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The paper proposes EXPLODE, a new model of exploratory learning environment for teaching and learning neural networks. The EXPLODE model is about pedagogically instrumenting a software development environment to transform it into an exploratory learning environment for neural networks. Such an environment is particularly aimed for students who are skilled in programming and meets typical challenges in teaching and learning neural networks, related to the lack of prerequisite knowledge in mathematics. By providing such students with a familiar learning environment and allowing them to programmatically experiment with neural networks, the EXPLODE model aims at improving the students' learning outcomes and learning experience. The effectiveness of the model was evaluated in an experimental study with 77 final-year IT students. The results have shown that the students from the experimental group, that is, those who were exposed to the EXPLODE model, scored higher on the knowledge test. Furthermore, the perceived learning experience of the experimental group was better than that of the control group. The results have also suggested that the proposed model helps students better understand learning topics that require practical experience and facilitates a deeper understanding of the internal operations of neural networks. [ABSTRACT FROM AUTHOR]

Chicana/Latina Feminist frameworks that center the lived experiences of Chicanas/Latinas/Mexicanas have helped to reshape profoundly the ways we think about the role and centrality of culture and identity in methods and methodology. However, this rich Chicana/Latina feminist cultural methodological and analytical framework has not been leveraged in conjunction with disciplinary learning, particularly in teacher education and teacher learning. This article is concerned with understanding how a rich cultural practice, feminista pláticas, can serve both as a cultural context for learning, as well as a tool for organizing human activity in which cultural ways of learning are centered. In this paper, through an empirically-informed vignette we show how feminista pláticas help organize participation in ways that make cultural knowledge a resource for future action towards equitable and justice-oriented math teaching and learning. [ABSTRACT FROM AUTHOR]

To design and develop a mobile application for pre-school readiness of children with autism and also to identify their learning pattern. Based on strong foundation of functional academics, we have developed a mobile application for providing an early educational intervention program to the children with autism. Three successive software trials have been conducted among 31 children with autism of age group of three to 10 years. The mobile app has been provided to educators and parents and they have been allowed to supervise the children during their learning phase for eight to 10 weeks. The imprint of learning pattern is recorded and learning progress profile is generated for individual child. Data analysis of learning progress profile shows that 90% of the participants preferred drag and drop or simple touch approach over conventional methods practised during classroom teachings. More than 84% of the children are found to adapt pre-requisite skills for writing like scribbling, tracing, dots joining, copying, etc. after using the app on their tablet who are reluctant to hold pencil and paper otherwise. Twenty-five percent of the participants are reported to reciprocate the greeting etiquettes in class such as greeting teachers and their peers. The mobile application made a valuable contribution to early intervention program for children with autism by imparting appropriate learning opportunities readily available to them. Performance metrics underlying each activity form a strong base of identification of learning patterns and formulation of revised individualized education plan (IEP). Children with autism need the mobile application as an educational intervention program for it is readily available and user friendly. Educators need the mobile application to quantify the performance parameters and there by monitor/evaluate the progress of the child. Overall, the present research has aimed to develop an easy reach app by which educating as well as handling challenging behaviour of the children with autism would be easier. [ABSTRACT FROM AUTHOR]

This article shares a paper presented as the keynote for the Terry L. Wood Memorial Conference that was held virtually on May 20, 2022. This paper starts with a reference to the project, The Coordination of a Psychological and Sociological Perspective, that was funded by the Spencer Foundation. The results of the research in this project are published in the book, The Emergence of Mathematical Meaning, edited by Cobb and Bauersfeld (1995). [ABSTRACT FROM AUTHOR]

Recent studies on classroom discourse have challenged the traditional classroom role set and emphasised equal contributions from the participants and the emergence of knowledge through active participation. Co-learning emphasises the process in which teachers and students attempt to adapt to one another's behaviour and learn from each other in order to produce desirable learning outcomes. Current research has paid little attention to the ways in which content teachers and students jointly negotiate new knowledge in bi/multilingual classrooms. Based on data collected from a linguistic ethnography in Hong Kong English-Medium-Instruction secondary mathematics classrooms, this paper uses translanguaging as an analytical perspective to analyse how the EMI teacher and students co-learn in the classroom. The data are analysed using Multimodal Conversation Analysis and triangulated with the video-stimulated-recall-interviews which are analysed using Interpretative Phenomenological Analysis. The paper argues that translanguaging creates a safe space for co-learning that emphasises equity in knowledge construction and challenges the hierarchical relationship between the teacher and the learner. [ABSTRACT FROM AUTHOR]

