Textbook Notes (363,236)
Canada (158,278)
Psychology (1,002)
PSYCH 312 (33)
Chapter 14

Chapter 14.docx

6 Pages
Unlock Document

University of Waterloo
Ernie Mac Kinnon

[ 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 - 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 NCTM Goals NCTM Numbers and  Understand #s, ways of presenting #s, rel’nshps among #s, and # sys’s Standards for operations  Understand meaning of op’ns and how they relate School  Compute fluently and make reasonable estimates Mathematics 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  Formulate q’ns tht can be addressed w/ data and collect, organize, and display probability 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  Recognize reasoning and proof as fundamental aspects of mathematics proof  Make and investigate mathematical conjectures  Dvlp and evaluate mathematical arguments and proofs  Select and use various types of reasoning and methods of proof LEARNING THEORIES FOR MATHEMATICS INSTRUCTION Active Involvement  Manipulate materials enable students to see, touch and move objects  Chinese proverb: ―I hear and I forget. I see and I remember. I do and I understand.‖ Progression from Concrete Learning to Abstract Learning  To help progression, 3 sequential levels of mathematics instruction are suggested 1.) Concrete level: students manipulate actual materials as they work out sol’ns to # problems 2.) Semi-concrete/representational level: use pictures/tallies to rep’ concrete objects as they work on problems 3.) Abstract level: use only #s to solve mathematics problems w/o help of semi-concrete pictures or tallies Direct Instruction of Mathematics  Comprehensive sys’ tht integrates curriculum design w/ teaching tm’s to produce instructional programs tht are highly organized and carefully sequenced  Teachers do the following: 1.) break tasks into small steps 2.) administer probes to drmn whether students are learning 3.) supply immediate feedback 4.) provide diagrams and pictures to enhance student understanding 5.) give ample (i) practice Learning Strategies Instruction 1. Provide elaborate explanations 2. Model learning processes 3. Provide prompts to use strategies 4. Engage in teacher-student dialogues 5. Ask processing q’ns Problem Solving  Identified as top priority for mathematics curriculum by NCTM  Implicit in teaching of problem solving are following underlying beliefs about math: 1.) no single way to do math 2.) no single way to organize math for instructional purposes 3.) important math concepts are actually learned t/ problem solving  Most difficult area of math for many students w/ math difficulties  Req’s students know how to apply math concepts and how to use computation skills in new/diff settings  Middle-grade st
More Less

Related notes for PSYCH 312

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.