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In this article, I will discuss a collective research project that I designed for my History of Mathematics course. My students, who are by and large pre-service teachers, explored online, digital versions of 18th-century British almanacs that contained question-and-answer sections for mathematics. In a multi-stage research process, they explored the primary sources, investigated selected mathematical problems from the almanacs, conducted prosopographies of the contributors to the almanacs, and finally surveyed secondary sources. They then presented their results in pairs to their classmates. Through these presentations, as well as the prosopographies and notes they shared on our online classroom management system, the working pairs of students wrote research papers that placed their findings within the context of the research of the whole class. This collective research project allowed my students to begin focused and purposeful research within the first week of classes. Moreover, this project encouraged them to become highly engaged with their primary sources and enabled them to work as a team. This collective research project framework could be applied to a variety of groups of primary sources from the history of mathematics (such as textbooks and journals), now widely available online, to a variety of mathematics courses. [ABSTRACT FROM PUBLISHER]

Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study method was employed to understand how different algebraic practices (abstracting, generalizing, justifying, and operating on symbols) and functional thinking types (recursive, covariational, and correspondence) were facilitated through working with multiple representations. Three 6th graders participated in the study by completing 12 algebra tasks and taking part in two interviews. The onto-semiotic approach guided the data analysis process that involved the identification of mathematical objects that emerged in the participating students' mathematical practices. Then, the configuration of objects and semiotic functions established by the students in the functional situations was examined to understand the role of representations in the students' development of algebraic thinking and practices. Findings showed that abstraction is an essential process for generalization. Thinking about far figures facilitated abstraction and generalization through helping students construct non-ostensive concrete/pictorial representations. Verbal representations interacted with all representations and preceded symbolic representations. Working with near figures promoted recursive and covariational thinking while examining the far figures usually resulted in correspondence thinking. Implications for the school curriculum are discussed in the paper. [ABSTRACT FROM AUTHOR]

In our study we exploit digital tools in order to foster a relational approach to mathematics undergraduate students. Specifically, we designed formative assessment workshops based on peer feedback, with the aim to promote self-assessment and reflection on one's own mathematical activity. In the paper we describe the design of an educational activity and investigate how the students perceived their experience with the designed formative assessment workshops. Furthermore, we provide evidence of the effectiveness of the designed workshops in terms of aligning students' feedback with the teacher's criteria. [ABSTRACT FROM AUTHOR]

This paper deals with the gender gap phenomenon as displayed by Italian students participating in mathematical competitions—gifted students. In particular, the results obtained by the entire student population participating in district competitions from 2017 to 2020 were analysed. The combined analysis of the competition results and of the final questionnaire allowed us to highlight and deepen possible causes of the gender gap. It has been observed that girls underestimate themselves, sometimes giving up participating in competitions. Particularly, during the upper secondary school years, increasingly fewer girls choose to attend mathematical competitions. Analysing the results, although the percentage of correct answers between the two genders is fairly similar, the rate of girls who prefer not to answer to avoid mistakes is higher than that of boys. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate how the contents related to the arithmetic of fractions, as described in the official curriculum issued by the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT), are implemented in actual teaching at the so-called Japanese supplementary school in Denmark. Additionally, at a methodological level, this case study demonstrates how so-called praxeological reference models can be developed at different levels of detail to describe classroom teaching at a particular grade level and the overall curriculum of primary school in a connected way. This study is based on the notions of praxeological reference models and moments of didactic processes from the Anthropological Theory of the Didactic. The findings reveal that (1) not much time is allocated to each moment and (2) the flow of gradually building up techniques, as intended by the textbook authors is to some extent disrupted in the lesson. [ABSTRACT FROM AUTHOR]

This paper clarifies contexts of probability in Egyptian primary and lower-secondary school textbooks and how the students prioritize them. Through preliminary general inductive analysis, it was apparent that the implemented curriculum of probability, represented by the students' textbooks, emphasized the conventional activities that require calculations and are suitable for employing theoretical probability. On the other hand, students highlighted environmental circumstances, such as weather forecasts, as the most practical context for the probability concept. In that sense, there is a need to refine the textbook activities so that they match students' viewpoints. [ABSTRACT FROM AUTHOR]

