Learning Difficulties Australia

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Numeracy

Key Research Papers
Programs & Resources
Useful Links

Key Research Papers

Journal of Learning Disabilities
Mathematics Education and Students with Learning Disabilities: Introduction to the Special Series - January/February 1997, Volume 30, No. 1
Author: Diane Pedrotty Rivera
This issue of the Journal focuses on issues relating to teaching maths to students with LD.
http://ldx.sagepub.com/content/vol30/issue1/
 
Educational Aspects of Mathematics Disabilities
Authors: Susan Peterson Miller, Cecil D. Mercer, EdD
Journal of Learning Disabilities, Vol. 30, No. 1, 47-56 (1997) DOI: 10.1177/002221949703000104
Research suggests that students with learning disabilities have significant difficulty acquiring and retaining math skills. A variety of factors seem to be contributing to the poor math performance of these individuals. The purpose of this article  is to discuss these factors and make recommendations that will enhance the likelihood of better math performance. The article begins with a discussion of national reform movements that have influenced math instruction (i.e., National Council of Teachers of Mathematics Standards, minimum competency testing, graduation requirements, inclusion). Next, learner characteristics are reviewed, then issues related to math instruction are described. Finally, ways to improve current practices in math education are discussed.
http://ldx.sagepub.com/cgi/content/abstract/30/1/47

Does Math Self-Efficacy Mediate the Effect of the Perceived Classroom Environment on Standardized Math Test Performance?
Authors: Lisa A. Fast, James L. Lewis, Michael J. Bryant, Kathleen A. Bocian, Richard A. Cardullo, Michael Rettig and Kimberly A. Hammond
Journal of Educational Psychology Volume 102, Issue 3, August 2010, Pages 729-740
We examined the effect of the perceived classroom environment on math self-efficacy and the effect of math self-efficacy on standardized math test performance. Upper elementary school students (N = 1,163) provided self-reports of their perceived math self-efficacy and the degree to which their math classroom environment was mastery oriented, challenging, and caring. Individual student scores on the California Standards Test for Mathematics were also collected. A series of 2-level models revealed that students who perceived their classroom environments as more caring, challenging, and mastery oriented had significantly higher levels of math self-efficacy, and higher levels of math self-efficacy positively predicted math performance. Analysis of the indirect effects of classroom variables on math performance indicated a small significant mediating effect of self-efficacy. Implications for research on self-efficacy and the perceived classroom environment are discussed.
http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ892642&ERICExtSearch_SearchType_0=no&accno=EJ892642  

Skill Development in Different Components of Arithmetic and Basic Cognitive Functions: Findings From a 3-Year Longitudinal Study of Children With Different Types of Learning Difficulties
Author: Ulf Andersson, Department of Behavioral Sciences and Learning, Linköping University, Linköping, Sweden
Journal of Educational Psychology Volume 102, Issue 1, February 2010, Pages 115-134
Arithmetic and cognitive skills of children with mathematical difficulties (MD-only), with comorbid reading difficulties (MD-RD), with reading difficulties (RD-only), and normally achieving children were examined at 3 points from Grades 3–4 to Grades 5–6 (age range, 9–13 years). Both MD groups displayed severe weaknesses in 4 domain-specific arithmetic components (factual, conceptual, procedural, and problem-solving skills) during all 3 measure points. Telling time and approximate arithmetic were also problematic for children with MD. Both MD groups displayed a small weakness related to visual–spatial working memory, and the MD-RD group also displayed small weaknesses related to verbal short-term memory, processing speed, and executive functions. The 4 groups developed at similar rates within all domain-specific components as well as basic cognitive functions. These findings demonstrate that children identified as having MD when they are 9 years old do not catch up with their normally achieving peers in later school grades, when they are 13 years old. They also continue to lag behind their peers with respect to the domain-general cognitive system. http://www.eric.ed.gov/ERICWebPortal/search/detailmini.jsp?_nfpb=true&_&ERICExtSearch_SearchValue_0=EJ876304&ERICExtSearch_SearchType_0=no&accno=EJ876304  

