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In language learning, learners engage with their environment, incorporating cues from different sources. However, in lab-based experiments, using artificial languages, many of the cues and features that are part of real-world language learning are stripped away. In three experiments, we investigated the role of positive, negative, and mixed feedback on the gradual learning of language-like statistical regularities within an active guessing game paradigm. In Experiment 1, participants received deterministic feedback (100%), whereas probabilistic feedback (i.e., 75% or 50%) was introduced in Experiment 2. Finally, Experiment 3 explored the impact of mixed probabilistic feedback (33% positive, 33% negative, 33% no feedback). The results showed that cross-situational learning of words was observed without feedback, but participants were able to learn structural regularities of the miniature language only when feedback was provided. Interestingly, the presence of positive feedback was particularly helpful for the learner, promoting more in-depth learning of the artificial language.

Researching how mathematical expression varies in different languages requires methodologies which allow investigation of languages on their own terms and the presentation of mathematical data in multiple languages. Perspectives and tools from linguistics can assist in identifying and describing mathematical expression in varied languages, particularly those without a school mathematics register. A typological approach, which deals with finding, describing and classifying languages according to their structural similarities and differences, is useful to investigate how a mathematical function or process is performed in different ways in different languages. Interactive structured tasks can elicit rich and targeted mathematical language data, where details of mathematically language are difficult to elicit through direct questions and interviewing. An interlinear morphemic gloss can be used to show more information about the structure of short texts in languages other than the publication language. Such research is an ideal forum for collaboration between mathematics education researchers and linguists.

Recently the prevailing language-as-resource metaphor has been problematised and theorised. Using the philosophical theory of inferentialism, we trace an epistemological dimension of multilingualism in mathematics education and add it to the current language-as-resource discussions. With data from two different settings--a mathematics classroom in Sweden and a workshop in an indigenous settlement in Colombia--we show that in encounters between language practices and plural mathematics, the semantic and the epistemological are two sides of the same coin. Inferentialism captures such encounters without dichotomising either languages or mathematics. We contend that epistemological issues move beyond the scope of language-as-resource approaches, but they are not paths to improving school achievement. Neither are they matters of distinguishing between formal and informal language use. Rather, an epistemological dimension is about shaping meta-understandings of language diversity that are liberated from mathematics as fixed and pre-stablished knowledge.

A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause, intonation and gestures, in ways that foreshadowed conclusions, shifted attention from known to less-known concepts and emphasized the logical structure of arguments. This suggests that multimodal poetic structures are experiential linguistic resources for expressing and animating mathematical insights.

By combining linguistic analysis with metaphors for mediating between a body of knowledge and teaching practice, we exemplify curriculum developers' voices in teacher guides. We discuss two types of voices, that of the Expert, who talks through the teacher and restricts the pedagogical agency of the teacher, and that of the Philosopher, who speaks to the teacher and affords the teacher agency in relation to pedagogical ideas and practices discussed in the teacher guide. An unexpected example of Expert voice was also found, where the developer talked past the teacher, leaving the teacher external to the teaching situation.

Spatial mental representations can be derived from linguistic and non-linguistic sources of information. This study tested whether these representations could be formed from statistical linguistic frequencies of city names, and to what extent participants differed in their performance when they estimated spatial locations from language or maps. In a computational linguistic study, we demonstrated that co-occurrences of cities in Tolkien's "Lord of the Rings" trilogy and "The Hobbit" predicted the authentic longitude and latitude of those cities in Middle Earth. In a human study, we showed that human spatial estimates of the location of cities were very similar regardless of whether participants read Tolkien's texts or memorized a map of Middle Earth. However, text-based location estimates obtained from statistical linguistic frequencies better predicted the human text-based estimates than the human map-based estimates. These findings suggest that language encodes spatial structure of cities, and that human cognitive map representations can come from implicit statistical linguistic patterns, from explicit non-linguistic perceptual information, or from both. (Contains 1 table, 2 figures, and 2 notes.)

This article examines the topicality of Library and Information Science (LIS) dissertations written between 1930 and 2009 at schools with American Library Association (ALA)--accredited university programs in North America. Dissertation titles and abstracts were examined for the presence of library-related keywords drawn from the core curricula of ALA-accredited schools, and trend data were created to describe the evolution of LIS doctoral research over the past eighty years. The results show that the percentage of dissertations found to contain no instance of any of the selected library keywords has steadily risen since 1980. Simultaneously, the percentage of dissertations found to contain instances of keywords in both the title and abstract has steadily declined. The results provide general empirical support for long-held anecdotal assertions that libraries are no longer the primary research focus at the doctoral level in LIS. (Contains 3 figures and 5 tables.)

