Responsiveness to Students’ Mathematical Thinking in Middle-Grades Classrooms

Responsiveness to students’ mathematical thinking is a characteristic of classroom discourse that reflects the extent to which students’ mathematical ideas are present, attended to, and taken up as the basis for instruction. Using the Mathematically Responsive Interaction (MRI) Framework and data from 11 middle-grades classrooms, we illustrate varied enactments of responsiveness and describe fluctuations in and relationships among different components of responsiveness. We found positive associations between different components of responsiveness, but they were not entirely predictive of one another. Individual classrooms appeared more or less responsive depending on which component was foregrounded. Our findings offer a more comprehensive characterization of responsiveness that documents the intertwined nature of teacher moves and student contributions during all whole-class instruction.

Analisis kendala pemahaman bahasa untuk mengembangkan kemampuan bernalar matematika siswa

Understanding of language is closely related to mathematical reasoning, because language has function as a means of communication to convey ideas or ideas to others. Submission of mathematical ideas delivered by students will show how far the level of student understading of the mathematical concepts they have. This research is a qualitative research with a descriptive approach which aims to describe the obstacles faced by students when using language on mathematical reasoning. Data obtained from observations, interviews, questionnaires, and documentations. Based on the results of the analysis conducted, it can be seen that constraints faced by students when using language on mathematical reasoning are feelings of shame and inferiority, difficulty understanding the sentence, and lack of vocabulary students have.

Transcultural Networks and Connectivities: The Circulation of Mathematical Ideas between India and England in the Nineteenth Century

The nineteenth century has been characterised as a period in which mathematics proper acquired a disciplinary and institutional autonomy. This article explores the intertwining of three intersecting worlds of the history of mathematics inasmuch as it engages with historicising the pursuit of novel mathematics, the history of disciplines and, more specifically, that of the British Indological writings on Indian mathematics, and finally, the history of mathematics education in nineteenth century India. But, more importantly, the article is concerned with a class of science and mathematics teaching problems that are taken up by researchers—in other words, science and mathematics teaching problems that lead to scientific and mathematical research. The article argues that over a period of 50 years, a network of scholars crystallised around a discussion on mathematics proper, the history of mathematics and education. This discussion spanned not just nineteenth-century England but India as well, involving scholars from both worlds. This network included Scottish mathematicians, East India Company officials and administrators who went on to constitute the first generation of British Indologists, a group of mathematicians in England referred to as the Analytics, and traditional Indian scholars and mathematics teachers. The focus will be on the concerns and genealogies of investigation that forged this network and sustained it for over half a century.

Domestication of Mathematical Pathologies

Certain mathematical objects bear the name “pathological” (or “paradoxical”). They either occur as unexpected and (temporarily) unwilling in mathematical research practice, or are constructed deliberately, for instance in order to delimit the scope of application of a theorem. I discuss examples of mathematical pathologies and the circumstances of their emergence. I focus my attention on the creative role of pathologies in the development of mathematics. Finally, I propose a few reflections concerning the degree of cognitive accessibility of mathematical objects. I believe that the problems discussed in the paper may attract the attention of philosophers interested in concept formation and the development of mathematical ideas.

Modernisation of urban governance: An approach of ‘Blockchain + Big Data’

Mathematics is a prerequisite for the development of blockchain technology. The deeply penetrated mathematical ideas support the establishment of the trust mechanism of the whole blockchain system, which makes the blockchain technology autonomous, decentralised, not so easy to tamper, open, anonymous and also possesses other characteristics. Due to these characteristics, the introduction of blockchain will greatly solve a series of problems faced by the quality and acquisition of big data in cities, and release more data vitality. Based on the perspective of chain blocks and big data fusion, this paper puts forward that data are the foundation of modern urban governance. Data management has become the key to modern urban governance. It puts forward that the building of a big data management system based on blockchain will strengthen the construction of the intelligent city and modernisation of urban governance capabilities.

Book Review: Geoffrey B. Saxe, Cultural Development of Mathematical Ideas.

A review of G Geoffrey B. Saxe, Cultural Development of Mathematical Ideas. Saxe offers a comprehensive treatment of social and linguistic change in the number systems used for economic exchange in the Oksapmin community of Papua New Guinea. By taking the cognition-is-social approach, Saxe positions himself within emerging perspectives that view cognition as enacted, situated, and extended. The approach is somewhat risky in that sociality surely does not exhaust cognition. Brains, bodies, and materiality also contribute to cognition—causally at least, and possibly constitutively as well (as argued by Clark & Chalmers; Renfrew & Malafouris). This omission necessarily excludes the material dimension of numeracy.

Number Concepts Are Constructed through Material Engagement: A Reply to Sutliff, Read, and Everett

I respond to three responses to my 2015 Current Anthropology article, “Numerosity Structures the Expression of Quantity in Lexical Numbers and Grammatical Number.” This study examined the categorical and geographical distribution of lexical numbers, also known as counting numbers, and grammatical number, the ability to linguistically distinguish singular and plural. Both these features of language conform to the perceptual experience of quantity, which consists of subitization, the ability to rapidly and unambiguously identify one, two, and three, and magnitude appreciation, the ability to appreciate bigger and smaller in the numerical quantity of groups when the difference lies above a threshold of noticeability. My reply to Sutliff disagrees with her contention that mathematical ideas are mentally innate on the grounds that this ignores their explicit construction through the interaction of human psychological, physiological, and behavioral abilities with materiality. My reply to Read expands on the idea that language obscures cross-cultural conceptual variability in number concepts because everything that translates as “three” does not necessarily have the same numerical properties. Finally, my reply to Everett notes that investigating numerical origins means discarding the deeply entrenched assumption of linguistic primacy on the grounds that material forms make numerical intuitions tangible, visible, and manipulable in ways that language cannot and, moreover, provide an alinguistic bootstrap mechanism that accounts for the emergence of both concepts of number and words for the concepts.

EKSPLORASI ETNOMATEMATIKA KONSEP POLA BILANGAN DALAM PERMAINAN TRADISIONAL

This study aims to study the relationship between mathematics and culture in Indonesia, one of which is the traditional game of Nasi Goreng Kecap and Mejikuhibiniu. This research is considered important because it teaches students to see real-world activities clearly by being integrated into mathematical ideas. This research uses an ethnographic approach and a library study (literature study) which is a type of qualitative research. The result of this research is that the traditional game Nasi Goreng Kecap and Mejikuhibiniu contains the concept of number patterns, which can be developed in a learning design for number pattern material so that it can change the student's paradigm that mathematics is still considered abstract science to be more fun mathematics