questions about Creating a Mathematical

Environment

Step Four Assess student learning and follow up

- What conclusions can be made from assessment

information? - How effective have instructional strategies been?
- What are the next steps for instruction?
- How will gaps be addressed?
- How will students extend their learning?

How Can I Support You?

- Formal Coaching
- Work with you one on one, for a four week

block, during your scheduled math time. - This would be Monday, Tuesday , Thursday,

Friday, - either in the morning or afternoon.
- Workshop Wednesdays
- Every Wednesday, from 400-530 I will

facilitate a workshop in various locations

throughout the division. The topics will come

from teacher surveys. - Work with individuals or a small group of

teachers with planning, assessment,

differentiated instruction, etc. - Resource lending library and math manipulatives.
- Support