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We were interested in exploring the extent to which advanced mathematics lecturers provide students with opportunities to play a role in considering or generating course content. To do this, we examined the questioning practices of 11 lecturers who taught advanced mathematics courses at the university level. Because we are unaware of other studies examining advanced mathematics lecturers’ questioning, we first analyzed the data using an open coding scheme to categorize the types of content lecturers solicited and the opportunities they provided students to participate in generating course content. In a second round of analysis, we examined the extent to which lecturers provide students with opportunities to generate mathematical contributions and to engage in reasoning that researchers have identified as important in advanced mathematics. Our findings highlight that, although lecturers asked many questions, lecturers did not provide substantial opportunities for students to participate in generating mathematical content and reasoning. Additionally, we provide several examples of lecturers providing students with some opportunities to generate important contributions. We conclude by providing implications and areas for future research. [ABSTRACT FROM AUTHOR]

This work shows the scope of concept maps in university students' learning by identifying the aspects and connections that arise in concept maps on different topics in mathematical education. It is part of a project that implements various methodologies at this level. This qualitative study considers teacher training students of an obligatory course in a Chilean university. The students produced concept maps on the notions of didactics, mathematics, and lesson design, and explained the reasons for the designs. The analysis considers three aspects: hierarchical organization, progressive differentiation, and integrative reconciliation. The results show a progression in the learning and processing of different classroomrelated concepts, changes in the location of key concepts in teacher training, and an integration of new concepts, which becomes more explicit in the last maps created. [ABSTRACT FROM AUTHOR]

In this mixed method study we investigate the impact of recorded lectures on passing rates in an online math course. For three years, we collected data from approximately 380 students enrolled in a first-year undergraduate online course, College Algebra. The data was used to compare the amount of time students spent watching recorded lectures and their final grades. The study reveals that students who watched more than half of the lectures were able to pass the course, and those who watched less than half of the lectures almost always did not pass the course. In this paper, we present the data and show the results. We also analyze the qualitative data and show the effects the recorded lectures had on student learning. [ABSTRACT FROM AUTHOR]

The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning. [ABSTRACT FROM AUTHOR]

Cognitive interviewing (CI) provides a method of systematically collecting validity evidence of response processes for questionnaire items. CI involves a range of techniques for prompting individuals to verbalise their responses to items. One such technique is concurrent verbalisation, as developed in Think Aloud Protocol (TAP). This article investigates the value of the technique for validating questionnaire items administered to young people in international surveys. To date, the literature on TAP has focused on allaying concerns aboutreactivity– whether response processes are affected by thinking aloud. This article investigates another concern, namely the completeness of concurrent verbalisations – the extent to which respondents verbalise their response processes. An independent, exploratory validation of the PISA assessment of student self-efficacy in mathematics by a small international team of researchers using CI with concurrent verbalisation in four education systems (England, Estonia, Hong Kong, and the Netherlands) provided the basis for this investigation. The researchers found that students generally thought aloud in response to each of the items, thereby providing validity evidence of responses processes varying within and between the education systems, but that practical steps could be taken to increase the completeness of concurrent verbalisations in future validations. [ABSTRACT FROM AUTHOR]

This in practice paper describes the experience of seven lecturers in a hybrid and flipped version of an introductory mathematics course for higher education. In a Mexican university, lecturers adapted to this innovation supported by an adjusted Massive Open Online Course. The experience revealed the relevance of leaving conventional assessment processes to make way for an understanding of lecturers as a collaborative team, trying to transform their own perspective about the learning of mathematics. This experience is an example of the reconceptualisation of the teaching of STEM education that contributes towards a non-formal educational context, promoting lecturers' education and dialogic transformative learning. [ABSTRACT FROM AUTHOR]

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos. [ABSTRACT FROM PUBLISHER]

Fostering students at the beginning of university studies is an important issue not only in the international context but also in Chile. However, high dropout rates show that the transition from secondary school to university in mathematics is supposed to be difficult for many students. Mathematical argumentation is a core activity in mathematics and also very complex. Therefore it could be one of the main reasons for the difficulty at the secondary-tertiary transition in mathematics. This study analyzes the quality of students' argumentations, the proof scheme, and the formalism in students' answers of N = 86 first-year students in mathematics in order to better understand where the problems are in detail. The results show that the quality of argumentation, the use of appropriate arguments, and mathematical formalism highly varies in the two reported tasks: on the one side, 10% of students are able to prove one of the given geometrical theorems, on the other, 65% proved the other theorem correctly. This indicates that students are in a phase of developing their argumentative abilities. Consequently, the process of proving and constructing analytical arguments should be explicitly discussed in university lectures, so that students can improve their abilities for mathematical reasoning. [ABSTRACT FROM AUTHOR]

