Effects of small-group tutoring with and without validated classroom instruction on at-risk students' math problem solving: Are two tiers of prevention better than one?

Abstract

The purpose of this study was to assess the effects of small-group tutoring with and without validated classroom instruction on at-risk (AR) students' math problem solving. Stratifying within schools, 119 3 rd -grade classes were randomly assigned to conventional or validated problem-solving instruction (Hot Math [schema-broadening instruction]). Students identified as AR (n = 243) were randomly assigned, within classroom conditions, to receive Hot Math tutoring or not. Students were tested on problem-solving and math applications measures before and after 16 weeks of intervention. Analyses of variance, which accounted for the nested structure of the data, revealed the tutored students who received validated classroom instruction achieved better than tutored students who received conventional classroom instruction (ES = 1.34). However, the advantage for tutoring over no tutoring was similar whether or not students received validated or conventional classroom instruction (ESs = 1.18 and 1.13). Tutoring, not validated classroom instruction reduced the prevalence of math difficulty. Implications for responsiveness-to-intervention prevention models and for enhancing math problem-solving instruction are discussed.Mathematics word problems require the transfer of knowledge to novel situations, and this form of transfer can be difficult to effect (cf. Bransford & Schwartz, 1999;Mayer, Quilici, & Moreno, 1999) especially for primary-grade children (Durnin, Perrone, & MacKay, 1997; Foxman, Ruddock, McCallum, & Schagen, 1991, cited in Boaler, 1993. Whereas a calculations problem is already set up for solution, a word problem requires students to use text to determine what information is unknown and to construct and solve a number sentence for finding that unknown information. So, although calculation skill is foundational to word problems (e.g., Fuchs et al., 2006), it seems likely that for some students, word-problem skill will not develop automatically from instruction on math calculations, but rather that instruction needs to be designed specifically to prevent difficulty with word problems.The context for preventing academic difficulty in the schools has changed over the past 5 years with the introduction of multi-tiered prevention systems. 1 Adapted from the health care system,

Inclusion Versus Specialized Intervention for Very-Low-Performing Students

“…Findings echo those of L. S. Fuchs, Fuchs, Craddock, et al (2008), which showed that although a state-of-the-art inclusive instructional program and a state-of-the-art specialized intervention both promote stronger mathematics word problem outcomes compared to typical inclusive word problem instruction, such specialized intervention is more active than such inclusive instruction in ameliorating initially at-risk students' risk status. The present analysis adds to this prior study in an important way, because although the 2008 L. S. Fuchs, Fuchs, Craddock, et al study sample was at risk, it was substantially higher performing than students in the present analysis.…”

Effects of a Multitier Support System on Calculation, Word Problem, and Prealgebraic Performance Among At-Risk Learners

“…An instructional model that incorporates explicit instruction with multiple visual representations, heuristics, and student verbalizations contributes to improved mathematics performance in this population of learners (Gersten et al, 2009). Most but not all tutoring studies that incorporate such practices have been associated with positive effects (e.g., Fuchs, Powell, et al, 2008; Jitendra, Hoff, & Beck, 1999; Powell & Fuchs, 2010; Tournaki, Bae, & Kerekes, 2008). For example, Bryant, Bryant, Gersten, Scammacca, Funk, et al (2008) conducted a regression-discontinuity study with first graders who were identified for tutoring due to low performance on a mathematics progress-monitoring measure.…”

Does calculation or word-problem instruction provide a stronger route to prealgebraic knowledge?

“…A secondary purpose of this study was to assess the efficacy of (a) the second-grade two-tiered calculation intervention, based in part on previously validated whole-class (Fuchs et al, 1997) and tutoring (Fuchs et al, 2009, 2011) programs at third grade, and (b) the second-grade two-tiered word-problem intervention, based in part on previously validated whole-class (Fuchs, Fuchs, Craddock, et al, 2008) and tutoring (Fuchs et al, 2009, 2011) programs at third grade. These programs are referred to, respectively, as Math Wise and Pirate Math .…”