The Effects of Schema-Based Instruction on the Mathematical Word-Problem-Solving Performance of Students with Learning Disabilities

“Some studies showed very high effect sizes (up to 12 or 14; Jitendra & Hoff, 1996; Van Luit & Van der Aalsvoort, 1985).”

“…to treatment Duration less than 12 weeks Inadequate outcome measure (continued) APPENDIX A (continued) Author Fuchs, Fuchs, Finelli, et al. (2006) Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp, et al. (2003) Fuchs, Fuchs, Prentice, et al. (2004) Jitendra et al. (1998) Jitendra & Hoff (1996)”

“…that instruction involving visual-spatial representation as a component does seem to improve math problem solving for students with LD (Hutchinson, 1993; Jitendra & Hoff, 1996; Marsh & Cooke, 1996; Montague, Applegate, & Marquard, 1993; Montague & Bos, 1986; Parmar, 1992; Zawaiza & Gerber, 1993).”

“…schema-based research studies reported in the literature have focused on teaching addition and subtraction word problems (i.e., change, group, compare; e.g., Jitendra et al., 1998; Jitendra & Hoff, 1996; Jitendra et al., 1999) or algebra word problems (Hutchinson, 1993; Maccini & Hughes, 2000).”

“Using a multi-probe-across-participants design with 3 students in third or fourth grade, Jitendra and Hoff (1996) used a similar instructional method to teach one-step change, compare, and group problems, which required single-digit adding or 157Exceptional Children subtracting for solution.”

“To investigate the effect of schema-broadening instruction for students at-risk for LD, Fuchs, Fuchs, Craddock, et al. (2008) randomly assigned 119 classrooms to receive schema-broadening instruction or to participate in a business-as-usual control group.”

“…for academic tasks (e.g., Case, Harris, & Graham, 1992), whereas other studies can be directly linked to information processing theory research (Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999) and the concern for metacognition in problem solving that arose in mathematics re- search in the…”

“We know that involving visual– spatial representations as a component of instruction does seem to improve math problem solving for students with LD (Hutchinson, 1993; Jitendra & Hoff, 1996; Marsh & Cooke, 1996; Zawaiza & Gerber, 1993).”

“However, later research by Jordan and Hanich (2000) cited problem simplicity as a limitation of their prior research, a factor which masked existing deficits in students with math LD under both conditions.”

“The second model, Schema-Based Strategy Instruction, was investigated in two studies involving elementary school students in grades two through five (Jitendra & Hoff, 1996; Jitendra et al., 1998).”

“In addition, Jitendra and colleagues used schematic diagrams as part of SBI to teach elementary and middle school students with disabilities and those at risk for mathematics difficulties (e.g., Jitendra, DiPipi, & Perron-Jones, 2002; Jitendra, Griffin, Deatline-Buchman, et at., 2007; Jitendra et al., 1998; Jitendra &…”

“alization, and maintenance (Case, Harris, & Graham, 1992; Jitendra et al., 2002; Jitendra & Hoff, 1996; Jitendra et al., 1999).”

“The current study, along with Saunders et al. (2016), provides a possible direction for teaching problem solving to students with ASD and moderate or severe ID by modifying SBI that has been used for students with high incidence disabilities (Jitendra & Hoff, 1996).”

“Prior research on schema-based word-problem intervention demonstrates positive effects at second and third grade (Fuchs et al., 2008; Fuchs et al., 2004; Jitendra et al., 2007; Jitendra & Hoff, 1996; Powell et al., 2019; Powell & Fuchs, 2010).”

“%) met or exceeded the minimum requirements for this indicator (Jitendra et al., 2002; Jitendra & Hoff, 1996; Neef et al., 2003; Rockwell et al., 2011).”

