Best Practices and Supporting Research
Anchored Instruction
Definition:The principal approach utilized for improving generalization of mathematics problem solving was "anchored instruction," which enables students to explore semantically rich learning environments with the knowledge they bring to the learning situation. These "anchors" help foster generalization by providing motivating and meaningful contexts in which students can develop their "intuitions" in combination with their computation and algorithmic skills to arrive at a plausible conclusion.
Objective:
Anchored instruction is intended to stimulate math problem solving of all students, including those who have had difficulty learning mathematics, by practicing skills that have applicability in the work environment and everyday life. It encourages students to “develop mathematical habits of the mind” and to explore, guess, and even make and correct errors so that they gain confidence in their ability to solve complex problems. Teachers are encouraged to structure learning experiences in contexts that students will recognize in new situations—a key to learning transfer.
The approach to this project will include the following elements:
- Train the resource room teacher: The Special Education Technology Center (SETC) trained the resource room teacher in conjunction with the identified mathematics teachers in the same building, in the use of strategies shown to be successful in remediation of writing, reading and mathematics areas. Additionally, the resource room teacher should have received training from individual Educational Service Districts in any relevant areas. This would include support from the math specialist to align their curriculum with the WA State Essential Academic Learning Requirements (EALR's).
- (Ideally, in addition) Train the mathematics and industrial technology teachers in the targeted school: The Special Education Technology Center hypothesized that technology used to help remediate the LD student's mathematical problem solving skills might also be useful for other students at risk. Therefore, it was helpful for the identified mathematics teachers and industrial technology teacher in the school to be trained with the same technology as the resource room teacher. This allowed for projects to be built and problems solved in a contextualized or anchored atmosphere for all students, including other students at risk in mathematics.
Research
A major goal of the national education reform movement is to promote problem solving performance assessments (PA). PAs require students to solve authentic problems by applying multiple skills and strategies to real-life situations. PAs pose many problems for students with learning disabilities (LD), in part because the assessments require reading as a foundation. Therefore, even though reading is not necessary to solve many real-life mathematical problems, reading deficits may lower PA scores in math testing as well as classroom work for students with LD. The nature of reading challenges posed by PAs has become more serious recently, as LD students are required to participate in statewide assessments, which increasingly incorporate PAs.
The lack of reading skills affects students with learning disabilities in every facet of their lives. They are of course at a disadvantage in classes that require reading to learn, such as social studies, English, or geography. In addition, reading disabilities impede learning in mathematically oriented classes. Reading and writing skills are needed to synthesize the recall and use of many steps, rules, and math facts. Reading disabilities also interfere with the capacity of many students with learning disabilities to solve word problems.
Even though the body of research on secondary learning-disabled student's mathematical problem solving skills is very limited, a synthesis of the research available indicates that the accommodation of providing "a reader" for students with LD, increases math test scores. (The term, "a reader," can mean teacher read, computer read or peer read.) Even with the use of a reader, the research still showed low scores, indicating a serious lack of problem solving capacity among secondary students with LD. Research in problem solving indicates that most secondary students with LD may not have progressed beyond the fourth grade level, in this area. Some researchers indicate that these low problem solving skills may be due to the lack of exposure to higher order thinking skills and problem solving curriculum in secondary math resource programs and/or to low math skills in general.
One researcher (Brian Bottge) notes that testing is frequently directed at student weaknesses rather than strengths. "This situation usually contributes to a sense of hopelessness and concomitant behavior problems. This is a recurring theme in education and continues despite emphasis on standards, authentic learning, and performance-based assessment. To make an impact on middle school and high school students' lives, we must move beyond the typical into contexts that promote and motivate student thinking. The power of technology matched to suitable learning tasks can lead to positive results for many disenchanted students. It is time to use our resources to make learning for all students more meaningful and attainable." (Bottge,B. (1999) Effects of Contextualized Math Instruction on Problem Solving of Average and Below-Average Achieving Students. Journal of Special Education Vol. 33., No. 2, 1999, pp.81-92) (For research references see References.)
We need to provide students with real math problems--problems that occur in their lives and prepare them to solve those problems.
References
Applegate, M., & Montague, M. (2000). Middle school students' perceptions, persistence, and performance in mathematical problem solving. Learning Disabilities Quarterly, 23(3), 215-235.
Bottge, B. (1999) Effects of Contextualized Math Instruction on Problem Solving of Average and Below Average Achieving Students. The Journal of Special Education, 33(2). 81-92.
Brunell, J.K., Manalo, E., & Stillman, J.A. (2000). The use of process mnemonics in teaching students with mathematics learning disabilities. Learning Disabilities Quarterly, 23(2), 137-156.
Calhoon, M.B., Fuchs, L.S., & Hamlett, C.L. (2000). Effects of computer based test accommodations on mathematics performance assessments for secondary students with learning disabilities. Learning Disabilities Quarterly, 23(4).
Higgins, E.L., Raskind, M.H., Staff, N.B., & Shaw, T.K. (1998). Assistive technology in the homes of children with learning disabilities: An exploratory study. Learning Disabilities, 9(2), 47-55.
Office of the Superintendent of Public Instruction. (2000). Organizing for success: Improving mathematics performance in Washington state. Olympia, Washington: Author.