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REGIONAL EDUCATIONAL LAB ~ REGIONAL EDUCATIONAL LAB ~ APPALACHIAAPPALACHIA

The Effects of Kentucky Virtual High School’s Hybrid Course in Algebra I on

Teaching Practices, Classroom Quality, and Adolescent Learning

On-Line CollaborationOctober 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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Welcome

Technology issues

Updates & other issues

Classroom visit results Hybrid instructional best practices from

Cohort I & II

Agenda

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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 – ⅓ x = ⅔ 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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Inverse Action/Operation• –• +• ÷• x• x²• • • x3

Exemplars

• Action/Operation

•+• –• X •÷• • x²• x³•

3

3

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Exemplars

Variable

• x

• - M

• T/2

• - x/4

• 2/2

• 0

Variable with Numerical

Coefficients

• 1 • x

• -1 • M

• ½ • T

• -¼ • x

• 2/5 • x

• 0 • x

Conceptual Model

5

2x

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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@education.ky.gov- KDE, Kari Welch: 502-564-4772 (#4501),

kari.welch@education.ky.gov- KDE, Grace Yeh: 502-564-4772 (#4537)

grace.yeh@education.ky.gov- Identify yourself as COHORT III HYBRID ALGEBRA

TEACHER

November On-Line Discussion: Thursday, November 12, 2009, 3:30 EST