Teaching Mathematics to tertiary students can be a challenge to educators, mainly because they must deal with learners' varying levels of readiness. Some of the factors attributing to the variability are learners' perceptions of mathematics, their previous learning experiences, and fear of failure. We implemented a teaching approach to facilitate student ownership through active peer involvement and flexibility with assessments. In this paper, we analyze students' perceptions of learning mathematics when using the new approach for three consecutive semesters. We discuss the results of our study and the factors that helped students overcome their inhibitions and appreciate mathematical concepts. [ABSTRACT FROM AUTHOR]

Mathematics is frequently considered as value-free, centring entirely on abstract reasoning. However, more often than not, the teaching of values in mathematics classrooms takes place implicitly through the actions of the teacher. The role values play in mathematics learning is also a growing area of interest and is now viewed by many as a contributing factor in the advancement of the quality of mathematics performance. This paper reports on part of a larger study aiming to establish the components that Grade 8–10 learners from a mathematics-and-science-focus school in Johannesburg value as important in the learning of mathematics. A quantitative survey was used to collect data from 249 participants. Principal component analysis was employed to analyse the data. The main findings revealed seven components that learners appeared to value in the learning of mathematics. Knowledge about what learners value in the learning of mathematics can inform teachers' pedagogical practices and the inculcation of values in mathematics teaching, which may, in turn, improve the quality of learning of mathematics. [ABSTRACT FROM AUTHOR]

This paper presents findings from a two-year qualitative study examining integration of computer science (CS) and computational thinking (CT) into elementary mathematics instruction. Integrated units were developed by elementary teachers and CS/CT coaches with support from university faculty with expertise in CS/CT and elementary mathematics. CS/CT instruction primarily relied on the Scratch environment, although some lessons made use of Code.org materials. This research primarily relied on two theories of integration (i.e. Kiray, 2012. A new model for the integration of science and mathematics: The balance model. Energy Education Science and Technology Part B: Social and Educational Studies, 4(3), 1181–1196) that provided insight into the level of interconnection between the disciplines and the relative amount of instructional time spent within each discipline. Findings revealed that cross-grade CS/CT concepts included sequencing, looping, and conditional logic. Within each category: (a) concepts were taught with increasing complexity across the grades, (b) the mathematics was dominant and CS/CT was important but secondary, and (c) three types of lessons emerged: No integration, partial integration, and full integration. Lastly, lessons generally included a transition from less integrated to more integrated activities with an initial focus on discipline-specific conceptual understanding prior to integrated activities. [ABSTRACT FROM AUTHOR]

In this paper, we pursue a materialist approach to tool use to account for the material dimensions of learning mathematics with technology while decentralizing the human body from activity. We root this vision in theoretical advances on embodied mathematics learning and tool use that have been recently offered as alternatives to traditional theories of learning that draw attention only to the individual learner or the mind. Focus is on the ways that learners, tools and mathematics are entangled in provisional reconfigurations of the world and on how the tool partakes in this movement. Starting from our theoretical commitment, we discuss some episodes from a research study in which grade 9 students were introduced to function through a graphical approach. The study took advantage of graphing motion technology, which allows working with couples of position over time graphs, capturing spatio-temporal relationships. The episodes provide insight into the complex nature of learning in this context, valuing the mobile way that mathematics emerges from activity with the tool. [ABSTRACT FROM AUTHOR]

This paper briefly overviews my research in supporting children to learn number concepts by relating number words, research-based visual supports, and math symbols. I first outline my approach to helping children build relationships between the use of concrete materials and the building of abstract concepts. I then focus on two crucial early aspects of building meanings for numbers: (1) understanding break-apart partners such as 5=3+2 that support addition and subtraction with small numbers and children's moving on to Level 2 counting on and algebraic problem representations, and (2) the use of visual five-groups in understanding numbers 1-1000 and in drawings to support multi-digit computations. The research-based learning path of visual-spatio supports is shown and discussed for each topic, including examples of children's math drawings for representing word problems algebraically and for multi-digit computations. I have found math drawings to be a key visual support that helps children transition to working meaningfully with symbols and words alone. I close with a brief discussion of the difficulties children have with the number line. This overview can provide a framework within which future research on number learning by individuals with trisomy 21/Down syndrome can proceed. [ABSTRACT FROM AUTHOR]

