Making Good Instructional Decisions Implementing Effective Teaching Practices Mathematics Success fo

1
Making Good Instructional
Decisions Implementing Effective Teaching
Practices Mathematics Success for
Students with Learning Problems!

• David Allsopp, Ph. D.
• Department of Special Education
• University of South Florida
• dallsopp_at_tempest.coedu.usf.edu

2
Agenda

• Introduction/Orientation of Handouts
• Importance of Meaning and Valuing Mathematics
  Instruction for Students with Learning
  ProblemsSelf-Reflection
• Why Do Students with Learning Disabilities Have
  Difficulty Learning Mathematics?
• 10 Powerful Teaching Techniques
• Where Do I Go From Here How Do I Get There?
  Long-Term Professional Development Introduction
  to Several Online PD Resources
• Questions/Discussion

3
Learning Objectives

• Self-relect on beliefs and preparedness to teach
  mathematics to students with learning
  disabilities.
• Prioritize several important areas for long term
  professional development.
• Identify learning characteristics that make
  learning mathematics difficult for students with
  learning disabilities.
• Identify powerful/effective instructional
  strategies determine how you can use at least
  one to improve mathematics learning for your
  students.
• Learn about several online resources and how to
  use them for my personal continuing professional
  development goals.

4
Topic 1 Introduction/Orientation of Handouts

• Participant Note-taking Guide/Activity packet
• Mathematic Teacher Placement Exam

5
Are You Good Enough?
Dont Be Last!
Work it Baby!!
FASTER!
Just
Try
98
FASTER!!
Harder!!!
FASTER!!!
The Last Group Was FASTER!
6
What Was Your Experience?...Implications for
Students with Learning Problems
7
Topic 2 Importance of Meaning Teacher
Self-Reflection

• Meaning...
• Why is meaning important?
• Some examples

8
Numbers, Numbers, Numbers... What Do They Mean?
9
Conceptual MeaningDirections Solve the
following two problems.
10
Can you explain your answer for each problem?
11
How can we enhance the meaning?
12
Use Language 2 x
4 ?two
groups of four Steelers is
how many Steelers 1/2 x
1/4
? one-half of a one-fourth piece
of pizza is how much pizza
13

• Provide Concrete Experiences
• 2 X 4
  ?
• two groups of four Nittany
  Lions is how many Nittany Lions

14
Provide Concrete Experiences 1/2
x 1/4
? one-half of
a one-fourth piece of pizza is how much
pizza
15

• What is...
• 435434544 ?
• even par! (Golf)

Contextual Meaning
16
Meaning and Disability

• Write a title for a short story you might write
  for the following picture...

17
(No Transcript)
18
Write Your Title

• Lets share
• our titles!-)

19
One thing I would like to remember from the
learning activities in Topic 2 is... ?
20

• Complete the Teacher Self-Reflection Activity
  Sheet in your packet. ?
• Brief Discussion

Teacher Self-Reflection
21
Recent Brain Research Implications
22
(No Transcript)
23
(No Transcript)
24
Topic 3 Why is it Difficult for Students with
Learning Problems to Learn Mathematics?

• Brief reflection on learning problems
• 7 Learning Characteristics That Are Barriers for
  Learning and Making Meaning of Mathematics

25
8 Learning Characteristics That Create Barriers
for Learning Mathematics

• ?Learned helplessness
• Passive approach to learning
• ?Metacognitive thinking deficits
• ?Attention problems
• ?Anxiety about learning mathematics
• ?Cognitive Processing deficits (auditory,
  visual/spatial, fine motor)
• ?Memory problems
• ?Low level of academic achievement (gaps)

?
26
Lets Reflect On Our Experiences with the Math
Quiz

• ?Learned helplessness
• ?Passive approach to learning
• ?Metacognitive thinking deficits
• ?Attention problems
• ?Anxiety about learning mathematics
• What is it?
• How does it impact learning mathematics?

27
How About the Other Learning Characteristics?

• ?Cognitive Processing deficits (auditory,
  visual/spatial, fine motor)?Memory problems
  ?Low level of academic achievement (gaps)

28
Cognitive Processing deficits (auditory,
visual/spatial, fine motor)?

• Auditory Processing Example What did he say?

The Blue Ardvark and the Pink Panther went to
the movie in a red convertible driven by the
White Ghost.
29
Memory Problems

• Storage
• Retrieval

30
Do you know the nicknames?Write down the
following names on a piece of paper

• Wichita State
• Kansas
• Bucknell
• Penn
• Western Kentucky
  
• Michigan
• Mississippi State
• Mississippi
• Florida
• Florida State
• Furman
• Idaho
• Northern Arizona
• Ferrum
• James Madison

31
The National College Nickname Memory Test
Wichita State Shockers
Kansas Jayhawks
Northern Arizona Lumberjacks
Florida State Seminoles
Mississippi State Bulldogs
Mississippi Rebels
Furman Paladins
Penn Quakers
James Madison Dukes
Bucknell Bison
Western Kentucky Hilltoppers
Ferrum Panthers
Michigan Wolverines
Florida Gators
Idaho Vandals
32
Lets Take the Test!!
Bucknell
Northern Arizona
Ferrrum
Mississippi State
Kansas
Florida
Western Kentucky
Furman
Idaho
Michigan
Florida State
Penn
Mississippi
Wichita State
James Madison
33
The National College Nickname Memory Test -
Answers

