Purpose: Research on interventions for secondary students with learning disabilities in math is limited. It has been estimated that between 5 to10 percent of students have a specific learning disability in math. Difficulties in math performance are often attributed to a combination of weak problem-solving, such as identifying relevant information, and computational skills, such as basic operations involving fractions. Research has suggested that students with disabilities in math gain, on average, only one year of achievement in math for every two years they are in school and for some math skills, there is little appreciable growth in the later school years.

Researchers in this study are evaluating Enhanced Anchored Instruction, a pedagogical approach that allows students additional opportunities to practice their skills as they solve new but analogous math problems in applied and challenging contexts. The development of the intervention was funded under the Cognition and Student Learning Research Program. The purpose of this study is to evaluate the intervention against a typical classroom curriculum.

Project Activities: Approximately 22 middle school teachers (classrooms) with 5 – 10 students with learning disabilities per classroom will participate in one of the two studies. In Study 1, special education teachers that teach middle school students with learning disabilities in special education instructional settings will participate. In Study 2, math teachers that teach middle school students with learning disabilities in inclusive math classrooms will participate. Classrooms will be randomly assigned to either the intervention condition or typical classroom instruction. Schools in Kentucky will participate. The intervention will be implemented for one year. Differential effects for computational and problem-solving outcomes will be determined for middle-school students with learning disabilities in the intervention and the typical classroom instruction condition. Researchers will also examine how child characteristics and fidelity of implementation are related to treatment outcomes. The research team will also examine the influences of specific teaching activities (teacher directed vs. group work) and student responses to these activities (level of student engagement and motivation in math) on the math skills of middle school students with math difficulties.

Products: Products from this study will include published reports and presentations describing the efficacy of Enhanced Anchored Instruction as measured by standardized and non-standardized measures of math skills in middle school students with learning disabilities in math.

Setting: Participating students will be from middle schools in Kentucky.

Population: Twenty-two middle school teachers (classrooms) with approximately 5–10 students with learning disabilities in math per classroom will participate in each of the two studies. In Study 1, special education teachers that teach middle school students with learning disabilities in special education instructional settings will participate. In Study 2, math teachers that teach middle school students with learning disabilities in inclusive math classrooms will participate. Students that receive special education services for a math learning disability will be eligible to participate in the study.

Intervention: The intervention, Enhanced Anchored Instruction, will be compared to typical classroom instruction. Enhanced Anchored Instruction uses a mix of video-based problems (called anchors) delivered on CD-ROM, hands-on projects (e.g., building skateboard ramps or hovercrafts), and explicit instructional units to develop the math skills of students with math learning difficulties. Each anchored problem consists of several sub-problems embedded in a realistic and motivating context. Students must first define and understand the problem, locate the relevant pieces of information for solving it, and then integrate this information into a solution. One module focuses on fraction computation and problem solving and the other module focuses on pre-algebraic concepts and problem solving. Teachers are provided daily lesson plans, taught strategies of how to teach with the multimedia tools, and hands-on projects. The intervention will be implemented in classrooms daily for 2–3 months.

Research Design and Methods: The research team will utilize a clustered randomized design to evaluate the computational and problem-solving outcomes of middle school students with math learning disabilities. Classrooms will be randomly assigned to either the Enhanced Anchored Instruction or typical classroom instructional approach.

Control Condition: The control condition will be the typical classroom instruction model.

Key Measures: The curriculum will be evaluated using commercial and non-commercial measures. Outcome measures include the Iowa Tests of Basic Skills math subtests. Non-commercial measures include measures of students' ability to perform rational number computations and problem-solving performance.Observational and fidelity measures will also be administered.

Data Analytic Strategy: Hierarchical linear models will serve as the primary data analytic strategy to determine improvements in computational and problem-solving skills. In addition, latent transition analysis will be used to examine changes in understanding of mathematics that arise as students participate in the intervention. Classroom observations and video analysis of selected classrooms will help to identify possible mediating and moderating variables.

Related IES Projects: Advancing the Math Skills of Low-Achieving Adolescents in Technology-Rich Learning Environments (R305H040032)

Products and Publications

Book chapter

Bottge, B. (2009). Anchored Instruction. In E.M. Anderman, and L.H. Anderman (Eds.), Psychology of Classroom Learning: An Encyclopedia (pp. 34–36). Detroit, MI: Macmillan Cengage Learning.

