REGIONAL EDUCATIONAL LAB ~ APPALACHIA

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REGIONAL EDUCATIONAL LAB APPALACHIA

• The Effects of Kentucky Virtual High Schools
  Hybrid Course in Algebra I on
• Teaching Practices, Classroom Quality,
• and Adolescent Learning
• On-Line Collaboration
• October 15, 2009
• Exemplar Classroom Practices
• 
  Classroom Visits

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Goals for On-Line Collaboration

• On-line Collaboration using Horizon Wimba
• Share teaching strategies/resources,
• Discuss planning instruction,
• Analyze student work,
• Share formative and summative assessment
  instruments/strategies that move learning
  forward,
• Provide instructional structures where feedback
  is focused on how students can improve related to
  learning goals,
• Others as defined by teachers and as need to
  address issues in the field including new
  learning that promotes student achievement.

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Agenda

• Welcome
• Technology issues
• Updates other issues
• Classroom visit results
• Hybrid instructional best practices from Cohort I
  II

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Cohort III Findings

• Using mathematical vocabulary
• Using note-taking/ tracking devices
• Opening activities for student engagement
• Simplifying expressions and/or solving equations
• Connecting the face-to-face learning with the
  on-line KYVS Lessons
• Reflecting and bringing the learning experience
  to closure

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Exemplars- Class Opener

• Before solving equations w/ variables on each
  side. (Lesson 4.3)
• Talk to your partner about what is different
  about the four equations from what you have
  previously seen or worked with?
• 3x 12 -1 5x x/2 2 -1 x/4
• -7 9x 7x 4 5 ? x ? x 3
• Sample student responses
• There are 2 variables on each side of the
  equation.
• There are fractions by x.
• Followed by guided practice, whole group
  discussion to solve each equation.
• Students responded and took notes.
• Alternate methods were encouraged and displayed.

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Observations to Note

• When speaking of EQUAL () use the term THE
  SAME AS to support the meaning of . Get
  students used to expressing mathematical
  relationships in their own language and in
  symbolic language.
• LISTEN to what students are saying. RESPOND to
  questions/comments allowing them to construct
  meaning and clarify misunderstandings.
  Acknowledge good thinking. Extend answers by
  asking for clarification or to provide an
  example(s). Ask Can you tell me why? Is there
  another way? Can you show me? What does inverse
  mean to you?

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Observations to Note

• Prior to entering the KYVS Lesson, teachers must
  communicate learning goals, expectations, and
  make connections prior to and after viewing the
  KYVS Lesson.
• Upon completing KYVS Unit I, Lessons 1- 4 (
  simplifying solving linear equations) skip KYVS
  Unit 2, Lessons 5 9 (linear inequalities
  absolute value) and go to KYVS Unit 3, Lesson 10
  - 14 (graphs of linear equations) to deepen and
  connect student understanding of Linear
  Equations. It will provide the NAGS model, thus
  enabling students to connect all models. The
  learning goal would then support students as they
  enter into solving linear inequalities and
  systems of equations.

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Algebra is the Study of Structures with Certain
Properties

• Associated Property
• Given
• Multiplication Prop. of
• Distributive Prop. of
• Subtraction Prop. of
• CLT Add. Inverse Prop.
• Addition Prop. of
• CLT Add. Inverse Prop.
• Division Prop. of
• Dividing out common factors

• Problem
• x/2 2 - 1 x/4
• 4(½x 2) 4(- 1 ¼ x)
• 2x 8 - 4 x
• 8 8
• 2x -12 x
• x x
• 3x -12
• 3 x -12
• 3 3
• x -4

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Increase Rigor Learning Expectations Through
Connections

• For x/2 1 -2 x/4
• Let x/2 1 y1
• -2 x/4 y2
• Display graphs using the OVHD
• graphing calculators.
• Allow the students to investigate and develop
  thinking skills around the graphs of each, ask
  what students they notice about the individual
  graphs and the two graphs together.

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Exemplars

• Inverse Action/Operation
• x
• x²
• x3

• Action/Operation
• X
• x²
• x³

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Exemplars

• Variable with Numerical
• Coefficients
• 1 x
• -1 M
• ½ T
• -¼ x
• 2/5 x
• 0 x

• Variable
• x
• - M
• T/2
• - x/4
• 2/2
• 0

Conceptual Model
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LESSON DESIGN USING KYVS LESSONS

• Learning Cycle Activating Prior Knowledge, New
  Learning, Reflections
• Vocabulary Critical to communicating
  understanding
• Multiple Representations NAGS where Numbers
  within the table of values, Algebra within the
  equation, Graph of the algebraic equation,
  Sentence to describe the mathematics
• Learning Goals Verbalizing these goals with
  students and connecting to the Program of Studies
• Tracking Tool used by students to track their
  understanding of key concepts within the Lesson.

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Hybrid Algebra Sites
Site Contents/Purpose
http//www.kyvs.org/ For the My Courses Tab Algebra Lessons (Semester I II), SpotLight on Algebra (ACT 1 -9, Blackline Masters, and other support materials) and the Hybrid/Blended Learning Community (videos of hybrid instructional practices) sites. For the e-Learning KY Tab KET EncycloMedia other instructional sources
http//hybridalgebra.wikispaces.com/ Site for posting research materials, announcements
http//67.202.209.114 On-Line Distance platform Office hours Professional learning conversations
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REMINDERS

• Office Hours Monday (9-10 EST) Tuesday (1-2
  EST)
• Help Line
• - Bb 866-590-9240
• - KDE, Paula White 502-564-4772(4512)
• paula.white_at_education.ky.gov
• - KDE, Kari Welch 502-564-4772 (4501),
  kari.welch_at_education.ky.gov
• - KDE, Grace Yeh 502-564-4772 (4537)
• grace.yeh_at_education.ky.gov
• - Identify yourself as COHORT III HYBRID ALGEBRA
  TEACHER
• November On-Line Discussion Thursday,
  November 12, 2009, 330 EST