Mathematics Workshop

Mathematics Workshop

Planning Student-Centered Mathematics Around

Big Ideas

Susan Muir K-4 Math Coach

Beginning with the end in mind…

Agenda Handshake Activity( warm-up)My Role as a Math CoachPlanning 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 ActivityIf 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 4+3+2+1=10 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 world’s 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.

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 AttitudeDevelop a positive attitude towards the

ability to understand mathematics and to use it to solve problems.

Four Strands

Number Patterns and RelationsShape and SpaceStatistics and Probability

Seven Processes Problem solvingReasoningCommunicatingConnectionsRepresentationsMental Math and EstimationTechnology

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 QuestionsWhat 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: PatternsMathematics is the science of patternsPatterning 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 RelationsOutcomesP2.1 Demonstrate understanding of

repeating patterns (three to five elements) by:

describingrepresenting patterns in alternate modesextendingcomparingcreating patterns using manipulatives,

pictures, sounds and actions.

Patterns And Relations cont.

OutcomesP2.2 Demonstrate understanding of increasing

patterns by:describingreproducingextendingcreating patterns using manipulatives,

pictures, sounds and actions (numbers to 100).

Patterns And Relations cont.

OutcomesP2.3 Demonstrate understanding of equality

and inequality concretely and pictorially (0 to 100) by:

relating equality and inequality to balancecomparing setsrecording equalities with an equal signrecording inequalities with a not equal

signsolving problems involving equality and

inequality.

Step Two: Determine how the learning will be observedWhat 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 student’s learning?

AssessmentAssessment should:reflect the mathematics that all children

need to know and be able to doenhance mathematics learningpromote equitybe an open processpromote valid inferences about

mathematical learningbe a coherent process.

AssessmentAssessment for LearningAssessment of LearningAssessment as Learning

http://www.wncp.ca/media/40539/rethink.pdf

Effective Questions for Understanding“. . . Questions stimulate thought,

provoke inquiry, and spark more questions—not 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 Mathematics Assessment

*Rubrics * Checklists

*Anecdotal notes/ Video

* Math J ournals

Math Journals

Portfolios

Each item in a collection of work should illustrate something important about a student’s 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 classroomChildren feel safe, valued and supported in

their learningAs a facilitator of learning we are responsible

for creating a classroom environment that will allow each student to experience success

InquiryA philosophical approach to teaching and

learningBuilds on students’ inherent sense of

curiosity and wonderDraws on students’ diverse background and

experiencesProvides opportunities for students to

become active participants in a search for meaning

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 AreaCentral 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 AreaWhat do you

think an effective meeting area

LOOKS LIKE?SOUNDS LIKE?

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

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 WednesdaysEvery Wednesday, from 4:00-5:30 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