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 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… =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.

Planning the Year Curriculum Documents 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 student’s 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

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

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 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

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

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?

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

Using a Variety of Manipulatives from 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 Wednesdays Every 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