This paper focuses on the importance of covariational reasoning within the processes of mathematics teaching and learning. Despite the internationally recognized relevance of covariation, research shows that only a small percentage of students and teachers is able to adopt covariational reasoning and the majority of mathematics curricula do not contain explicit references to covariational skills. In particular, when covariational reasoning manifests as conceptual knowledge, it becomes challenging to assess, and the need for innovative methods of assessment emerges; there is a need for suitable assessment to highlight the characteristics of covariation and capture the various features that characterize conceptual understanding. Comparative judgement (CJ) is an innovative assessment method based on collective expert judgements of students' work rather than requiring scoring rubrics. Due to its holistic approach, CJ is particularly suitable for assessing complex mathematical competencies, and, as we shall see in this study, it proved to be appropriate for the covariation's assessment. In details, our study aims to investigate the perception and relevance attributed by mathematics teachers to covariation as a theoretical construct and the way CJ can help in the assessment of covariational reasoning skills underlying a less structured modelling task. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Educational Thought / Revue de la Pensée Educative is the property of University of Calgary, Faculty of Education and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper aims to illustrate a design cycle of inquiry-based mathematics activities. We highlight a series of questions that we use when creating inquiry-based materials, testing and evaluating those materials, and revising the materials following this evaluation. These questions highlight the many decisions necessary to find just the right tasks for our students. Throughout the paper the use of multiple representations (graphical, numerical, symbolic, and narrative) and the distinction between facts, skills, methods, and conceptual understanding is explained and illustrated with examples. Additionally, we present evidence of student learning through excerpts from student journals and exam analysis. [ABSTRACT FROM PUBLISHER]

In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers. [ABSTRACT FROM AUTHOR]

Mathematics results in South Africa are of serious concern. The reports by TIMSS [Trends in International Mathematics and Science Study] prove that the teaching of mathematics remains a challenge in the South African schooling system. In their attempts to improve mathematics results and to cope with the many curriculum changes since the start of democracy in 1994, mathematics teachers are experiencing increased levels of stress and anxiety. Diversity is a critical issue in education and learners suffer the consequences if teachers do not recognise the importance of diversity. Democracy leads to curriculum change and causes socio-cultural diversity among the learners in a classroom. Mathematics teachers faced ousting of their power in the classroom through the learner-centred strategies that they were expected to implement. In this study, three semi-structured interviews and a focus group discussion were deployed to generate data. The dualistic theoretical lenses used in this paper are based on the theory of culturally responsive teaching and theory of cultural capital. The findings that emerged from the data show that mathematics teachers are ill-equipped to meet the needs of the socio-culturally diverse learners in their differing classrooms. Further research in exploring ethnomathematics as a culturally responsive teaching strategy will reveal new dynamics in socio-cultural deficit thinking. [ABSTRACT FROM AUTHOR]

The transition from studying mathematics at school to university is known to be challenging for students. Given the desire to increase participation in science, technology, engineering and mathematics subjects at degree level, it is important to ensure that the school mathematics curriculum is providing suitable preparation for the challenges ahead, and yet remains both accessible and popular. This two-part study investigates student choices of studying the post-16 A-level Mathematics and Further Mathematics qualifications in the UK and their impact on the transition from school to university mathematics. Student opinions were accessed via a survey of undergraduate students and also individual interviews. This first part of the study considers the responses of mathematics undergraduate students and finds that both those who studied Further Mathematics and those who did not perceive studying Further Mathematics as advantageous for their degree courses. However, the advantages identified mostly relate to the familiarity with topics, while students still feel unprepared for studying more abstract and proof-based mathematics. The study found that some factors which may be beneficial for transition currently lie outside the mainstream school mathematics syllabus and include studying through blended learning provided by the Further Mathematics Support Programme, practicing more advanced extension exam papers and attending university outreach events. The choice of Further Mathematics is found to be influenced by the attitudes of the students, their teachers and their parents, to both mathematics as a subject and to Further Mathematics as a qualification as well as student perceptions of Further Mathematics and their plans in terms of degree and university choice. [ABSTRACT FROM AUTHOR]

