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American Educational Research Journal
April 2018, Vol. 55, No. 2, pp. 362–414
DOI: 10.3102/0002831217737028
2017 AERA. http://aerj.aera.net
How Readability Factors Are Differentially
Associated With Performance for Students
of Different Backgrounds When Solving
Mathemati

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How Readability Factors Are Differentially Associated With Performance for Studentsof Different Backgrounds When SolvingMathematics Word Problems
Candace Walkington
Southern Methodist University
Virginia Clinton
University of North Dakota
Pooja Shivraj
Coppell Independent School District
The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics prob-lems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how readability factors—such as length, word difficulty, and pronouns—interact with stu-dent background characteristics—such as race/ethnicity, mathematics achievement, and socioeconomic status. Textual features that make prob-lems more difficult to process appear to differentially negatively impact
C
ANDACE
W
ALKINGTON
is an assistant professor in the Department of Teaching andLearning at Southern Methodist University, 6401 Airline Rd., Dallas, TX, 75205;e-mail:
cwalkington@smu.edu
. Her research examines how mathematical tasks canbecome grounded in students’ interests, experiences, and prior knowledge suchthat they become easier for students to grasp. She examines mathematics assessmentsand curricula and designs interventions for mathematics learning in Grades 6through 10. V
IRGINIA
C
LINTON
is an assistant professor of educational foundations and research atthe University of North Dakota. She holds a master’s degree in teaching English tospeakers of other languages from New York University and a doctorate in educa-tional psychology from the University of Minnesota. Dr. Clinton’s research focuseson affective factors in student cognition and learning.P
OOJA
S
HIVRAJ
is the director of research and evaluation at Coppell IndependentSchool District, a midsized school district in the north Dallas area. Her work largely entails evaluating district effectiveness using multiple measures and sources. In addi-tion, her research interests primarily involve the design, interpretation, and use of assessments.
American Educational Research Journal April 2018, Vol. 55, No. 2, pp. 362–414 DOI: 10.3102/0002831217737028
2017 AERA. http://aerj.aera.net
struggling students, while features that make language easier to process appear to differentially positively impact struggling students. It is critical that readability along various dimensions be considered when designing instruction and assessment.
K
EYWORDS
: achievement gap, language comprehension/development,NAEP, mathematics education
T
he strong relationship between reading and mathematics achievement is well known (e.g., Crawford, Tindal, & Stieber, 2001; Hecht, Torgesen, Wagner, & Rashotte, 2001; Jiban & Deno, 2007; Lerkkanen, Rasku-Puttonen, Aunola, & Nurmi, 2005). For example, analyses of student performance onthe Programme for International Student Assessment (PISA; Kelly, Nord, Jenkins, Chan, & Kastberg, 2013), known to have a particularly high readingdemand in its mathematics items, show a correlation of 0.95 between PISA mathematics country mean scores and PISA reading country mean scores(Wu, 2010). This correlation was higher than the country by country correla-tion between PISA mathematics scores and mathematics scores on the Trendsin International Mathematics and Science Study (TIMSS) international assess-ment. This suggests that measures of reading achievement may actually pre-dict mathematics achievement well and in fact be better predictors thansome complementary measures of mathematics achievement.One reason why mathematics achievement may be so closely linked toreading is that many mathematics problems involve considerable readingdemands. Mathematical information is often presented in verbal (ratherthan symbolic) formats, with significant unraveling and decoding of theEnglish language needed to extract relevant relations. Indeed, mathematics word problems (i.e., problems where a mathematical scenario is posed usinglanguage rather than or in combination with symbols) have long been con-sidered notoriously difficult (Cummins, Kintsch, Reusser, & Weimer, 1988),and U.S. mathematics teachers cite word problems as a major weakness of students (Loveless, Fennel, Williams, Ball, & Banfield, 2008). A subset of word problems are story problems, which are situated in ‘‘real-world’’ con-texts that reference concrete people, places, and objects. International com-parisons suggest U.S. students struggle with mathematics word problems(OECD, 2010).Large-scale mathematics assessments in the United States, such as theNational Assessment of Educational Progress (NAEP), have also revealedenduring achievement gaps between different student groups. Relatively small achievement gaps between males and females, favoring males, persistin some grade levels of mathematics (Robinson & Lubienski, 2011). Large,persistent, and widening achievement gaps between students of low andhigh socioeconomic status (SES) are particularly troubling (Reardon, 2011),as are continued gaps between Caucasian and Hispanic or African
Readability and Student Background
363