“In the area of mathematics, interventions such as cover-copy-compare (Skinner, Turco, Beatty, & Rasavage, 1989), reciprocal peer tutoring (Fantuzzo, King, & Heller, 1982), classwide student tutoring teams (Harper & Maheady, 1999), and schema-based problem solving ( Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999 )…”

“Study n Grade Participant status Test for identifying MD Test for identifying RD Design Cassel and Reid (1996) 2 3 MD, MD + RD WIAT: Broad math WIAT: Reading MPD Jitendra and Hoff (1996) 2 3 MD California Achievement Test: math operation; Key Math MPD Marsh and Cooke (1996) 3 3 MD + RD Woodcock-Johnson Psycho-Educatio…”

“As Jitendra and Hoff (1996) and Zawaiza and Gerber (1993) noted, students must be directly taught to process the problem schemata (or the definitive characteristics, features, and facts) necessary to recognize and represent the situation described in a problem.”

“Several studies using this approach have reported (Jitendra& Hoff,1996;Jitendra,Hoff,&Beck,1999;Jitendra,DiPipi,& Perron-Jones,2002;Jitendraetal.,1998).”

“…effectiveness of using SBI to improve the additive word problemsolving performance of students with learning disabilities in both resource room and inclusive settings (e.g., Jitendra et al., 2007; Jitendra et al., 1998) and have shown maintenance of the skill across time (Jitendra & Hoff, 1996).”

“…2002; Jitendra, Griffin, Deatline-Buchman, & Sczesniak, 2007; Jitendra et al., 2007; Jitendra, Griffin, McGoey, Gardill, Bhat, & Riley, 1998; Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999; Lewis, 1989; Willis & Fuson, 1988; Xin, 2008; Xin, Jitendra, & Deatline-Buchman, 2005; Xin…”

“Diagrams have been used to supplement explicit teaching of steps of a problem-solving chain in the context of computer programs (Jaspers & van Lieshout, 1994) or direct instruction (e.g., Jitendra & Hoff, 1996).”

“Five single-case design studies (i.e., Jitendra et al., 2002; Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999; Sharp & Dennis, 2017; van Garderen, 2007) and one group design (Walker & Poteet, 1990) included only participants with LD.”

“My colleagues and I have successfully taught the graphic representational strategy to students with disabilities in elementary and middle schools in our research investigations (Jitendra et al., 1998; Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999).”

“…to map the problem features to the corresponding schema and then solve the problems (e.g., Jitendra, Griffin, Deatline-Buchman, & Sczesniak, 2007; Jitendra & Hoff, 1996; Jitendra et al., 1998), or use equation models to represent mathematical relations in the problem (e.g., Xin, Jitendra, &…”

“…(d) did not report findings of an intervention study targeting WPS (e.g., Woodward & Baxter, 1997) or evaluated word problem outcomes but did not include WPS-focused interventions (e.g., Strand Cary et al., 2017); (e) employed non–group research designs, such as SCD (e.g., Jitendra & Hoff, 1996).”

“As in the previous two studies, Jitendra and Hoff (1996) and Jitendra et al. (1998) taught students to draw diagrams to discriminate between different problem types.”

“However, some studies have suggested advantages related to visual-schematic representations over more general-heuristic approaches (e.g., Jitendra & Hoff, 1996; Jitendra et al., 2011).”

“…42 47 S Broad 1,200 R PPW/C/C Fuchs et al. (2010) 131 139 Cl Broad 1,838 R PPW/C/C Griffin and Jitendra (2008) 30 30 MP Based 1,500 Tr PPW/C/C Jitendra and Hoff (1996) 13 10 MP Based 765 Tr PPW/C/C Jitendra et al. (1998) 17 17 S Based 765 R PPW/C/C Jitendra, Griffin, Haria, et al. (2007) 45…”

“Jitendra and colleagues (Jitendra et al., 1998; Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999) have used a schema-based approach to improve word problem-solving abilities in students who are at risk and students who have learning disabilities.”

“Schema-based instruction in problem solving has many proponents (e.g., Chen 1999; Fuchs et al. 2004a, b; Jitendra and Hoff 1996; Marshall 1995).”