Trends in curriculum reform recognise the need to develop skills and competencies in addition to specifying what knowledge should be taught and when. However, a balance between skills and knowledge is sometimes difficult to achieve. In this paper which takes mathematics as the focus, we consider reform currently underway in Wales, from the perspective of a 'knowledge approach' and from the perspective of the Successful Futures report which is, we argue, driven more by a skills approach at the heart of which are 'four purposes': developing young people as ambitious, capable learners; enterprising, creative contributors; ethical, informed citizens; and healthy, confident individuals. Our interest is in the contribution that mathematics makes to the four purposes; and contribution that the four purposes make (or do not make) to the development of a school mathematics curriculum. After outlining the background and context, the paper consults literature and experts to consider what mathematics is and how the learning of mathematics can be seen to fulfil the four purposes. The study contributes to understanding the difficulties of re-contextualising school subjects from the academic disciplines and proposes that operating with a curriculum driven by big ideas or overarching statements places higher demands on teacher knowledge. [ABSTRACT FROM AUTHOR]

This paper reports on a study set in Wales where the Further Mathematics Support Programme Wales supports the provision of an advanced qualification in mathematics for 16- to 18-year-old students with courses delivered in reduced teaching time. The study aimed to understand how the students experienced the Further Mathematics (FM) courses which are delivered either face-to-face or online and, more generally, to negotiate a place of alternative forms of delivery in post-16 mathematics curriculum. Sixteen students, eight of whom studied through the online course, were interviewed; overall, although they found the course challenging both in terms of the content and relatively limited teaching time, they enjoyed it and appeared to perceive benefits from taking the course. Most volunteered 'tips' about coping with the challenges of the course and the tips can be seen as strategies of self-regulation. Self-regulation strategies were reported more strongly by the students taking the course online than those attending face-to-face classes. In view of the evidence of technology creating new learning environments perceived as advantageous by students, it is hypothesized that introducing blended learning as part of post-16 mathematics curriculum could be beneficial. Improving learner self-regulation is discussed as means of improving access to FM. Other findings included the importance of support from peers, parents and schools and gender differences. [ABSTRACT FROM AUTHOR]

Formulas are involved in most parts of the mathematical curriculum in upper secondary education and in everyday mathematics classrooms, but research shows that students have difficulties using formulas adequately. When students are presented with a task, the task activates a conceptual frame in the students, making them perceive formulas in a specific way, thereby affecting their mathematical behaviour. In this paper, building ideal types of patterns of mathematical behaviours is used to conceptualise 'view on formula' specified by several specific views. The concept of 'view on formula' is applied in an analysis of a classroom episode pointing to reasons for the difficulties students have with handling formulas. When views are either missing or not used in a flexible way this can lead to an unsuccessful handling of formulas. Also, students' views on formula may indicate what knowledge is missing for solving a task involving formulas. Taken together, this points to the importance of paying attention to views on formulas in the everyday mathematics classroom. [ABSTRACT FROM AUTHOR]

An introduction is presented in which discuss various articles in the issue on topics including relation between inquiry-based learning, equity and student experiences; enrichment in first-year courses for academically strong mathematics students; and issues surround mathematics education.

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]

The school system in both the Republic of Ireland [ROI] and Northern Ireland [NI] is configured to accommodate children into discrete educational bands at different stages on their learning journey. Research has consistently shown that the transition from primary to post-primary, which typically occurs between the ages of 11 and 13, is the most challenging transition with the negative effects more pronounced for mathematics than any other subject. This cross-border study investigates this transition in mathematics education from the final year of primary school to first year of post-primary school from the perspective of teachers involved with these year groups. It examines teachers' knowledge of the mathematics curriculum and teaching strategies employed in the other phase. The majority of primary teachers reported being unfamiliar with the curriculum and teaching approaches employed in the first year of post-primary and the differences between the two jurisdictions were not significant. However, a difference was noted in the responses of second level teachers. Teachers in NI appeared more confident in their knowledge of the curriculum and teaching approaches adopted in the final year of primary school than their ROI colleagues. In this paper, the authors will elaborate on these findings; outline possible reasons for the differences across jurisdictions and share what impact teacher knowledge is having on classroom practices. [ABSTRACT FROM AUTHOR]

