REGIONAL EDUCATIONAL LAB ~ APPALACHIA

1
REGIONAL EDUCATIONAL LAB APPALACHIA

• The Effects of Kentucky Virtual High Schools
  Hybrid Course in Algebra I on
• Teaching Practices, Classroom Quality,
• and Adolescent Learning
• ACT 6
• Systems of Equations
• On-Line PD
• July 8, 2008

2
Agenda

• Welcome and Introductions
• Equipment check-in
• Updates
• Synthesis from Act 5 Responses
• Discussion of Act 6
• Unit Planning
• Assignment for Act 7 Discussion
• Wednesday, July 17

3
Equipment Check

• What is the current status for your school
  regarding computer access for the KVHS Algebra I
  course?

4
Synthesis of Act 5 Responses

• 1 Is x y lt 6 equivalent to 6 lt x y ?
• Attending to the process of reading for
  inequalities and graphs from left to right and
  once a mathematical sentence may require
  reversing that process students have trouble.
• Putting in the y mx b form to assist with
  making meaning such as y lt -x 6 as opposed to
  y gt -x 6
• Reviewing the Property of Symmetry for equalities
  states that if A B, then B A while that
  Property does not hold true for inequalities.
• Substituting numerical values such as x 2 and y
  -4 assist students in determining the nature of
  the equivalency.

5
Act 5 5, Importance of NAG

• Importance of using graphs or diagrams in
  explaining mathematical ideas. How will pictures,
  diagrams, or tables assist with solving word
  problems?
• Multiple Representations make connections for
  students and provide a critical visual for making
  meaning.
• Connections from the visual to the abstract
  assist in understanding the concept and serve as
  a way to verify solutions.
• Organizes thinking.
• Addresses various learning styles.
• Pictures, diagrams, and tables provide models
  that can assist with translating the words into
  mathematical symbols and creating possible
  solution pathways.

6
Act 5 6, The Distance Problem

• Takes Maria between 4.9 hours and 6.5 hours to
  complete the trip to her brothers house.
• Time is a conjunction, intersection, betweenness
  statement 4.9 lt Time lt 6.5 Hours.
• It should take Marie some where between 5 and 6
  hours to get to her brothers house which is 320
  miles away.

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Act 5 10, Proof for 0 gt 3

• Using numerical values to demonstrate that for
  some a gt 3 the proof is not valid.
• Providing justification/truthfulness for each
  statement while showing that by dividing both
  sides by a 3 (which is a negative number
  because a gt 3), the order of the inequality must
  be switched.
• http//mathforum.org/library/drmath/view/53142.ht
  ml provides a rationale for why the inequality
  is switched when multiplying/dividing by a
  negative.

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Act 5, General Comments

• Preciseness of communicating mathematical ideas
  uses mathematical language that supports and
  mirrors that Algebra is the Study of Structures
  with certain properties. For example, rather
  than
• - flip around an equation speak of the
  Symmetry Property that allows one to equate the
  left to the right or right to the left sides if
  A B, then B A.
• - plug in speak of substituting equivalent
  values because of the Substitution Property.
• - cancel, speak of terms adding out or
  dividing out because of the additive or
  multiplicative properties of equality.
• Graphs, Pictures, Models, Equations, Tables make
  connections to equivalent forms all should tell
  the same story (solution).
• Always have students to show their thinking and
  provide pictures and models of their
  understanding. When asked to explain your
  reasoning, expect mathematical work including
  equations, tables, models (graphs, labeled
  pictures), language that explains their
  reasoning.
• Model for them how to demonstrate mathematical
  thinking and reasoning write while they write
  show them your thinking.

9
Small Group Discussion of Act 6

• Highlights regarding
• Content
• Instructional Strategies
• Reflections from Act 6
• Share-out
• Negotiate someone to speak for the group for each
  strand
• 2-3 main points for each

10
Act 6 Scene 1

• How do I teach this?
• Rafting Problem
• Overlapping Circles
• Practicing Skills

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Getting Students to Connect to Solving Equations

• Multiple Representations
• Number Sense
• Diagrams (labeled drawings)
• Charts/Tables (charting ordered pairs)
• Symbolic Expressions (use of Real Number
  properties)
• Manipulatives (Algebra Tiles)
• Graphs (use of graphing calculators)
• Trace
• Y1Y2
• Spreadsheets
• Words
• Intentional/Transparent/Model

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Act 6 Helping Students

• Scene 1
• Anticipating Student Difficulties
• Scene 3
• Shannons Work

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KVHS Algebra I to Spotlight

• Connections KVHS Algebra I to Spotlight
• Systems of Equations and Inequalities
• Unit 4, Lessons 15-19 in KVHS
• Act 6 in Spotlight on Algebra

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Planning Lessons using KVHS Algebra I Skill Set
from Spotlight on Algebra

• How will you bundle your Units for 08-09?
• What are the structures you will put in place to
  support instructional strategies that motivate
  students to engage in learning Alg I?
• Refer to Strategies listed behind TAB 14
• For each structure, plan what formal feedback you
  will provide to move students into their
  zone of proximal development.
• See Linking Formative Assessment to
  Scaffolding, p 1

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Planning Instruction Using KVHS Alg. I

• What do you want the students to know and be able
  to do?
• How will you know that they know and can do?
• Formative
• Summative
• How will you use KVHS ALG I what lesson and in
  what context? Will Spotlight on Algebra help?
  How?
• How will you access prior knowledge?
• What is the new learning? How will students keep
  track and/or organize this learning?
• What form of student/teacher reflection will you
  use?
• See Research Standards behind TAB 2

16
Use of the Graphing Calculator within an
Authentic Context

• Cell Phone Problem

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Expectations for Next Steps

• Work through all of Act 7 take notes and be
  prepared to discuss for the Pedagogy Quiz post
  responses to Numbers 1, 7- 8, 10.
• Investigate KET Encyclomedia find one segment
  that provides an access point for some critical
  ALG I concept. Be prepared to share site location
  and ALG I concept addressed.
• Fill out the School Technology Database and send
  to Roland by Thursday, July 17, 2008
• Group Times will alternate 9-11 Group becomes
  the 2-4 Group while the 2-4 Group becomes the
  9-11 Groups.
• Have graphing calculators, notes from Act 7, and
  research binders nearby.
• Have open Spotlight on Algebra and the KVHS
  Algebra I Course.
• Make sure that ACT 5 6 Pedagogy Quiz responses
  have been posted.

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• Thanks for sharing your thinking!
• See you Thursday, July 17, 2008