La enseñanza del álgebra en la escuela secundaria argentina desde una perspectiva traspositiva

This study investigated the Effect of Metacognitive Self-Assessment Strategy on Performance in Algebra among Senior Secondary School Students, Dutsin-Ma Education Zone, Katsina State, Nigeria. The study was guided by two research questions and two hypotheses. A quasi-experimental research design involving two groups (experimental and control) was used. The study population comprised three thousand six hundred and ninety-one (3691) senior secondary school two (SSS 2) students of the public secondary schools in Dutsin-Ma Education Zone of Katsina State. Two (2) coeducational schools were selected using simple random sampling technique. Two intact classes were also selected using the simple random sampling from the SSS 2 arm from which 102 students participated as sample for the study with 77 males and 25 females. An instrument: Algebra Performance Test (APT) with a reliability coefficient of 0.82 was used for data collection. The research questions were answered using descriptive statistics of mean and standard deviation while the corresponding research hypotheses were tested using inferential statistics of t-test at ρ ≤ 0.05 level of significance. It was found from the results that there was a significant difference between the performance of the experimental and control groups in favour of the experimental group who were exposed to the Metacognitive Self-Assessment Strategy, but no significant difference in the performance of male and female students when exposed to Metacognitive Self-Assessment Strategy. The study therefore concluded that the Metacognitive Self-Assessment Strategy is effective in the teaching and learning of algebra in senior secondary schools and it is a gender friendly teaching method. Based on the findings it was recommended among others that Teachers should employ metacognitive self-assessment strategy in the teaching of algebra in secondary schools to enhance students’ academic performance.

Both international examination results and scientific evidence related to the teaching and learning of school algebra point to the necessity for analyzing mathematical practice in the classroom. In this context, we have formulated the research objective of characterizing the mathematical work that teachers favor based on the examples that they implement in the teaching of topics within the domain of secondary school algebra. To this end, this study is situated within the interpretive paradigm utilizing an instrumental collective case study approach. The study design entails the selection of two representative cases of mathematics teachers in Chilean schools, with the objective of understanding and describing their mathematical work in the secondary school classroom based on the examples they present. The results show that the first teacher utilizes varied examples that activate distinct forms of mathematical thinking, promoting the activation of both instrumental and discursive genesis. In contrast, the second teacher follows a more traditional approach, with the use of examples to illustrate and motivate, and a direct presentation of knowledge, activating primarily semiotic genesis, in which a transition between the numerical and the algebraic is lacking. Ultimately, the results highlight the importance of deeper consideration of the choice of examples in the teaching of algebra and how these examples can influence students’ learning. Furthermore, additional ideas are put forward for future work in this line of research associated with the use of examples in the classroom.

Contents: C. Kieran, S. Wagner, The Research Agenda Conference on Algebra: Background and Issues. Part I:Past Research and Current Issues. J.A. Thorpe, Algebra: What Should We Teach and How Should We Teach It? J.R. Leitzel, Critical Considerations for the Future of Algebra Instruction. C. Kieran, The Early Learning of Algebra: A Structural Perspective. L.R. Booth, A Question of Structure. N. Herscovics, Cognitive Obstacles Encountered in the Learning of Algebra. D. Tall, Different Cognitive Obstacles in a Technological Paradigm. S. Chaiklin, Cognitive Studies of Algebra Problem Solving and Learning. R.B. Davis, Three Ways of Improving Cognitive Studies in Algebra. J.H. Larkin, Robust Performance in Algebra: The Role of the Problem Representation. P.W. Thompson, Artificial Intelligence, Advanced Technology, and Learning and Teaching Algebra. M.W. Lewis, Intelligent Tutoring Systems: First Steps and Future Directions. J.J. Kaput, Linking Representations in the Symbol Systems of Algebra. D. Kirshner, Critical Issues in Current Representation System Theory. J.T. Fey, School Algebra for the Year 2000. S.L. Senk, Toward School Algebra in the Year 2000. Part II:A Research Agenda. S. Wagner, C. Kieran, An Agenda for Research on the Learning and Teaching of Algebra. L.R. Booth, The Research Agenda in Algebra: A Mathematics Education Perspective. M.W. Lewis, The Research Agenda in Algebra: A Cognitive Science Perspective. S.L. Rachlin, The Research Agenda in Algebra: A Curriculum Development Perspective. Part III:Theoretical Considerations. R.B. Davis, Research Studies in How Humans Think About Algebra. J.H. Larkin, Eight Reasons for Explicit Theories in Mathematics Education. D. Wheeler, Contexts for Research on the Teaching and Learning of Algebra.

