Transcript October 2009 PP97 version - hybridalgebra

REGIONAL EDUCATIONAL LAB ~
APPALACHIA
The Effects of Kentucky Virtual High School’s 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?
x/ + 2 = -1 – x/
3x + 12 = -1 – 5x
2
4
-7 + 9x = 7x – 4
5–⅓x=⅔x+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
Problem
+ 2 = - 1 – x/4
4(½x + 2) = 4(- 1 – ¼ x)
x/
2
2x + 8
–8
2x
+x
3x
3x
÷3
=
=
=
=
=
=
-4 –x
–8
-12 – x
+x
-12
-12
• Given
•
•
•
•
•
•
•
Multiplication Prop. of =
Distributive Prop. of =
Subtraction Prop. of =
CLT; Add. Inverse Prop.
Addition Prop. of =
CLT; Add. Inverse Prop.
Division Prop. of =
÷3
x = -4
• Dividing out common factors
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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
• Action/Operation
•+
•–
• X
•÷
•
• x²
• x³
•3
Inverse Action/Operation
• –
• +
• ÷
• x
• x²
•
• 3
• x3
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Exemplars
Variable
Variable with Numerical
Coefficients
• x
• 1•x
• -M
• -1 • M
•
• ½•T
T/
2
• - x/4
•
2x
2/
5 2
• 0
Conceptual Model
• -¼ • x
•
2/ •
5
x
• 0•x
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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)
[email protected]
- KDE, Kari Welch: 502-564-4772 (#4501),
[email protected]
- KDE, Grace Yeh: 502-564-4772 (#4537)
[email protected]
- Identify yourself as COHORT III HYBRID ALGEBRA
TEACHER
 November On-Line Discussion: Thursday, November 12, 2009,
3:30 EST
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