Identifying obstacles is not enough for everybody—Differential efficacy of an intervention fostering fifth graders’ comprehension for word problems
Introduction
How can innovations be developed and implemented that help students to overcome typical challenges? We focus this major question on word problems, a typical type of tasks that play an important role in mathematics classrooms as they can enhance or assess reality-oriented considerations. The process of reading, understanding and solving mathematical word problems has widely been described, e.g. by Reusser (1997) for arithmetic word problems. Empirical studies contributed to identifying students’ challenges with word problem in various obstacles (Reusser, 1997; Verschaffel, Greer, & de Corte, 2000). Obstacles, defined as potentially challenging features, were shown to occur in various dimensions, among them mathematical, semantical, structural, strategic, conceptual and language obstacles (Daroczy, Wolska, Meurers, & Nuerk, 2015; Reusser, 1997; Verschaffel et al., 2000).
As a consequence of identifying obstacles, effective instructional approaches have been developed and evaluated for mastering conceptual obstacles in word problems (e.g., Van Dooren, De Bock, Hessels, Janssens, & Verschaffel, 2004), for mastering mathematical, structural and semantical obstacles (Rudnitsky, Etheredge, Freeman, & Gilbert, 1995; Xin & Jitendra, 1999; Zheng, Flynn, & Swanson, 2013), and also for strategic and/or habitual obstacles (e.g., Prediger & Krägeloh, 2015; Reusser, 1997; Verschaffel, Greer, Dooren, & Mukhopadhyay, 2010).
This article focuses on language obstacles which comprise e.g. unfamiliar vocabulary or specific meanings of words (e.g. of prepositions or technical terms) on the word level or passive voice and complexe subclauses on the sentence level (Daroczy et al., 2015). So far, empirical findings on language obstacles have been mainly used for avoiding language biases in assessments for students with limited academic language proficiency (e.g. Abedi & Lord, 2001; Haag, Heppt, Roppelt, & Stanat, 2015). Although this reductionist approach is important for fair assessments, it is not sufficient for learning situations, as already Austin and Howson (1979) have argued: “An alternative to simplifying textual material is that of providing children with special reading instruction intended to help them approach and assimilate mathematical vocabulary and phraseology with greater confidence and facility” (p. 173). The call for amplifying approaches has resulted in various approaches for enhancing students’ comprehension strategies (see above), but not many approaches focus on language obstacles on a structural level (as summarized by Erath et al., 2021; Solano-Flores, 2010). Thus, limited empirical evidence exists so far for the efficacy of instructional approaches for fostering students’ competency in overcoming language obstacles.
This article intends to reduce this research gap by investigating the efficacy and implementability of a language-responsive intervention focusing on fifth graders’ strategies and language awareness. The designed teaching-learning arrangement aims at fostering reading and understanding of word problems on two levels of reading processes: (1) on the text level, i.e. fostering subject-specific reading and understanding strategies through strategic scaffolding with concept maps as a strategic scaffold (Hannafin, Land, & Oliver, 1999) and (2) on the sentence level, i.e. fostering syntactic language awareness through the variation principle (Marton & Pang, 2006).
Whenever innovations are implemented in classroom practice, the big question is how much support teachers need for implementing the innovation (Pellegrini, Lake, Inns, & Slavin, 2018; Saxe, Gearhart, & Nasir, 2001). Is it enough to inform the teachers about typical obstacles, or do they also need support in realizing fostering approaches? In our evaluation study, the language-responsive intervention is compared to an information-problems-only intervention (in which teachers were informed about typical language obstacles, but not supported to foster their students in overcoming them), and a no-treatment control group. The teachers’ preparation for both intervention groups is in line with teachers’ demands for the possibilities of direct implementation of PD themes and data into their teaching practice (Wayman & Jimerson, 2014).
The following section introduces the empirical and theoretical background on typical language obstacles, and specifies comprehension strategies and language awareness required for overcoming them. This is the base for justifying the design principles underlying the language-responsive intervention presented in the second section. Its efficacy is investigated by a cluster-randomized controlled trial for which the research design of the evaluation study and the methods are explicated in the third section. The empirical section then presents the differential results for students with high and low general reading proficiency of the study.
Section snippets
Theoretical and empirical backgrounds on language obstacles in word problems
Empirical research on students’ processes of solving arithmetic word problems have identified crucial steps and located typical obstacles in these steps (Plath & Leiß, 2018; Reusser, 1997):
- (1)
Understanding of the textbase includes reading competencies on a basic level. Potentially, language obstacles but also habitual obstacles can occur in this step (Prediger, Wilhelm, Büchter, Gürsoy, & Benholz, 2018).
- (2)
Understanding of the situation requires generating a mental model of the situation model and a
Language-responsive design principles for fostering comprehension strategies and language awareness for mathematical word problems
As Heid et al. (2006) have emphasized in their strategic position paper, research should not stop with identifying obstacles and specifying learning contents, i.e. components of word problem comprehension, but should bridge the gap to classroom practices by collaboratively developing instructional approaches and concrete teaching units for fostering the learning contents. For language in mathematics classrooms, various teaching approaches are summarized by Erath et al. (2021).
With respect to
Overview
Fig. 5 gives an overview of the design of the cluster-randomized controlled trial with pre- and post-test with n = 275 students and n = 22 teachers of middle schools in urban areas. Two competing interventions served as the independent variable compared to a no-treatment control group. Students’ comprehension of word problems and especially their syntactic language awareness were the dependent variables. Language background (multilingual background and reading proficiency) were considered as
Significantly higher learning gains in the language-responsive intervention
Research question RQ1 asks for the overall efficacy of the interventions compared to each other. The results in the first lines of Table 2 reveal that both intervention groups had highly significant learning gains (Ftime/LRI (1, 117) = 89.00 with p < 0.01 and η2 = 0.20; Ftime/IPI (1, 40) = 13.86 with p < 0.01 and η2 = 0.09). Also the NTG group show significant differences from pre- to post-test (Ftime/NTG (1, 117) = 9.77 with p < 0.01), but these baseline gains have very low effect size (η2
Discussion
Students’ difficulties with word problems are well identified with respect to several obstacles. Whereas effective intervention programs have been developed with respect to conceptual and habitual obstacles (Verschaffel et al., 2000), and sometimes strategic obstacles (e.g., Reusser, 1994; Schukajlow et al., 2015), language obstacles on the word, sentence and text level have been mainly discussed with respect to reductive approaches of simplifying texts.
This paper, in contrast, reports on a
Funding
This study was conducted within the MuM-research group (Mathematics learning under conditions of language diversity) at TU Dortmund University. It was partly funded by the German Ministry for Research and Education (Grant No. 03VP02270), partly by a grant by the German Telekom Foundation, both to S. Prediger. We thank our colleague Henrike Weinert for her statistical support.
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