# Effects of Blended Instructional Models on Math Performance

## Article excerpt

The National Assessment of Educational Progress (NAEP; National Center for Education Statistics, 2011) reported that almost two thirds (65%) of students with disabilities in eighth grade scored below the Basic level compared to 23% of students without disabilities. To achieve Basic on the NAEP, students must have an understanding of arithmetic operations with whole and rational numbers and be able to solve "real world" problems using charts, graphs, and technology tools such as calculators and computers.

Much of the students' low math performance can be traced to computing with fractions and problem solving (see Misquitta, 2011), two areas of difficulty that have been identified for many years on large-scale assessments and in research studies. For example, results of the 1996 NAEP (Silver & Kenney, 2000) indicated many eighth grade students (65%) could not order five fractions less than 1 from least to greatest and more than one third of students (35%) did not choose 1/3 as the fraction equivalent to 4/12. In problem solving, students have difficulty focusing on relevant parts of problems (Kauffman, 2001), organizing information (Geary, 2004), and monitoring their work (Gallico, Burns, & Grob, 1991; Montague, Bos, & Doucette, 1991).

These findings have put more pressure on teachers to emphasize in earlier grades complex math concepts such as fractions and algebra (e.g., Butler, Miller, Crehan, Babbitt, & Pierce, 2003; Scheuermann, Deshler, & Schumaker, 2009). The Common Core State Standards for Mathematics (CCSS-M, National Governors Association Center for Best Practices, Council of Chief State School Officers 2010) recommends that students develop understanding of fractions in Grade 3, equivalence in Grade 4, and fluency with adding and subtracting fractions by the end of Grade 5. Stressing the importance of fractions, the Brookings Institution (2004) and the National Mathematics Advisory Panel (NMAP, 2008) have suggested adding more fraction items on the NAEP test noting their underrepresentation.

In problem solving, the National Council of Teachers of Mathematics (NCTM; Briars, Asturias, Foster, & Gale, 2012) recommends that all students have opportunities to solve quality problems that are motivating and help students build confidence in their ability to figure things out on their own. Problem solving poses special challenges for low-performing students because problems are typically embedded in text that is difficult to decipher for students with comorbid difficulties in reading and math (Knopik, Alarcon, & DeFries, 1997; Parmar, Cawley, & Frazita, 1996).

Over a decade ago we began testing the effects of enhanced anchored instruction (EAI), an instructional method we developed for improving the computation and problem solving skills of middle students with disabilities in math. EAI is based on the concept of anchored instruction (AI; Cognition and Technology Group at Vanderbilt, 1997) and follows closely the theoretical base in our model for teaching and learning math (Bottge, 2001). Realistic problems (i.e., anchors) are embedded in interesting contexts and presented in interactive, video-based formats. The anchors consist of an 8- to 15-min video in which adolescents are shown attempting to solve a challenging problem.

First versions of EAI included one video-based problem and one simple hands-on application. Based on a series of studies, we made improvements to EAI by adding more complex hands-on applications (enhancements) to help students "visualize" abstract concepts, a strategy that aligns closely with recommendations in the Institute of Education Sciences' Practice Guide for Organizing Instruction to Improve Student Learning (Pashler et al., 2007). The hands-on projects afforded multiple opportunities for students to improve their procedural skills and helped them gain a deeper understanding of the math concepts embedded in each problem. …

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