Academic journal article School Psychology Review

Assessing the Instructional Level for Mathematics: A Comparison of Methods

Academic journal article School Psychology Review

Assessing the Instructional Level for Mathematics: A Comparison of Methods

Article excerpt

Abstract. This study compared the mathematics performance of 434 second-, third-, fourth-, and fifth-grade students to previously reported fluency and accuracy criteria using three categories of performance (frustration, instructional, and mastery). Psychometric properties of the fluency and accuracy criteria were explored and new criteria for the instructional level were empirically derived. Two sets of mathematics probes were administered to the students and delayed alternate-form reliability coefficients were obtained from multiskill probes. Results suggested that fluency data were significantly more reliable than accuracy data. Slopes from the single-skill probes were used to categorize students as high responders, and the mean fluency scores from that group's multiskill probes were used to suggest an alternative instructional level of 14-31 digits correct per minute for second- and third-graders and 24-49 digits correct per minute for fourth- and fifth-graders. Implications for practice and suggestions for future research are discussed.


Recent empirical attention to academic intervention has focused primarily on reading (Badian, 1999; Daly & McCurdy, 2002). Research related to mathematics assessment and instruction has lagged comparably behind, yet the need for evidence in effective mathematics assessment and intervention is pressing because fewer than one third of fourth-grade students met or exceeded the proficiency standard on the 2003 mathematics test of the National Assessment of Educational Progress (Manzo & Galley, 2003).

Panels convened to recommend reform in mathematics assessment and instruction have emphasized, among other factors, the need for data that are useful to teachers in planning and delivering math instruction (National Council for Teachers of Mathematics, 2000). Moreover, assessment data can be used for progress monitoring and to facilitate attainment of desired outcomes (Algozzine, Ysseldyke, & Elliott, 1997). Thus, instructionally relevant assessment data are critical to effective mathematics instruction and intervention.

Academic difficulties can result from a mismatch between student skill and the curriculum or instructional material (Daly, Martens, Kilmer, & Massie, 1996; Daly, Witt, Martens, & Dool, 1997; Enggren & Kovaleski, 1996; Gravois & Gickling, 2002). Instructional material that is too difficult results in student frustration, and material that is not challenging enough, or is too easy, results in student boredom. The "window of learning" (Tucker, 1985, p. 201) between boredom and frustration is called the "instructional level" and occurs when instructional materials provide an appropriate level of challenge. Research has consistently found that providing appropriately challenging teaching material, at the instructional level, has led to improved student outcomes for reading (Burns, 2002; Gickling & Rosenfield, 1995; Shapiro, 1992; Shapiro & Ager, 1992) and mathematics (Burns, 2002; Gickling, Shane, & Croskery, 1989).

An appropriate level of challenge (or instructional level) is one of the essential components of an effective learning environment (Ysseldyke & Christenson, 2002), but research has yet to adequately define an instructional match for mathematics. Gickling and Thompson (1985) suggested an accuracy approach in which mathematics assignments should contain 70-85% known items to represent an instructional level task. Deno and Mirkin (1977) suggested that the instructional level for mathematics be determined with fluency (i.e., accuracy plus speed) measures instead of accuracy data alone. They further estimated that 10-19 digits correct per minute (dc/min) would represent an instructional level for students in the 1st through 3rd grades, whereas 20-39 dc/min would equal an instructional level for children in the 4th through 12th grades. Meta-analytic research has found strong effects from studies using the accuracy criterion of 70-85% known items for mathematics, but also found strong effects for other proposed accuracy criteria such as 50% known and 90% known (Burns, 2004). …

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