Mathematics Computing Environment on the Web

The 2014 World Health Organization guidelines for human immunodeficiency virus postexposure prophylaxis (PEP) are the first to combine recommendations for all populations and exposures. To inform the development of these guidelines, we gathered views of end users on key aspects of PEP provision. A mixed-methods approach was used to gather views from the populations for whom the guideline will be of relevance. Data gathered from an online survey, focus group discussions, and previously collected data from in-depth interviews with key populations were used to inform the development of recommendations, in particular where there is a paucity of evidence to assess the benefits and harms of an intervention. This was a successful method to gather end users' views and preferences; however, limitations exist in the generalizability and reliability of the evidence. Future guideline development processes should consider methods to include the views of end users to guide the decision-making process.

This study analyzes the mathematical knowledge of 40 pre-service Chilean Early Childhood and Primary Education teachers when designing mathematical tasks on patterns, in the context of teaching early algebra. Based on the domains of the Mathematical Knowledge for Teaching (MKT) model, we have adopted a descriptive qualitative methodological approach that relies on the content analysis technique. The results show that pre-service teachers exhibit little mathematical knowledge in the description of the mathematical tasks they pose, addressing partial aspects of the subdomains of specialized content knowledge and knowledge of content and teaching. We conclude that training experiences should be given that allow students to further their acquisition of mathematical knowledge in order to achieve effective learning of the contents that early algebra promotes, such as patterns, in Early Childhood and Primary Education classrooms.

A primary virtue of a communications system is transparency of the transport network to the person using the system. The layered structure of SNA provides for the separation of the transport network, called path control, from higher level functions involving the end users of the network. This paper describes the structure of the path control layer of SNA, focusing on connectivity, routing, and flow control. The end user's view of these architectural concepts is presented, as well as a discussion of the underlying formats and protocols.

This review is based for the most part on conference proceedings. It begins with a look at recent developments in interlending in Australasia, with a comparison of interlending statistics, and papers from a resource‐sharing conference in New Zealand reporting Australian and New Zealand interlending practice. Unresolved attempts to define an interlending plan for Australia are discussed together with the present situation. Two delegates' papers at a conference in Western Australia report contrasting developments there. Turning to the UK, four papers from an interlending conference consider the current UK situation, financial aspects, the end user's view and future development of interlending. Finally, a world‐wide collection of ‘proceedings’ is reviewed, dealing with different interlending systems in the UK, FRG, GDR, USA, Netherlands, Denmark, Sweden, China and the European Communities' DOCDEL project, with particular reference to Patent information in Germany and the TRANSDOC project in France.

This study aims to identify the level of technological pedagogical content knowledge (TPCK) of mathematics trainee teachers at Universiti Pendidikan Sultan Idris (UPSI) and explore their teaching practices during practical training at school. The study was conducted in two phases using a mix-method research. In the first phase, a survey method using a questionnaire was carried out on 156 trainee teachers of Bachelor of Mathematics Education (AT14) and Bachelor of Science (Mathematics) with Education (AT48). The instrument used was a questionnaire that measures the level of content knowledge, pedagogy, technology and TPCK of mathematics. Data were analyzed using descriptive statistics, namely the mean. While in the second phase, the interview method involved four trainee teachers were performed. The instrument used was the semi-structured interview protocol to assess the trainee teacher's TPCK integration in their teaching practice. Data were analyzed using the content analysis. The findings showed that the level of knowledge of TPCK among trainee teachers was moderate with overall mean score of 3.60. This level did not show significant differences between the two programs with mean scores of 3.601 for the AT14 group and 3.603 for the AT48 group. However, there was a difference for gender classification such that the female trainees had mean score of 3.58 and male trainees with mean score of 3.72. Although students' TPCK level was moderate, the level of content knowledge (CK), technological knowledge (TK) and pedagogical knowledge (PK), showed a higher level with overall mean scores of 3.75, 3.87 and 3.84 respectively. The findings also showed that in terms of content knowledge, trainee teacher's learning mathematics background was good, but the knowledge of mathematics was limited in the curriculum, philosophy and application aspect. In terms of pedagogical content knowledge, all respondents tend to use lecture and discussion methods in teaching Trigonometry topic in almost the entire teaching and learning sessions. In terms of using technology in teaching and learning process, all respondents were more likely to use PowerPoint presentation as well as assisted by the use of a scientific calculator. The use of PowerPoint was limited in explaining the title and its content and the calculators were used during practice sessions. The four trainee teachers were still at the recognizing and acceptance levels of TPCK integration during their teaching practice. This study indicates that UPSI trainee teachers should be given exposure in the use of information and communication technology and trained to provide alternative teaching strategies in more creative ways if there are obstacles when integrating technology in teaching and learning process.

