Teaching Mathematics for Learning

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Teaching Mathematics for Learning A Standards
Aligned System

• Elementary Mathematics Teacher Leadership Academy

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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.

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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?

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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

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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

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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.

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Standards Aligned Systems
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Clear Standards

• Establish what all
• students should know
• and be able to
• accomplish.

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Fair Assessments

• Aligned to PA Standards
• Summative
• Formative
• Diagnostic
• Benchmark

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Curriculum Framework

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

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Instruction

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

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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.

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Interventions

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

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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

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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.

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CompetenciesAnswer the Question

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

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

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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?

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MCF Supporting SAS Framework Knowledge Networks
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Third Grade
Estimate and verify measurements.
Tell time to the minute.
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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?

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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.

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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.
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Building a System of Tens
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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

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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.

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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.

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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.

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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.