To promote and facilitate the teaching of math modeling throughout the K–16 setting, the Consortium for Mathematics and Its Applications and the Society for Industrial and Applied Mathematics recently published the GAIMME (Guidelines for Assessment and Instruction in Mathematical Modeling Education) Report. This paper provides insight into how the GAIMME report can be a valuable asset to undergraduate faculty in terms of better understanding how K–12 students engage in math modeling and how to create a continuum so that college mathematics courses, both pre-existing and perhaps newly developed, can support and further develop those skills. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to describe the design and development of a final year undergraduate mathematics module designed to address professional skills development at a UK university, including via input to curriculum and assessment from employers, and to investigate student acquisition of skills from this module. Design/methodology/approach: Literature on skills development in mathematics informs module design and development. Students optionally completed Likert-style competency questionnaires before and after the taught module content, and reflected on skills development via an end of module questionnaire. Data collection took place over three academic years. Findings: Several key competencies exhibit median increases over the course of the module in each academic year, indicating a perceived skills development. Problem solving and presentation skills are particularly highlighted. Research limitations/implications: Numbers of students were small, though the study is repeated with three different cohorts. Some students study mathematics jointly with another discipline and hence may have experience in skills development from the other subject. Practical implications: This study indicates that innovations in teaching style and assessment in mathematics modules can enhance student confidence and competence with key professional skills. Originality/value: Undergraduate modules in mathematics which have a focus on professional skills development are still fairly rare in UK universities. Often such modules do not embed the professional skills development activities with subject-specific technical tasks and projects as this module does. There are few formal studies of the effectiveness of this style of module, especially longitudinal studies covering several academic years. [ABSTRACT FROM AUTHOR]

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument that students need to see problem-clarifying strategies in conjunction with problem-solving techniques, as the former are essential for making progress when engaging a mathematics problem where an explicit solution is not apparent. The other facet aiming to promote student agency is providing them opportunities to work with their own practical/professional concerns as students so as to become more creative and productive artists of their mathematics experience. [ABSTRACT FROM AUTHOR]

This paper compares sections on functions and linear functions from two Korean textbooks and an American standards-based textbook (University of Chicago School Mathematics Project [UCSMP] Algebra) to understand differences and similarities among these textbooks through horizontal and vertical analyses. We found that these textbooks provide different opportunities to learn (OTL). UCSMP Algebra places strong emphasis on real-life applications of linear functions rather than on pure mathematics andmathematical algorithms. Also, compared to Korean textbooks, UCSMP Algebra offers more OTL for students to solve, explain, and reason about higher level cognitively demanding mathematics problems than Korean secondary text books. Contradictory results, compared to previous studies about East Asianmathematics textbooks indicate the need for further study to compare secondary textbooks from more East Asian countries. Also, with the results of this study, we need to understand the results of international assessments more carefully. [ABSTRACT FROM AUTHOR]

With the rapidly increasing scale of normal students in Chinese local universities, the higher quality of education of normal students is required urgently. As the base of cultivating normal students, curriculum offered by university plays an extremely important role in the entire training process. By taking a local university in China --- Hunan University of technology, as an example, this paper establishes the related indexes of curriculum satisfaction in the questionnaire, and explores the factors affecting normal students' curriculum satisfaction. Especially for normal students with different gender, statistical analysis on their difference to the satisfaction of curriculum configuration, structure and evaluation is subsequently made to provide practical countermeasures for improving the current mathematics normal curriculum system. [ABSTRACT FROM AUTHOR]

This paper presents findings from a larger research project that provides insight into the attitudes of high-school students who were taught using different types of mathematics curricula when they were in middle school. A total of 44 12th-grade students from 10 high schools in the same urban school district were interviewed. Eighteen (41%) of them had been taught using a reform curriculum in middle school and 26 (59%) had been taught using a more traditional curriculum. Using Di Martino and Zan’s three-dimensional model for attitude, we found that the high-school seniors who had been taught using the reform curriculum in middle school harbored attitudes toward mathematics that differed significantly from the attitudes of those who had been taught using a traditional curriculum in middle school. Our analysis of the student interviews culled seven themes that provide fine-grained information about the students’ attitudes toward mathematics. Significantly greater percentages of reform students than traditional students had a relational Vision of mathematics as opposed to an instrumental Vision; however, there was no significant difference between the proportions of reform and traditional students who had a positive Emotional Disposition toward mathematics or a positive Perceived Competence in mathematics. [ABSTRACT FROM AUTHOR]