This paper considers the effects of both free optional mathematics learning support and engagement on the mathematics performance in a foundation mathematics subject of a cohort of engineering students entering university with poor mathematical skills. New engineering students were directed to either a foundation or standard mathematics subject based on the results of a placement test. For students in the foundation subject, it was found that high levels of learning support were associated with greater improvement over the semester. Some form of learning support was used by 57.9% of the students, a reasonably high proportion of the cohort. Some factors for this high level of use of learning support are considered. One possible factor, the placement test, appears to have had a positive effect. Engagement in the subject activities as measured by tutorial attendance and learning management system use was found to have a positive association with final mark. Students who utilized a high level of learning support were more likely to be more engaged with the subject, making it impossible to draw conclusions about improvements being solely due to the use of learning support. [ABSTRACT FROM AUTHOR]

Inquiry-based pedagogies have a strong presence in proof-based undergraduate mathematics courses, but can be difficult to implement in courses that are large, procedural, or highly computational. An introductory course in statistics would thus seem an unlikely candidate for an inquiry-based approach, as these courses typically steer well clear of proof, have a list of required topics, and depend critically on computational software. On the other hand, the American Statistical Association (ASA) has long advocated the sort of active and exploratory class design that in many respects parallels traditional inquiry-based learning (IBL). This paper reports on the author’s recent attempt to implement an inquiry-based course in introductory statistics that fuses established IBL techniques with the specific pedagogical recommendations of the ASA. A signature feature of this course is that many of the inquiry-based activities are explicitly tied to computer work in the open source language R. [ABSTRACT FROM PUBLISHER]

Mathematics teachers across the Western world are faced with an expectation that they make significant change to their teaching, but repeated attempts have shown little embedded success. This paper draws on a longitudinal study of two apparently well-placed English mathematics departments attempting to make change aligned with both policy and internationally-valued ‘good practice’. It suggests deep teacher change draws on a wide range of both social and affective characteristics, as well as sophisticated professional skills and knowledge. The study supports a construct of ‘(mathematics) teacher capacity for change’ at both individual and group levels within teachers’ ‘personal domains’, synthesising the range of characteristics apparently needed by teachers in times of change. In particular, it argues for the development of dispositions for collaborative learning and of other learning-supportive affects. Such an approach has the potential to place teachers in a better position to respond to demanding aspirations. [ABSTRACT FROM PUBLISHER]

Students are expected to learn mathematics such that when they encounter challenging problems they will persist. Creating opportunities for students to persist in problem solving is therefore argued as essential to effective teaching and to children developing positive dispositions in mathematical learning. This analysis takes a novel approach to perseverance by conceptualizing it as collective enterprise among learners in lieu of its more conventional treatment as an individual capacity. Drawing on video of elementary school children in two US classrooms (n = 52), this paper offers: (1) empirical examples that define perseverance as collective enterprise; (2) indicators of perseverance for teachers (and researchers) to support (and study) its emergence; and (3) evidence of how the task, peer dynamics, and student-teacher interactions afford or constrain its occurrence. The significance of perseverance as collective enterprise and as an object of design in developing effective learning communities, is discussed. [ABSTRACT FROM AUTHOR]

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching techniques – (a) variation theory and (b) representations of subject matter – on the design of learning objects for secondary school algebra concept learning. The results of this study showed that the experimental group performed significantly better than the control group on algebra learning achievement. The results also showed that only the experimental design with the addition of the instructional approach resulted in higher-order mathematical thinking skills and improved procedural skills of the students. Further analysis reveals that concept learning was simplified when multimedia learning principles were applied and the information was presented by the instructional approach. [ABSTRACT FROM AUTHOR]

Metacognition as a dimension of learning ranks highest in the revised Bloom’s Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly to evaluate their own progress and review their development in light of their personal goals. We observed positive affective changes (including engagement levels) in the students through the course of the semester. We argue that the weekly metacognitive and self-reflective activities helped students keep their focus on learning deeply and allowed them to remain engaged and motivated through the semester. A brief theoretical discussion is included, and other possible contexts suitable for the described activities are suggested. [ABSTRACT FROM PUBLISHER]