Choi, H-J., Cohen, A. S., & Bottge, B. A. (2016). An Application of a Random Mixture Nominal Item Response Model for Investigating Instruction Effects.

Book chapter, edition specified

Bottge, B. (2010). Math Instruction for Children With Special Needs. In P. Peterson, E. Baker, and B. McGaw (Eds.), International Encyclopedia of Education (2nd ed., pp. 767–773). Oxford: Elsevier. doi:10.1016/b978–0–08–044894–7.01126–x

Journal article, monograph, or newsletter

Bottge, B. A., Cohen, A. S., and Choi, H. J. (2017). Comparisons of Mathematics Intervention Effects in Resource and Inclusive Classrooms.

Bottge, B.A., and Cho, S.-J. (2013). Effects of Enhanced Anchored Instruction on Skills Aligned to Common Core Math Standards. Learning Disabilities: A Multidisciplinary Journal, 19(2): 73–83.

Bottge, B.A., Grant, T.S., Rueda, E., and Stephens, A.C. (2010). Advancing the Math Skills of Middle School Students in Technology Education Classrooms. NASSP Bulletin, 94(2): 81–106. doi:10.1177/0192636510379902

Bottge, B.A., Ma, X., Gassaway, L., Butler, M., and Toland, M.D. (2014). Detecting and Correcting Fractions Computation Error Patterns. Exceptional Children, 80(2): 237–255. doi:10.1177/001440291408000207

Bottge, B.A., Ma, X., Gassaway, L., Toland, M., Butler, M., and Cho, S.J. (2014). Effects of Blended Instructional Models on Math Performance. Exceptional Children, 80(4): 423–437. doi:10.1177/0014402914527240

Bottge, B.A., Rueda, E., Grant, T.S., Stephens, A.C., and LaRoque, P.T. (2010). Anchoring Problem-Solving and Computation Instruction in Context-Rich Learning Environments. Exceptional Children, 76(4): 417–437. doi:10.1177/001440291007600403

Bottge, B.A., Rueda, E., Kwon, J.M., Grant, T., and LaRoque, P. (2009). Assessing and Tracking Students’ Problem Solving Performances in Anchored Learning Environments. Education Technology Research and Development, 57(4): 529–552. doi:10.1007/s11423–007–9069–y

Bottge, B.A., Toland, M.D., Gassaway, L., Butler, M., Choo, S., Griffen, A.K., and Ma, X. (2015). Impact of Enhanced Anchored Instruction in Inclusive Math Classrooms. Exceptional Children, 81(2): 158–175.

Cho, S.-J., and Bottge, B.A. (2015). Multilevel Multidimensional Item Response Model With a Multilevel Latent Covariate. British Journal of Mathematical and Statistical Psychology, 68(3): 410–433. doi:10.1111/bmsp.12051

Cho, S.J., Bottge, B.A., Cohen, A.S., and Kim, S.H. (2011). Detecting Cognitive Change in the Math Skills of Low-Achieving Adolescents. Journal of Special Education, 45(2): 67–76. doi:10.1177/0022466909351579

Cho, S.J., Cohen, A.S., and Bottge, B.A. (2013). Detecting Intervention Effects Using a Multilevel Latent Transition Analysis With a Mixture IRT Model. Psychometrika, 78(3): 576–600. doi:10.1007/s11336–012–9314–0

Cho, S.J., Cohen, A.S., and Kim, S.-H., and Bottge, B. (2010). Latent Transition Analysis With a Mixture Item Response Theory Measurement Model. Applied Psychological Measurement, 34(7): 483–504. doi:10.1177/0146621610362978

Li, F., Cohen, A. S., Bottge, B. A., and Templin, J. (2016). A Latent Transition Analysis Model for Assessing Change in Cognitive Skills. Educational and Psychological Measurement, 76(2): 181–204. doi:10.1177/0013164415588946 Full text

Suh, Y., Cho, S. J., and Bottge, B. A. (2017). A Multilevel Longitudinal Nested Logit Model for Measuring Changes in Correct Response and Error Types. Applied Psychological Measurement. doi:10.1177/0146621617703182 Full text