New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge; knowledge of particulars, language and rhetoric in mathematics. These developments also include a recognition of the philosophical import of the social context of mathematics, and are part of the diminished domination of the field by absolutist philosophies. From an epistemological perspective, all knowledge must have a warrant and it is argued in the paper that tacit knowledge is validated by public performance and demonstration. This enables a parallel to be drawn between the justification of knowledge, and the assessment of learning. An important factor in the warranting of knowledge is the means of communicating it convincingly in written form, i.e., the rhetoric of mathematics. Skemp’s concept of ‘logical understanding’ anticipates the significance of tacit rhetorical knowledge in school mathematics. School mathematics has a range of rhetorical styles, and when one is used appropriately it indicates to the teacher the level of a student’s understanding. The paper highlights the import of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in the area.

The purposes of this study were (1) to explore the relationship between mathematics education and the rural context and (2) to determine the usefulness of a social theory of learning (Wenger, 1998) to account for students' participation in advanced high school mathematics courses. Qualitative methods were used to gather data in a small, rural high school in the Pacific Northwest. Data gathered included a student survey, interviews with students and mathematics teachers, observations in mathematics classes, and documents related to the curriculum, the school, and the community. The findings suggest that high school mathematics education is related to the rural context in two ways. First, the small size produces characteristics unique to rural high schools. Specifically, a small number of mathematics teachers has considerable ability to shape the curriculum, instruction, and students' views of mathematics. The mathematics course offerings reflect a college preparatory curriculum with few mathematics electives offered. Students' experiences are quite similar and their beliefs about the nature and usefulness of mathematics are fairly uniform. Second, mathematics education is related to the socioeconomic aspects of a rural community. Students' knowledge of mathematics that is used in adults' work and daily life comes from experiences with parents and community members. The usefulness of mathematics, and advanced high school mathematics specifically, may not be apparent for students living in communities without mathematics-intensive jobs. Rural high school students studying advanced mathematics are likely exceeding the formal mathematical education level of their parents. The findings also indicated that Wenger's notions of identity and three modes of belonging provided a useful framework for understanding whether or not students participated in advanced mathematics classes. Students' participation in advanced math classes was related to their engagement in the day-to-day practice of mathematics education in the classroom, the place their engagement fit within the broader experiences of life in their imagination, and the alignment of their energies.

Growing awareness of the importance of education in the early years has led professional organizations and policy makers to consider the effectiveness of mathematics education for young children. Factors such as educational environments, early years curricula and teacher education are some of the many aspects that have been examined. This paper describes the types of mathematical content knowledge that 25 prospective primary teachers developed as they designed, taught and reflected upon early number lessons. This Lesson Study approach involved two mathematics educators and 25 prospective primary teachers designing, teaching and re-teaching five early number lessons in two elementary classrooms with 4–5 year old children. The results suggest that effective teaching of early number concepts draws on mathematical knowledge that is specialized and unique to teachers; in other words Specialized Content Knowledge (SCK). The study found that engaging in Lesson Study promoted mathematics SCK development in two primary ways, notable by: (1) raising awareness of the complex relationships between early number concepts that contribute to developing robust early number understandings and (2) developing expertise in identifying the nature and source of children’s mathematical errors. The development of participants’ early number SCK is described and recommendations are made for the design of experiences in Initial Teacher Education (ITE) to support teachers in the provision of high quality mathematics experiences to young learners.

