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Mathematics II. Days 4 and 5 Training: Compressed Provided by First District RESA Winter 2009. Assumptions. Participants will teach Mathematics II or are responsible for the delivery of Mathematics II instruction

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Mathematics ii

Mathematics II

Days 4 and 5 Training: Compressed

Provided by First District RESA

Winter 2009


Assumptions
Assumptions

  • Participants will teach Mathematics II or are responsible for the delivery of Mathematics II instruction

  • Participants attended Days 1, 2, and 3 of Mathematics II training in May 2008 or have heard about the training

  • Participants are comfortable with the level of content in Mathematics II


Certainties
Certainties

  • Participants will hear information today that they already know

  • The DOE has prepared many resources including frameworks, curriculum maps, and pacing guides to assist teachers in providing instruction

  • More planning and collaboration will need to be done at the local level before implementation

  • FDRESA will assist as requested


Contingencies
Contingencies

  • Not all students will present themselves in Mathematics II as prepared as we would prefer

  • Continuous monitoring and adjusting of implementation plans will be necessary

  • Plans for teacher and student support will be made based on local needs


Enduring understandings
Enduring Understandings

  • Teaching and learning in a standards-based classroom require strategies that span the instruction/processing continuum from “sage on the stage” through constructivism

  • Instructional and assessment decisions are based on content complexity and student readiness while maintaining a focus on the standard


Essential questions
Essential Questions

  • How do the parts of performance standards inform the level of rigor in content, processes, and student expectations?

  • How does the assignment of standards and elements to Mathematics I, II, and III impact instructional planning?

  • How can collaboration facilitate analysis of instructional strategies for use in accelerated, regular, and support classes?


Performance standards
Performance Standards

Content and Process Standards

Tasks

Student Work

Commentary


Content standards
Content Standards

  • Content standards identify the understandings and big ideas of student learning

  • Elements provide further details about what students should know and be able to do


Process standards
Process Standards

  • Promote Mathematical Literacy

    • Problem Solving

    • Reasoning and Proof

    • Communicating

    • Making Connections

    • Using Multiple Representations


Tasks
Tasks

  • Tasks provide examples of the level of rigor and reasoning required for the standard

    • Give detail to the elements

    • Provide depth of understanding

    • Maintain high cognitive demand

    • Exemplify the kind of performance expected of students


Student work
Student Work

  • Reflects the level students should attain by end of course

  • Further defines content standards

  • Illustrates the kind of performance expected of students

  • Relates to a strand or topic rather than a single standard, embodying many concepts


Commentary
Commentary

Identifies the mathematics involved in the task

Identifies evidence of understanding related to a specific standard

Informs the teacher in understanding the depth, detail, and rigor in work that meets the standard

Guides students in comparing and judging the quality of their own work


Course content parameters
Course Content Parameters

Arrange the standards within strands across Mathematics 1, 2, and 3; check with key.

Using the GPS booklet, examine the algebra standards in grade 8 to decide how these lead to the algebra standards in M1.

What are the benefits of knowing the standards parameters by course?


Task analysis and planning
Task Analysis and Planning

In school or system groups, use the guiding questions to analyze the task segment provided.

Jot notes about suggestions.

Be prepared to share responses with the total group.


Rigorous relevant reasoning
Rigorous, Relevant Reasoning

Complete each problem, and answer the following questions.

Which mathematics standards and elements are the focus of the item?

As presented, the items are “constructed response” or mini-tasks. How can the item be changed to multiple choice? Create some logical choices.

Create a multiple choice item addressing the same content at a lower depth of knowledge level.


Instructional approaches
Instructional Approaches

  • Use tasks in a constructivist approach as presented in frameworks: warm up, opening, work, summary.

  • Present entire task in “chunks” as a guided activity.

  • Use only selected parts of tasks.

  • Provide instruction along the continuum and engage students in processing activities from algorithms through higher depth of knowledge problems.


Teacher-Focused

Student-Focused

Instruction/Processing Continuum

Constructivism

Lecture

Mastery Lecture

Direct Instruction

Concept Attainment

Discovery

Inquiry


Necessities
Necessities

  • Teach/revisit all standards and elements

  • Ensure that all assessments have about 55% higher level questions and that processing opportunities have been provided at the higher levels

  • Remember that collaboration with other teachers facilitates decisions about instruction and assessment


Support models
Support Models

All models for support can be classified based on the number of regular mathematics teachers a student has.

In groups, use the handout to decide how each model impacts the state-identified components of support and to list benefits and detractors of each model.


Collaboration in support
Collaboration in Support

  • All teachers who instruct Mathematics Support students should collaborate in an ongoing manner about:

    • Individual Student Progress

    • Curriculum Expectations

    • Instructional Strategies

    • Assessment


Individual student progress
Individual Student Progress

  • Discuss grades, strengths and weaknesses based on standards, mathematical disposition, and work habits


Curriculum expectations
Curriculum Expectations

  • Discuss specific standards to be addressed based on a timeline, prerequisite skills, vocabulary, and potential misconceptions


Instructional strategies
Instructional Strategies

  • Share or develop specific strategies for teaching mathematics concepts in both courses to provide consistency and understanding for teachers and students


Assessment
Assessment

  • Discuss content and assessment formats that are being used to evaluate students for specific standards


Summary essential questions
Summary: Essential Questions

How do the parts of performance standards inform the level of rigor in content, processes, and student expectations?

How does the assignment of standards and elements to Mathematics I, II, and III impact instructional planning?

How can collaboration facilitate analysis of instructional strategies for use in accelerated, regular, and support classes?


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