Recommendations for Teaching Mathematics

Recommendations for Teaching Mathematics

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

Recommendations for Teaching Mathematics

Tasks include– Rich learning situations– Reading and writing

Discourse includes– Talking– Listening

Recommendations for Teaching Mathematics

Tools include– Models– Manipulatives– Technology

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

NCTM's Standards for Teaching Mathematics

Professional Standards for Teaching Mathematics

National Council of Teachers of Mathematics, 1991

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

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 

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....

 

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

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

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

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

1. Size

2. Time

3. Level of Support

4. Input

5. Difficulty

6. Output7. Participation8. Alternate Goals9. Substitute Curriculum

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

Active Teaching and Learning

6. Be clear; provide relevant examples and non-examples.

7. Ask many "why", "how", and other high level questions.

8. Be organized; foster time-on-task.

9. Allow time for guided seatwork before independent seatwork.

10. 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:

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 MathematicsNational Council of Teachers of Mathematics, 1991, pp. 3,

Manipulatives: The teacher should be certain that:

1. manipulatives have been chosen to support the lesson's objectives.

2. students have received orientation concerning the manipulatives and classroom procedures.

3. the lesson involves active participation of each student.

4. 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

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.

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.

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?

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?