The current study examines the personal epistemology of fourth-grade elementary school teachers from Germany (n = 10) and the United States (n = 10) to gain a more nuanced understanding of teachers' beliefs about knowledge and knowing through a cross-cultural lens. Analyses of semi-structured interviews reveal similarities and differences in the…

To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three…

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

There are infinitely many ways of talking about infinity. The assortment of discourses on learning infinity is infinite as well. When the author says "way of talking" or "discourse," she is concerned with much more than the question of how words are chosen and combined. Ways of talking are not just innocent "auxiliaries" to thinking--they shape…

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…

This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…

Subject-verb agreement is a computation that is often difficult to execute perfectly in the first language (L1) and even more difficult to produce skillfully in a second language (L2). In this study, we examine the way in which bilingual speakers complete sentence fragments in a manner that reflects access to both grammatical and conceptual…

Research on the production of subject-verb number agreement in monolinguals suggests differences between and within languages in how it proceeds as a function of morphological richness. When agreement morphology is relatively rich, the influence of conceptual number over grammatical number is less than when it is relatively poor. Within the…

The authors compared performance on two variants of the primed lexical decision task to investigate morphological processing in native and non-native speakers of English. They examined patterns of facilitation on present tense targets. Primes were regular (billed-BILL) past tense formations and two types of irregular past tense forms that varied…

Spanish-English bilingual lexical organization was investigated using masked cognate and non-cognate priming with the lexical decision task. In Experiment 1, three groups of bilinguals (Spanish dominant, English dominant and Balanced) and a single group of beginning bilinguals (Spanish) were tested with Spanish and English targets primed by…

This study aims to examine the influence of multiple translations of a word on bilingual processing in three translation recognition experiments during which French-English bilinguals had to decide whether two words were translations of each other or not. In the first experiment, words with only one translation were recognized as translations…

The apparent optionality in the use of null and overt pronominal subjects and the apparently free word order or distribution of preverbal and postverbal subjects in Spanish obey a number of discourse-pragmatic constraints which play an important role in Spanish L2 subject development. Although research on subject properties at the syntax-discourse…

For bilinguals born in an English-speaking country or who arrive at a young age, English (L2) often becomes their dominant language by adulthood. This study examines whether such adult bilinguals show equivalent performance to monolingual English native speakers on three English auditory processing tasks: phonemic awareness, spelling-to-dictation…

We investigated the consequences of bilingualism for verbal fluency by comparing bilinguals to monolinguals, and dominant versus non-dominant-language fluency. In Experiment 1, bilinguals produced fewer correct responses, slower first response times and proportionally delayed retrieval, relative to monolinguals. In Experiment 2, similar results…

This study investigated the possibility that lifelong bilingualism may lead to enhanced efficiency in the ability to shift between mental sets. We compared the performance of monolingual and fluent bilingual college students in a task-switching paradigm. Bilinguals incurred reduced switching costs in the task-switching paradigm when compared with…