1. Recommendations for Teaching Mathematics

2. Recommendations for Teaching Mathematics
Expectations include
Sense making
Focus on Processes
High expectations for all
Reflection
Master 3-1: Recommendations for Teaching Mathematics

3. Recommendations for Teaching Mathematics
Tasks include
Rich learning situations
Reading and writing
Discourse includes
Talking
Listening
Master 3-1: Recommendations for Teaching Mathematics

4. Recommendations for Teaching Mathematics
Tools include
Models
Manipulatives
Technology
Master 3-1: Recommendations for Teaching Mathematics

5. 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
Master 3-1: Recommendations for Teaching Mathematics

6. NCTM's Standards for Teaching Mathematics
Professional Standards for Teaching Mathematics
National Council of Teachers of Mathematics, 1991
Master 3-2: NCTM's Standards for Teaching Mathematics

7. 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
Master 3-2: NCTM's Standards for Teaching Mathematics

8. The Importance of Planning
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 
Master 3-3: The Importance of Planning

9. 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 to 9-29
24 Ch. 4-division whole/dec to 11-2
3 Election project-statistics to 11-7
12 Ch. 5-metric measurement to 11-22
5 Ch. 7-customary measurement to 12-1
13 Ch. 9,10-geometry to 12-20
2 Holiday ornaments-space figures 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 to 2-21
8 Ch. 7-fractions, multiply to 3-3
etc....
Master 3-4: Levels of Planning

10. Unit 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 6th
grader like?" Predict, determine survey
questions
Master 3-4: Levels of Planning

11. Unit Chapter 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
Master 3-4: Levels of Planning

12. 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
Master 3-5: Components of Lesson Planning

13. Investigative Lesson Plan Outline
Launch
Investigate
Summarize
Master 3-6: Investigative Lesson Plan

14. Direct Instruction Lesson Plan Outline
Launch
Instruct
Summarize
 Master 3-7: Direct Instruction Lesson Plan

15. Nine Types of Adaptations
Size
Time
Level of Support
Input
Difficulty
Output
Participation
Alternate Goals
Substitute Curriculum
Master 3-8: Adaptations

16. Active Teaching and Learning
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.
Master 3-9: Active Learning/Teaching
Thornton and Wilson, 1993, p. 274

17. 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.
Master 3-9: Active Learning/Teaching
Thornton and Wilson, 1993, p. 274

18. Questions: Include questions that help students:
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.
Master 3-10: Questions
Professional Standards for Teaching Mathematics
National Council of Teachers of Mathematics, 1991, pp. 3,

19. 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.
Master 3-11: Manipulatives
Ross and Kurtz, 1993, p. 256

20. 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.
Master 3-12: Educational Software

21. 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.
Master 3-12: Educational Software

22. 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?
Master 3-13: Find a Pattern

23. 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?
Master 3-13: Find a Pattern