Recommendations for Teaching Mathematics

1. Recommendations for Teaching Mathematics

2. Recommendations for Teaching Mathematics • Expectations include • Sense making • Focus on Processes • High expectations for all • Reflection

3. Recommendations for Teaching Mathematics • Tasks include • Rich learning situations • Reading and writing • Discourse includes • Talking • Listening

4. Recommendations for Teaching Mathematics • Tools include • Models • Manipulatives • Technology

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

6. NCTM's Standards for Teaching Mathematics Professional Standards for Teaching Mathematics National Council of Teachers of Mathematics, 1991

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 andLearning

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 

9. 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....

10. 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

11. 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

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

13. Investigative Lesson Plan Outline • Launch • Investigate • Summarize

14. Direct Instruction Lesson Plan Outline • Launch • Instruct • Summarize

15. Nine Types of Adaptations • Size • Time • Level of Support • Input • Difficulty Output Participation Alternate Goals Substitute Curriculum

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 materialthrough active engagement of the students • Involve students in problem solving, estimation, mental math, and mathematical extensions. • Communicate the expectation that students willbe able to master the material if they attend. 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 levelquestions. • Be organized; foster time-on-task. • Allow time for guided seatwork before independentseatwork. • Regularly assign a small amount of homework orseatwork to develop fluency, stimulate thinking,or provide open-ended challenges. 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 solveproblems. • connect mathematics, its ideas, andits applications. 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 proceduresfor evaluation that reflect anemphasis on the development ofreasoning skills. 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.

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.

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 theright, 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 conjectureabout the 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?