This article presents some of the results from one master's thesis. We intend to analyze how the curricular organization influences production of meanings that high school math teachers attribute in a proposal based in the critical mathematics education (CME). Teachers engaged in the development, implementation and evaluation of a hypothetical trajectory learning (HTL) of statistical measures. This is a strictly qualitative nature study. From the empirical material, we infer that the teachers gave some meanings to the developed proposal: a strange activity, that bothers, that generates anxiety, which stresses, that needs a lot of knowledge to be accomplished. The demand of the curricular organization, as well as teacher training, is taken as important factor in the attribution of these meanings. [ABSTRACT FROM AUTHOR]

In this article we aim to explain some methodological aspects of the original notions of the Study and Research Path (PER), which the first two authors adapted as part of their thesis research methodology. The theoretical discussions are those that appear in the original texts, in the French language, of which we translate some sections. The theoretical notions of didactic devices of Guided Personal Work, Study and Research Activities and Study and Research Path guide the textual body of the article. we present the methodological adaptations of the PER that led the researches of the two doctoral theses. The conclusions indicated that the methodology of the PER, with the appropriate adaptations, allows an initial and continuous formation process of teachers of mathematics intermediated by the pedagogy of questioning, as predicted by this didactic and methodological device. [ABSTRACT FROM AUTHOR]

As we studied how trainers in Mathematics Degree courses constitute their own professional identity, we faced another question: what factors were / are essential to the construction of the professional identity of teacher educators in Mathematics Degree courses? The subject is formed a professor by experiencing and internalizing different learning, in different environments and different times. Thus, we analyzed socialization processes experienced by teacher trainers from a Mathematics Degree course. Five teachers were interviewed through a qualitative approach. We noted that such a professional is formed through family issues, experiences that took place during elementary education, higher education, in the professional field, among others. [ABSTRACT FROM AUTHOR]

The present work presents a part of a research developed in the Theory and Pedagogical Practice classes of the Mathematics Degree course of the State University of Maringá - UEM, in order to verify: a) what has been the contribution of these disciplines in the process of knowledge construction Teachers and in the development of a more communicative and reflexive pedagogical practice in the classroom. Taking into account the issues established for this study we developed a qualitative research focusing aspects of discourse analysis. The observation and analysis of these practices shows that the predominance of teacher discourse often does not allow moments and / or activities that allow students to rethink about a more communicative and reflexive pedagogical practice to be developed in the classroom. [ABSTRACT FROM AUTHOR]

In this article we present an investigation about the perception of the students that study in the Bachelor of Mathematics at the Eduardo Mondlane University, in Mozambique, about the willing to be a Mathematics teacher. The methodology is part of the qualitative approach and the instrument of the production of the information was a questionnaire composed by essay questions. The corpus of the research was examined by the Discourse Textual Analysis method, which is allowed showing affinity with the mathematics from the high school as a factor that boosted the pleasure of the subject mentioned above and about the desire to learn and teach as a way to share knowledge and contribute with the mathematics formation. [ABSTRACT FROM AUTHOR]

This article presents a study performed for the graduation task of the course of Mathematics in the University of Santa Cruz do Sul and aims to study how learning is acheved at different levels of education in relation to the daily calculations present in their contexts: from subjects who attended school for a short period to those with complete basic education. The study is based on qualitative research, application of questionnaires and problematization of a practical situation with the participants, taking in consideration methods such as case study. From this study one may observe that the people dominate the mathematical contents that are necessary to them, besides that this learning is a construction from the social coexistence. [ABSTRACT FROM AUTHOR]

This paper presents the effects of a cognitive acceleration program in mathematics classes on Tongan students' achievements, motivation and self-regulation. Cognitive Acceleration in Mathematics Education (CAME) is a program developed at King's College and implemented worldwide with the aim of improving students' thinking skills, mathematics performance and attitudes. The first author adapted the program materials to Tongan educational context and provided support to participating teachers for 8 months. This study employed a quasi-experimental design with 219 Year 8 students as the experimental group and 119 Year 8 students as the comparison group. There were a significant differences in the mean scores between the pre-test and post-test of the three instruments that were employed in the study, indicating that learning mathematics under the CAME program had a positive effect on levels of students' self-regulation, motivation and mathematics achievement. Students also reported changes to the ways they learn mathematics. [ABSTRACT FROM AUTHOR]

