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"Mathematics interventions at the Tier 2 (secondary prevention) level of a multi-tier prevention system must incorporate six instructional principles: Instructional explicitness Instructional design that eases the learning challenge A strong conceptual basis for procedures that are taught An emphasis on drill and practice Cumulative review as part of drill and practice Motivators to help students regulate their attention and behavior and to work hard This article describes each of these principles and some of their research underpinnings, with consideration given to how the principles can be implemented in real-world teaching contexts. The first principle of effective intervention in mathematics at the secondary prevention level is instructional explicitness. Typically developing students profit from the general education mathematics program even though it relies, at least in part, on a constructivist, inductive instructional style. Students who are at risk for serious mathematics deficits, however, fail to profit from those programs in a way that produces understanding of the structure, meaning, and operational requirements of mathematics. A meta-analysis of 58 math studies (Kroesbergen & Van Luit, 2003) revealed that students with math disability benefit more from explicit instruction than from discovery-oriented methods. Therefore, effective intervention in Tier 2 requires an explicit, didactic form of instruction in which the teacher directly shares the information the child needs to learn. Explicitness is not, however, sufficient. A second and often overlooked principle of effective secondary mathematics intervention is instructional design that eases the learning challenge. The goal is to anticipate and eliminate misunderstandings by means of precise explanations and with the use of carefully sequenced and integrated instruction. The purpose is to close the achievement gap as quickly as possible. This may be especially import

"Studies in New Zealand (Young-Loveridge, 1991) have shown that children who have limited basic mathematical concepts on entry to school are unlikely to make rapid improvements. Initially, the viability and success of early mathematics intervention was investigated (Young-Loveridge, 1993). It was not only in New Zealand that such research was taking place. In Australia, between 1992 and 1995, Mathematics Recovery (Wright, Martland, Stafford & Stanger, 2002; Wright, Stanger, Cowper & Dyson, 1996) was developed in New South Wales. This is both a recovery program for students in their second year of school and a specialised professional development program for teachers. 'Mathematics Recovery has been adopted by school systems in 15 states in the USA, in nine Local Education Authorities in the north of England, and the Bahamas and Scotland' (Wright, 2002, p. 31). At the same time, however, there was research showing that all children would benefit if the way mathematics was taught were changed, and the Count Me In Too (CMIT) program was implemented in New South Wales government schools from 1996. 'Development of CMIT drew extensively on the theory and methods that had been developed for Mathematics Recovery' (Wright, 2002, p. 31). Initial evaluations of the CMIT program were positive (Bobis & Gould, 1998) and by 2003 the program was available in about 1800 primary schools in New South Wales; in other Australian states; and in 2000 it was implemented in 81 New Zealand schools on a trial basis (Wright, 2002). During the late 1990s and early 2000s, the Numeracy Development Project in New Zealand was developed, building on the CMIT program."

"Center on Instruction www.centeroninstruction.orgBack to Top The Center on Instruction offers materials and resources on mathematics to build educators' knowledge of instruction for students with low achievement in mathematics, improve professional development models for math teachers, and build teachers' skills in monitoring student growth toward important math outcomes."

This page summarises the NZ NUmeracy project

a range of resources, strategies and research into internvention programs

intervention program for 5-11 year olds

Implications for Classroom Teachers The importance of the Mathematics intervention program to students "mathematically at risk" cannot be over-emphasised. As stated by the National Statement (Australian Education Council, 1991): "Whether a particular student gains the full benefit from mathematics may be influenced by a range of personal characteristics and circumstances. It will also depend on the quality of the mathematics offered" (p.8). Steffe and his colleagues (Steffe et al., 1983; 1988) have indicated that 6 year-old children below Stage 3 of the counting stages may require up to two years to progress to Stage 5 and even then there is no guarantee that all children will attain this level. Considered in this light the results achieved by children in a quarter of that time are a positive indication of the viability of the Mathematics Intervention program.

A good place to start researching

good site to start other research listing of 5 studies

summary of research into succesful mathematics intervention programs

UK information

"Australia, the Czech Republic, Hong Kong SAR,1 Japan, the Netherlands, Switzerland, and the United States."

Summary of CRA

"A Resource for Teaching Mathematics to Struggling Learners "

"Other areas of research on the use of manipulatives show generally positive impacts when manipulatives are combined with (1) virtual manipulatives software, (2) reflective practices, (3) cooperative learning, or (4) learning activities that are exploratory and deductive in their approach. And we believe that manipulatives can indeed benefit student achievement in regular mathematics classrooms (as opposed to special education environments) when used in conjunction with instructional practices that develop a concept of a symbolic nature and don't simply mirror a process or algorithm."