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, 2008 Series

Exemplar Classroom Practices &

Classroom Visits

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.

Nuts & Bolts

Technology Issues

Control Panel Hints

Reactions/Additions to the September Synthesis

WALKTHROUGH INDICATORS FOR SCHOOL VISITS

• Content Standards

• Classroom Instructional Practice

• Classroom Technology Practice

• On-line Student Interaction

PLANNING INSTRUCTION USING KYVS ALGEBRA I

• What do you want the students to know and be able to do [Program of Studies]?

• How will you know that they know and can do?– Formative Assessment (conversations, written work, questions posed)– Summative Assessment ( tests, projects, group work)

• How will you use KVHS ALG I – what lesson and in what context? How does it support the Program of Studies and connect with the text? Will Spotlight on Algebra or other links help? How?

• How will you access prior knowledge? What can students expect to experience in the KVHS Lesson?

• What is the new learning? How will students keep track and/or organize this learning? What can they expect to see in the KVHS Lesson? How will you provide support?

• What will you do when students need redirection and/or more support?

• What form of student/teacher reflection will you use?

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.

Inverse Action/Operation• –• +• ÷• x• x²• • • x3

Exemplars- Note-taking

• Action/Operation

•+• –• X •÷• • x²• x³•

3

3

Exemplars- Note-taking

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

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.

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

Increase Rigor & Learning Expectations Through Connections

•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.

• For x/2 + 1 = -2 – x/4

Observations to Note

When speaking of ‘=‘ use the term “THE SAME AS” to support the meaning of ‘=‘.

Insist that students SHOW THE WORK on the tracking tool, homework, and quizzes. Can print out the homework problems, have students complete, then enter the computer to insert answers. [Note: KVHS grades the homework but does not include the grade in the gradebook.]

LISTEN to what students are saying. RESPOND to questions/comments allowing them to construct meaning and clarify misunderstandings. Go beyond your agenda and be responsive to what you hear. 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?

Observations to Note

Prior to entering the KYVS Lesson, teachers must communicate learning goals, expectations, and make connections prior to and after viewing the KVHS Lesson.

Upon completing KYVS Unit I, Lessons 1- 4 ( simplifying & solving linear equations) skip KVHS Unit 2, Lessons 5 – 9 (linear inequalities & absolute value) and go to KVHS 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.

KYVS Outline for Units 1-3 (Linear Equalities & Inequalities)

Unit 1: Basic algebra principles Lesson 1: Real numbers & algebraic expressions Lesson 2: Simplifying expressions Lesson 3: Solving equations Lesson 4: More on solving equations Unit 2: Inequalities & absolute values Lesson 5: Sets, intersections & unions Lesson 6: Inequalities & their graphs Lesson 7: Using inequalities Lesson 8: Solving equations involving absolute values Lesson 9: More solving inequalities involving absolute values Unit 3: Graphs of linear equations Lesson 10: Graphing linear equations Lesson 11: Slope in graphs & equations Lesson 12: Linear & nonlinear equations Lesson 13: Finding the equation of a line Lesson 14: Parallel & Perpendicular lines, & linear inequalities

Additional Comments

• “Students sometimes fuss about using KVHS but it is forcing them to become independent learners while increasing their reading, note-taking, and listening skills.”

• “The KYVS Lessons support learning diversity. My students are at various spots within any one Lesson. The format allows a student to go back if they do not understand a concept and thus differentiated learning.”

• “I need to see your beautiful face.”• “I need your eyes. If I do not see your eyes, I

cannot tell you are listening to me.”• “What are your questions? Give me one.”

Using the Hybrid Wiki for Sharing

URL: http://hybridalgebra. wikispaces.com/

Basics- Adding a page- Adding a link- Posting a file

Reminders

Office Hours (Mondays & Tuesdays)

Help Line:- Bb: 866-590-9240- KDE, Paula White: 502-564-4772(#4512)

paula.white@education.ky.gov- KDE, Kari Welch: 502-564-4772 (#4546),

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

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

TEACHER, COHORT II November 17, 19, & 20: On-Line Collaboration will include a discussion on Mathematical Discourse - Academic Dialogue and Questioning Techniques.