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The aim of this study was to investigate differences in student teachers’ and experienced teachers’ professional vision in natural settings and to elicit clues of the relation of in-the-moment noticing and instruction quality of students’ understanding of rational number concept. Rational number concept challenges both students and teachers because of natural number bias that learning of rational numbers is vulnerable to. Accurate professional vision and adequate instructions are needed to enhance students’ understanding of rational number concept. Mobile eye-tracking technique enables video recording of natural teaching situations from a teacher’s perspective with more specific information of teacher’s in-the-moment noticing. Combined with cued retrospective reporting, this approach can gather more explicit evidence of teachers’ professional vision and instructions. Results indicated that both student teachers and experienced teachers attended to mathematical and fraction-related aspect similarly but differed in interpreting and instructing students’fraction understanding. Student teachers made more advanced interpretations but their instructions were less adequate, whereas among experienced teachers, it was just the opposite. Furthermore, student teachers made more attempts to shared attention when using fraction understanding non-supporting instructions, whereas experienced teachers’ attempts to shared attention were related to fraction understanding supporting instructions. Results indicate student teachers’ difficulty to transfer pedagogical content knowledge from noticing to actions and experienced teachers to have more enhanced in-the-moment professional vision and its application to teaching. Practical implications for teacher training as well as methodological decisions of in-the-moment professional vision studies in natural settings are discussed.

BackgroundEarly numeracy development is supported by linguistic features such as mathematics-specific vocabulary. Researchers have established a link between the amount and quality of children’s exposure to mathematics-specific vocabulary and their numeracy learning. Studies have also shown that children from low socio-economic status are less exposed to mathematics-specific vocabulary and also tend to underperform on mathematics assessments. South African children consistently perform poorly on local and international mathematics assessments.AimTo describe associations between numeracy and mathematics-specific vocabulary of the sample who participated in the study.SettingParticipants in this study are from Quintile 1 schools and receive social grants from the South African government.Method133 Grade 1 and 2 children completed assessments for (1) early numeracy (MARKO-D SA), (2) mathematics-specific vocabulary (MMLT) and (3) early reading (EGRA). Correlation analyses were conducted to investigate associations between variables and developmental continuity of number concept development and reading skills were described.ResultsAn association between numeracy and mathematics-specific vocabulary was found. The data confirm that number concepts and reading skills develop hierarchically. Although English-speaking children performed better on the numeracy assessment, isiZulu and Sesotho speakers performed better on the reading test.ConclusionMathematics-specific vocabulary is a key tool for early number concept development, also in isiZulu and Sesotho. Teachers’ pedagogical content knowledge (PCK) should include how number concept development intersects with mathematics-specific vocabulary. Explicit teaching of mathematics-specific vocabulary should be included in the Foundation Phase curriculum.

BackgroundTeachers teach mathematics by focusing on procedural knowledge (what steps to follow when doing mathematics) and pay scant attention to the conceptual understanding that underlies these procedures such as double-digit addition or subtraction and overall additive and multiplicative relations. They teach concepts in a haphazard way instead of looking at them from a convergent perspective of concepts that a child builds, one after the other.AimThis study explores what Grade R teachers know about young children’s specific developmental numerical cognition and if they infuse their understanding of number concept development in their pedagogy.SettingSamples of 15 female Grade R teachers were purposefully selected from five schools in what was previously a racially segregated living area in South Africa.MethodsThis research design is a descriptive case study. Data were collected using semi-structured interviews and observation notes documented during workshops and when the teachers implemented their learnings in their classrooms.ResultsThe main finding was that although teachers could reflect on the model of number concept development they had learned, they found it hard to infuse their knowledge into a strictly structured curriculum.ConclusionDespite the Meerkat Maths programme offered to the teachers, they could not rely on their intuitive pedagogy, coupled with the model of number concept development that they had learned because of the strict demands of the school curriculum content with which they had to comply.

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4 to 14 years, this correlation was r = .443. The correlation increased with age, mainly because it was higher for fractions than for whole numbers. The correlation remained stable across a wide range of task variants and mathematical competence measures (i.e., counting, arithmetic, school achievement). These findings demonstrate that the task is a robust tool for diagnosing and predicting broader mathematical competence and should be further investigated in developmental and experimental training studies.

