Transcript Recommendations for Teaching Mathematics

Recommendations for Teaching
Mathematics
Recommendations for Teaching
Mathematics
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Expectations include
– Sense making
– Focus on Processes
– High expectations for all
– Reflection
Recommendations for Teaching
Mathematics
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Tasks include
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Rich learning situations
Reading and writing
Discourse includes
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Talking
Listening
Recommendations for Teaching
Mathematics
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Tools include
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Models
Manipulatives
Technology
Recommendations for Teaching
Mathematics
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Learning Environment includes
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Safety and intellectual stimulation
Students learning at different rates
Positive attitudes toward mathematics
Class organized to facilitate learning
NCTM's Standards for Teaching
Mathematics
Professional Standards for
Teaching Mathematics
National Council of Teachers
of Mathematics, 1991
NCTM's Standards for Teaching
Mathematics
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Standard 1:
Standard 2:
Standard 3:
Standard 4:
Standard 5:
Standard 6:
Worthwhile Mathematical Tasks
The Teacher's Role in Discourse
Students' Role in Discourse
Tools for Enhancing Discourse
Learning Environment
Analysis of Teaching and Learning
The Importance of Planning
1.
2.
3.
4.
5.
6.
Establishes goals, ensures all essential content is included
Permits scheduling feasible units of time in a sensible
sequence
Ensures an interesting beginning and involvement of each
child.
Aids in holding the children's interest and attention.
Helps avoid unnecessary repetition.
Creates a feeling of confidence for the teacher
Levels of Planning: Grade 6 Example
Year
# Days
16
6
24
3
12
5
13
2
24
5
7
8
Topic/Chapter
Ch. 3-multiplication whole/dec
District computer unit
Ch. 4-division whole/dec
Election project-statistics
Ch. 5-metric measurement
Ch. 7-customary measurement
Ch. 9,10-geometry
Holiday ornaments-space figures
Ch. 6-fractions, add/subtract
State assessment tests
Ch. 11-statistics
Ch. 7-fractions, multiply
etc....
Date
8-30 to 9-21
9-22 to 9-29
10-2 to 11-2
11-3 to 11-7
11-8 to 11-22
11-27 to 12-1
12-4 to 12-20
12-21 to 12-22
1-3 to 2-3
2-6 to 2-10
2-13 to 2-21
2-22 to 3-3
Unit
Chapter 11: Statistics (7 days)
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Day 1
Day 2
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Day 3
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Intro, review collecting and displaying data-text
Interpreting data-Mean, Median, Mode, Range
text, cubes, calculators, family size problem
Groups-begin project "What is a typical 6th
grader like?" Predict, determine survey
questions
Unit
Chapter 11: Statistics (7 days)
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Day 4,5
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Day 6
Day 7
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Collect and display data - (remember to
reserve computer lab and survey and
graphing software)
Group presentations and discussion
Update portfolios and performance
assessment
Components of Lesson Planning
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Clearly state the objective(s)
Decide how to organize the class: whole class, small
group, or individual
Determine procedures to be followed
Decide how much time to spend
Decide how to assess or evaluate
Write the plan for the lesson
Investigative Lesson Plan Outline
I.
Launch
II.
Investigate
III.
Summarize
Direct Instruction Lesson Plan Outline
I.
Launch
II.
Instruct
III.
Summarize
Nine Types of Adaptations
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2.
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5.
Size
Time
Level of Support
Input
Difficulty
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Output
Participation
Alternate Goals
Substitute Curriculum
Active Teaching and Learning
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Be proactive with long and short range plans.
Make students aware of the objectives.
Spend at least half the period developing material
through active engagement of the students
Involve students in problem solving, estimation,
mental math, and mathematical extensions.
Communicate the expectation that students will be
able to master the material if they attend.
Thornton and Wilson, 1993, p. 274
Active Teaching and Learning
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Be clear; provide relevant examples and non-examples.
Ask many "why", "how", and other high level
questions.
Be organized; foster time-on-task.
Allow time for guided seatwork before independent
seatwork.
Regularly assign a small amount of homework or
seatwork to develop fluency, stimulate thinking, or
provide open-ended challenges.
Thornton and Wilson, 1993, p. 274
Questions: Include questions that help
students:
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5.
work together to make sense of mathematics.
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,
Manipulatives: The teacher should be
certain that:
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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
Types of Educational Software
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Drill and Practice provides practice for a skill
already taught.
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Tutorial provides instruction on new skills.
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Simulation allows students to experience events or
environments that would not otherwise be available.
Types of Educational Software
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Educational Game includes an opportunity to win
or overcome an obstacle.
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Problem-Solving aids in the development of
higher-order thinking.
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Tool provides assistance with graphing, computing,
visualizing.
Can you find the pattern?
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Select any number on the hundred board and mark it
using a color tile.
Circle the numbers directly above, directly below, to the
right, and to the left of your selected number. These
numbers form your four-point square.
What is the average of these four vertex numbers?
Select another number and repeat the averaging process.
After trying several examples, do you have a conjecture
about the pattern?
Can you find the pattern?
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Use your conjecture to answer the following
question:
The vertex numbers of a four-point square add to
224.
What number is at the center of the square?
Can you explain why the pattern works?