planning and teaching chapter 3 to accompany helping children learn math cdn ed, reys et al. ©2010...

Planning and Teaching

Chapter 3Chapter 3

To accompany Helping Children Learn Math Cdn Ed, Reys et al.©2010 John Wiley & Sons Canada Ltd.

Guiding Questions

1. What questions must an elementary mathematics teacher answer before beginning to plan?

2. Why does the teacher plan mathematics lessons so carefully?

3. What levels of planning does the teacher create? What are three types of lessons used to teach mathematics, and what is the purpose of each?

5. How can the teacher meet the needs of all students?

6. How does the teacher integrate planning with assessing and analysis?

Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,Canadian Edition, © 2010

Preparing to Teach:Questions to Ask Before Planning Begins

• Do I understand the mathematics I am teaching?

• What are the developmental characteristics of my students?

• What do my students already know?Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,

Canadian Edition, © 2010

Preparing to Teach (cont.)

• What kinds of tasks will I give my students? – Focus on the mathematics.– Provide necessary practice.

• How will I encourage my students to talk?– What kind of questions will I ask?– How will I group my students?


Preparing to Teach (cont.)

• What materials will my students and I use?– Provincial curriculum documents– Textbook lessons– Children’s literature– Manipulatives– Technology


Effective Mathematical Tasks • Are often authentic in that they come from the

students’ environment• Are challenging yet within students’ reach• Pique the students’ curiosity• Encourage students to make sense of mathematical

ideas• Encourage multiple perspectives and interrelated

mathematical ideas• Nest skill development in the context of problem

solving(Reys and Long, 1995)


Include Questions that Help Students: • work together to make sense of mathematics.• learn to 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.

Professional Standards for Teaching MathematicsNational Council of Teachers of Mathematics, 1991, pp. 3,4


ManipulativesThe 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 Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math,

Canadian Edition, © 2010

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(cont’d)

• Educational Games include an opportunity to win or overcome an obstacle.

• Problem-Solving aids in the development of higher-order thinking.

• Tool software provides assistance with graphing, computing, visualizing.


Planning for Effective Teaching

• Importance of Planning• Levels of Planning– Planning for the Year– Planning Units– Planning for Daily Lessons

• Planning Different Types of Lessons– Investigative– Direct Instruction– Exploration


Planning for Effective Teaching Cont.

Meeting the Needs of all Students• Teaching students from other cultures• Teaching English-language learners• Teaching students with identified special needs

Assessment and Analysis in 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…

Example Unit PlanChapter 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 grade 6 student like?" – Predict and determine survey questions


Chapter 11: Statistics (7 days) (cont’d)

• Day 4 & 5: Collect and display data - (remember to reserve computer lab and locate survey and graphing software)

• Day 6: Group presentations and discussion• Day 7: Update portfolios and performance

assessment


Generalized Lesson Plan

• 1. Introductory Information• Grade Level• Date• Topic/Title• Objective(s)• Assessment• Gearing Down• Gearing Up• Materials


Generalized Lesson Plan (cont.)• Lesson Outline– Launch (setting the stage)

– Investigate (for investigative lessons)or

Instruct (for direct instruction lessons)or

Explore (for exploration lessons)

– Summarize (closure)


Investigative Lesson Plan Outline

• Launch

• Investigate

• Summarize


Direct Instruction Lesson Plan Outline

• Launch

• Instruct

• Summarize


Exploration Lesson Plan Outline

• Launch

• Explore

• Summarize


Meeting the Needs of All Students: Teaching Students from Other Cultures • Be aware of the learning preferences of other

cultures• Connect mathematics to the cultural roots of

your students• Students enjoy learning about how math was

developed by people in other countries• Students see the relevance of math when it is

tied to art, literature, technology and games


Meeting the Needs of All Students: Teaching English Language Learners

• Give students comprehensible input (i.e., language they will understand).

• Give students opportunities to increase verbal interaction during class activities (i.e., to talk more with you and with the other children).

• Teach in a way that contextualizes language.


Teaching English Language Learners (cont.)

• Use teaching strategies and groupings that reduce the anxiety of students.

• Assign activities in the classroom that offer students opportunities for active involvement.

(Herrell, 2000, p. xiv)


Meeting the Needs of All Students: Potential Barriers for Students with

Special Needs • Memory: visual memory, verbal/auditory

memory, working memory

• Self-regulation: excitement/relaxation, attention, inhibition of impulses

• Visual Processing: visual memory, visual discrimination, visual/spatial organization, visual-motor coordination


Potential Barriers for Students with Special Needs (cont.)

• Language Processing: expressive language, vocabulary development, receptive language, auditory processing

• Related academic skills: reading, writing, study skills

• Motor Skills: writing legibly, aligning columns, working with small manipulatives, using one-to-one correspondence, writing numerals

• (Karp and Howell, 2004, p. 120)


Meeting the Needs of All Students:Nine Types of Adaptations

• Size• Time• Level of Support• Input• Difficulty

• Output• Participation• Alternate Goals• Substitute

Curriculum


Assessment and Analysis inPlanning

• Assessment should be an integral aspect of mathematics instruction.

• Many teachers also find it helpful to keep an evaluative record of the effectiveness of their lessons.


Copyright

Copyright © 2010 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (The Canadian Copyright Licensing Agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons Canada, Ltd. The purchaser may make back-up copies for his or her own use only and not for distribution or resale. The author and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these programs or from the use of the information contained herein.

planning and teaching chapter 3 to accompany helping children learn math cdn ed, reys et al. ©2010...

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