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According to Bialystok, mathematical competence. Furthermore, solving mathematical word level of proficiency in the instructional language predicted problems may not only be an ecologically valid but also a sensitive achievement on mathematics word problems in the same language. As illustrated earlier, problem solving in math- metic skills, general cognitive ability, and socioeconomic status ematics is characterized by a process of cognitive modeling.

In was controlled. We also expected that our measure of oral order to construct an adequate situational and mathematical model, proficiency in the language of instruction would be a stronger students need to identify and extract the relevant pieces of infor- predictor of mathematics problem solving in that language than mation from a given problem context and, at the same time, reading comprehension.

Furthermore, we tested whether bilingual children structure differed strongly according to the level of the ambiguity with an immigrant background would show a cognitive benefit, as of the context. Then Tom gave him 5 more in those tasks which especially require attentional control skills, marbles. How many marbles does Joe have now? Yesterday Dane and arithmetic skills were controlled. How many marbles does Dane have now?

The former type was derived from a set of empirically tested word Participants problems with established solution rates for primary school stu- dents of various ages Stern, For the latter type, we artifi- Participants were 78 third graders from five primary schools in cially enriched common problems by including numerical infor- urban districts of Berlin and Frankfurt with a high percentage of mation that was not needed for solving the problem distractors : Turkish immigrants.

Altogether, the marbles cost with a Turkish—German background and 34 were German mono- 90 cents. Then Hans gave her 5 marbles. They cost 1. The bilingual sample consisted of 20 female and 24 male How many marbles does Maria have now?

In the group of monolingual tional control processes are particularly called for as children need students, there were 14 female and 20 male students with a mean to suppress the misleading numerical information in order to age of 8. The Turkish—German bilingual students and half extract the relevant data. The other half of the proficiency instead of the reading comprehension measure that has monolingual sample was recruited from two schools in Frankfurt.

As reported previously, The sample consisted of three subsamples. The third sample was tested in January mains including mathematics. In these studies, however, language Frankfurt. Subsample 1 consisted of 43 students 32 bilingual, 11 proficiency was indicated only by reading comprehension rather monolingual ; Subsample 2, tested in the consecutive year, con- than being assessed with language tests.

Reading comprehension is sisted of 16 additional students 12 bilingual, four monolingual. Compar- depends on cognitive skills unrelated to language but critical to isons with regard to the control measures used socioeconomic school-related learning.

In fact, it has been shown that perfor- status, cognitive ability, mathematics achievement; see the instru- mance of poor readers on math tests increased significantly when ments listed in the Materials section revealed no statistically the test items were presented orally e. Furthermore, language profi- dents of Subsamples 1 and 2 as well as between the monolingual ciency was usually only measured for the language of instruction students of Subsamples 1, 2, and 3.

Therefore, we will refer to the but not for the native language. Therefore, it remains unclear what entire sample in the following sections. In the present study, we thus used oral establish the comparability of the monolingual and bilingual sam- proficiency measures in both the instructional and the native ples on the various control measures.

A set of nine word Turkish background. Although this was not a bilingual school problems, consisting of three exchange problems, three compari- setting, we assumed that the additional instruction in the Turkish son problems, two complex comparison problems, and one com- language would contribute to the development of a reasonable plex combination problem, was employed. All problems were level of Turkish proficiency in the participating bilingual students.

The categorization of word problems addition and subtraction with respect to the situational model exchange, The instruments employed can be divided into language measures comparison, and combination was originally provided by Riley, language proficiency, reading comprehension , measures of the de- Greeno, and Heller Solution rates for the different kinds of pendent variable mathematical word problems , and control mea- problems were obtained in several large-scale studies with children sures cognitive ability, arithmetic skills, socioeconomical status.

For the present study, it was thus possible to choose a set of Test of language proficiency. Its three subtests are derived and the complex combination problem was reported with an item from the Woodcock Language Proficiency Battery—Revised difficulty of. All problems had been presented in written Woodcock, It is suited for persons from age five to format in previous studies.

The to the bilingual group in both the Turkish and the German versions, complex version requires an additional step of calculation as more and to the monolingual group in the German version only.

