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At the end of Primary 6, students in Singapore schools take a national examination, the Primary School Leaving Examination (PSLE). Society at large view the PSLE as a highstakes examination. In addition to out-of-class work assigned by mathematics teachers for students to prepare for the PSLE mathematics, parents may also draw on out-ofschool practice books to further support their children's preparation for the examination. A study of two main types of such books show that these books do generally support students in reviewing content knowledge for the examination and test preparation.

Emergent graphical shape thinking (EGST) entails conceiving a graph as being dynamically generated via the trace of a moving point constrained by two changing quantities. As such, Paoletti et al. (2023) argue that meanings for quantities within a situation and meanings for graphical representations must be connected, or bridged, to engage in EGST. In this report, we explore this bridging process through a case study investigating how two students made connections that bridge their situational and graphical meanings during their work on a mathematical task. We found that the pair's connections between situational and graphical meanings emerged most prominently only after recursive engagement with reasoning in both contexts. We discuss the implications of these findings for researchers and practitioners seeking to support students as they develop EGST. [For the complete proceedings, see ED657822.]

We previously (Gantt et al., 2023; Paoletti et al., 2021) identified items from the publicly released TIMSS 2011 assessments that had potential for students to employ covariational reasoning as a solution strategy. In this report, we explore the extent to which fourth-grade students' performance on such items in mathematics differed among 26 nations. Using multilevel modeling, we conclude that, in general, fourth-grade students were less successful on mathematics items for which covariational reasoning was a viable strategy than on items for which we could not identify a possible covariational reasoning strategy. However, three countries (Finland, Sweden, and the Netherlands) did not follow this pattern. [For the complete proceedings, see ED657822.]

Despite significant research exploring students' quantitative reasoning, few studies have explored the semiotic processes that mediate its development. In this report, we present a case study to show how one student constructed a semiotic chain for a quantity as he worked with a mathematical task. Importantly, we connect frameworks for quantitative reasoning and semiotics to make sense of this process. Our findings show how our case student constructed a sign for a chunk of change in a triangle to support his later construction of the quantity of amount of change of area. We also describe how the case student leveraged these signs to bolster his development of the quantity of total area. We emphasize the role of artifacts, such as physical manipulatives, a digital applet, and a diagram, in this process. Finally, we discuss the implications of this analysis for future studies that explore students' constructions of quantity. [For the complete proceedings, see ED630210.]

Emergent graphical shape thinking (Moore & Thompson, 2015) is a way of reasoning that is critical across numerous STEM fields. However, evidence indicates that the underlying component ideas for emergent thinking are underdeveloped in school mathematics education (e.g., Thompson & Carlson, 2017), and few studies directly report on students' development of this way of thinking. We present the results of a teaching experiment conducted with eighth-grade students to support stable meanings for emergent graphical shape thinking. We focus on the in-the-moment meanings expressed by a pair of students as they engaged in a sequence of tasks that we conjecture could support stable meanings for constructing and interpreting graphs. [For the complete proceedings, see ED630060.]

We describe how we supported middle-school students developing meanings for quadratic growth by bringing together three theoretical framings and designing a task sequence grounded in that framework. Specifically, this framework was assembled from the research on students' quantitative and covariational reasoning, Realistic Mathematics Education, and the theory of designing for mathematical abstraction. We present data from a teaching experiment to highlight how this task sequence supported students as they imagined constant increases in the amounts of change in one quantity, a kind of change they later understood to be a defining characteristic of quadratic growth. We conclude with a discussion of our findings and how our integration of the three frameworks proved useful to design a productive task sequence. [For the complete proceedings, see ED629884.]

Researchers have identified students' difficulties reasoning about inverse functions. Through our review of this literature, three meanings stand out: a formal, 'undoing', and quantitative meaning. Using these meanings as a guide, we analyzed student work collected from a lesson on the topic of inverse functions taught by an experienced high school mathematics teacher, using a novel task. In analyzing the data, we noticed tensions between students' understanding of the context and of inverse function as treated in curricula. In this paper, we illustrate these tensions and describe potential implications for students' productive construction of the meanings of inverse function. [For the complete proceedings, see ED629884.]

This study employs Sfard's (2008) socio-cultural theory of Commognition to analyse student teachers' thinking and communicating practices. Specifically, we investigate the effectiveness of the student teachers' communication of a particular mathematical proof with reference of the four features of the commognitive framework (i.e., word use, visual mediators, narrative and routines). In this paper, we can report on the routine of the discourse to analyse the quality of mathematical discourse in two situations of "Expert-to-Novice" and "Novice-to-Novice".