The Imperative of Evidence-based Practices for the Teaching and Assessment of Numeracy
Author: Kenneth J. Rowe, MSc PhD
Invited submission to National Numeracy Review July 2007 Australian Council for Educational Research (ACER)
The rationale for this submission was motivated by at least three major considerations pertinent to Australian and international contexts. First, despite findings from existing and emerging research for educational effectiveness in terms of instructional effectiveness and its impact on teaching and learning, there is a disturbing level of ignorance among school leaders and teachers at all levels of educational provision related to what works and why – especially as they relate to the teaching of literacy and numeracy.
Second, prevailing ideologies in schools and universities surrounding effective teaching practice are typically not grounded in findings from evidence-based research. Such ideologies are not only endemic in Australian schools and higher education institutions, but throughout the world, with the possible exception of South-East Asian and several Eastern European jurisdictions.
Third, current pre-service teacher education and subsequent in-service professional development (PD) is characterised by very narrow conceptions about how teachers should teach – aided and abetted by the content of Australian State and Territory curriculum documents. This has resulted in teachers not being equipped with an evidence-based repertoire of pedagogical skills that are demonstrably effective in meeting the developmental and learning needs of all students – regardless of students' intrinsic characteristics, socioeconomic and socio-cultural backgrounds.
http://www.acer.edu.au/documents/Rowe-NNRSubmission.pdf  

Applications and Misapplications of Cognitive Psychology to Mathematics Education
Authors: John R. Anderson, Lynne M. Reder, Herbert A. Simon
Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213
There is a frequent misperception that the move from behaviorism to cognitivism implied an abandonment of the possibilities of decomposing knowledge into its elements for purposes of study and decontextualizing these elements for purposes of instruction. We show that cognitivism does not imply outright rejection of decomposition and decontextualization. We critically analyze two movements which are based in part on this rejection ˆ situated learning and constructivism. Situated learning commonly advocates practices that lead to overly specific learning outcomes while constructivism advocates very inefficient learning and assessment procedures. The modern information-processing approach in cognitive psychology would recommend careful analysis of the goals of instruction and thorough empirical study of the efficacy of instructional approaches.
http://act-r.psy.cmu.edu/papers/misapplied.html

Mathematics Learning Difficulties: Research & Teaching
Authors: Brenda Dalheim, and Dr John Munro
Early Learning, Development and Inclusion Cluster, Melbourne Graduate School of Education
(A version of the paper was published as: Munro, J. (2003). Information processing and mathematics learning disabilities. Australian Journal of Learning Disabilities, 8 (4), 19-24.)
http://online.edfac.unimelb.edu.au/selage/pub/mathsld.htm

Educational Aspects of Mathematics Disabilities
Authors: Susan Peterson Miller, Cecil D. Mercer, EdD
Journal of Learning Disabilities, Vol. 30, No. 1, 47-56 (1997) DOI: 10.1177/002221949703000104
Research suggests that students with learning disabilities have significant difficulty acquiring and retaining math skills. A variety of factors seem to be contributing to the poor math performance of these individuals. The purpose of this article is to discuss these factors and make recommendations that will enhance the likelihood of better math performance. The article begins with a discussion of national reform movements that have influenced math instruction (i.e., National Council of Teachers of Mathematics Standards, minimum competency testing, graduation requirements, inclusion). Next, learner characteristics are reviewed, then issues related to math instruction are described. Finally, ways to improve current practices in math education are discussed.
http://ldx.sagepub.com/cgi/content/abstract/30/1/47

A Longitudinal Investigation of the Relationship Between Reform-Oriented Instruction and Student Achievement
(USA) Rand Corporation, 2006
This impressive study comes up with some surprisingly candid observations about constructivist math and science.
http://www.rand.org/pubs/monographs/2006/RAND_MG480.pdf

The Effects of a 15-minute Direct Instruction Intervention in the Regular Mathematics Class on Students’ Mathematical Self-efficacy and Achievement  
Author: Rhonda Farkota
Doctoral research into DI, mathematics and self-efficacy was described by the examiner, Professor DH Schunk, Dean of Education, University of North Carolina, as an outstanding thesis on a topic of great theoretical and applied significance.
http://www.acer.edu.au/documents/FarkotaThesis.pdf

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Programs & Resources

A Comparison of Three K-6 Mathematics Programs
Authors: David Klein, Professor of Mathematics, California State University
Jennifer Marple Mathematics Teacher Monroe High School, California
In this report we evaluate and compare the following three K-6 mathematics programs for
grades 2 and 5:
Sadlier-Oxford: Progress in Mathematics
Saxon: Math, An Incremental Development, Third Edition
SRA McGraw-Hill: Explorations and Applications
http://mathematicallycorrect.com/k6books.pdf

Ten Myths About Math Education And Why You Shouldn't Believe Them - May 4, 2005
Authors: Karen Budd, Elizabeth Carson, Barry Garelick, David Klein, R. James Milgram, Ralph A. Raimi, Martha Schwartz, Sandra Stotsky, Vern Williams, and W. Stephen Wilson
Written in association with New York City HOLD and Mathematically Correct, two education advocacy organizations of parents, mathematicians, and K-12 educators.
http://www.nychold.org/myths-050504.html