Numeracy entails a facility for communicating mathematical knowledge in diverse contexts. Indeed, large scale standardised assessments have demonstrated that numeracy is associated with both mathematics and language proficiency. And yet, while research in mathematics education in schools has demonstrated the utility of taking a discursive view of mathematics, similar developments in higher education studies are scarce. Moreover, as teaching interventions in numeracy may lead to tensions between mathematical and disciplinary knowledge, the prospect of including language proficiency development is challenging. Taking a discursive multimodal view, this study reports on a pilot teaching intervention that introduced explicit language proficiency development into numeracy teaching activities at a prominent South African university. The study found that the participants produced coherent descriptions of statistics when mathematical concepts were related to vocabulary and grammar. These observations suggest that language proficiency development has the potential to realise the goal of teaching mathematical knowledge within disciplinary curricula.

Although studies of teacher preparation programs have documented positive changes in mathematical knowledge for teaching with preservice teachers in mathematics content courses, this study focused on the impact of a mathematics methods course and follow-up student teaching assignment. The presumption was that preservice teachers would show growth in their mathematical knowledge during methods since the course was structured around active participation in mathematics, research-based pedagogy, and was concurrent with a two-day-per-week field experience in a local elementary school. Survey instruments utilized the computer adaptive test version of the Mathematical Knowledge for Teaching (MKT) measures from the Learning Mathematics for Teaching Project, and the Attitudes and Beliefs (towards mathematics) survey from the Mathematical Education of Elementary Teachers Project. A piecewise growth model analysis was conducted on data collected from 176 participants at 5 time-points (methods, 3 time-points; student teaching, 2 time-points) over a 9 month period. Although the participants' demographics were typical of U.S. undergraduate preservice teachers, findings suggest that initial low-level of mathematical knowledge, and a deep-rooted belief that there is only one way to solve mathematics problems, limited the impact of the methods and student teaching courses. The results from this study indicate that in (a) number sense, there was no significant change during methods (p = .392), but a significant decrease during student teaching (p < .001), and in (b) algebraic thinking, there was a significant decrease during methods (p < .001), but no significant change during student teaching (p = .653). Recommendations include that the minimum teacher preparation program entry requirements for mathematical knowledge be raised and that new teachers participate in continued professional development emphasizing both mathematical content knowledge and reform-based pedagogy to continue to peel away deep-rooted beliefs towards mathematics.

The investigation of research trends in mathematics education in the global landscape has been prominent in the recent years. However, there is a dearth of literature in investigating research trends in mathematics education in the Philippine setting. Thus, this bibliometric analysis on the research in mathematics education in the Philippines from 2013 to 2023 was conducted. This paper aimed to present scientific information about the distribution pattern of research on mathematics education in terms of discipline, the profile of prominent authors, the key subject areas which given emphasis, and the direction of research. A total of 993 articles were obtained from the Scopus database and were analyzed using the VOSviewer software application to see the research trends in mathematics education in the Philippines. Research articles emerged as the predominant document type, followed by conference papers. The pinnacle of mathematics education research in the Philippines was in 2014. Notably, the research trend in the Philippines for the last five years have observable decrease in mathematics education. Results show that in terms of discipline, problem solving, teacher professional development, and curriculum were typically the key areas of emphasis. Moreover, the top author with the greatest number of citations since 2013-2023 is a female researcher from Mindanao. Furthermore, the mathematics subjects that have the most attention are algebra, proof, calculus, technology, geometry, and modeling. Finally, this paper foresees continued growth in mathematics education research in the Philippines, particularly in the realms of professional development and problem-solving.