“Interventions in which students receive direct structured instruction have been frequently found to be very effective (e.g., Harris et al., 1995; Jitendra & Hoff, 1996; Van Luit, 1994; Wilson et al., 1996).”

“…as cover–copy–compare (Skinner, Turco, Beatty, & Rasavage, 1989), reciprocal peer tutoring (Fantuzzo, King, & Heller, 1992), classwide student tutoring teams (Harper & Maheady, 1999), and schema-based problem solving (Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999) were found in both groups.”

“According to Riley et al. (1983), the acquisition of problem-solving skills is primarily an improvement in children's ability to represent the relationships among quantities described in the problem situation.”

“…clear evidence that when these students are explicitly taught such strategies, they can develop their word problem-solving knowledge and skills (Jitendra & Hoff, 1996; Jitendra, DiPipi, & Perron-Jones, 2002; Montague, 1992; Montague & Bos, 1986; Xin, Jitendra, & Deatline-Buchman, 2005; Zawaiza…”

“…been conducted that focus on schema (Fuchs, Fuchs, Hamlett, & Appleton, 2002; Fuchs et al., 2004a; Fuchs, Fuchs, Finelli, Courey, & Hamlett, 2004b; Jitendra & Hoff, 1996; Jitendra et al., 1998; Jitendra, Hoff, & Beck, 1999; Xin, Jitendra, & Deatline-Buchman, 2005; Jitendra et al., 2007; Jitendra,…”

“…interventions included several instructional strategies, such as story mapping (Idol, 1987), listening passage preview (Rathvon, 1999), collaborative strategic reading (Vaughn & Klingner, 1999), and schema-based word problem solving (Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999).”

“SBI uses a conceptual teaching approach that combines mathematical problem solving and reading comprehension strategies (Jitendra & Hoff, 1996).”

“This particular enhancement is supported by research with students with learning disabilities, revealing positive effects for the use of manipulatives and visual representations during mathematics instruction (e.g., Jitendra & Hoff, 1996; Kroesbergen & Van Luit, 2003).”

“One study implemented SI and was included in our study (Jitendra & Hoff, 1996).”

“…consistent with previous research associated with CRA, the FAST strategy, and schema-based interventions (Cassel & Reid, 1996; Jitendra, DiPipi, & Perron-Jones, 2002; Jitendra, George, Sood, & Price, 2010; Jitendra & Hoff, 1996; Jitendra et al., 2013; Jitendra, Sczesniak, & Deatline-Buchman, 2005).”

“Similar problem types (i.e. change, group, and compare problems) were used in studies by Jitendra and colleagues (Griffin & Jitendra, 2009; Jitendra & Hoff, 1996; Jitendra, Griffin, Haria, et al., 2007; Jitendra et al., 1998; Leh & Jitendra, 2013).”

“…model, educators successfully taught school age children with learning disabilities how to solve mathematical problem using different strategies (Jitendra & Hoff, 1996; Jitendra & Xin, 1997; Montague & Di-etz, 2009; Montague, Enders, & Dietz, 2011; Xin & Jitendra, 1999; Xin, Jitendra, &…”

“…2009; Jitendra et al., 2009) as well as those with learning disabilities (Griffin & Jitendra, 2009; Jitendra, DiPipi, & Perron-Jones, 2002; Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck,1999; Jitendra et al., 2007; Na, 2009; Xin, 2008; Xin, Jitendra, & Deatline-Buchman, 2005), emotional…”

“…the experimental group generalized the procedural knowledge they gained from the TIP strategy to solve functional mathematical problems that involved using percentage values in a different context immediately following the intervention (Case et al., 1992; Hutchinson, 1993; Jitendra & Hoff, 1996).”

“Yet, when the question is changed a little bit or students confront with a new question, this approach may fail to solve the problem (Viennot &Moreau, [82] Jitendra &Hoff, [40]; Steele & Johanning,[75].”

“…solving has demonstrated that effective methods include explicit instruction in self regulated strategies (Case, Harris, & Graham, 1992; Wilson & Sindelar, 1991) CRA coupled with direct instruction that utilized mnemonic devices (Cassel & Reid, 1996) , or schema training (Jitendra & Hoff, 1996).”

