Abstracts - Earli

as a control measure. Children with VCFS were significantly slower in accessing magnituderepresentations from symbolic number, as evidenced by slower performance on numbercomparison. This difference could not be attributed to a slower number identification as childrenwith VCFS did not differ from controls in number reading. Children with VCFS also performedsignificantly slower on single-digit addition and subtraction and were significantly less accuratelyin solving multidigit calculations and word problems. Number comparison was related to most ofthe response time data on the other math tasks in children with VCFS. These associations wereparticularly prominent for single-digit addition and subtraction. To conclude, the speed ofaccessing magnitude representations appears to be an important correlate of the development ofMD in children with VCFS. Therefore, these children may benefit from educational interventionsthat foster the development of magnitude representations.Students’ interpretations of algebraic expressions in inequalitiesKonstantinos Christou, University of Athens, GreeceStella Vosniadou, University of Athens, GreeceIn this paper we present results from a study which investigated students’ interpretations ofalgebraic expressions and their effects on evaluating algebraic inequalities. Algebraic expressionsuse literal symbols to stand for numbers and in that way they can be considered as externalrepresentations. We adopt a constructivist position to analyse how the individuals interpretexternal representations. More specifically, we argue that the individuals understand externalrepresentations on the basis of what they already know. If so, prior knowledge about naturalnumbers can hinder students’ understanding that a literal symbol in algebra can stand for any realnumber. The study was based on individual interviews with 10th grade students who were asked totest the validity of six algebraic inequalities. The results showed that none of the students used theformal way of solving an inequality. Instead, all students substituted numbers for the literalsymbols in order to test whether the inequality was valid or invalid. The majority of the students’responses (60%) substituted only natural numbers for the literal symbols. In those cases studentscame up with erroneous responses concluding that the inequality was either valid or invalid forany number in all cases where the inequality was valid or invalid respectively for natural numbers.Another 28% of the students’ responses substituted integers for the literal symbols. In those casesstudents came up with the erroneous conclusion that the given inequality was valid for positivenumbers and invalid for negatives or vice versa. Only 12% of the students’ responses substitutedrational numbers for the literal symbols. These results are consistent with previous findings andsupport our hypothesis that students’ prior knowledge of natural numbers affects the way theyinterpret the algebraic expressions and this reflects on their performance in mathematical taskssuch as the evaluation of algebraic inequalities.Multiple external representations and internal representations: Why subjective goals matter!Alexander Renkl, University of Freiburg, GermanyRolf Schwonke, University of Freiburg, GermanyKirsten Berthold, University of Freiburg, GermanyAn (often implicit) assumption of educational and psychological laypersons as well as researchersin these fields is that there is a relatively direct correspondence between externally providedrepresentations (e.g., as learning materials) and internal representations. Against this backgroundmultiple external representations are often regarded as facilitating learning and leading to multipleinternal representations. For example, the theory of Päivio suggests that pictures lead to internallyrepresented imagens and language leads to logogens. Although the different subsystems containing– 293 –