Just like physical skills, cognitive skills grow rusty over time unless they are regularly used and practiced. This means that school breaks can have quite negative consequences on student learning. The Keeping in School Shape (KiSS) program is an engaging, innovative and cost-effective intervention that uses push technology to help students maintain proficiency over breaks from school, while also promoting a growth mindset. Theoretically, the KiSS program draws on the well-documented benefits of retrieval practice -- the notion that recalling previously material is a very effective way of maintaining cognitive performance. The KiSS program embodies retrieval practice by sending students a multiple-choice mathematics question daily via text messaging or email. A positive mindset regarding the benefits of effort is promoted through feedback messages that encourage program resource use, such as choosing to view a hint and retry a problem instead of giving up. This paper reports on a few aspects of the implementation of the KiSS program at a large university during the summer break for students enrolled in an engineering introductory calculus course sequence. [ABSTRACT FROM AUTHOR]

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students’ pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities. [ABSTRACT FROM PUBLISHER]

A summary of an experimental course on algebraic curves is given that was held for young learners at age 11. The course was a part of Epsilon camp, a program designed for very gifted students who have already demonstrated high interest in studying mathematics. Prerequisites for the course were mastery of Algebra I and at least one preliminary year in a prior Epsilon camp. The summary gives an overview of the flow of teaching, the achieved results and some evaluation of the given feedback. [ABSTRACT FROM AUTHOR]

Stanley Erlwanger's Case of Benny is seen by many as particularly influential in the mathematics education research community. This paper reports the results of a study designed to describe the nature of that influence. Through an analysis of academic references to the Case of Benny from the past 40 years, five primary purposes for citing the case were identified. These purposes revolve around the themes of student mathematical conceptions, the relationship between correct answers and understanding, the value of qualitative research, the impact of a behaviorist-based curriculum, and students as sense makers. The paper concludes by using these themes to reflect on the past 40 years and to look ahead to the future of research in mathematics education. [ABSTRACT FROM AUTHOR]

Differences in definitions of limit and continuity of functions as treated in courses on calculus and in rigorous undergraduate analysis yield contradictory outcomes and unexpected language. There are results about limits in calculus that are false by the definitions of analysis, functions not continuous by one definition and continuous by another, and continuous functions with discontinuities. This paper uncovers these issues and resolves them in five guided classroom discoveries ideal for students in a first course in real analysis, an honors calculus course, or a course on transitions to higher-level mathematical thinking. The conclusion provides definitions consistent with analysis in a setting for the general student of calculus. [ABSTRACT FROM PUBLISHER]

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving investigation and discovery activities. This paper presents the mathematical thinking processes and pre-service teachers' experiences in the course of investigation and discovery activities. The pre-service teachers claimed that they learned new mathematical concepts, as also how to apply their mathematical knowledge. Finally, some useful examples of the mathematical processes experienced by the students during their project work are presented. [ABSTRACT FROM AUTHOR]

This article presents the findings of a case study that introduced online quizzes as a form of assessment in pure mathematics. Rather than being designed as an assessment of learning, these quizzes were designed to be an assessment for learning; they aimed to academically support students in their transition from A-Level mathematics to university-level pure mathematics by providing an extrinsic motivation to engage them with their learning material early on and to emphasize the small details within proofs, such as defining notation, which are not necessarily emphasized by written homework assignments. The results obtained during the 2-year study using online quizzes show e-assessment to be a powerful complementary tool to traditional written homework assignments. [ABSTRACT FROM AUTHOR]

Good stories, literary or mathematical, have the ability to keep the reader engaged and wanting for more. However, poorly designed stories may also elicit a negative aesthetic reaction and thereby reduce engagement. By drawing on literary theory and Dietiker's (For the Learning of Mathematics 33(3):14–19, 2013; Educational Studies in Mathematics 90(3):285–302, 2015) theoretical framework of mathematical stories, this essay conceptualises two aspects of mathematical stories that are likely to be perceived by the readers as aesthetic deficiencies: mathematical cheap plot tricks and mathematical plot holes. Additionally, examples of them are proposed from various areas of mathematics curriculum and some ideas of how they can be avoided, so as not to hinder engagement, are offered. [ABSTRACT FROM AUTHOR]

Applying a retrospective, qualitative, longitudinal approach, this study identified aspects of teaching and learning in mathematics and science courses that were the focus of reflections for faculty who were involved early in a STEM improvement effort at an institution oriented toward change. Results indicated an emphasis on instructional considerations but variability in participants' focus on student learning before, during, and after participating in a yearlong faculty learning community. Implications are described that relate to building on faculty's sense of caring, so as to centre professional development experiences on student considerations and on fostering change in undergraduate STEM education through a 'propagation' approach. [ABSTRACT FROM AUTHOR]