Infants are adept at tracking statistical regularities to identify word boundaries in pause-free speech. However, researchers have questioned the relevance of statistical learning mechanisms to language acquisition, since previous studies have used simplified artificial languages that ignore the variability of real language input. The experiments reported here embraced a key dimension of variability in infant-directed speech. English-learning infants (8-10 months) listened briefly to natural Italian speech that contained either fluent speech only or a combination of fluent speech and single-word utterances. Listening times revealed successful learning of the statistical properties of target words only when words appeared both in fluent speech and in isolation; brief exposure to fluent speech alone was not sufficient to facilitate detection of the words' statistical properties. This investigation suggests that statistical learning mechanisms actually benefit from variability in utterance length, and provides the first evidence that isolated words and longer utterances act in concert to support infant word segmentation.

This study examined the theoretical controversy on the impact of syllables and bigrams in handwriting production. French children and adults wrote words on a digitizer so that we could collect data on the local, online processing of handwriting production. The words differed in the position of the lowest frequency bigram. In one condition, it coincided with the word's syllable boundary. In the other condition, it was located before the syllable boundary. The results yielded higher movement durations at the position where the low-frequency bigram coincided with the syllable boundary compared to where the low-frequency bigram appeared before the syllable boundary. Syllable-oriented strategies failed with the presence of a very low-frequency bigram within the initial syllable. Further analysis showed that children in grades 3 and 4 privileged syllable-oriented programming strategies. The production times of children in grade 4 were also affected by syllable frequency and, to a lesser extent, bigram frequency. The adults writing durations were modulated by bigram frequency. Therefore, both bigrams and syllables regulate handwriting production although the influence of bigrams was stronger in adults than children. In the light of these results, we propose a psycholinguistic model of handwriting production. (Contains 1 table and 5 figures.)

Syriac translations and Syriac scholars played an important role in the transmission of the sciences, including the mathematical sciences, from the Greek to the Arabic world. Relatively little, unfortunately, remains of the translations and original mathematical works of earlier Syriac scholars, but some materials have survived, and further glimpses of what once existed may be gained from works of later authors. The paper will provide an overview of the earlier materials that have survived or are known to have existed. This will be followed by an account of some of the later materials, which will include an example illustrating how further earlier materials can be recovered from the writings of later authors, and a mention, by way of an epilogue, of an instance where a Syriac scholar was involved in a major historical and scientific event in the West, namely the reform of the calendar by Gregory XIII. (Contains 66 footnotes.)

The term "recursion" is used in at least four distinct theoretical senses within cognitive science. Some of these senses in turn relate to the different levels of analysis described by David Marr some 20 years ago; namely, the underlying competence capacity (the "computational" level), the performance operations used in real-time processing (the "algorithmic" level), and the neural implementation (the "hardware" level). It is demonstrated here that the current focus of the artificial grammar learning literature on recursion blurs the different levels, resulting in three main corollaries: (1) the literature cannot tell us anything about the first level, as the explanation for the role of recursion therein lies elsewhere; (2) it has not studied the possible recursive processing of artificial strings properly, as studies have so far focused on the correct processing of the internal hierarchy of recursive structures, but none have attempted to probe the underlying processing operations; and (3) as a consequence, much cannot in fact be known about the neural basis of recursion. It is furthermore argued that, in general, these studies can actually tell us very little about the language faculty, and some programmatic remarks are described and defended towards a more coherent study. (Contains 2 figures, 1 table and 16 footnotes.)

In discussion-oriented classrooms, students create mathematical ideas through conversations that reflect growing collective knowledge. Linguistic forms known as indexicals assist in the analysis of this collective, negotiated understanding. Indexical words and phrases create meaning through reference to the physical, verbal and ideational context. While some indexicals such as pronouns and demonstratives (e.g. "this", "that") are fairly well-known in mathematics education research, other structures play significant roles in math discussions as well. We describe students' use of entailing and presupposing indexicality, verbs of motion, and poetic structures to express and negotiate mathematical ideas and classroom norms including pedagogical responsibility, conjecturing, evaluating and expressing reified mathematical knowledge. The multiple forms and functions of indexical language help describe the dynamic and emergent nature of mathematical classroom discussions. Because interactive learning depends on linguistically established connections among ideas, indexical language may prove to be a communicative resource that makes collaborative mathematical learning possible. (Contains 1 table.)