Tina has 4 euros. Kai and Nina have regard to the range of vocabulary tested; yet, specific vocabulary 9 euros altogether. Nina has 3 euros. How many euros do Paul and items may differ in difficulty according to their frequency of use. Kai have altogether? Then Philip gave her 5 euros. How many menter had presented orally. In the second subtest, oral vocabu- euros does Sabine have now?

In the subtest of verbal analo- known, and initial quantity unknown—all of which were used in gies, the children had to finish sentences on the basis of analogies this study. These problems are the standardized testing procedure, individual testing in each of the the most difficult ones for students to solve because besides a subtests continued until a child made four consecutive errors.

Max has 8 stickers. How many more stickers does Max on the so-called consensus translation and standardization process have than Beate? The complex versions of the comparison verbal analogies. In addition to the word is a German reading comprehension test for children in problems without distractors, we constructed a parallel set of nine Grades 1— 6.

It consists of three subtests: a word comprehension, word problems that were artificially enriched by numerical infor- b sentence comprehension, and c text comprehension. For the mation that is not necessary for solving the problem distractors. The marbles cost 90 cents. Then Hans gave topic of everyday life and then have to answer several compre- her 5 marbles. How many marbles does hension questions on the text in multiple-choice format. This test Maria have now? The two sets of nine problems each were then translated into Measures of the dependent variable: Mathematical word Turkish by a fluent speaker of Turkish and German.

The resulting problems. To assess mathematical problem solving abilities, we set of nine word problems without distractors and nine word used two types of mathematical word problems: problems without problems with distractors showed a satisfactory internal consis- distractors and problems with distractors. For each word problem, a score of 2 was the language measures and the control measures, we conducted assigned if a child provided a correct solution after the first two separate multivariate analyses of variance MANOVAs , with presentation of the word problem.

If the problem had to be pre- univariate post hoc tests for the language measures and the control sented a second time due to nonresponse, incorrect response, or measures. There was no significant difference between the mono- misunderstanding after the first presentation , a score of 1 was lingual and the bilingual groups with respect to the control mea- assigned for a correct solution.

After two incorrect answers or sures of books at home, cognitive ability, and arithmetical skills, nonresponses, a score of 0 was assigned. As expected, we found a attain a maximum of 18 points per set of word problems with or significant difference in the MANOVA on language proficiency without distractors. The Test of cognitive ability.

The CFT20 is a nonverbal test and is consid- [. For the group of ered to be culture-fair. The four employed subscales of a series bilingual students, the difference between scores of the German continuation, b classification, c matrices, and d topologic and Turkish BVAT versions suggests that these students were reasoning were presented in a graphical format.

Its reported reli- more proficient in German than in Turkish. Table 1 provides a ability for children in Grade 3 is. Test of arithmetic skills. Only subtests that test the basic arithmetic Research Question 1: Does the Level of Proficiency in operations of addition and subtraction were used.

The children the Instructional Language Predict Achievement on were required to work on eight arithmetic problems that dealt with Mathematical Word Problems Presented in That two-digit numbers up to The reported reliability internal Language? Indicator of socioeconomic-status SES.

Children in Grade 3 can answer this question quite Table 1 reliably Schnepf, In the item that was presented, the Means and Standard Deviations of the Groups of Monolingual children could choose between five pictures showing book and Bilingual Students shelves with about 10 books, 25 books, books, books, and more than books.

Reading comprehension ELFE 1—6 9. German In Session 2, we administered a test of cognitive ability, arithmetic skills, and, for the bilingual students, Note.

Ability Test. Books at home — 2. Cognitive ability. Oral proficiency German. Word problems without distractors. Word problems with distractors. In the main analyses, we employed only problems without problems with distractors were used as the dependent variable re- distractors as the dependent variable because these are the ones that vealed the same pattern as the analyses of problems without distrac- have been empirically validated in other studies.

In Model 2, we additionally in- language Turkish. Table 4 lists the a further predictor, language proficiency in German in Model 3. Table 5 lists the results of Models 1—3.

The inclusion of rates of word problems than did reading comprehension alone. Additional analyses in which contributed to problem solving in Turkish to a greater degree than Table 3 Intercorrelations Among Measures for the Group of Bilinguals Variable 1 2 3 4 5 6 7 8 9 10 1.