“Through this instruction, children could learn to pay attention to the features of the situation mentioned in the word problems and linked them with relevant mathematic concepts (Jitendra & Hoff, 1996).”

“SBI helps students learn to use schematic diagrams when solving word-problems (Jitendra & Hoff, 1996; Jitendra, Sczesniak, et al., 2007).”

“Schema-based strategy instruction has been demonstrated as effective with students with mathematical difficulties in Grades 2‐8 ( Jitendra & Hoff, 1996; Jitendra, DiPipi, & Perron-Jones, 2002; Jitendra et al., 1998; Jitendra, Hoff, & Beck, 1999).”

“…regular and strategic education (Montague, 2007; 2008; Whitby, 2009), students with mental disabilities should be taught appropriate strategies that help them to solve problems within the process (from planning to reaching the final solution) (Jitendra & Hoff, 1996; Karabulut & Özmen , 2018).”

“Third, many of the single-case studies were implemented one-to-one and with 30–40min intervention sessions (Jitendra & Hoff, 1996; Jitendra, Hoff, & Beck, 1999; Rockwell, Griffin, & Jones, 2011).”

“…Prentice, Burch, Hamlett, Owen, & Schroeter, 2003; Fuchs, Seethaler, Powell, Fuchs, & Hamlett, 2008; Griffin & Jitendra, 2009; Jitendra, Griffin, et al., 2007; Jitendra et al., 1998; Jitendra & Hoff, 1996; Leh & Jitendra, 2013; Owen & Fuchs, 2002; Seo & Bryant, 2012; Wilson & Sindelar, 1991).”

“While prompting drawing production has sometimes yielded mixed results (see Ver-schaffel, 2016, for a discussion), this line of interventions using teacher-imposed constraints on the drawings has also shown encouraging results (Jitendra & Hoff, 1996; Ng & Lee, 2005; Verschaffel et al., 2020).”

“Dolayısıyla süreç temelli, düzenli ve stratejik bir eğitimle (Montague, 2007, 2008) öğrenme güçlüğü olan öğrencilere problem çözümü için planlamadan çözüme ulaşana kadar tüm süreçte yardımcı olacak uygun stratejiler öğretilmelidir (Jitendra & Hoff, 1996; Özkubat vd., 2020).”

“Studies emphasize that visual representation improves mathematical problem solving for students with SLD (Hutchinson, 1993; Jitendra & Hoff, 1996; Zawaiza & Gerber, 1993).”

“Compare story situations are statements of the problems in which there is no unknown (Jitendra & Hoff, 1996).”

“Integrating the word problem-solving processes into schema theory, Jitendra and Hoff (1996) presented a three-stage schema-based processing model in mathematical word problem-solving.”

“A progressive approach to helping at-risk students learn how to solve WPs, which has been improved over the last 30 years, is the use of a 'schematic diagram' to solve WPs (e.g., Fuchs et al., 2004; Jitendra & Hoff, 1996).”

“At the beginning of the instruction, story sessions, without unknown quantities in the statements, were conducted with the objective of providing procedural guidance on the use of the materials (Jitendra and Hoff 1996).”

“The survey model aims to reveal a current situation as it is, and the researcher cannot have any manipulative influence in this model (Karasar, 2002). The second research question, “What types of errors do the primary fourth-grade students make while converting problem sentence in verbal form into visuals?” was answer…”

“As for Jitendra et al.’s (2007) recent study, the SBI diagrams presented were not fundamentally different from the SBI initially presented in Jitendra and Hoff (1996) or summarized in Jitendra (2002), as students still were expected to make distinctions among various additive problem types (i.e.,…”

“Once the underlying semantic relations have been identified, students can determine the components that make up the semantic relations, such as beginning, change, and ending quantities, and select the appropriate arithmetic operation to solve the problem (Jitendra & Hoff, 1996).”