In our work in teacher education and professional development, we aim to help teachers to learn to participate in, and create, classroom ecologies that support students' learning. In this article we focus on the challenges of developing a classroom ecology that provides mathematical sustenance for students. We pay particular attention to the ways in which classroom language can impede the development of a classroom ecology--one where all students are heard and where knowing is understood as participatory. We present recommendations for teaching practice drawn from an ecological reading of the classroom discourse during a series of lessons on measurement in a Grade 3 classroom. (Contains 2 figures.)

Accurate teacher evaluations of student performance are crucial for effective teaching. This study examined whether students' immigration and language background affect teachers' evaluations. Multilevel analyses tested whether teachers overestimate the performance of immigrant relative to that of non-immigrant students. As part of the German PISA 2003 assessment, 305 teachers predicted the performance of seven of their students on two mathematics problems of different linguistic complexity. Results revealed an interaction effect of students' language background and linguistic complexity of the problem on teachers' predictions. Teachers overestimated the performance of bilingual students more than the performance of monolingual immigrant or non-immigrant students on a linguistically complex problem. Teachers need to consider both students' language background and linguistic demands of the material used to appropriately support bilingual students. (Contains 3 figures and 2 tables.)

Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very reliably observed in the data, but to date it escaped satisfactory theoretical explanation. This article suggests that Zipf's law may result from a hierarchical organization of word meanings over the semantic space, which in turn is generated by the evolution of word semantics dominated by expansion of meanings and competition of synonyms. A study of the frequency of partial synonyms in Russian provides experimental evidence for the hypothesis that word frequency is determined by semantics. (Contains 6 figures, 2 tables, and 14 notes.)

This study analyzes the procedural explanations written by remedial college mathematics students. Relevant literatures suggest that six communication activities might be key in effective procedural explanations in mathematics writing: (a) orienting the learner, (b) providing kernels or definitions of concepts and procedures, (c) using exemplars or worked examples, (d) providing descriptions of the process or procedure, (e) solidifying learner understanding, and (f) facilitating linguistic control of mathematical terms. Using this framework, 18 practices or types of difficulties were discovered in students' written explanations. Independent experts consistently evaluated student explanations more highly when the explanations contained arithmetic or algebraic exemplars, described specific actions and their meanings, linked new with prior knowledge, and used descriptive language; experts evaluated student explanations more negatively when students displayed difficulties reasoning with kernels, reasoning with exemplars, or with describing processes. (Contains 2 tables.)

Much has been written to convince content-area teachers to include literacy instruction as part of their regular content instruction. The purpose of this study was to determine how the messages available in the literature are framed and how they might be viewed by content-area teachers, especially mathematics teachers. The analysis revealed that messages available to content-area teachers about literacy neglect, deemphasize, or misrepresent mathematics and/or mathematics education. These findings may help explain why content-area teachers, particularly mathematics teachers, resist ideas related to content-area literacy instruction. (Contains 1 table.)

This study examined whether singular/plural marking in a language helps children learn the meanings of the words "one," "two," and "three." First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.

This article presents a Vygotsky-inspired analysis of how a teacher mediated a "thinking aloud" whole-group discussion in a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers as a phase towards building recursive and direct algebraic formulas. By a "thinking aloud" discussion we mean a conversation wherein students exchange and further develop ideas-in-the-making with their peers under the teacher's guidance. Drawing upon Halliday's systemic functional linguistics (SFL), we treated the selected discussion as a text. We then analyzed how the teacher mediated the conjoined making of this text so that it served as an interpersonal gateway for students to practice searching for patterns and signifying these patterns in propositional form. This analysis was guided by the following questions: How did the discussion as a text-in-the-making mean what it did? What was the role of the teacher in the conjoined making of this text? Our study illustrates the power of SFL for capturing the inner grammar of instructional conversations thus illuminating the complexities and subtleties of the teacher's role in mediating semiotic mediation in mathematics classrooms.

This paper examines the change in young children's understanding of "equal", "more", "less", and "between", words commonly used in equivalent and non-equivalent situations, over a 3-year period. Seventy-six children participated in the longitudinal study. Each year they were asked to share their understanding of these four words. Past research has indicated that many children have limited understanding of "equal" as quantitative sameness. The results of this research suggested that many children also have limited understanding of "more" and "less" and that these understandings did not significantly change over the 3-year period.

There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of (1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning; (2) the fact that the main mathematics-related skill needed in our computerized, information saturated society is a proper mind-set rather than knowledge of some facts or techniques. The proposed definition of mathematics can enrich debates on its nature, in particular, connecting natural human psychological characteristics with philosophical questions of the origin of mathematics.

