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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

- 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
- 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”

- 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

Communication ideas

Reasoning

Everyday applications

Reasonableness

Estimation

Computational skills

Algebraic thinking

Measurement

Geometry

Statistics

Probablity

- 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

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

- Teach to understand concepts
- 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
- 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
- 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

- 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

- 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

- 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

- 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

- 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

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

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

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

- 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
- Interactive practice, group rewards

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

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

- 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

- 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

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

- 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
- 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
- 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

- 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.