Undergraduate mathematics students are expected to spend a substantial amount of time outside class studying proofs independently. Yet, little is known about how such expectations shape instruction in proof-oriented courses. This paper investigates this issue in a case study of an experimental teaching strategy, designed by a mathematics professor, for scaffolding student independent proof reading. On the basis of interviews and classroom observations we scrutinize the instructor’s course image – his envisioning of the teaching and learning activities, inside and outside class, throughout the course. We examine a representative case of proof presentation through the lens of the instructor’s course image. Our analysis reveals complex relationships between various teaching and learning activities in the course, and demonstrates that unpacking these relationships can provide valuable insights into specific teaching practices. Findings suggest that the concept of course image can be useful in enhancing our understanding of mechanisms underlying collegiate mathematics instruction. [ABSTRACT FROM AUTHOR]

Education in the 21st century faces the challenge of digitalization; therefore, the acquisition and development of digital skills in students is indispensable, not only for their learning processes but also for their lives. This study aims to validate the test "ECODIES", which was used to assess the level of development of digital competence in students in a public high school in Bogotá (Colombia). The test is based on the DigCom model and was administered to a sample of 777 students aged between 11 and 18. The results obtained in the exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and reliability analysis show the quality of the test. Therefore, in this study it is concluded that "ECODIES" is a test with the reliability and validity to assess digital competence in the Colombian context; in this way, we hope to gain enough research about this topic to contribute to the development of digital competence in Colombian students. We conducted an instrumental study for the analysis of the psychometric properties of the questionnaire. [ABSTRACT FROM AUTHOR]

This research aimed to identify the effect of immediate and delayed feedback in virtual classrooms on mathematics students' higher-order thinking skills. To achieve the objective of the research, the experimental method was used. The research sample consisted of students from Mathematics Department, College of Science and Arts, Najran University in the course of Computer in Education. Fifty students were selected and distributed into two equal experimental groups randomly. The first experimental group studied the (Computer in Education) course through virtual classrooms using immediate feedback while the second experimental group studied through virtual classes using delayed feedback. The higher-order thinking skills test was used as the study instrument to collect data. The results showed that there were statistically significant differences between the mean scores of the participants in the two groups (the first and second experimental groups) in favor of the second experimental group. This indicates the effect of the delayed feedback on enhancing students' higherorder thinking skills. Therefore, this result may contribute to the study and practice of some forms of interaction and its impact on different learning outcomes in the context of virtual classrooms during the emerging corona pandemic and the future. In light of the current result, the researchers recommended enhancing the skills of faculty members to use immediate feedback in virtual classrooms, through targeted short training sessions. Also, they should be trained in using other methods of interaction to develop students' higher-order thinking skills and measure the extent of their impact. [ABSTRACT FROM AUTHOR]

This descriptive study sought to determine the least mastered topics in Mathematics in the Modern World (MMW) course and describe the students' perception of new normal mathematics learning. It was conducted in a State University in the Western Visayas region in the Philippines with 77 freshmen college students as participants. Researcher-made test and asynchronous focus group discussion guide were used as instruments of the study which were analyzed through frequency count, percentage, and bar graph for quantitative data and thematic analysis for qualitative data. Results revealed that the least mastered topics of freshmen college students in MMW were statistics concepts, problem solving, and logic. In addition, students' perceptions of new normal mathematics learning include difficult and challenging; willingness to learn despite the crisis; interesting and exciting mathematics in the new normal; and positive attitude towards mathematics learning. Hence, higher educational institutions might explore possibilities of curricular innovations, technology integration in mathematics instruction, pedagogical retooling for teachers, and recalibration of instructional materials to respond to the demands of the new normal or the next normal education. The least mastered topics may inform teachers handling MMW in Philippine Higher Education Institutions (HEI's) to design ways on how to make these concepts more comprehensive and easier to understand by freshmen students. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem about calculating the volume of a solid of revolution. Representational fluency was used as a lens to analyze the conceptions of the students. Results indicated that the students imagined certain aspects of one main summation conception of the definite integral at different times in calculating the volume of the solid. They also used the conceptions of function matching and perimeter and area/boundary and volume. The students were comfortable explaining what they were doing in the solution if their conceptions of the definite integral allowed them to understand integral notation and build representational fluency. Implications based on the different conceptions that the students used and the representational fluency that they developed were discussed. [ABSTRACT FROM AUTHOR]

