Recommendations for Teaching Mathematics

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Recommendations for Teaching Mathematics
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Recommendations for Teaching Mathematics

• Expectations include
• Sense making
• Focus on Processes
• High expectations for all
• Reflection

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Recommendations for Teaching Mathematics

• Tasks include
• Rich learning situations
• Reading and writing
• Discourse includes
• Talking
• Listening

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Recommendations for Teaching Mathematics

• Tools include
• Models
• Manipulatives
• Technology

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Recommendations for Teaching Mathematics

• Learning Environment includes
• Safety and intellectual stimulation
• Students learning at different rates
• Positive attitudes toward mathematics
• Class organized to facilitate learning

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NCTM's Standards for Teaching Mathematics

• Professional Standards for Teaching Mathematics
• National Council of Teachers of Mathematics, 1991

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NCTM's Standards for Teaching Mathematics

• Standard 1 Worthwhile Mathematical Tasks
• Standard 2 The Teacher's Role in Discourse
• Standard 3 Students' Role in Discourse
• Standard 4 Tools for Enhancing Discourse
• Standard 5 Learning Environment
• Standard 6 Analysis of Teaching and Learning

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The Importance of Planning

1. Establishes goals, ensures all essential content
   is included
2. Permits scheduling feasible units of time in a
   sensible sequence
3. Ensures an interesting beginning and involvement
   of each child.
4. Aids in holding the children's interest and
   attention.
5. Helps avoid unnecessary repetition.
6. Creates a feeling of confidence for the teacher 

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Levels of Planning Grade 6 ExampleYear
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....
 
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UnitChapter 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 6th
  
• grader like?" Predict,
  determine survey
• questions

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UnitChapter 11 Statistics (7 days)

• Day 4,5 Collect and display data - (remember to
• reserve computer lab and
  survey and
• graphing software)
• Day 6 Group presentations and discussion
• Day 7 Update portfolios and performance
• assessment

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Components of Lesson Planning

• 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

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Investigative Lesson Plan Outline

1. Launch
2. Investigate
3. Summarize

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Direct Instruction Lesson Plan Outline

1. Launch
2. Instruct
3. Summarize

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Nine Types of Adaptations

1. Size
2. Time
3. Level of Support
4. Input
5. Difficulty

1. Output
2. Participation
3. Alternate Goals
4. Substitute Curriculum

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Active Teaching and Learning

1. Be proactive with long and short range plans.
2. Make students aware of the objectives.
3. Spend at least half the period developing
   material through active engagement of the
   students
4. Involve students in problem solving, estimation,
   mental math, and mathematical extensions.
5. Communicate the expectation that students will be
   able to master the material if they attend.

Thornton and Wilson, 1993, p. 274
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Active Teaching and Learning

• 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
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Questions Include questions that help students

1. work together to make sense of mathematics.
2. rely more on themselves to determine whether
   something is mathematically correct.
3. learn to reason mathematically.
4. learn to conjecture, invent, and solve problems.
5. connect mathematics, its ideas, and its
   applications.

Professional Standards for Teaching
Mathematics National Council of Teachers of
Mathematics, 1991, pp. 3,
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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
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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.

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Types of Educational Software

• Educational Game includes an opportunity to win
  or overcome an obstacle.
• Problem-Solving aids in the development of
  higher-order thinking.
•  Tool provides assistance with graphing,
  computing, visualizing.

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Can you find the pattern?

• 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?

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Can you find the pattern?

• 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?