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Teaching Mathematics for Learning A Standards

Aligned System

- Elementary Mathematics Teacher Leadership Academy

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.

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?

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

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

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.

Standards Aligned Systems

Clear Standards

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

Fair Assessments

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

Curriculum Framework

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

Instruction

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

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.

Interventions

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

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

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.

CompetenciesAnswer the Question

- What is the truly important mathematics at this

grade level or in this course?

Navigating the Website http//www.pdesas.org/

(No Transcript)

- Number of Mathematics Topics Intended

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?

MCF Supporting SAS Framework Knowledge Networks

Third Grade

Estimate and verify measurements.

Tell time to the minute.

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?

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.

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.

Building a System of Tens

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

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.

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.

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.

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.