Chapter
3
Planning and Teaching
To a c c o m p a n y H e l p i n g C h i l d re n L e a r n M a t h C d n E d , R e y s e t a l .
©2010 John Wiley & Sons Canada Ltd.
Guiding Questions
1. What questions must an elementary mathematics teacher
answer before beginning to plan?
2. Why does the teacher plan mathematics lessons so carefully?
3. What levels of planning does the teacher create? What are
three types of lessons used to teach mathematics, and what is
the purpose of each?
5. How can the teacher meet the needs of all students?
6. How does the teacher integrate planning with assessing and
analysis?
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Preparing to Teach:
Questions to Ask Before Planning Begins
• Do I understand the mathematics I am
teaching?
• What are the developmental characteristics of
my students?
• What do my students already know?
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Preparing to Teach (cont.)
• What kinds of tasks will I give my students?
– Focus on the mathematics.
– Provide necessary practice.
• How will I encourage my students to talk?
– What kind of questions will I ask?
– How will I group my students?
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Preparing to Teach (cont.)
• What materials will my students and I use?
– Provincial curriculum documents
– Textbook lessons
– Children’s literature
– Manipulatives
– Technology
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Effective Mathematical Tasks
• Are often authentic in that they come from the
students’ environment
• Are challenging yet within students’ reach
• Pique the students’ curiosity
• Encourage students to make sense of mathematical
ideas
• Encourage multiple perspectives and interrelated
mathematical ideas
• Nest skill development in the context of problem
solving
(Reys and Long, 1995)
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Include Questions that Help Students:
• work together to make sense of mathematics.
• learn to rely more on themselves to determine
whether something is mathematically correct.
• learn to reason mathematically.
• learn to conjecture, invent, and solve
problems.
• connect mathematics, its ideas, and its
applications.
Professional Standards for Teaching Mathematics
National Council of Teachers of Mathematics, 1991, pp. 3,4
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Manipulatives
The teacher should be certain that:
• manipulatives have been chosen to support
the lesson's objectives.
• students have received orientation concerning
the manipulatives and classroom procedures.
• the lesson involves active participation of each
student.
• the lesson plan includes procedures for
evaluation that reflect an emphasis on the
development of reasoning skills.
Ross and Kurtz, 1993, p. 256
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Types of Educational Software
• Drill and Practice provides practice for a skill
already taught.
• Tutorial provides instruction on new skills.
• Simulation allows students to experience
events or environments that would not
otherwise be available.
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Types of Educational Software
(cont’d)
• Educational Games include an opportunity to
win or overcome an obstacle.
• Problem-Solving aids in the development of
higher-order thinking.
• Tool software provides assistance with
graphing, computing, visualizing.
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Planning for Effective Teaching
• Importance of Planning
• Levels of Planning
– Planning for the Year
– Planning Units
– Planning for Daily Lessons
• Planning Different Types of Lessons
– Investigative
– Direct Instruction
– Exploration
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Planning for Effective Teaching Cont.
 Meeting the Needs of all Students
• Teaching students from other cultures
• Teaching English-language learners
• Teaching students with identified special needs
 Assessment and Analysis in Planning
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Levels of Planning: Grade 6 Example Year
# Days Topic/Chapter
Date
16
Ch. 3-multiplication whole/dec
8-30 to 9-21
6
District computer unit
9-22 to 9-29
24
Ch. 4-division whole/dec
10-2 to 11-2
3
Election project-statistics
11-3 to 11-7
12
Ch. 5-metric measurement
11-8 to 11-22
5
Ch. 7-customary measurement
11-27 to 12-1
13
Ch. 9,10-geometry
12-4 to 12-20
2
Holiday ornaments-space figures
12-21 to 12-22
24
Ch. 6-fractions, add/subtract
1-3 to 2-3
5
State assessment tests
2-6 to 2-10
7
Ch. 11-statistics
2-13 to 2-21
8
Ch. 7-fractions, multiply
2-22 to 3-3
Etc…
Example Unit Plan
Chapter 11: Statistics (7 days)
• Day 1: Intro, review collecting and displaying
data-text
• Day 2: Interpreting data-Mean, Median, Mode,
Range
• text, cubes, calculators, family size problem
• Day 3: Groups-begin project "What is a typical
grade 6 student like?"
– Predict and determine survey questions
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Chapter 11: Statistics (7 days)
(cont’d)
• Day 4 & 5: Collect and display data (remember to reserve computer lab and
locate survey and graphing software)
• Day 6: Group presentations and discussion
• Day 7: Update portfolios and performance
assessment
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Generalized Lesson Plan
• 1. Introductory Information
•
•
•
•
•
•
•
•
Grade Level
Date
Topic/Title
Objective(s)
Assessment
Gearing Down
Gearing Up
Materials
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
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Generalized Lesson Plan (cont.)
• Lesson Outline
– Launch (setting the stage)
– Investigate (for investigative lessons)
or
Instruct (for direct instruction lessons)
or
Explore (for exploration lessons)
– Summarize (closure)
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Investigative Lesson Plan Outline
• Launch
• Investigate
• Summarize
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Direct Instruction Lesson Plan Outline
• Launch
• Instruct
• Summarize
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Exploration Lesson Plan Outline
• Launch
• Explore
• Summarize
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Meeting the Needs of All Students:
Teaching Students from Other Cultures
• Be aware of the learning preferences of other
cultures
• Connect mathematics to the cultural roots of
your students
• Students enjoy learning about how math was
developed by people in other countries
• Students see the relevance of math when it is
tied to art, literature, technology and games
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Meeting the Needs of All Students:
Teaching English Language Learners
• Give students comprehensible input (i.e.,
language they will understand).
• Give students opportunities to increase
verbal interaction during class activities (i.e.,
to talk more with you and with the other
children).
• Teach in a way that contextualizes language.
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Teaching English Language Learners
(cont.)
• Use teaching strategies and groupings that
reduce the anxiety of students.
• Assign activities in the classroom that offer
students opportunities for active involvement.
(Herrell, 2000, p. xiv)
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Meeting the Needs of All Students:
Potential Barriers for Students with
Special Needs
• Memory: visual memory, verbal/auditory
memory, working memory
• Self-regulation: excitement/relaxation,
attention, inhibition of impulses
• Visual Processing: visual memory, visual
discrimination, visual/spatial organization,
visual-motor coordination
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Potential Barriers for Students
with Special Needs (cont.)
• Language Processing: expressive language, vocabulary
development, receptive language, auditory processing
• Related academic skills: reading, writing, study skills
• Motor Skills: writing legibly, aligning columns, working
with small manipulatives, using one-to-one
correspondence, writing numerals
•
(Karp and Howell, 2004, p. 120)
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Meeting the Needs of All Students:
Nine Types of Adaptations
•
•
•
•
•
Size
Time
Level of Support
Input
Difficulty
•
•
•
•
Output
Participation
Alternate Goals
Substitute
Curriculum
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
Assessment and Analysis in
Planning
• Assessment should be an integral aspect of
mathematics instruction.
• Many teachers also find it helpful to keep an
evaluative record of the effectiveness of their
lessons.
Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,
Canadian Edition, © 2010
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