The mathematics education literature shows that encouraging students to develop multiple solutions for given problems has a positive effect on students’ understanding and creativity. In this paper, we present an example of multiple-solution problems in statistics involving a set of non-traditional dice. In particular, we consider the exact probability mass distribution for the sum of face values. Four different ways of solving the problem are discussed. The solutions span various basic concepts in different mathematical disciplines (sample space in probability theory, the probability generating function in statistics, integer partition in basic combinatorics and individual risk model in actuarial science) and thus promotes upper undergraduate students’ awareness of knowledge connections between their courses. All solutions of the example are implemented using the R statistical software package. [ABSTRACT FROM PUBLISHER]

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A survey was done focusing on students’ struggle to pass a course in analogue electronics by introducing a top-down perspective and the revised taxonomy of Bloom. From a top-down perspective you can create learning environments from any spot in the taxonomy using a step-by-step approach of the verbsunderstandandapply.Three textbooks with a top-down perspective on analogue electronics are analysed on the concept of amplifying with a transistor circuit. The study claims issues when losing the top-down perspective to present concepts and procedures of the content to be learned. [ABSTRACT FROM PUBLISHER]

This article details an initial analysis of the transition of a second level curriculumreform to higher education in Ireland. The reform entitled 'Project Maths' involved changes to what second level students learn in mathematics, how they learn it, and how they are assessed. Changes were rolled out nationally on a phased basis in September 2010. Students who were taught and assessed through the new curriculum first entered third level education in September 2012. It is important that third level mathematics lecturers are aware of the changes to the curriculum since certain topics such as vectors and matrices are no longer taught at second level.Hence, third level coursesmay need to be adapted accordingly. This study investigates mathematics lecturers' awareness of Project Maths and whether they have made any adaptions to their course content, teaching and assessment approaches as a result of the new curriculum being introduced. The findings, from a return rate of 23% of eligible respondents, show that although many lecturers are mindful of the concept of ProjectMaths, they are not aware of the changes in full and how it affects their own course content, teaching and assessment strategies. Accordingly, the gap between second and third level education remains.This study highlights that more needs to be done to ensure there is coherent and uniform approaches to the teaching, learning and assessment ofmathematics in the transition from second to third level education. [ABSTRACT FROM AUTHOR]

This study investigated how 38 secondary mathematics prospective teachers modified textbook tasks for convergent and divergent thinking while learning to teach mathematics during university coursework. The coursework focused prospective teachers' attention on their analyses of textbook tasks in terms of potential affordances and constraints for creativity education and implementation of textbook task modification and micro-teaching. Prospective teachers were asked to consider studies from general perspectives on creativity education, studies on enhancing creativity by increasing or maintaining levels of cognitive demands in tasks, and studies about encouraging creativity thinking by facing and dealing with ambiguity or pathologies and misconceptions when modifying textbook tasks and micro-teaching. Findings indicated that prospective teachers had different types of textbook task modification for creativity education that fell into four categories: no meaningful change, blind variability, orthodoxy, and creativity. In addition, prospective teachers actively linked theory and practice centered on textbook tasks and textbook task modification for creativity education and the citations to which they referred varied according to the task quadrant into which their textbook task modification was categorized. [ABSTRACT FROM AUTHOR]

In our study, we examine the factors influencing the implementation of a mathematics coaching initiative at four high schools including the assets an instructional coach brings to the position and the challenges unique to each school. In our case study we include data collected in individual interviews with instructional coaches, focus groups with Algebra I teams, and coaching logs. Four models of coaching behavior emerged from the data collected in the study: coach as facilitator, coach as mediator, coach as dictator, and coach as victim. No role was associated exclusively with any particular instructional coach. However, which role the coach assumed hinged on one or more factors: the coach’s leadership style, the context in which the coach served, and the dynamics of the situation. [ABSTRACT FROM AUTHOR]

The ability to interpret graphs is highly important in modern society, but has proven to be a challenge for many people. In this paper, two teaching methods were used to remediate one specific misinterpretation: the area misinterpretation of box plots. First, we used refutational text to explicitly state and invalidate the area misinterpretation of box plots. Second, we used multiple external representations (MERs): Histograms were used as an overlay on box plots in order to give students a better insight in the way box plots represent data distributions. Third, we combined refutational text and MERs. We found that refutational text was successful in improving students’ interpretation of box plots, but that the use of MERs did not improve students’ interpretation of box plots. The addition of MERs also did not increase the effect of refutational text. [ABSTRACT FROM PUBLISHER]

The present research, of qualitative nature, aims to identify how the curricula of mathematics undergraduate courses in Brazil contemplate the teaching of hyperbolic geometry. In addition, we try to make a parallel between these curricula and the curricular proposals of basic education about the teaching of the non-Euclidean geometries. In this sense, they were analyzed the curricular proposals of thirty-five courses and as the curricular guidelines of the states in which such courses are allocated. The results show that hyperbolic geometry does not yet have the same space occupied by Euclidean geometry in both higher education and basic education. Despite the possibility of the utilization of dynamic geometry softwares in the teaching of non- Euclidean geometries, no references were found to the use of this tool in the analyzed curricula. [ABSTRACT FROM AUTHOR]

