Planning and Teaching CHAPTER 3 Tina Rye Sloan To accompany Helping Children Learn Math9e, Reys et al. ©2009 John Wiley & Sons

Focus 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? 4. 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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Preparing to Teach (cont.) What kinds of tasks will I give my students? ▫ Focus on the mathematics. ▫ Provide necessary practice. ▫ Use the strategic moment. How will I encourage my students to talk, what kind of questions will I ask, and how will I group my students? Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Preparing to Teach (cont.) What materials will my students and I use? ▫ Textbook lessons ▫ Standards-based Curricula ▫ Children’s Literature ▫ Manipulatives ▫ Technology Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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 Mathematics National Council of Teachers of Mathematics, 1991, pp. 3,4 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Types of Educational Software (cont’d) 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. Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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  Meeting the Needs of all Students  Assessment and Analysis in Planning Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Levels of Planning: Grade 6 Example Year # DaysTopic/ChapterDate 16Ch. 3-multiplication whole/dec 8-30 to District computer unit 9-22 to Ch. 4-division whole/dec 10-2 to Election project-statistics 11-3 to Ch. 5-metric measurement 11-8 to Ch. 7-customary measurement to Ch. 9,10-geometry 12-4 to Holiday ornaments-space figures to Ch. 6-fractions, add/subtract 1-3 to 2-3 5State assessment tests 2-6 to Ch. 11-statistics 2-13 to Ch. 7-fractions, multiply 2-22 to 3-3 etc.... Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Unit Chapter 11: Statistics (7 days) Day 1Intro, review collecting and displaying data-text Day 2Interpreting data-Mean, Median, Mode, Range text, cubes, calculators, family size problem Day 3Groups-begin project "What is a typical 6 th grader like?" Predict, determine survey questions Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Unit Chapter 11: Statistics (7 days) (cont’d) Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009 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 Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Investigative Lesson Plan Outline I.Launch II.Investigate III.Summarize Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Direct Instruction Lesson Plan Outline I.Launch II.Investigate III.Summarize Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Exploration Lesson Plan Outline I.Launch II.Investigate III.Summarize Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

Meeting the Needs of All Students: Nine Types of Adaptations 1.Size 2.Time 3.Level of Support 4.Input 5.Difficulty 6.Output 7.Participation 8.Alternate Goals 9.Substitute Curriculum Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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? Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009

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? Can you model with blocks or a number line? Reys/ Lindquist/ Lamdin/ Smith, Helping Children Learn Math, 9 th Edition, © 2009