Research Overview

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   Mathematics Recovery (Wright, 2000; 2003; 2009) draws significantly on an extensive program of research into young children’s number learning and instruction undertaken by Steffe and colleagues (e.g. Steffe, 1992; Steffe, von Glasersfeld, Richards, & Cobb, 1983; Steffe, Cobb, & von Glasersfeld, 1988) and related research (e.g. Wright, 1992; 1994; Wright, Stanger, Cowper, & Dyson, 1996). An important focus of Mathematics Recovery is provision of extended and on-going programs of professional development and school renewal related to both intensive intervention for low-attainers and whole-class instruction. Detailed descriptions of the theory and practice of Mathematics Recovery are available (See Wright, Martland, & Stafford, 2006; Wright, Martland, Stafford, & Stanger, 2006; Wright, Stanger, Stafford, Martland, 2006).
   As outlined in the previous paragraph, Mathematics Recovery has its origins in an extended and coherent body of research and practice undertaken over the last 25 years. At the same time, Mathematics Recovery is continually undergoing a program of review, revision and extension (e.g. Ellemor-Collins & Wright, 2007, 2008; Tabor, 2008). Leaders and teachers are annually offered conferences and the Mathematics Recovery Summer Institute. This enables them to keep abreast of the latest domestic and international research and the instructional implications of such research. For example, in recent years, design research related to early number instruction (Gravemeijer, Bowers, & Stephan, 2003) and the work of researchers at the Freudenthal Institute in The Netherlands (Gravemeijer, 2004; Van den Heuvel-Panhuizen, 2001) have significantly influenced the theory and practice of Mathematics Recovery, related to two-digit addition and subtraction.

Kentucky Math Intervention Initiative
   In the school year of 2006 /2007, Mathematics Recovery was implemented in 13 schools as part of an initiative of the Kentucky State Department of Education, focusing on early math intervention. In each of the 13 schools, a teacher undertook the year-long, professional development program for Math Recovery specialists. This included administering cycles of intensive, one-on-one instruction to up to six low-attaining first-graders. Participants’ progress was gauged via several assessments including the nationally-normed Terra Nova Assessment (CTB McGraw-Hill) which generated pre- and post- national percentile scores for each student.
   An analysis of student progress was undertaken by the Evaluation Services Center at the University of Cincinnati. In the report (details below) of the analysis, the outcomes relevant to Math Recovery are those for intervention at the first-grade level (see pp. 6-7 in the report) because, in the Kentucky initiative, Math Recovery intensive intervention was implemented at first-grade level only. The table below (adapted from p. 7 in the report) underlines the very significant progress of the Math Recovery participants, progressing from an average percentile of nine on the pre-assessment to an average of 70 on the post-assessment.

Pre- and Post- Terra Nova scores for first-graders in three groups – Math Recovery, an alternative intervention program, and comparison first-graders

Source: 2006/2007 Terra Nova Scores (p. 7). Available in pdf format from:
http:/www./kentuckymathematics.org/research.asp (retrieved 17th February 2009).

An evaluation of the effectiveness of Mathematics Recovery professional development
   MacLean (2003) evaluated the relative effectiveness of three different professional development models on low-achieving first-graders, in a large urban school district. The first model consisted of a full Math Recovery implementation. The full implementation included intensive one-on-one tutorial intervention provided to selected, low-achieving, Title 1 first-grade children as well as on-going professional development for classroom teachers provided by the on-site Math Recovery leader. This professional development took the form of presentations, joint planning sessions, model and team teaching. The second model involved those same Math Recovery leaders conducting on-going professional development in Math Recovery theory, strategies, and activities to classroom teachers from schools without an on-site, one-on-one tutorial component. These strategies and activities were adapted for use in the classroom setting. The third model involved schools in which classroom teachers received periodic, one-shot professional development and conference attendance. This professional development was provided by both in-district math leaders and by outside consultants and speakers. The teachers from this model were not exposed to any of the Math Recovery theory and methods. MacLean (2003) found that the full Math Recovery implementation model significantly out-performed both the on-going professional development only model as well as the periodic, one-shot model. The school district is currently in the process of conducting a longitudinal study to follow those children as they take the state mandated assessments. MacLean’s findings replicate similar findings by other researchers (Phillips et al., 2003).

The impact on one school of a comprehensive implementation of Math Recovery
   Commencing in the 2005 school year, Wyoming Indian Elementary School (WIES) underwent a three-year implementation of Mathematics Recovery. This involved (a) intervention specialists who undertook a year-long training program; and (b) classroom teachers who undertook a training program focused on the application of Math Recovery theory and practice to classroom teaching. Over the course of three school years, this implementation of Math Recovery had a dramatic effect on student achievement as gauged by the Wyoming state assessments in mathematics. The table below shows the percentages of 3rd, 4th and 5th graders achieving a level of proficient or advanced in the school years of 2006 and 2007. As shown, the 3rd grade cohort of 2006 advanced from 23% in 2006, to 63% in 2007. As well the 3rd grade cohort of 2007 achieved 78% proficient or advanced.

