VIEWS FROM THE FIELD
Helping Students with Disabilities Participate in Statewide Math Assessments
The 1997 Reauthorization of the Individuals with Disabilities Education Act (IDEA) provides that students with disabilities will participate in state and districtwide assessments, with accommodations and modifications as necessary. These largescale assessments reflect standards that all students are expected to meet. Most State and districtwide assessments tap mathematical knowledge and skills. Emerging research is shedding light on what practitioners can do to ensure that students with disabilities participate and achieve their potential on such assessments.
Making Assessment Accommodations for Math Assessments
"IDEA '97 has heightened the need for research findings on the effects of assessment accommodations," says Martha Thurlow, director of the National Center on Educational Outcomes (NCEO). "The complexity of the many studies on test changes made it evident that a searchable database was needed to cull the information for addressing specific accommodations, specific groups of students, specific ages, or combinations of these and other factors." Under Thurlow's leadership, NCEO launched a searchable data base of accommodations (http://education.umn.edu/NCEO/AccomStudies.htm).
The online database houses an accommodations bibliography that allows users to search a compilation of empirical research studies on the effects of various testing accommodations for students with disabilities.
"You can search the bibliography for specific accommodation research studies by typing in keywords related to the accommodation, disability, test content area, or student age," Thurlow describes. Currently, the database contains 173 documents, covering the years through 2001.
Type "math" in the search category and the database yields 59 references that cover such accommodations as the use of calculators (when the test does not measure computation) and reading the test aloud. At this point, users may click on any of the references for more information. Brief summaries of each study are provided and include information on the accommodation, participants, dependent variable, and major findings of the study.
RESOURCE
NATIONAL CENTER ON EDUCATIONAL OUTCOMES (NCEO)
The OSEPfunded NCEO was established in 1990 to provide national leadership in designing and building educational assessments and accountability systems that monitor educational results for all students, including students with disabilities and students who are English language learners. To this end, NCEO produces a variety of publications (e.g., researchbased technical reports and syntheses) that may be downloaded from its web site at http://education.umn.edu/NCEO.
One of NCEO's activities involves examining the participation of students with disabilities in national and state assessments. In a 2001 technical report, On the Road to Accountability: Reporting Outcomes for Students with Disabilities, NCEO researchers reviewed mathematics performance information from state education reports (n=35). Selected results include:
 On normreferenced math tests, students with disabilities received percentile rank scores approximately 25 percentile points below the average of all students in that grade in the state. Average scores for all elementary students ranged form the 47th to the 68th percentile, whereas average scores for students with disabilities ranged from the 18th to the 38th percentile. In higher grade levels, the difference between the scores of students with disabilities and their peers was even greater.
 On state benchmarks for mathematics proficiency, the percentage of all students meeting criteria for proficiency ranged from 11% to 87%, whereas the percentage of students with disabilities meeting proficiency requirements ranged from 2% to 77%. Beyond elementary school, only a fraction of students with disabilities met proficiency in any state (with the exception of middle school students in Texas).

Student Performance on Math Assessment: Implications for Standards
"If students with disabilities are to meet high standards, they will need support," says Rene Parmar.
With OSEP funding, Parmar and her colleagues Barbara Signer and John Cawley set out to explore the discrepancy between the desire for higher standards of student performance in mathematics and current data showing that students with disabilities tend not to meet expectations. "We looked at mathematical proficiency in relation to NCTM standards, which are aligned into groupings for PreK2, 35, 68, and 912," Parmar explains. "We found that significant numbers of general education students and those with mild disabilities do not demonstrate proficiency in many of the topics introduced or expected to be mastered (e.g., division) at a specific grade level." For Parmar, the implication is that schools should replace the gradebygrade level system with a multigrade level format. "Unfortunately," Parmar adds, "the commercial materials provided to the schools and the curriculum guides of the states and districts continue to specify gradebygrade level content."
Parmar sees other practical implications as emerging from this research. "Students need support in thinking about and understanding math concepts," According to Parmar, traditional assessments that yield passfail data are rarely useful instructionally. "Even with rubrics, teachers seldom have sufficient information to identify specific student difficulties that require instructional intervention," Parmar asserts. "Teachers need information that answers questions such as, What is the student thinking when he or she is encountering math?"
RESOURCE
MATH FLUENCY
According to researcher Ted Hasselbring of the University of Kentucky, students with disabilities often have difficulty developing fluency. Students without math disabilities can recall more facts from memory than their peers with math disabilities. This discrepancy increases with age, resulting in students falling further and further behind in their ability to recall basic math facts from memory.
To help alleviate this, Hasselbring and his colleagues created the Math Fluency Program with OSEP funding. The program— is still as current today as it was more than a decade ago— systematic instruction and practice for developing student ability to recall the answers to basic math facts accurately and fluently. It embodies several unique design features that make it particularly attractive to students with disabilities.
For more information, contact Hasselbring at Special Education Technology, University of Kentucky, 229 Taylor Education Building, Lexington, KY 40506, tsh@uky.edu. 
One suggestion for teachers is to assess the student by testing with items that occur between the last item correct and the first item failed to determine the type of item and type of error. Using the principle of least error correction, the teacher determines if the error was one of calculation or faulty use of an algorithm, and then corrects only the dominate error. For example, if a student completes an item by going from lefttoright and makes an error in calculation, use of the lefttoright algorithm would not be addressed.
When assessing student errors, Parmar encourages teachers to talk to students about what they are thinking. "Teachers need to understand the cognitive aspects of the math problem so that they can intervene if necessary." For example, when solving story problems, consider the following:
 Problem recognition. When the student thinks about the story problem,
what does he or she see? Some students may not see a representation
of a math problem in a word problem.
 Problem definition. If the student knows that addressing the problem
requires math, does he or she know how to apply math (e.g., multiply,
calculate an angle)
 Some students do not know or they guess. They continue to fail because
they started out thinking erroneously.
 Problem comprehension. Does the student comprehend the language of
math
 Phrases may have special meaning in math, such as "of these," which
means a subset in math.
RESOURCE
MEET THE MATH WHIZ
Using multimedia capability, OSEPfunded researchers Jean Andrews and Donald Jordan at Lamar University, developed the Meet the Math Wiz CDROM series for students who use American Sign Language (ASL) to communicate. In addition to signing the content, the program also is translated in Spanish.
Meet the Math Wiz helps students focus on math word problems over six grades of math difficulty using multicultural names, stories, and themes. For example, the program features Chris Kurtz, a math teacher who is deaf. He welcomes users to his castle, where he describes, among other things, a fourpoint plan for solving math word problems. He leads users into eight demonstrations per CD, giving them an ASL translation of the problem, an animation hint, and an explanation of how to solve the problem in ASL. Math words are linked to an ASL sign and explanation dictionary.
Materials can be ordered from: Curriculum Publications Clearinghouse, Horrabin Hall 46, Western Illinois University, 1 University Circle, Macomb, IL 61455, 8003223905. For more information, contact Andrews at jandrews47@aol.com. 
