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Mathematics Instruction PowerPoint Presentation

Mathematics Instruction

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### Mathematics Instruction

EDCI 5474

In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

Guiding Questions mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- What factors impair performance?
- How do standards impact students?
- What math skills are essential?
- What teaching strategies can be applied?
- What methods are effective for teaching basic math facts?
- What methods are effective for problem solving?

Knowing and Doing Math mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Knowing
- Comprehend basic principles
- More than one way to explain
- More than one acceptable answer
- “Difference between 2 numbers”

- Doing
- Apply strategies to complete item
- “take away”

Factors mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000 Procedural & representational Failure to understand concepts, lack pre-requisite skills, maintain facts Need direction instruction, strategic

- 60% of students with LD
- Reading, writing, attending, memory, language, motivation
- (Montague, Bos, & Doucette, 1991)

- (Geary, 1993)

- (Cox, 1975; Miller & Milam, 1987; et. al)

Problem solving mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

Communication ideas

Reasoning

Everyday applications

Reasonableness

Estimation

Computational skills

Algebraic thinking

Measurement

Geometry

Statistics

Probablity

NCTMEffective Instruction mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Appropriate math content
- Problem solving, communicating ideas, everyday applications, computation

- Establish goals & expectations
- Assessment

- Systematic & explicit instruction
- Demonstrate-prompt -practice sequence
- Highly organized, step by step presentation what, when and why use target skill
- Insure understanding and task demands
- Use learning principles
- Attention, reinforcement, varied practice motivation

Efficient Teaching mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Demonstrate
- Guided practice with prompts/feedback
- Independent practice with feedback
- Advanced organizers
- Mastery of skill as generalization level

- Teach to understand concepts mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Concrete-representational-abstract sequence
- Learning concepts and rules
- e.g. communative property of addition, inverse relationship, place value, # time 0 = 0

- Monitor progress
- Check for understanding, interact, demonstrate

- Provide feedback
- Essential promote learning, mastery, independent learning, plan activities, motivation, confidence abilities
- Immediate, basic & elaborate

- Teach to mastery mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Automaticity
- Benefits – retention, higher level skills, completion, positive feelings

- Independent practice
- Games, peers, computers, self monitor

- Teach problem solving skills
- Math knowledge, application, engage thinking
- Strategy instruction parallel

- Teach generalization mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Perform different situations
- Motivation to apply, discuss why and how used, varied examples, mastery to use rather than remember

- Positive attitude
- Goal setting, success on prior skills, progress chart, high expectations, enthusiasm, reinforcing

Math Curricula mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Distar Arithmetic – SRA
- Connecting Math Concepts
- Edmark
- Project MATH
- Real Life Math
- Strategic Math
- Touch Math
- Rapid, sequenced, scripted, direct instruction
- 1 2 3 4 5 6 7 8 9

Strategic Math mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Pretest lesson
- Teach concrete application
- Teach representational application
- DRAW (Discover, Read problem, Answer with drawing, Write answer)
- Teach abstract application
- Posttest
- Provide practice to fluency
- Strategic Math Series, Mercer & Miller, 1991

Math Methods for SWD mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Curriculum-based Assessment & Error Analysis
- Spiral curriculum
- Fast paced, insufficient practice, developmental sequence gaps, order of concepts, number of concepts

- Performance: frustration < 70 to success 90%
- Construct probes for error patterns
- “Slice back” to re-teach lower skill

- Spiral curriculum

Concrete to Seimconcrete mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Manipulatives rather than pictures or numerals and symbols
- Repeated opportunities
- Relate manipulatives to numbers immediately
- Build understanding of concepts
- Questions and verbalize thinking
- Check answers with manipulatives

Direct Instruction mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Focused, explicit, interactive
- Tasks analyzed, clear examples (models), questions & feedback
- Hi success
- Models, demonstration, time delay

- Systematic practice in real world contexts
- Provide calculators as postsecondary level

Sequence & Rule Based mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Resequence texts
- e.g. teach “zero” facts earlier

- Sameness to reduce memorization
- E.g. 0 times any number = 0

Build Strategies mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Self instruction & mnemonics
- Good with direct instruction
- Associate pictures, visual imagery
- Should not substitute for practice for mastery
- Good for rote memory deficits

Motivation for Practice mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Games
- Bingo, blackjack, jeopardy, math basketball

- Real Life
- Newspapers, internet, technical courses, solve real life problems

- Self-Monitoring, Goal Setting
- Record, graph, choice of goals, conference, self-talk

- Cooperative Learning mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Interactive practice, group rewards

- Computer Instruction
- Tutorial, drill & practice, software
- With teacher directed instruction

Teacher Student Dialogues mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Math reasoning & problem solving
- Explicit modeling centered on concepts
- Verbal rehearsal, feedback, guided practice, check for understanding
- Think alouds, scaffolded practice

Instructional Tips mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Number Sense – numbers to objects
- One to one correspondence
- Readiness skill

- Numeration
- Number values

- Seriation
- Ordinal, less/more

- Place value
- Ones, tens, hundreds

- One to one correspondence

Basic Facts & Operations mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Addition
- Sticks, counters, dots on cards, Touch Math, sums of ten, number lines, 1-5 w/9-5 below

- Subtraction
- Counters, sticks, number line, tally marks, Touch Math,

- Multiplication
- Groups in rows, Geoboards-cubes, teach rules, fingers

- Division
- Counters, number line to 25

Complex Operations mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Understand place value, regrouping, state the operation, graph paper
- Addition with regrouping
- Concrete manipulatives, mnemonic or visual reminders

Other Essential Skills mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Fractions
- Need systematic practice, examples
- Explicitly define whole, fractions equal parts
- Fair sharing
- Formal symbols, ½ or ¼
- Concrete aids before teaching rules
- Mastering Fractions – interactive videodisc
- Need more time

- Decimals mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Concrete manipulatives
- Represent fractions with denominators 10 or 100
- Visual representation less that whole

- Algebra
- Direct instruction, think alouds, concrete to abstract, strategy (FOIL)

- Arithmetic Word Problems mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000
- Group problems around familiar themes
- Pictures & manipulatives of the problem
- Attack word problems
- Emphasize understanding with visuals, question for important information, model strategies for solving, give feedback during process - SOLVE

Enhance Instruction mathematics will have significantly enhanced opportunities and options for shaping their futures. NCTM, 2000

- Increase instructional time, reduced independent practice
- Review, directed instruction, guided practice, independent practice with feedback
- Use concrete objectives
- Teach key math terms, “sum”
- Small group instruction
- Real life examples
- Varied reinforcement styles, process rather product
- Lock, R.H. (1996). Adapting Mathematics Instruction in General Education for Students with Mathematics Disabilities, CLD.

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