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Mathematics Workshop Mathematics Workshop

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Mathematics Workshop Mathematics Workshop Planning Student-Centered Mathematics Around Big Ideas Susan Muir K-4 Math Coach * Begin with the Handshake Activity. – PowerPoint PPT presentation

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Title: Mathematics Workshop Mathematics Workshop


1
Mathematics Workshop Mathematics
Workshop
  • Planning Student-Centered
  • Mathematics Around
  • Big Ideas
  • Susan Muir
  • K-4 Math Coach

2
Planning Student-CenteredMathematics
Instruction
  • Beginning with the end in mind

3
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)

4
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?

5
Handshake Activity
  • People of Handshakes
  • 5 ___
  • 10 ___
  • 20 ___
  • Strategies?

6
Strategies.
  • 5 432110 handshakes
  • n(n-1) of people ( of
    people- yourself)
  • 2 repeated handshakes
  • 5(5-1)
  • 2

7
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.

8
Where Do I Begin???
9
Planning for Outcome-Based Curriculum
  • What is it that the student needs to know,
    understand and be able to do?

10
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?

11
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.

12
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.

13
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)

14
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.

15
Logical Thinking
  • Develop and be able to apply mathematical
    reasoning processes , skills and strategies to
    new situations and problems.

16
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.

17
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.

18
Mathematical Attitude
  • Develop a positive attitude towards the ability
    to understand mathematics and to use it to solve
    problems.

19
Four Strands
  • Number
  • Patterns and Relations
  • Shape and Space
  • Statistics and Probability

20
Seven Processes
  • Problem solving
  • Reasoning
  • Communicating
  • Connections
  • Representations
  • Mental Math and Estimation
  • Technology

21
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)

22
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

23
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.

24
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)

25
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.

26
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).

27
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.

28
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?

29
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.

30
Assessment
  • Assessment for Learning
  • Assessment of Learning
  • Assessment as Learning
  • http//www.wncp.ca/media/40539/rethink.pdf

31
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.

32
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

33
Rubrics and Checklists
34
Math Journals
35
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).

36
Math Tubs for Centers
37
Math Invitation Tables
38
Carefully select your items based on the
curriculum outcome.
39
Math at Home
40
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?

41
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

42
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43
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

44
Climate and EnvironmentCreating a Mathematical
Community in the Classroom
45
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.

46
Floor Plan
47
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.

48
Using the Meeting Area
  • What do you think an effective meeting area
  • LOOKS LIKE?
  • SOUNDS LIKE?

49
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50
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

51
Storage of Materials
52
Math Word Wall
53
Math Word Wall
54
Using a Variety of Manipulativesfrom the
Environment
55
Math Mini Offices
56
Questions about Creating a Mathematical
Environment
57
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?

58
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
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