American students (National Center for Educational Statistics [NCES], 2013;Provasnik et al., 2012). Achievement gaps also exist with respect toEnglish language learners (ELLs; Fry, 2007), a fast-growing segment of theU.S. population. Finally, research has placed increasing emphasis on theimportance of students’ attitudes toward mathematics—particularly theirinterest in learning mathematics—and its positive association with achieve-ment (Kim, Jiang, & Song, 2015).These gaps in mathematics achievement may in part be explained by differences in reading and language background between student groups.Indeed, recent work highlights that students who have weak language skillshave difficulty understanding the text in word problems (Vilenius-Tuohimaa, Aunola, & Nurmi, 2008) and that accommodations that reduce the readingdemands of mathematics problems can result in higher performance forstruggling students (e.g., Helwig, Rozek-Tedesco, Tindal, Heath, & Almond, 1999). When considering that all students, including those from dif-ferent demographic backgrounds, should understand mathematics and beassessed on their progress, it is critical to investigate how readability charac-teristics of mathematics problems may be differentially associated withperformance.In the present study, we use almost 20 years of mathematics achieve-ment data from the NAEP and TIMSS to examine how the reading level of mathematics word problems is differentially associated with performancefor students from different demographic backgrounds. Examining approxi-mately 1,000 problems solved by three-quarters of a million fourth- andeighth-grade U.S. students, we look at the interaction of word problem read-ability, focusing on several key text-based indicators identified in priorresearch, and student background characteristics, focusing on characteristics where achievement differences are well established. Pilot work we reviewsuggests that readability measures do matter for students’ performance onmathematics word problems. Thus, investigating whether these readability factors are differentially impacting students from different backgrounds isimportant for understanding and acting on persistent achievement differen-ces between groups.
Literature Review
Theoretical Framework
Theoretical work on cognitive models for solving word problems hasexplicated why readability may be important. Early research revealed thatslight variations in mathematics problem wording result in children usingdifferent strategies (Carpenter, Fennema, Franke, Levi, & Empson, 1999;Carpenter & Moser, 1984). Kintsch and Greeno (1985) developed a modelof story problem solving where students first translate from a problem
Walkington et al.
364
statement to a
propositional textbase
, which is a conceptual representation of the relationships in the text. Students then form a
problem model
or
situationmodel
that infers the information needed to solve the problem based onknowledge of the domain. Later research (Hegarty, Mayer, & Monk, 1995)recognized that unsuccessful problem solvers use
direct translation strate- gies
, operating on numbers and keywords from the text and bypassing inter-mediate formation of a model of the situation. In contrast, successfulproblem solvers use problem model strategies where they form a mentalrepresentation of the situation and use this model to plan and assess theirstrategies.Following this work, Nathan, Kintsch, and Young (1992) proposeda model of story problem solving where students coordinate three levelsof representation: (a) the textbase or the propositional information given;(b) the situation model or mental representations of the relationships,actions, and events; and (c) the problem model of formal mathematical oper-ands, numbers, and variables. The situation and problem models are thoughtto be mutually supportive, with students iteratively moving between the tworepresentations. Thus, if students are able to extract a meaningful situationmodel from the problem’s text, this situation model can support andimprove their formal mathematical computations. However, forming this sit-uation model is heavily dependent on comprehension of the text itself, which is impacted by readability.Cognitive load theory also gives an important and related way of under-standing the demands of solving mathematics word problems.
Cognitive load
refers to the amount of mental effort expended in a learning or assess-ment task as working memory is utilized (Sweller, van Merrienboer, & Paas,1998). While
intrinsic cognitive load
is the inherent difficulty level associated with understanding and processing particular mathematical concepts ina word problem,
extraneous cognitive load
describes the way in which cog-nitive load is further impacted by the manner in which the concepts are pre-sented. Problem texts that are difficult to read may increase extraneouscognitive load as students struggle to decode the written language to forma situation model. For example, Walkington, Clinton, Ritter, and Nathan(2015) describe a story problem where a character wakes up to find theirbasement flooded and ends up comparing the rate of two plumbers. Thecontextual information at the beginning of the problem may have contrib-uted to extraneous cognitive load as such factors may not be directly relatedto learners’ processing and retrieval of relevant schemas. Thus, extraneouscognitive load from readability factors that are unrelated to retrieval of sche-mas may monopolize working memory, making these schemas more diffi-cult to access. However, it is important to note that readability characteristics are not always extraneous—it may be unavoidable to addreading demands when explaining a complex mathematical situation, andconfronting such problems may intrinsically involve reading skills.
Readability and Student Background
365

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