• Wichita State Shockers
• Kansas Jayhawks
• Bucknell Bison
• Penn Quakers
• Western Kentucky Hilltoppers
• Michigan Wolverines
• Mississippi State Bulldogs
• Mississippi Rebels
• Florida Gators
• Florida State Seminoles
• Furman Paladins
• Idaho Vandals
• Northern Arizona Lumberjacks
• Ferrum Panthers
• James Madison Dukes

34
Reflection Your Experiences

• How many nicknames were you able to recall?
• What either helped or inhibited your ability to
  recall the nicknames?
• What role does memory play in doing mathematics?
• Multi-step operations
• Multiple meanings for a math symbol or term
• Recalling formulas
• Employing problem solving strategies

35
Low Level of Academic Achievement/Gaps in
Understanding

• Solve the following problem
• Onewa ayda wota riendsfa entwa ota eirtha
  avoritefa usicma oresta, Lanpa Inena Usicma.
  Eromeja ikesla iphaopha osa eha oughtba eethra
  EDsa. Owna, Eronicava ikesla ythmrha anda uesbla
  osa eshea oughtba wota EDsa. Etha otalta ostca
  ofa etha EDsa aswa irtytha evensa ollarsda. Ifa
  othba Eromeja anda Eronicava aidpa etha amesa
  orfa eacha EDsa, owha uchma dida eacha EDsa
  ostca?

36
Ok, Lets Try it Again...

• 3c 2c 37
• 5c 37
• c 7.40

37
Implication for Mathematics?

• Language
• Ability to process the Language of Mathematics?

38
One thing I would like to remember from the
learning activities in Topic 3 is... ?
39
Topic 4 Powerful Teaching Techniques

• What are they?
• Key instructional features
• Examples
• How do they help students with learning
  disabilities?

40
10 Powerful Teaching Techniques

• Support Student Connections Between New
  Mathematics Concepts Prior Knowledge/Experiences
  
• Provide Explicit Models of Target Mathematics
  Concepts, Skills, Processes
• Imbed Instruction and Practice in Authentic
  Contexts
• Teach Problem Solving Strategies
• Cue Important Features of a Mathematics
  Concept/Skill Using Multisensory Methods
• Use Language Experiences to Enhance Meaning
  Understanding
• Ground Abstract Concepts Processes in Concrete
  Experiences
• Provide Students Many Opportunities to Respond
• Monitor Student Learning Provide Them Concrete
  Ways to Visualize Their Learning
• Provide Continuous Maintenance Activities for
  Previously Mastered Concepts/Skills

41
PTT 1 Support Student Connections Between New
Mathematics Concepts Prior Knowledge/Experiences

• 
  Where we are
• Where our students are

42
Meet Your Students Where They Are...

• L - I - P
• L ink to prior knowledge/previous experiences.
• I dentify what students will learn.
• P rovide meaning/rationale.

43
L I P

• Where we are Where our
  students are

44
PTT 2Provide Explicit Models of Target
Mathematics Concepts, Skills, Processes

• You cant hit what you cant see...

Student
Mathematics Concept
45
Make the mathematics concept accessible to your
students by...

• Student
  Mathematics Concept
• Multiple Senses
• Cue Important Features/Steps
• Examples Non-examples
• Think Aloud
• Engage Student Thinking

46
PTT 3Imbed Instruction and Practice in
Authentic Contexts

• Age/Grade
• Interests/Hobbies
• Family/Culture
• Student Interest Inventory

47
Student Interest Matrix (See Special Connections
Website)
48
Mathematics Class Interest Matrix(see Special
Connections Website)
49
PTT 4Teach Problem Solving Strategies

• ?Students with learning disabilities do not
  naturally employ problem solving strategies like
  successful mathematics students do...

50
What Are They?

• An efficient learnable process for
• 1) solving a particular type of problem
• 2) developing conceptual understanding of
  important mathematics concepts
• What do they include?
• limited number of steps (3 to 7 steps)
• accurately reflect the problem/concept
• provide cueing
• actions thinking
• they are taught

51
Strategy Examples

• MathVIDS

52
Example Chart to Help Students Generate
Problem-Solving Strategies
53
Example Helping Students Think About/Monitor
Their Use of Different Strategies
54
PPT 5Cue Important Features of a
Mathematics Concept/Skill Using Multisensory
Methods

• Visual
• Auditory
• Tactile (Touch)
• Kinesthetic (Movement)
• Cognitive/Thinking

55
Examples of Visual Cuing

• color
• words/language
• pictures
• cue sheets
• 1/2 one of
  two equal parts

56
(No Transcript)
57
Example Cue Sheet to Enhance A Students
Independent Practice
58
PPT 6Use Language Experiences to Enhance
Meaning Understanding

• Incorporate the following language expression
  modalities
• Speech
• Writing
• Drawing
• Acting Out/Drama
• Song
• Videotape, phoography/technology

