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Teaching Mathematics for Learning

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Teaching Mathematics for Learning A Standards Aligned System Elementary Mathematics Teacher Leadership Academy Teaching Mathematics for Learning – PowerPoint PPT presentation

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Title: Teaching Mathematics for Learning


1
Teaching Mathematics for Learning A Standards
Aligned System
  • Elementary Mathematics Teacher Leadership Academy

2
Teaching Mathematics for Learning A Standards
Aligned System
  • GOALS for the year for you, as participants
  • Understand and use the Standards Aligned System
    in Mathematics.
  • See that mathematics is about thinking and that
    you have mathematical thoughts.
  • Recognize students as mathematical thinkers.
  • Learn how to analyze students ideas.
  • Learn how to engage a whole class in analysis of
    student ideas.
  • Whatever processes are envisioned for mathematics
    classrooms, are also envisioned for this group of
    adults.

3
Norms for Learning
  • What can you do to make this a good learning
    experience for yourself?
  • What can you do to make this a good learning
    experience for others?

4
Professional Practice Norms
  • Listening to and using others ideas
  • Keeping records of professional work
  • Adopting a tentative stance toward practice -
    wondering versus certainty
  • Backing up claims with evidence and providing
    reasoning
  • Talking with respect yet engaging in critical
    analysis of teachers and students portrayed
  • Seago Mumme, 2003

5
PA Standards Aligned System
  • GOALS
  • Define Standards Aligned Systems, identify its
    purpose, and understand all segments of the
    system
  • Investigate the relationship between the PA
    standards and assessment anchors to the Big
    Ideas, Concepts, and Competencies
  • Explore the Big Ideas in math to search for links
    within curriculum and instruction

6
What Is SAS?
  • The Pennsylvania Standards Aligned
  • Systems (SAS) is a collaborative product
  • of research and good practice that
  • identifies six distinct elements which, if
  • utilized together, will provide schools and
  • districts a common framework for continuous
  • school and district enhancement and
  • improvement.

7
Standards Aligned Systems
8
Clear Standards
  • Establish what all
  • students should know
  • and be able to
  • accomplish.

9
Fair Assessments
  • Aligned to PA Standards
  • Summative
  • Formative
  • Diagnostic
  • Benchmark

10
Curriculum Framework
  • A framework specifying Big Ideas,
  • Concepts, and Competencies
  • in each subject area/at
  • each grade level.

11
Instruction
  • Aligned with standards in order
  • to identifying strategies that
  • are best suited to help
  • students achieve the
  • expected performance.

12
Materials Resources
  • Chosen as a guide for selecting
  • only material from textbooks,
  • reading materials, software,
  • and any other instructional
  • resources that are needed
  • to fit the framework
  • and match the standards.

13
Interventions
  • A safety net/intervention
  • system ensures
  • all students meet standards

14
Why do we need a Standards -Aligned System in
Pennsylvania?
  • To support districts with Curriculum, Assessment,
    Instruction
  • To provide Professional Development
  • To promote an ongoing learning community
  • To help all students to meet and when possible,
    exceed the PA Academic Standards

15
Definitions
  • Big Ideas A declarative statement of enduring
    understandings, for all students at each grade
    level/course. They are essentail to provide focus
    on specific content for all students.
  • Concepts What students should know, key
    knowledge, as a result of this instruction,
    specific to grade level.
  • Competencies Describe what students should be
    able to do, key skills, as a result of this
    instruction, specific to grade level.

16
CompetenciesAnswer the Question
  • What is the truly important mathematics at this
    grade level or in this course?

17
Navigating the Website http//www.pdesas.org/
18
(No Transcript)
19
  • Number of Mathematics Topics Intended

20
So.
  • How can we identify and organize a few essential
    learnings at each grade level?
  • What might the curriculum look like as its
    organized around essential learnings in
    mathematics?

21
MCF Supporting SAS Framework Knowledge Networks
22
Third Grade
Estimate and verify measurements.
Tell time to the minute.
23
Standards Aligned System Mathematics
  • Take a few minutes to look at the big ideas,
    concepts and competencies for one grade level,
    which you will find in your binder under day 1.
  • What did you notice?

24
Standards Aligned System Mathematics
  • The Pennsylvania Standards Aligned
  • Systems (SAS) is a collaborative product
  • of research and good practice that
  • identifies six distinct elements which, if
  • utilized together, will provide schools and
  • districts a common framework for continuous
  • school and district enhancement and
  • improvement.

25
How People Learn Mathematics
Key Findings for Students Key Findings for Teachers
First Students come to classrooms with preconceptions about what mathematics is. Recognize preconceptions and adjust instruction.
Second Students must have a deep foundation of usable knowledge and understand facts in the context of a conceptual framework. Understand the context and conceptual framework for a discipline.
Third Students must be explicitly taught to take control of their own learning by monitoring their progress. Teach metacognitive skills.
26
Building a System of Tens
27
Building a System of Tens
  • GOALS for the year
  • Understand and use the Standards Aligned System
    for Mathematics
  • Explore mathematics for yourselves
  • Examine print and video cases to learn how
    students develop these ideas
  • Investigate and share your own students work

28
Students Addition and Subtraction Strategies
  • Goals for this session of BST
  • Examine different strategies for addition and
    subtraction.
  • Determine which strategies rely on the underlying
    structure of the base ten system.
  • Look at verbal descriptions, base ten models, and
    number line models that underlie each approach.

29
Professional Discourse
  • Low-level talk focuses on
  • How to use curriculum materials
  • How to organize classrooms for instruction
  • General discussions of how lesson went.
  • High-level talk focuses on
  • Pedagogical principles underlying instructional
    approaches
  • Nature of students mathematical and scientific
    thinking
  • Understanding of mathematical and scientific
    concepts.

30
Professional Discourse
  • To support instructional improvement,
    professional learning community talk should be
    about how students learn content and what
    teachers can do to ensure that ALL students
    learn.

31
This material is based on work supported by the
National Science Foundation under Grant No.
EHR-0314914. Any opinions, findings,
conclusions, or recommendations expressed in this
publication are those of the authors and do not
necessarily reflect the views of the granting
agency.
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