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Chapter 14

School

University of WaterlooDepartment

PsychologyCourse Code

PSYCH312Professor

Ernie Mac KinnonChapter

14This

**preview**shows pages 1-2. to view the full**6 pages of the document.**[ CHAPTER FOURTEEN ] MATHEMATICS DIFFICULTIES

THEORIES

MATHEMATICS DIFFICULTIES

6-7% of students in GEC show evidence of serious mathematics difficulty

Ca. 26% of WLD exhibit problems in area of math

Dylscalculia – severe disability in mathematics w/ medical connotations

EARLY NUMBER CONCEPTS AND NUMBER SENSE

Learning mathematics is a sequential process, and children must acq’ skills at an earlier stage before going

on to the next stage

Early # learning includes skills in (1) spatial rel’nshps, (2) visual-motor and visual-perception skills, and

(3) concepts of time & direction

Spatial Relationships

Play activities w/ objects help dvlp sense of space, sequence, and order

Parents of children w/ math difficulties often report their child dN enjoy/play w/ blocks, puzzles, or models

Visual-Motor and Visual-Perception Abilities

Visual-motor abilities combine motor mvmt w/ what one sees

i.e. copying figure/shape

Visual perception refers to ability to interpret what one sees

i.e. perceive geometric shape as complete and integrated entity

For a child w/ visual perception difficulty, a square may not appear as a square shape, but rather as four

unrelated lines

Concepts of Time and Direction

Have difficulty estimating time span of hr/min/week

May not be able to judge and allocate time needed to complete assignment

Sometimes forget whether it’s morning/afternoon and may even go home during recess period, thinking

school day has ended

CHARACTERISTICS OF MATHEMATICS DISABILITIES

Information-Processing Difficulties

Motor problems problems in writing #s, illegible, slow, and inaccurate

Attention problems poor attention during instruction

Problems in memory and retrieval cannot remember math facts

Problems in visual-spatial processing problems aligning #s and thus, miscalculations

Problems w/ auditory processing difficulty ―counting-on‖

Language and Reading Abilities

Lang problem may cause them to confuse math terms

i.e. plus, take away, minus, borrowing

Math Anxiety

Emotion-based reac’n to math, which causes indvdls to freeze up when they confront math problems/tests

Guidelines for dealing w/ math anxiety:

- use competition carefully

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

- provide abundant practice w/ ~ tests

- use clear instructions

- avoid unnecessary time pressures

- try to remove pressure from test-taking situations

MATHEMATICS DISABILITIES AT THE SECONDARY LEVEL

High school math req’mts for grad becoming more rigorous (geometry, statistics, calculus)

- adolescents w/ LD and RMD cont’ to have memory deficits tht interfere w/ AT learning of

computation facts

Effective instructional strategies in math for 2 students:

- provide many examples

- provide practice in discriminating various problem types

- provide explicit instruction

MATHEMATICS STANDARDS

High Standards and Annual Testing

Scores tht students receive on these math tests affect high-stakes decisions, such as whether student will be

promoted to next grade o will receive high school diploma

In general, students w/ mathematics disabilities dN fare well under high stakes assessment approach to

math edu’ w/o sp’ considerations and accommodations

Mathematics Principles and Standards From the national Council of Teachers of Mathematics (NCTM)

NCTM principles & standards intended for all students

Table 14.2

NCTM

Standards for

School

Mathematics

NCTM Standards

NCTM Goals

Numbers and

operations

Understand #s, ways of presenting #s, rel’nshps among #s, and # sys’s

Understand meaning of op’ns and how they relate

Compute fluently and make reasonable estimates

Algebra

Understand patterns, rel’ns, and f’ns

Rep’ and analyze mathematical situations and structures using algebraic symbols

Use mathematical models to rep’ and understand quantitative rel’nshps

Analyze change in various contexts

Geometry

Analyze char’s and properties of 2D & 3D geometric rel’nshps

Specify locations and describe spatial rel’nshps using coordinate geometry and

other rep’nal sys’s

Apply transformations and use symmetry to analyze math situations

Use visualization, spatial reasoning, and geometric modeling to solve problems

Measurement

Understand measurable attributes of objects and the units, sys’s and processes of

measurement

Apply appropriate tm’s, tools, and formulas to dtrmn measurements

Data analysis and

probability

Formulate q’ns tht can be addressed w/ data and collect, organize, and display

relevant data to answer them

Select and use appropriate statistical methods to analyze data

Dvlp and evaluate inferences and predictions tht are based on data

Understand and apply basic concepts of probability

Problem solving

Build new mathematical knowledge t/ problem solving

Solve problems tht arise in mathematics and in other contexts

Apply and adapt a variety of appropriate strategies to solve problems

Monitor and reflect on process of mathematical problem solving

Reasoning and

proof

Recognize reasoning and proof as fundamental aspects of mathematics

Make and investigate mathematical conjectures

Dvlp and evaluate mathematical arguments and proofs

Select and use various types of reasoning and methods of proof

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