Percentage of students at WEIS proficient or advanced in 2006 and 2007

Changing teachers’ practice. Williams (2001) found that Mathematics Recovery significantly changes teacher practice in the classroom. Teachers participating in the Mathematics Recovery professional development became much more reform oriented in their teaching.

References

• Ellemor-Collins, D., & Wright, R. J. (2008). From counting by ones to facile higher decade addition: The case of Robyn. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the Joint Meeting of PME 32 and PME-NA XXX (Vol. 2, pp. 439-446). Mexico: Cinvestav-UMSNH.
• Ellemor–Collins, D. & Wright, R. J.  (2007).  Assessing student knowledge of the sequential structure of numbers as a significant aspect of multi-digit addition and subtraction.  Educational and Child Psychology, 24(2), 54-63.
• Gravemeijer, K. P. E. (2004). Local instruction theories as means of support for teachers in reform mathematics education. Mathematical Thinking & Learning, 6(2), 105-128.
• Gravemeijer, K. P. E., Bowers, J. S., & Stephan, M. L. (2003). Continuing the design research cycle: A revised measurement and arithmetic sequence. In M. L. Stephan, J. S. Bowers, P. Cobb & K. P. E. Gravemeijer (Eds.), Supporting students' development of measuring conceptions: Analyzing students' learning in social context: Journal for Research in Mathematics Education: Monograph number 12 (pp. 103-122). Reston, VA: National Council of Teachers of Mathematics.
• MacLean, H. E. (2003). The effects of early intervention on the mathematical achievement of low-performing first grade students. Unpublished Doctor of Education dissertation, University of Houston, Houston, TX.
• Phillips, V. J., Leonard, W. H., Horton, R. M., Wright, R. J., & Stafford, A. K. (2003). Can Math Recovery save children before they fail? Teaching Children Mathematics, 10(2), 107-111.
• Steffe, L. P.  (1992a).  Learning stages in the construction of the number sequence. In J. Bideaud, C. Meljac, & J. Fischer (Eds.), Pathways to number: Children's developing numerical abilities, (pp. 83-88).  Hillsdale, NJ:  Lawrence Erlbaum.
• Steffe, L., von Glasersfeld, E., Richards, J. J., & Cobb, P. (1983). Children's counting types: Philosophy, theory and application. New York: Praeger Publishers.
• Steffe, L. P., Cobb, P., & von Glasersfeld, E. (1988). Construction of Arithmetical Meanings and Strategies. New York: Springer-Verlag.
• Tabor, P.D. (2008). An investigation of instruction in two-digit addition and subtraction using a classroom teaching experiment methodology, design research, and multilevel modeling. Lismore, NSW, Australia: Southern Cross University, Doctoral dissertation (published on-line at http://epubs.scu.edu.au/theses/68/).
• Van den Heuvel-Panhuizen, M. (Ed.). (2001). Children learn mathematics: A learning-teaching trajectory with intermediate attainment targets. Utrecht, The Netherlands: Freudenthal Institute.
• Williams, L. A. G. (2001). The influences of participation in a Mathematics Recovery program on classroom practices. Unpublished Doctor of Education dissertation, University of Virginia, Charlottesville, VA.
• Wright, R. J. (1992).  Number topics in early childhood mathematics curricula: historical background, dilemmas, and possible solutions.  The Australian Journal of Education, 36, 125-142.
• Wright, R. J. (1994). A Study of the Numerical Development of 5-year-olds and 6-year-olds.  Educational Studies in Mathematics, 26, 25-44.
• Wright, R. J. (2000).  Professional development in recovery education.  In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action:  Building on the pioneering work of Ernst von Glasersfeld (pp. 134-151).  London:  Falmer.
• Wright, R. J. (2003). Mathematics Recovery: A program of intervention in early number. Australian Journal of Learning Disabilities, 8(4), 6-11.
• Wright, R. J. (2009).  An overview of mathematics recovery.  In A. Dowker (Ed.), Mathematics difficulties: Psychology, neuroscience and intervention.  San Diego, CA:  Elsevier.
• Wright, R. J., Martland, J., & Stafford, A.  (2006).  Early numeracy:  Assessment for teaching and intervention (2nd Ed.).  London:  Paul Chapman Publications /Sage.
• Wright, R. J., Martland, J., Stafford, A, & Stanger, G.  (2006).  Teaching number:  Advancing children’s skills and strategies, (2nd Ed.).  London:  Paul Chapman Publications /Sage.
• Wright, R. J., Stanger, G., Cowper, M. & Dyson, R. (1996).  First-graders' progress in an experimental mathematics recovery program.  In J. Mulligan & M. Mitchelmore, Research in early number learning:  An Australian Perspective (pp. 55-72).  Adelaide: Australian Association of Mathematics Teachers.
• Wright, R. J., Stanger, G., Stafford, A., & Martland, J. (2006).  Teaching number in the classroom with 4- to 8-year-olds.  London:  Paul Chapman Publications /Sage.