Systems of equations are an important topic in school mathematics. However, there is limited research examining productive ways of supporting students' understandings of systems of equations. In this paper, we first present a conceptual analysis of potential ways students may leverage their quantitative and covariational reasoning to graph systems of relationships. We then describe results from a design experiment in which we examined the potential of supporting middle-grades students in reasoning in ways compatible with this conceptual analysis. We highlight two different ways of reasoning students engaged in as they compared the relative magnitudes of two quantities with respect to a third quantity and leveraged this reasoning to graphically represent two relationships on the same coordinate system. We draw implications from these results for the teaching and learning of systems of equations. [For the complete proceedings, see ED606556.]

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a conceptual analysis of different ways students may reason about graphs and coordinate systems. Specifically, we describe two different uses of coordinate systems--spatial and quantitative--students might leverage and two ways of reasoning--static and emergent--students might engage in as they construct or interpret graphs. We characterize how a student may engage in each kind of reasoning in each use of coordinate system. We intend this paper to serve as a theoretical lens for future empirical studies examining students' developing graphing understandings. [For the complete proceedings, see ED606531.]

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of coordinate systems. We discuss the implications of the framework for student learning, curriculum design, and teaching. [For the complete proceedings, see ED606531.]

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing the literature on students' inverse function meanings, I provide my theoretical perspective, including a description of a quantitative approach in the context of inverse relations. I then present one student's activity in a teaching experiment designed to support her in reasoning about a relation and its inverse as representing the same relationship. The student's quantitative reasoning supported her in developing productive meanings for inverse function, although this required her to reorganize her understanding of various mathematical ideas. [For the complete proceedings, see ED583989.]

Researchers have identified challenges students face when modeling dynamic situations. This report discusses the results of semi-structured clinical interviews with ten prospective secondary mathematics teachers who were provided with a dynamic image of a growing and shrinking cone. We asked the students to graph the relationship between the surface area and the height of the cone. We identify four themes in the students' solution approaches and discuss the implications of these approaches. Specifically, we discuss the themes with respect to relationships between the students' solutions and their images of the growing and shrinking cone, including the extent that they leveraged this image to determine their solutions. [For the complete proceedings, see ED583989.]

In this preliminary theoretical paper, we describe our use of conjecture mapping (Sandoval, 2014) to guide the design of a digital task sequence to support 6th graders’ meanings for points as a simultaneous representation of the amount-ness of two quantities. The conjecture map ultimately serves as a theoretical framework with testable conjectures about how the design of the digital task sequence might promote the intended learning outcomes. [ABSTRACT FROM AUTHOR]

In this theoretical report, we leverage a radical constructivist perspective to explain how designing learning environments in which students work towards making sense of others’ mathematical solutions may support learning. We elaborate on radical constructivist constructs—social goals, cognitive perturbations, and reflective abstraction—and use these constructs to model how engagement with others’ mathematical solutions may engender learning. We illustrate our model with a task we designed to promote students’ meanings for spatial coordinate systems. We conclude with implications for research and teaching. [ABSTRACT FROM AUTHOR]

We examined students’ thinking of graphs around a graphing task from 14 individual interviews, in terms of three layers—frames of reference, coordinate systems, and graphs—and explored their productive and intuitive strategies. As a result, we present a framework that offers a characterization of students’ graphing activities. We then discuss implications of the framework. [ABSTRACT FROM AUTHOR]

As graph literacy continues to be necessary to communicate in STEM fields, conventions around such graphs have developed for students to work and reason with. We describe a fifth grader’s, Emma’s, thinking through non-conventional graphical representations of a linear relationship. We argue that Emma relied on mathematical reasoning when faced with conflict in conventions and was able to make sense of unconventional graphs by using quantitative strategies. Although Emma acknowledged her known conventions of graphing, she was not bound by these conventions but rather leaned on her reasoning about quantities and flexible use of reference frames. We use Emma’s activity to argue possible implications for research and teaching regarding graphing conventions. [ABSTRACT FROM AUTHOR]

Graphical representations are commonly used in everyday life and are important in STEM fields. Interpreting graphs entails understanding the underlying structures of graphs, including coordinate systems and reference frames. In this report, we characterize one student’s constructions of coordinate systems. These constructions indicate two distinct types of reference frames not currently distinguished in the literature: (a) continuous and (b) ordered-discrete. Using data from a 10-session teaching experiment, we discuss the interplay of a student’s perception of tasks, the reference frames she reasoned with, and differences in those reference frames. We consider how the interplay of the aforementioned items may have influenced the quantities she considered as well as the coordinate systems she constructed. We conclude with suggestions for research and teaching that support students’ productive graphing activity. [ABSTRACT FROM AUTHOR]

