A concrete–semiconcrete–abstract (CSA) instructional approach derived from discovery learning (DIS) was embedded in a direct instruction (DI) methodology to teach eight elementary students with math disabilities. One-minute abstract-level probes were the primary metric used to assess student performance on subtraction problems (minuends 0–9). A single-subject, multiple-baseline across-participants design was used to identify the differential effects of discontinuing instruction at crossover (i.e., the point when the correct response rate exceeded the incorrect response rate). Results indicate that the commonly accepted practice of teaching an entire CSA unit of lessons may not be the most efficacious approach for classroom teachers. Instead, through daily data collection and application of the “crossover decision rule” (discontinue rule), teachers can selectively target those students appropriate for additional concrete- and/or semiconcrete-level instruction and those students for whom continued practice at the abstract level is more appropriate. Implications for teaching computational skills are examined.

Preservice special education teacher candidates in higher education training programs are given little or no specific training in the use of basic native language or cultural academic instructional techniques to support the learning needs of students who have not reached a level of English proficiency. Preservice special education students are also not assessed for their effective level of application of culturally responsive language techniques to classroom field placement settings when working with diverse children with disabilities. The purpose of this study was to investigate the transfer of basic Spanish language culturally responsive academic math problem solving instruction strategies from the university classroom to field placements by three preservice student teachers in a special education training program in mild/moderate disabilities. This study employed an experimental single-subject multiple baseline design across subjects. Data were collected on the frequency of use of basic culturally responsive Spanish language behavior in the areas of (a) concept bridging, (b) task directional, and (c) praising language. After five sessions of explicit targeted Spanish language training all subjects significantly increased their levels of the use of the Spanish targeted language approach when teaching small groups of students in their classroom field placement settings.