Recommendations for Teaching Mathematics

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

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

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

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

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

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

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

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.... Master 3-4: Levels of Planning  

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

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

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

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

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

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

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

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

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,

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

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

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

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

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