Space for society: How Eurisy’s activities and research support publicawareness raising on satellite applications in meeting societal needs

probably studies only a small part of the material which is available at his stage of education. Even at an earlier stage, the interpretation of the mathematical curriculum varies from school to school so that even here it is difficult to say precisely what the content is. (For example, what really is expected in basic numeracy? Presumably it includes the ability to divide one positive integer by another but does it include the ability to divide one decimal number by another (non-zero) decimal? And what about I/tn?) It is clear that the union of all mathematics syllabuses is not a workable definition of Mathematics in Education. With the present discussions of core syllabuses, I wish to steer clear of the details of the intersection of syllabuses as they are or as they should be; in any case, the core and the intersection of syllabuses are unlikely to be the same. I shall adopt as my starting point for Mathematics in Education that body of mathematical knowledge which is taught to a pupil up to degree level because it encourages, and hopefully transmits, an understanding of at least some fundamental concepts of mathematics. It indicates not only the applicability of these concepts but it also shows their importance as abstract ideas; the development of the pupil's own mathematical skill is an essential part of this process. If the task of defining the Mathematics in Education (of my title) is difficult, it is nevertheless incomparably easier than the task of defining the Mathematics of Industry. The term is generally understood to go well beyond the mathematics of the engineering industry and takes in the mathematics of commerce. Probably the mathematics of administration and nursing should be included. It is possible that the term really means the Mathematics of Work, but this then includes the mathematics of catering which is related to the mathematics of cooking which is related to the mathematics of running a home which includes how to protect yourself against those with calculators in their hands. The whole subject seems amorphous. This does not mean that attempts have not been made to discover what mathematical skills and knowledge are used in particular sections of industry and commerce; in the last io years significant progress has been made in this direction. A stumbling block in the search has been the belief, by many responsible for industrial and commercial processes, that mathematics is not used at all. (A number of years ago, when the Oxford undergraduate syllabus in mathematics was being thoroughly revised, I asked in a large industrial firm what topics the faculty should consider including; the reply was that it did not greatly matter as long as Bessel functions were there.)

This study arose from a desire to investigate initial teacher education for primary school mathematics teachers in Hong Kong. A conceptual framework for analyzing pre-service teachers’ mathematical knowledge and beliefs informed this qualitative investigation. The purpose of the study was to scrutinize both the cognitive and affective domains in mathematics teaching of pre-service primary teachers within the analytical framework. This paper seeks to capture three cases of Hong Kong pre-service primary teachers holding different views about mathematics teaching and learning as revealed by a beliefs survey. Their mathematical knowledge was examined along with a questionnaire, individual interviews, and an analysis of the lesson plans they provided. Through triangulation, it was found that these pre-service teachers’ beliefs about mathematics teaching and learning correspond to their pedagogical content knowledge to some extent. The results of lesson plan analysis were mostly consistent with those in the questionnaire and interviews although some of the interview data were inconsistent with the questionnaire results. Such inconsistency seemed to suggest that pre-service teachers’ reform-oriented mathematical beliefs were impacted by some traditional values such as Confucianism. Implications are discussed regarding the relationship between knowledge and beliefs in mathematics education as well as the theory of teacher competencies.

There has been substantial research undertaken on the integration of computational thinking (CT) in K-12 mathematics education in recent years, particularly since 2018 when relevant systematic reviews were conducted on the topic. Many empirical studies in this area have yet to elaborate clearly and explicitly on how CT may support mathematics learning, or otherwise, in CT-based mathematics activities. Addressing this research gap, we conducted a systematic review on the integration of CT in K-12 mathematics education with a focus on CT-based mathematics instruction and students learning under such instruction. The Web of Science database was searched for in terms of studies published from 2006 to 2021, from which 24 articles were selected to provide illustrations of CT-based mathematics instruction and related student learning, and they were further analyzed according to education levels and contexts, programming tools, learning outcomes in CT and mathematics, and the mutual relationship between CT and mathematics learning. Among the results, this review found that geometrized programming and student-centered instructional approaches were facilitators of productive learning in CT and mathematics. Moreover, CT-based mathematics learning entails an interactive and cyclical process of reasoning mathematically and reasoning computationally, which can occur when: (1) applying mathematics to construct CT artefacts; (2) applying mathematics to anticipate and interpret CT outputs; and (3) generating new mathematical knowledge in parallel with the development of CT. The findings contribute to an in-depth understanding of what, and how, CT-based mathematics instruction impacts student learning in K-12 contexts.