Previous studies have produced several typologies of teacher questions in mathematics. Probing questions that ask students to explain are often included in the types of questions. However, only rare studies have created subtypes for probing questions or investigated how questioning differs depending on whether technology is used or not. The aims of this study are to elaborate on different ways of asking students to give explanations in inquiry-based mathematics teaching and to investigate whether questioning in GeoGebra lessons differs from questioning in other lessons. Data was collected by video recording 29 Finnish mathematics student teachers’ lessons in secondary and upper secondary schools. The lesson videos were coded for the student teachers’ probing questions. After this, categories for the types of probing questions were created, which is elaborated in this paper. It was found that the student teachers who used GeoGebra emphasized conceptual probing questions during the explore phase of a lesson slightly more than the other student teachers. [ABSTRACT FROM AUTHOR]

The notion of flow of a proof encapsulates mathematical, didactical, and contextual aspects of proof presentation. A proof may have different flows, depending on the lecturer's choices regarding its presentation. Adopting Perelman's New Rhetoric (PNR) as a theoretical framework, we designed methods to assess aspects of the flow of a proof. We present a case study from a Number Theory class at the beginning undergraduate level, focusing on an intervention concerning one lesson given in two consecutive years. The intervention consisted of a discussion with the lecturer about findings from Year-1 and potential changes in the flow of the proof before the Year-2 lesson. We analyze two aspects of the flow of the proof: the scope and organization of the argumentation and the presence (in the PNR sense) of different elements. Our analysis revealed that the intervention caused global and local changes in the flow and that PNR enables us to capture these changes. [ABSTRACT FROM AUTHOR]

Two sections of a college discrete mathematics class were taught using cooperative learning techniques throughout the semester. The 33 students attending these sections were randomly assigned into groups of three. Their final examination consisted of an individual and group blended examination where students worked in their groups and discussed questions, but each student had a different version of the examination and their own questions to answer. Afterwards, students were given a questionnaire and one group from each section was interviewed to see how they rated blended assessment. The majority of students preferred the blended examination over an individual examination, however not every student felt this way. One benefit of the blended examination was being able to verbalize test questions, which led to a better understanding of them. Concerns about the blended examination such as time, fairness, and difficulty concentrating were raised. [ABSTRACT FROM AUTHOR]

It is presented the analysis the developed the mathematical arguments in a group of students, interacting with a didactic sequence about the inappropriate integral. The study was motivated by the detected difficulties in the students in the use of the concept of inappropriate integral in the solution of typical problems of its career. It was designed and put into practice a didactic sequence with students that studied the second semester of Industrial Engineering in the Superior Technological Institute of Tantoyuca, Veracruz. It was used the ACODESA Methodology from HITT y GONZÁLEZ-MARTÍN (2015) for its development and in the study of the data, was used the argumentative pattern, TOULMIN, (1958), which allowed to describe the construction, content and structure of the arguments of the students in spontaneous representations of the verbal and visual type, and that it favors the transition to the algebraic, graph and numeric representations during its solution, what was carried out using a technological atmosphere. The integration of these three elements (ACODESA methodology, the Toulmin pattern and the technological atmosphere, specifically the Geogebra software) in a cooperative learning, where the scientific debate conjugated with a technological atmosphere it is sustained as main hypothesis of the work the formation of mathematical arguments in the students, with emphasis in those that refer to the inappropriate integral. [ABSTRACT FROM AUTHOR]

A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the “complex precalculus” part of the course. In June 2014, a faculty group started developing a variant of the “transition to higher mathematics” course in which the complex numbers play a central role. The new textbook and syllabus would support variations of the course, depending on instructors and students. This paper presents the outline of the course, a rationale for its potential value to mathematics programs, a description of how goals for the transition course would be met by the proposed course, and some key topics described with some detail. [ABSTRACT FROM AUTHOR]

Educational modules can play an important part in revitalizing the teaching and learning of complex analysis. At the Westmont College workshop on the subject in June 2014, time was spent generating ideas and creating structures for module proposals. Sharing some of those ideas and giving a few example modules is the main purpose of this paper. The author has started to constructMathematica-based educational modules for complex analysis, one of which is available in the online repository of supplemental materials for this article. The author has also begun work on a website calledThe Complex Moduli Projectto make modules in complex analysis available worldwide, and invites others to join him in this endeavor. [ABSTRACT FROM AUTHOR]