59
Examples - Describe what numbers symbols mean

• Describe what numbers symbols mean
• 1/2 x 1/4 1/8
• one-half of one-fourth is one-eighth
• 1/2 4 1/8

60

• Combine Language with Color-Coding and Concrete
  Materials or Drawings/Pictures
• 2 X 4
  ?
• two groups of four Steelers is how many
  Steelers

61
How? Create stories that represent mathematics
conceptsExamples Create Stories/Examples
That Communicate Understanding

• Example Intersect of x y coordinates on a
  plane.
• Speech/Words - The place on the football field
  where the Steelers kickoff.
• Drawing (x, y) where x15 y 0 x-15 y0

62
Meaningful Story Problems
The Gators quarterback threw a long pass to his
favorite receiver. The play started with the ball
on the Gators 5 yard line. Use the following
ordered pairs to find out where on the field the
pass was caught, how many yards the ball flew in
the air, and how many yards the Gators gained on
the play (5, 11) (10, 21), (15, 31), (20, 41)
63
Use Structured Dialogue Sheets-Patterns

• I looked at ____________ patterns.
• ? My first pattern used _______________ .
  Draw a picture of your pattern here
• When I labeled my pattern, I found that it had an
  ____________ pattern. Label your pattern.?My
  second pattern used _______________ . Draw
  a picture of your pattern here
• When I labeled my pattern, I found that it had an
  ____________ pattern. Label your pattern.
• My patterns were alike/different because
  ____________________________.
• I

64
Structured Dialogue Sheets - Algebra Expressions

• The variable in the problem is _________.I read
  the problem and ________ is on the left side of
  the sign and __________ is on the right
  side.There is a ______________ next to the
  variable. This means that ________________________
  __________________________________________________
  __________________.I can describe the expression
  with the following words or picture

65
PTT 7Ground Abstract Concepts Processes in
Concrete Experiences

• Manipulatives
• Teach Drawing Strategies

66
Manipulative Examples (Discrete)

• Attributes more accessible
• Can be manipulated more easily

67
Teach Drawing Strategies

• Start with concrete experiences
• Move to drawing representations of concrete
  experiences

68
Drawing Example
3x 4
16
x 4
69
Other Drawing Examples(see MathVIDS website)
70
Enhance Abstract Understanding

• Reasons for DifficultyLack of conceptual
  understandingMemory problemsOrganization/writing
  /visual processing problems
• Provide Many Practice Opportunities/Link to
  concrete drawing experiences! MASTERY

71
PTT 8Provide Students Many Opportunities to
Respond

• The more opportunities students with learning
  disabilities have to respond to a learning task,
  the more likely it is they will master that
  learning task...

72
How?

• Ensure that...
• students have a motivational context
• the practice activity focuses on the target math
  concept/skill
• students have multiple opportunities to respond
• teachers have a way to evaluate student responses
• Examples
• Instructional Games
• Self-correcting Materials
• Structured Peer-Mediated Learning Groups
• Structured Language Experiences
• Planned Discovery Experiences

73
Math Instructional Games/Self-Correcting
Materials - A Few Ideas

74
Example Simple Algebraic Thinking Board Game
75
Example Algebraic Thinking Board Game

• Football Game
• Flash Cards with ordered pairs
• Students take turns moving their football
• Touchdown scored when football crosses goal line

76
What Instructional Game Ideas Can You Create for
Your Students?

• Groups of 3-4
• Choose a mathematics concept/skill your students
  need to learn.
• Create an instructional game idea.
• Share your idea...

77
PPT 9Monitor Student Learning Provide Them
Concrete Ways to Visualize Their Learning

• At least 2-3 times weekly
• Incorporate at concrete, drawing abstract
  levels
• Use short, easy to evaluate probes
• Pinpoint key concepts for monitoring
• Teach students to chart their learning
• Use as a way to engage students in setting
  learning goals
• CELEBRATE SUCCESS!!

78
How?
79
Examples

• Abstract Level
• Probe/Curriculum Slice

80
goal line

• Visual Display
• corrects
• incorrects
• What does this learning picture show?

81
Learning Picture Example Student Use of
Strategies
82
PTT 10Provide Continuous Maintenance
Activities for Previously Mastered Concepts/Skills

• Purposefully plan maintenance opportunities
• Emphasize foundational concepts for the
  mathematics curriculum you teach
• Make sure target maintenance concepts are ones
  students have previously mastered
• Vary the type of activities
• Avoid drill practice
• Include students in developing ideas for
  maintenance activities
• Emphasize connections between abstract concrete
• Engage students in talking/writing/drawing
  about target maintenance concepts

83
One thing I would like to remember from the
learning activities in Topic 4 is ... ?
84
Topic 5 Long-term Professional Development
Resources

• http//coe.jmu.edu/mathvidsr
• The Learning Toolbox
• http//coe.jmu.edu/learnngtoolbox
• http//www.specialconnections.ku.edu/cgi-bin/cgiwr
  ap/specconn/index.php

85
One thing I would like to remember from the
learning activities in Topic 5 is... ?
86
Topic6 Questions/Discussion

• ?