We previously (Gantt et al., 2023; Paoletti et al., 2021) identified items from the publicly released TIMSS 2011 assessments that had potential for students to employ covariational reasoning as a solution strategy. In this report, we explore the extent to which fourth-grade students' performance on such items in mathematics differed among 26 nations. Using multilevel modeling, we conclude that, in general, fourth-grade students were less successful on mathematics items for which covariational reasoning was a viable strategy than on items for which we could not identify a possible covariational reasoning strategy. However, three countries (Finland, Sweden, and the Netherlands) did not follow this pattern. [ABSTRACT FROM AUTHOR]

In algebra, operating with symbols meaningfully depends upon a student's quantitative and deductive reasoning. Students can engage in these types of reasoning in different combinations, which has not yet been well conceptualized by mathematics education research. In this report, we present a framework that describes different combinations of how students use quantitative reasoning, deductive reasoning, and/or operating with algebraic symbols. We describe and illustrate each combination using examples from extant literature. [ABSTRACT FROM AUTHOR]

Constructing quantities and coordinating covarying quantities is a central component of STEM learning and development. We examined 323 publicly released fourth- and eighth-grade mathematics and science TIMSS 2011 assessment items to explore the extent to which such items could potentially elicit such reasoning. We found items potentially eliciting covariational reasoning across all four assessments, as well as an increase in number and complexity of such questions from fourth to eighth grade regardless of content domain. Further, we highlight the diverse content domains that leveraged graphical representations in such items. We discuss implications of our findings for the teaching and learning of middle-school STEM and for future study of covariational reasoning through international assessments. [ABSTRACT FROM AUTHOR]

In this report, we present results from semi-structured clinical interviews with a preservice secondary teacher which were conducted prior to and after a teaching experiment intended to support the student in developing emergent graphical thinking. We illustrate how the student engaged in static shape thinking in the pre-clinical interview to describe relationships represented graphically. In the post-clinical interview, the student used both static and emergent reasoning to describe relationships. Hence, we provide an empirical example of a student developing more sophisticated graphing meanings while underscoring the importance of probing students' shapebased thinking. [ABSTRACT FROM AUTHOR]

In this paper, we draw a distinction between two uses of inequalities, comparative and conditional inequalities, that emerged from our interactions with students. We highlight that despite reasoning quantitatively to make accurate statements with both types of inequalities, conventional notations for conditional inequalities were not sensible from the students’ perspective. We describe a third notation we introduced which the students were able to understand and use in later teaching episodes. [ABSTRACT FROM AUTHOR]

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of coordinate systems. We discuss the implications of the framework for student learning, curriculum design, and teaching. [ABSTRACT FROM AUTHOR]

Supporting students developing understandings of function has been a notoriously elusive task. In this report, we present Thompson and Carlson's (2017) description of a covariational meaning of function and provide an empirical example of a student who maintains meanings compatible with this description. We use this students' activity to illustrate nuances in Thompson and Carlson's description and to highlight how such meanings can be powerful. [ABSTRACT FROM AUTHOR]

I extend the body of research investigating students' quantitative reasoning by examining the interplay between a student's meanings developed through her school experiences and her quantitative reasoning in the context of inverse functions. I present one student's activities in a teaching experiment designed to support her in reasoning about a relation and its inverse function as representing an invariant relationship. Although the student engaged in such reasoning, her school mathematics experiences constrained her in relating this reasoning to her inverse function meanings. I conclude with implications and areas for future research. [ABSTRACT FROM AUTHOR]

Automated grading of fruit is an important industrial task that is expanding rapidly in its uptake. Machine learning-based techniques are increasingly being applied to this domain in order to formulate effective solutions for complex classification tasks. The inherent variability in the visual appearance of fruit and its quality-determining features, contributes to it often being a challenging classification task with much potential for improving the predictive accuracies for many fruit varieties. Additionally, the usability of many sophisticated machine learning algorithms in the form of tunable parameters and interpretable outputs is low, thus presenting a real barrier for the uninitiated. We address these problems by decomposing the overall machine learning task into subproblems. We propose combining a more sophisticated boosting algorithm (AdaBoost.ECC) with low interpretability for the learning of fruit-surface characteristics, whose outputs can then be combined with rule induction algorithms (RIPPER and FURIA) that learns the overall fruit grading rules with outputs of high interpretability for the operators to both review and revise. Our initial experiments considered four fruit datasets. We compared the results of our approach with that from a commercial system using manual calibration of the fruit grading parameters and found that our strategy can improve the accuracy over the current industry methods while providing high usability and interpretability of outputs. [ABSTRACT FROM AUTHOR]