Mathematics is a central part of school curricula around the world. There has been much interest in linguistic aspects of the teaching and learning of mathematics, both from mathematics educators and from applied linguists. This short paper introduces a set of five articles exploring the intersection between these two communities. The articles all discuss two texts: an extract from the guidance issued to primary school mathematics teachers in the UK; and an extract from a primary school mathematics lesson. This paper begins by summarising some of the research on language in the mathematics classroom, before introducing the two texts.

I draw attention to the distinction between reductionist views of "language" and the rich and complex ways in which we might approach language as social practice and suggest the latter view is evident in the set of papers collected here. Socially oriented linguists, including those in New Literacy Studies (NLS), look beyond reductionism, to consider more complex "social" features of language and literacy. This perspective includes: viewing language and literacy as a process rather than as a fixed entity and as a resource rather than as a set of rules; exploring the role of language and literacy in implementing social agendas and in establishing relations between participants, such as their role in establishing and challenging power relations; and the relation of language and literacy to other means of communication and meaning making, such as visual, gestural, and iconic, that are usually woven in with language use. I consider how appropriate it might be to apply aspects of these approaches and in particular of the "academic literacies" approach linked to them, to what we might term the "academic numeracies" at play in the texts under consideration. These perspectives entail an assumption that participants deploy "hidden knowledge" of the features of language, literacy and numeracy in order to accomplish their social ends and that the task of the researcher is to bring into view and to unpack these hidden dimensions. Identifying such "hidden" features of classroom discourse can, then, help teachers and policy makers recognise important communicative features of classroom interaction that are missed when the focus is on "correctness", "definition", formal features of language and "lack of ambiguity", as in some curriculum documents and approaches.

National Numeracy Strategy (NNS) guidance appears to characterise mathematical language as a set of specialist words with unambiguous definitions, yet analysis of the classroom transcript suggests that at least some mathematical concepts cannot be captured by such definitions. This paper explores the notion of definition within mathematics, considering both school mathematics and the field of academic mathematics research. Extracts of texts from these domains are analysed using tools drawn from systemic functional linguistics. The more advanced texts show definitions to be constructed and used in creative and purposeful ways. This contrasts with the one-to-one word-concept relationship apparent in the NNS guidance and in a text for "Intermediate Level" secondary students. This finding raises the question of the extent to which the linguistic models implicit in the texts for less advanced school students and their teachers allow students to learn more powerful aspects of mathematics.

Recommends a change in the way mathematics is taught to engineers and scientists. Espouses a shift away from traditional methods to an approach that makes significant use of algebra packages. Suggests that teaching the language comprised of the notation and grammar of mathematics would be of more use and more accessible than focusing entirely on teaching mathematical techniques. (Contains 11 references.) (Author/NB)

Contrasts students' presymbolic and symbolic procedures in generalizing activities. Uses the semiotic-cultural theoretical approach and focuses on the role of body, discourse, and signs when students refer to mathematical objects. Identifies types of generalizations and discusses a specific kind of rupture in the ostensive gestures and contextually based key linguistic terms underpinning presymbolic generalization. (Author/KHR)

Describes theoretical points concerning the idea of semiotic means of objectification. Analyzes classroom activity by observing the interface between the spoken and the seen. Discusses the role of a category of linguistic terms related to actions of showing or pointing out something that constitute a key element in the mathematical discursive meaning production processes. (KHR)

Explores policy, practice, and research issues related to teaching and learning mathematics in multilingual classrooms in South Africa. Focuses on code-switching in multilingual mathematics classrooms. Points to the significance of language as power in mathematics education settings. Demonstrates the need for researching the relationship between language and the teaching and learning mathematics in South African classrooms from a political perspective. (KHR)

Explores how to develop children's understanding of mathematical vocabulary. Presents a lesson in which the class works on the concept of dimension, and issues raised by a discussion of applied linguistics and mathematics education. Discussion was stimulated by advice from the National Numeracy Strategy (NNS) vocabulary book. (KHR)

Suggests that trivialized versions of constructivism are promulgated due to misunderstandings of vocabulary adopted by its advocates. Discusses specifics of frustrations in an effort to communicate the insights and implications of radical and social constructivist theories to preservice and practicing teachers. Presents a classroom episode to show how to work with teachers to foster deep appreciation of how learning is reframed as dependent on teaching. (Author/KHR)

Reports on the clarity rating of Chinese, English, and "Chinglish" (Chinese words translated into English) mathematical words. The inherent compound word structure of the Chinese language seems well suited to portray mathematical ideas. Examines the relations among the clarity of Chinese mathematical terms, U.S. urban junior high school students' Chinese reading ability, and their mathematics performance. (Author/MM)