1. Planning and Teaching Chapter 3 To accompany Helping Children Learn Math Cdn Ed, Reys et al. ©2010 John Wiley & Sons Canada Ltd.

2. 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

3. 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

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

5. Preparing to Teach (cont.) What materials will my students and I use? – Provincial curriculum documents – Textbook lessons – Children’s literature – Manipulatives – Technology Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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

7. 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 Mathematics National Council of Teachers of Mathematics, 1991, pp. 3,4 Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

8. 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. Ross and Kurtz, 1993, p. 256 Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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

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

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

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

13. Levels of Planning: Grade 6 Example Year # DaysTopic/ChapterDate 16Ch. 3-multiplication whole/dec8-30 to 9-21 6District computer unit9-22 to 9-29 24Ch. 4-division whole/dec10-2 to 11-2 3Election project-statistics11-3 to 11-7 12Ch. 5-metric measurement11-8 to 11-22 5Ch. 7-customary measurement11-27 to 12-1 13Ch. 9,10-geometry12-4 to 12-20 2Holiday ornaments-space figures12-21 to 12-22 24Ch. 6-fractions, add/subtract1-3 to 2-3 5State assessment tests2-6 to 2-10 7Ch. 11-statistics2-13 to 2-21 8Ch. 7-fractions, multiply2-22 to 3-3 Etc…

14. Example Unit Plan 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 grade 6 student like?" – Predict and determine survey questions Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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

16. Generalized Lesson Plan 1. Introductory Information Grade Level Date Topic/Title Objective(s) Assessment Gearing Down Gearing Up Materials Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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

18. Investigative Lesson Plan Outline Launch Investigate Summarize Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

19. Direct Instruction Lesson Plan Outline Launch Instruct Summarize Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

20. Exploration Lesson Plan Outline Launch Explore Summarize Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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

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

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

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

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

26. Meeting the Needs of All Students: Nine Types of Adaptations Size Time Level of Support Input Difficulty Output Participation Alternate Goals Substitute Curriculum Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

27. Assessment and Analysis in Planning 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. Reys/ Lindquist/ Lambdin/ Smith/ Colgan, Helping Children Learn Math, Canadian Edition, © 2010

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