How regular maths teaching assume working memory abilities
Presenter: Dr John Munro
Handout at the CHERI Hippocrates and Socrates XVI conference - September 2011
Title: The role of working memory in mathematics learning and numeracy

Junior Elementary Math Mastery (JEMM)
Author: Rhonda Farkota
OZMATH Press 2010
Ideally suited for middle primary, and upper primary remedial students
Requires daily 10–15 minutes to implement, plus 3–7 minutes for instant feedback
JEMM features 80 lessons. Students answer one question per strand daily with Lesson 1 introducing:
 Whole number addition
 Whole number subtraction
 Number facts
 Place value
 Number patterns
Building on these base strands the following lessons introduce:
 Lesson 21 Money
 Lesson 31 Measurement
 Lesson 41 Fraction
 Lesson 51 Time
 Lesson 61 Chance and data
https://shop.acer.edu.au/acer-shop/product/5136BK

Elementary Math Mastery (EMM)
Author: Rhonda Farkota
McGraw-Hill Australia 2003
Ideally suited for upper primary, first year secondary and secondary school remedial students
Requires daily 15–20 minutes to implement, plus 5–10 minutes for instant feedback
EMM features 160 lessons, each composed of 20 strands. Students answer one question per strand daily.
https://shop.acer.edu.au/acer-shop/product/5126BK/X

Count On is a vast collection of games (e.g. Memory Spin), resources, news, problem solving, and information ñ e.g. a whole section on codebreaking - all to do with maths.
http://www.counton.org

Singapore Maths
Get the latest editions of the best Singapore Math textbooks and workbooks that Singaporeans use today direct from Singapore™
Find out why Singapore schools have switched completely to the new and improved Singapore Math.
Singapore is number one in Mathematics and number two in Science worldwide in the Third International Mathematics And Science Study (TIMSS) 1999. 93% and 80% of our students are in the international top half for Mathematics and Science respectively.
The mathematics and science curriculum in Singapore has been found to be more comprehensive than that of many countries. Singapore's rigorous curriculum is continually reviewed to ensure that it remains relevant for our students.
http://www.sgbox.com/singaporemath.html

Khan Academy
A free world-class education for anyone anywhere.
The Khan Academy is an organization on a mission. We're a not-for-profit with the goal of changing education for the better by providing a free world-class education for anyone anywhere.
All of the site's resources are available to anyone. It doesn't matter if you are a student, teacher, home-schooler, principal, adult returning to the classroom after 20 years, or a friendly alien just trying to get a leg up in earthly biology. The Khan Academy's materials and resources are available to you completely free of charge.
Arithmetic and Pre-Algebra
The first math topic. Start here if you want to learn the basics (or just want to make sure you know these topics). After this, you should be ready for algebra. This topic includes videos from the former developmental math playlists.
Basic Addition
Adding and subtracting fractions
Basic Multiplication
Converting fractions to decimals
Converting fractions to decimals
And 205 more videos...

Singapore Math @ Khan Academy
Lectures based on the Singapore Math curriculum.
http://www.khanacademy.org/

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Useful Links

Mathematically Correct
This web site is devoted to the concerns raised by parents and scientists about the invasion of our schools by the New-New Math and the need to restore basic skills to math education.
http://www.mathematicallycorrect.com/

Mathletics: one of Australia's most popular websites
A next generation of learning, helping students enjoy maths and improve their results. Mathletics covers the full K-12 curriculum and while highly recommended for home use, with a weekly report emailed to parents, is trusted by more than 3000 schools worldwide.
http://www.mathletics.com.au  

New York City HOLD National
(Honest Open Logical Decisions) on Mathematics Education Reform
Today's flagship web site for the mathematics education advocacy community
We are a national nonpartisan advocacy organization that provides parents, K-12 educators, mathematicians and scientists, and others information resources and networking opportunities to support systemic improvements in the quality of mathematics education in our nation's schools.
http://www.nychold.com/

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. On this website you will find thousands of our free mathematics enrichment materials (problems, articles and games) for teachers and learners from ages 5 to 19 years. All the resources are designed to develop subject knowledge, problem-solving and mathematical thinking skills. The website is updated with new material on the first day of every month. This site also includes a section of research and education articles and an ask a mathematician service / forum.
http://nrich.maths.org/public/index.php

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