Arithmetic ability. Oral proficiency Turkish. Word problems without distractors German. Word problems with distractors German. Word problems with distractors Turkish. Thus, the findings of Model 3 suggest that the bilinguals vs. As covariates we entered SES, cog- importance of the instructional language cannot be simply gener- nitive ability, and arithmetic skills.

As expected, the results alized to problem solving in another language i. In the regression analysis, the addition of the Bilinguals variable of instructional language in Model 3 did not contribute to 16 a significant change of R2 in Model 2.

This seems to suggest that 14 there are no switching costs in mathematical word problem solving in bilingual students of this age since achievement in word prob- 12 lems is apparently influenced solely by language proficiency in the Scores on Word Problems language of testing.

However, in previous research on this issue 10 e. Our sample of bilingual students, in con- 6 trast, comprised students of varying proficiencies in native lan- guage and instructional language. Thus, having a group of rather 4 proficient bilinguals performing on a level comparable to that of monolinguals may be needed to test the existence of switching 2 costs.

In contrast, students with a weak command in the instruc- 0 tional language may actually use their native language in order to Without Distractors With Distractors compensate for deficits in the instructional language when solving word problems in the instructional language.

In order to test these Figure 1. Means and standard deviations on German word problems with hypotheses, we divided our bilingual sample into three equal parts distractors and without distractors for monolinguals and bilinguals.

The bars indicate standard deviation. Leaving the middle third aside, we now had two groups that we analyzed in detail. In other words, the restricted in variance in the entire sample see Table 6 for descrip- substantial disadvantage of bilinguals for problems without dis- tives of the two resulting groups. A multivariate ANOVA re- tractors relative to monolinguals diminished for problems with vealed no significant differences between the groups regarding the distractors.

A re- as in the former analyses confirmed that the monolingual students peated measures ANOVA with Language of Testing problems outperformed the bilingual students on word problems without without distractors in German vs. Yet for problems with In addition, there was a significant tional control.

German language proficiency Arithmetic skills 4. This analysis picks up on Research Question 1 second Note. It is interesting that students in is consistent with the regression analyses underlining the impor- the low-proficiency group tended to show higher scores when the tance of language proficiency for problem solving in the respective problems were presented in Turkish rather than German.

In other language. Post hoc tests for the Turkish. In the present research, we examined the relation between However, the latter group showed a reversed trend of switching bilingualism and school-related learning. In particular, we aimed costs, with higher means when tested in Turkish than when tested to disentangle the possible costs and benefits of bilingualism with in German.

To this end, we compared their achievement on results as for problems without distractors: Language of Testing, mathematical word problems with that of their monolingual peers.

Again, dominant bilinguals scored higher when tested in was mostly realized by self-reports or via the assessment of read- German than when tested in Turkish, while the reverse trend was ing comprehension, we used a measure that directly tapped oral observable with weak bilinguals see Table 6 for means and language proficiency. Regression analyses with the sample of standard deviations. In fact, language proficiency explained as much vari- German Word problems ance as arithmetic skills did and far more variance than was Turkish Word problems explained by cognitive ability, SES, and reading comprehension.

In sum, students who were rather proficient in German were much more likely to solve 12 mathematical word problems in German correctly than students Scores on Word Problems with poor German language skills. A similar pattern appeared for 10 Turkish word problems as a criterion. Accordingly, we cannot presume a generalized effect of learning processes in German to solution processes in Turkish.

Second, our data indirectly support the assumption that bilin- 0 gualism has beneficial effects even for students who are not highly Dominant Bilinguals Weak Bilinguals proficient in both languages and who are from a lower socioeco- Figure 2. Error bars indicate monolinguals, they performed as well as their monolingual peers standard deviation.

Since these students nev- ertheless performed better when tested in Turkish, we can presume Mathematics that further factors such as motivation or the frequency of aca- Our data confirm the important role of language proficiency in demic language use in Turkish may have influenced their perfor- school-related learning established by prior research in general and mance on Turkish word problems.

This interpretation would be in in solving mathematical word problems, in particular. As de- line with results of our regression analyses on Turkish word scribed in the introduction, the influence of language proficiency problem in Research Question 1.

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