The current quantitative study, a naturalistic field experiment, was conducted in a public primary school in Soweto, Johannesburg, with the objective to examine how children’s achievement on four assessments at the beginning of Grade R, namely their numeracy, their mathematics-specific vocabulary, their executive functions, and their logical reasoning capabilities, predicted their performance on a numeracy assessment at the beginning of Grade 1. A purposive intact group of 59 participants was assessed at the beginning of their Grade R year and again when they entered Grade 1. The results of the study indicate that, apart from existing or prior numeracy knowledge at the beginning of Grade R, mathematics-specific vocabulary was the strongest predictor for numeracy attainment at the beginning of Grade 1. We suggest that early grade teachers consider young children’s number concept development as a cognitive, developmental psychology phenomenon and that they help learners build a lexicon of mathematics-specific qualifiers in their teaching with words that represent concepts of, among others, space, position, comparison, inclusion, sequence and magnitude.

The primary goal in this study was to examine maternal support of numerical concepts at 36 months as predictors of math achievement at 4½ and 6-7 years. Observational measures of mother-child interactions (n = 140) were used to examine type of support for numerical concepts. Maternal support that involved labeling the quantities of sets of objects was predictive of later child math achievement. This association was significant for preschool (d = .45) and first-grade math (d = .49), controlling for other forms of numerical support (identifying numerals, one-to-one counting) as well as potential confounding factors. The importance of maternal support of labeling set sizes at 36 months is discussed as a precursor to children's eventual understanding of the cardinal principle.

This innovative text offers a unique approach to making mathematics education research on addition, subtraction, and number concepts readily accessible and understandable to pre-service and in-service teachers of grades K–3. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book provides educators with the knowledge and tools needed to modify their lessons and improve student learning of additive reasoning in the primary grades. Based on research gathered in the Ongoing Assessment Project (OGAP), this engaging, easy-to-use resource features practical resources such as: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess, and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding; A focus on the OGAP Addition, Subtraction, and Base Ten Number Progressions, based on research conducted with hundreds of teachers and thousands of pieces of student work; In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research; End-of-chapter questions to allow teachers to analyze student thinking and consider instructional strategies for their own students; Instructional links to help teachers relate concepts from each chapter to their own instructional materials and programs; An accompanying eResource, available online, offers an answer key to Looking Back questions, as well as a copy of the OGAP Additive Framework and the OGAP Number Line Continuum. A Focus on Addition and Subtraction marks the fourth installment of the popular A Focus on… collection, designed to aid the professional development of pre-service and in-service mathematics teachers. Following from previous volumes on ratios and proportions, multiplication and division, and fractions, this newest addition is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.

In this paper the authors demonstrate how play can serve as a space for assessing and promoting children’s mathematical thinking. Analyzing data from a larger study of professional development to support culturally and developmentally responsive mathematics teaching in preschool, we found that through Learning Stories, a holistic narrative assessment tool, teachers describe how they explicitly identify the mathematical practices children engage with during play. The structure of Learning Stories provided teachers with a way to think about how they identify and reflect on children’s mathematical practices and, based on that understanding, develop strategies for supporting children’s mathematical understanding. The purpose of this paper is not to argue for play as the only space for teaching and assessing mathematics in preschools but to provide evidence of what is possible when teachers attend to children’s mathematical thinking and mathematize play.

As people increasingly move to cities, their lifestyles profoundly change. Sonnenburg and Sonnenburg review how the shift of recent generations from rural, outdoor environments to urbanized and industrialized settings has profoundly affected our biology and health. The signals of change are seen most strikingly in the reduction of commensal microbial taxa and loss of their metabolic functions. The extirpation of human commensals is a result of bombardment by new chemicals, foodstuffs, sanitation, and medical practices. For most people, sanitation and readily available food have been beneficial, but have we now reached a tipping point? How do we “conserve” our beneficial symbionts and keep the pathogens at bay? Science , this issue p. eaaw9255 The human body is an ecosystem that is home to a complex array of microbes known as the microbiome or microbiota. This ecosystem plays an important role in human health, but as a result of recent lifestyle changes occurring around the planet, whole populations are seeing a major shift in their gut microbiota. Measures meant to kill or limit exposure to pathogenic microbes, such as antibiotics and sanitation, combined with other factors such as processed food, have had unintended consequences for the human microbial ecosystem, including changes that may be difficult to reverse. Microbiota alteration and the accompanying loss of certain functional attributes might result in the microbial communities of people living in industrialized societies being suboptimal for human health. As macroecologists, conservationists, and climate scientists race to document, understand, predict, and delay global changes in our wider environment, microbiota scientists may benefit by using analogous approaches to study and protect our intimate microbial ecosystems.