The aim of this study is to assess the relationship between elementary school students' academic performance, gender and video gaming habits. More specifically, we seek to examine the usefulness of a distinction between addiction and high engagement and assess the predictive validity of these concepts in the context of scholastic achievement. Three hundred and thirty three children aged 8 - 12 years from two primary schools in Singapore were selected to participate in this study. A survey utilizing Danforth's Engagement-Addiction (II) scale and questions from DSM-IV was used to collect information from the schoolchildren, while their grades were obtained directly from the teachers. The findings suggest that boys spend more time playing video games and are more likely to report higher levels of addiction and engagement. The results also indicate that addiction tendencies are consistently negatively related to scholastic performance, while no such relationship is found for either time spent playing games or for video game engagement. The implications of these findings are discussed. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

This paper aims to show that the gendered practices of states not only affect the lives of men and women differentially, but that they produce a politics of gender which embody people's conceptualizations of the state and the greater good of society. Drawing on the case of family policies in Singapore, I show that despite the salience of gender as a principle of division, and the awareness of gender inequality, gender as principle identity around which to resist or organize vis-à-vis the state is largely disarmed. Embedding gender norms, values, and practices under the broader categories of "the family," "tradition," and "values," the effect of family policies is to produce not a sense that women have different interests than men, but that Singaporeans all have interests as families. This in turn is embedded in a broader conceptualization of the state as doing its best to produce a meaningful development wherein the twin and contradictory goals of "modernity" and "tradition" are balanced. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

We know that organizations of different but related kind greatly influence each other's evolution. Although empirical findings abound, the theories behind them are still being developed. We advance a model of ecological interdependence between emergent and established populations based on three main ideas. First, we consider related populations— those that overlap in identity and resource space and simultaneously exhibit competitive and mutualistic relationships. Second, we build on the idea that legitimated forms codify prescriptive sanctions for deviations from identity blueprints and predict that when an emergent population overlaps with an established one in identity space, its early proliferation will manifest violations of established social identities and will trigger prescriptive sanctions. Third, we rely on the notion of a focused identity to argue that organization-level changes affect external perceptions of the population's collective identity and hamper legitimacy. [ABSTRACT FROM AUTHOR]

The paper analyzes Singaporeans? negotiations of state policies around the family. It argues that state policies aimed at increasing rates of marriage and reproduction, while not directly ?effective,? have the latent effect of producing ideal citizens who take for granted the link between the family and the nation, and who are willing to tolerate the state?s high degree of intervention in their personal lives because they see this as the only way for continued economic development. This, in turn, is experienced as the basis of the nation?s existence. [ABSTRACT FROM AUTHOR]

Prior literature asserts that scope, crowding, and focused identity have pivotal effects on organizational mortality and position change. We argue that the mechanism through which the relationships between these features (i.e., scope, crowding, and focused identity) and mortality/position change unfold is innovation. To clarify the relationships between these three features and position change, we examine how these features affect the rate of innovation and how such innovations affect the rate of position change. Furthermore, we determine whether the effects of the three features depend on the type of innovation (i.e., incremental versus radical innovation). Then, we examine how innovations at both the focal firm level and the population level affect a firm's rate of position change. Our analyses are conducted in the context of longitudinal innovation dynamics of American automobile manufacturers from 1886-1981. On the basis of our findings, we draw some general implications regarding innovation and organizational change. [ABSTRACT FROM AUTHOR]

This paper investigates the mechanisms by which the Singaporean state rules. Specifically, it looks at how the state frames the problem of women and their fertility, and how it then tries to resolve the supposed problem. It argues that the state approaches the problem by balancing rhetoric and practice; by emphasizing inclusion rather than exclusion; and by trying to convince citizens that they should behave in particular ways for the good of the nation. [ABSTRACT FROM AUTHOR]

Electrospinning is the process for producing different type of fibers with nano and micro diameter. In usual electrospinning the nanofibers collect on the surface of flat or drum grounded collector and the final nanofiber web have 2D structure with some micrometer thickness. In the present research, some new methods based on the liquid support system and jet controlling are introduced for modifying the process to obtain 3D random and oriented structures. The main advantages of this system are the ability of producing continues aligned bundle of nanofibers as yarn and some other bulk structures. Some preliminary studies, especially on the set-up conditions were done to show the feasibility of these techniques for designing the nanofiber structures. [ABSTRACT FROM AUTHOR]

An abstract of the article "Changing Cones: Students' Images of a Dynamic Situation" by Teo Paoletti and colleagues is presented.

The article presents a study of 25 pre-service teachers with the use of an interview protocol that comprised contextualized and decontextualized tasks which included graphical or analytical representations. It shows that only five of 25 students were able to identify a viable interpretation of the inverse function they determined analytically in a contextual situation, even though each of the 25 students applied a consistent technique in analytic, decontextualized tasks.