This study aims to examine mathematics teachers' interpretations of students' thinking within the scope of teaching experiments as a professional development activity. The method used in this study is a teaching experiment. The participants are 3 elementary school mathematics teachers. The teaching experiment consists of 5 teaching episodes and clinical interviews in each episode. The study was conducted in 15 weeks. The data collection tools consist of student solution sheets, written opinion forms, and video recordings of interviews and observation notes taken in clinical interviews after the application. Conceptual analysis of the data obtained from the teaching experiment was conducted as retrospective and prospective analysis. The results show that teachers developed the interpretation level of students' thinking by not only describing/commenting on students' solutions but also making appropriate comments on students' solutions in the process of teaching experiments. Considering that teachers can structure the content of their courses and classroom interaction based on students' different ways of thinking, it is believed that this study will provide foresight for future studies. [ABSTRACT FROM AUTHOR]

This guided discovery project provides high school math students an opportunity to solve a real-world problem by applying tools they have learned in geometry and, optionally, calculus. The task is to determine the volume, surface area, and other properties of a certain form of folded paper container, such as those used by Wendy's for sour cream. Students first construct the containers, and then are challenged to find a geometric way to determine the volume of these objects, which do not fit conventional volume formulas. They next find surface area and, optionally, angles of the container. In the process, 2- and 3-dimensional visualization skills are exercised. Calculus students are asked to find the volume by the method of slabs, and subsequently to determine the dimensions that optimize the surface-to-volume ratio. Several additional extensions are suggested, and core curriculum standards are listed. Diagrams and calculations are provided. While much support material is provided, it is hoped that the teacher will encourage students to explore, discover and invent as much as possible on their own. [ABSTRACT FROM AUTHOR]

The aim of this study is to measure the effects of teaching problem-solving strategies as an integrated part of the mathematical content prescribed by the curriculum. By implementing the designs principles developed in the previous study, we carry out a one-year-long teaching intervention in a Swedish upper secondary school. Pre- and post-tests are used to compare the development of the experimental group with a control group. The results show that the development in mathematical knowledge in general is similar for the experimental group and the control group. However, the experimental group has a significantly better development in problem-solving ability. This study presents relevant implications to practitioners and other educational designers on how to enhance problem-solving ability by focusing on teaching problems-solving strategies integrated throughout the curriculum. [ABSTRACT FROM AUTHOR]

During 46 lessons in Euclidean geometry, sixth-grade students (ages 11, 12) were initiated in the mathematical practice of inquiry. Teachers supported inquiry by soliciting student questions and orienting students to related mathematical habits-of-mind such as generalizing, developing relations, and seeking invariants in light of change, to sustain investigations of their questions. When earlier and later phases of instruction were compared, student questions reflected an increasing disposition to seek generalization and to explore mathematical relations, forms of thinking valued by the discipline. Less prevalent were questions directed toward search for invariants in light of change. But when they were posed, questions about change tended to be oriented toward generalizing and establishing relations among mathematical objects and properties. As instruction proceeded, students developed an aesthetic that emphasized the value of questions oriented toward the collective pursuit of knowledge. Post-instructional interviews revealed that students experienced the forms of inquiry and investigation cultivated in the classroom as self-expressive. [ABSTRACT FROM AUTHOR]

Abstract: Usually the first course in mathematics is calculus. It''s a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the prior fear of mathematics. The students today can’t live without using computer technology. The uses of computer for teaching and learning can transform the boring traditional methodology of teach to more active and attractive method. In this paper, we will show how we can use Excel in teaching calculus to improve our students’ learning and understanding through different types of applications ranging from Business to Engineering. The effectiveness of the proposed methodology was tested on a random sample of 45 students from different majors over a period of two semesters. [Copyright &y& Elsevier]

The article focuses on the response by students to mathematical modeling, which is an important part of advanced mathematics courses. It says that 302 mathematics students took part in the investigation, where they were asked to work on pairs in finding solution to knot problems. It also states that the responses of the students to the problems were categorized as no logic, scaling with lengths, and volume approach.