Progress monitoring measures in mathematics: a review of the literature.

This review of literature on progress monitoring was designed to examine the full array of curriculum-based measures (CBMs) in mathematics for students from preschool to secondary schools. We organized the article around two primary concerns: the approach used to develop the measures (curriculum sampling or robust indicators) and the type of research necessary to establish the viability of the tasks. Our review addressed the technical adequacy of the measures as indicators of performance and progress, as well as teachers' use of the measures to improve achievement. The largest number of studies has been conducted at the elementary level, with less work in early mathematics or at the secondary level. In general, the measures have acceptable levels of reliability; the criterion validity of mathematics CBMs appears to be lower than that for reading CBMs. One important finding that emerged was the relatively low degree of consensus on the best approach to use in developing mathematics CBMs. We discuss probable reasons for this, along with implications for practice and research.

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Continuous monitoring of individual student academic progress has long been an important aim within the field of special education (Deno, 1985; Fuchs, 2004). Curriculum-based measurement (CBM) represents an empirically supported system of progress monitoring that has produced demonstrated effects on student achievement, particularly in reading (Fuchs, Deno, & Mirkin, 1984; Fuchs, Fuchs, & Hamlett, 1989b; Jones & Krause, 1988). In recent years, as general educators and policymakers have emphasized greater accountability for schools' efforts to teach all children, many researchers and practitioners have asserted the utility of progress monitoring--particularly in reading--for increasing numbers of students, regardless of disability status (Deno, 2003). Given growing attention to student achievement in mathematics, the practice of continuous progress monitoring should be similarly scaled up in this content domain. To do so, education professionals need to take stock of the empirical evidence for mathematics progress monitoring measures with regard to technical adequacy and instructional utility.

The purpose of this article is to review the existing empirical literature on mathematics progress monitoring measures. As we began our work on the mathematics strand of the Research Institute on Progress Monitoring (RIPM), we sought to identify the areas of greatest need in which to focus our research. A review of the literature provided the best means of evaluating the current status of research in mathematics CBMs. We have organized our article using two concerns identified by Fuchs (2004): (a) strategies for developing CBM tasks and (b) stages of research necessary to establish the viability of those tasks.

Two Approaches for Developing CBMs in Mathematics

Fuchs (2004) described two broad approaches for the development of CBM tasks. This categorization is particularly useful in the area of mathematics. In one approach, termed curriculum sampling, researchers have developed measures by constructing representative samples of the year's mathematics curriculum--taking at second grade, for instance, a larger proportion of addition and subtraction problems and, at sixth grade, a sampling that includes more advanced skills, such as division of decimals or addition of fractions. The curriculum sampling approach has been applied to computation, as well as to conceptual problems and applied mathematics skills. For the second approach, termed robust indicators, researchers have sought to identify measures that represent broadly defined proficiency in mathematics. Using this approach, effective measures are not necessarily representative of a particular curriculum, but are instead characterized by the relative strength of their correlations to various overall mathematics proficiency criteria. Measures in this second approach attempt to parallel in mathematics the kind of "robustness" that the oral reading CBM task offers in the area of reading: not necessarily drawn from the student's yearly curriculum, yet offering strong correlations to a host of criterion measures of overall subject area proficiency. In the following section, we consider the relative merits of each approach and their implications for the development of mathematics CBMs. Practitioners will need to weigh these advantages and disadvantages when making decisions about which mathematics measures to use for progress monitoring.

A primary advantage of the curriculum sampling approach is the direct link it provides to the instructional curriculum, which facilitates the means to provide teachers with diagnostic feedback about a student's performance with regard to specific skills or concepts. These data may assist teachers in designing effective remedial instruction. This direct link to the curriculum also engenders limitations associated with this approach. Given the high level of curriculum specificity in mathematics, the curriculum sampling approach requires that different measures be developed to mirror each year's mathematics curriculum. As a result, the measures model student growth only within a single year, not across multiple years of learning. Moreover, current curriculum programs implemented in the nation's schools are quite diverse, with little consensus on placement of concepts in an instructional sequence or relative emphasis among topics (Reys, Dingman, Sutter, & Teuscher, 2005). The curriculum sampling approach may result in measures that are wedded to a particular curriculum program, necessitating the development of multiple CBM systems, each linked to a specific mathematics curriculum.