Research Roundup (LD News: January 2007)

By Dr. Sheldon H. Horowitz
Director of Professional Services, NCLD

Math & LD: Support for Early Identification

In an earlier Research Roundup column (October 2005) I provided a brief overview of the area of math and LD and bemoaned the limited progress we've made in understanding the science underlying early math learning and instruction in comparison to our now robust knowledge in the area of early reading. The steps we refer to when talking about "breaking the code" (an expression often used to mean 'learning to read') appear to be very different when it comes to math, and much research still needs to be done before we can, with confidence, know which specific skills are the essential building blocks for math learning, in what order they are best learned, and through what strategies and activities they are best taught.

The National Mathematics Advisory Panel
While NCLD's current research efforts focus on early math instruction and recognizing and responding to young students who struggle with math learning, the federal government has commissioned a National Mathematics Advisory Panel (NMAP) whose task is to:

• examine and summarize the scientific evidence related to the teaching and learning of mathematics, with a specific focus on preparation for and success in learning algebra and
• issue two reports containing policy recommendations on how to improve mathematics achievement for all students.

The National Math Panel is scheduled to issue an interim report by January 31, 2007 (and a final report no later than February 28, 2008), on topics including:

• the critical skills (and skill progressions) needed to learn algebra and prepare for more advanced courses,
• the role and design of standards and assessments in promoting student competence in math,
• the processes by which students of various abilities or backgrounds learn math,
• how the training, selection, placement and professional development of math teachers affect student achievement,
• instructional practices, programs and materials that have proven effective in improving math learning and
• research needs in support of math education.

NCLD's Math & LD Initiative
In June 2005, NCLD convened a meeting of prominent Math & LD researchers to:

• review the available research in the area of mathematics and LD,
• identify gaps in current knowledge,
• identify assessments and instructional interventions that have proved to be effective for struggling learners of math and
• recommend the development of new specific tools and strategies that can be used to ensure that children who struggle to learn math receive effective instruction.

The long-term goal of this work will be to delineate the core knowledge and skills that are necessary for students to benefit from mathematics instruction in kindergarten and the elementary grades, and to disseminate this knowledge through high-quality educational products and services, professional development activities, and replication and dissemination activities.

In an effort to begin to answer some of the 'big questions' asked in my earlier column, NCLD commissioned a paper titled Early Identification of Math Difficulties and Disabilities: Beginnings of a Scientific Foundation (PDF). As the principal investigator and leader of NCLD's Math & LD Initiative, Dr. Russell Gersten (former member of NCLD's Professional Advisory Board and member of the NMAP) authored this research synthesis with Dr. Benjamin Clark (Pacific Institutes for Research) and Dr. Nancy Jordan (University of Delaware). This paper is a first step toward 'unpacking' what we know about math learning in young children and how early math learning lays the foundation for later acquisition of mathematical concepts.

We cannot yet say that the same students who struggle with math at the end of first grade are the ones who are likely to remain weak for the rest of their academic careers. There is some evidence to suggest (and it makes logical sense) that the numerical concepts children acquire in early childhood lay the foundation for later acquisition of mathematical concepts. And professional wisdom tells us that successful early experiences in math learning have a powerful affect on the interest and confidence students bring to new opportunities for math learning.

While there are surely students whose underlying struggles in math learning are due to learning disabilities, we also believe that providing carefully tailored individual or small group instruction together with additional practice, explanation and feedback might be sufficient for many students who are lagging behind their peers in learning critical foundational skills in math. To help identify young students who are in need of special attention in math, NCLD is exploring the possibility of developing a screening tool that will point to at-risk behaviors and document math difficulties (or early signs of disabilities) so that carefully targeted and intentional opportunities for instruction can be provided to students who show early signs of struggle.

An Unfolding Body of Knowledge
Without going into great detail, here are some of the key findings from the research paper:

-- Currently available screening and assessment measures being used by educators appear to tap a variety of different and overlapping skills with varying levels of success. This is not a bad thing! (at least not until we have better empirical evidence about the critical aspects of early math development).

-- Underlying all math learning is the need for thirty or more skills or components including:

• fluency in estimating and judging magnitude,
• the ability to recognize unreasonable results,
• flexibility when mentally computing and
• the ability to move among different number representations and to use the most effective one.

-- Of all of the abilities gleaned from the synthesis of early math learning, two appear to be key variables for success:

• strategic counting (note: a child who demonstrates "knowledge of counting" e.g. by rote, may not necessarily have "skill in counting" e.g., counting objects) and
• magnitude comparisons (e.g., understanding of more/less and its impact in real life situations).

-- Other skills that appear to be important for later math learning include:

• number recognition (linking numerals with names),
• retrieval of basic arithmetic facts (without having to count) and
• word problems.

-- Preliminary evidence suggests that achievement in a first grade math curriculum may be a strong predictor of future math outcomes.

-- Some young students will learn at acceptable levels and begin to show signs of struggle once the content moves to more abstract levels.

-- Some young students (for example, those who have difficulty with visual-spatial skills) may show signs of struggle when task demands include measurement and an appreciation of the forms and shapes that are common, well before the formal introduction of geometry).

-- Successful mastery of skills at one grade level does not guarantee success in later grades.

-- While we know that certain cognitive attributes (e.g., working memory) contribute to math learning, we are not yet able to tap this underlying attribute in an efficient and accurate way (with a screening tool or set of structured activities).

-- While still inconclusive, some research points to the possibility that 'timed' screening measures may be more potent than those that are untimed.

To Be Continued...

The research in early math assessment is in its infancy, but we now have an emerging knowledge base that allows us to begin to draw conclusions, guide future research and inform current practice.

The limited research that is available in the area of early math instruction and learning suggests that there are significant differences between kindergarten and first grade when it comes to math. While exposure to math concepts and opportunities for practice appear to be important variables in preparing students for success in this area, a menu of critical variables is just now being developed.  Hopefully this knowledge will be incorporated into screening measures and instructional approaches and incorporated into wide-spread practice throughout kindergarten and first grade practice.

Some Resources
In addition to the resources listed in the earlier Research Roundup column and the LD InfoZone, visit the following online resources:

Early Learning in Mathematic: A Prevention Approach
This poster session was offered at the 2006 IES Research Conference. It describes the development and preliminary evaluation of a kindergarten mathematics curriculum designed to support the development of young children's understanding of number, number operations, geometry, measurement, and mathematical vocabulary.

A review of math research for the Exceptional Children publication
In October 2004, a group of educators began reviewing and evaluating mathematics research. Although there were only 26 valid studies (as defined by using experimental or quasi-experimental group designs and studies with LD samples) as of 1998, the research provided a backdrop for Foundation Level Training in Mathematics for Exceptional Children.

Mathematical Disabilities: What We Know and Don't Know

Math Learning Disabilities

Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities

Components of Effective Mathematics Instruction

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