Curricular policy documents generally communicate guidelines regarding the teaching of algebra. Those policy documents may not represent what teachers, currently teaching mathematics, consider significant. Teachers' views are more likely to provide information about what they emphasise in their mathematics classrooms. This paper reports on practising Teachers' beliefs about what is important in the teaching of algebra. Data were collected from 306 practising mathematics teachers, who were registered in an Algebra module in an Advanced Certificate in Education (ACE) programme. The teachers were asked to discuss and list aspects in school algebra that they considered to be important. Qualitative analysis methods were used to code the Teachers' responses according to categories that were subsequently grouped into larger themes. The emergent themes were considered in light of curriculum documents to better understand the Teachers' negotiated views about important aspects in the teaching and learning of algebra. While many of their responses reflected aspects of algebra that have been identified both internationally and historically, a number of responses included aspects that are not part of the algebra curriculum. In general, the Teachers' comments emphasized the basic procedures in algebra (i.e., symbolic manipulations) rather than the key concepts in algebra or the general processes associated with doing algebra (e.g., reasoning or representing ideas algebraically).

In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides these three stages of expressing algebraic ideas, there are four more conceptual stages which have happened along side of these changes in expressions. These stages are the geometric stage, where most of the concepts of algebra are geometric ones; the static equation-solving stage, where the goal is to find numbers satisfying certain relationships; the dynamic function stage, where motion seems to be an underlying idea, and finally, the abstract stage, where mathematical structure plays the central role. The stages of algebra are, of course not entirely disjoint from one another; there is always some overlap. We discuss here high points of the development of these stages and reflect on the use of these historical stages in the teaching of algebra.

This research explored the implementation of Queensland's Education and Training Reform from the perspective of teachers and administrators in one rural Secondary School. Within the context of educational reform and vocational education, the specific aims were to explore how teachers and administrators responded to a changing educational environment, and catered for a broader range of students in Senior Schooling. Four research questions were generated from a review of the literature. These were: (1) What leadership is in practice in the implementation of the ETRF? (2) What are the perspectives of the teachers and school leaders with regards to how the ETRF was implemented in the school? (3) How do teachers change as a consequence of the Education and Training Reform? (4) How does the Education and Training Reform influence teacher pedagogy? The overarching question that guided this study was: 'How do administrators and teachers respond to and implement current educational reforms?' Case study methodology was utilised as it allowed for detailed exploration of lived experiences of the participants in relation to their educational context. Fifty-eight teaching staff (full time and part time) were invited to participate in the study. Twenty four of these staff responded to a survey. Seven staff were selected for in-depth interviews. This group consisted of the principal, two heads of departments and four teachers. The teachers and heads of department represented 'vocational education' and 'academic education'. These participants were interviewed in a semi-structured format at the beginning of the year and an informal format at the end of the year. In addition, at the conclusion of the study, four staff participated in a focus group interview. The study concluded that the successful implementation of new reforms is complex, long term and must be inclusive of all participants.;Some teachers resist change and engaging in professional development activities and some teachers are unable to cope with rapid change. For these teachers, there is a need for greater support from the principal, heads of department and fellow teachers, as the increased student diversity resulting from the reform resulted in many teachers implementing coping strategies in the classroom. Thus the ongoing provisions of resources and sustained collaboration between all parties (including the employing authority) are essential in promoting the policies and implementation of reform.

This study investigated the effect of the Concrete Representational Abstract (CRA) instructional strategy on form two students’ achievement in Algebra in Secondary Schools in the South West Region of Cameroon. The research questions were: What is the difference in the mean achievement scores of form two students taught directed numbers using the Concrete Representational Abstract (CRA) instructional strategy as compared to those taught using the Conventional Abstract Instruction (CAI)? What is the difference in the mean achievement scores of form two students taught simplification of algebraic expressions using the Concrete Representational Abstract (CRA) instructional strategy as compared to those taught using the Conventional Abstract Instruction (CAI)? The study made use of a quasi-experimental non-randomized pre-test, post-test research design. The target population of this study was made up of form two students of all public secondary schools in Meme and Fako Divisions. The accessible population consist of form two students of Government High School (GHS) Bokwango and Cameroon College of Arts and Science (CCAS) Kumba. The Sample comprised of 464 Form 2 students with 215 students from GHS Bokwango and 249 from CCAS Kumba. Three research instruments were used namely: The Algebra Achievement Test (AAT) and Algebra Interest Inventory (AII) for students and the interview guide for 2 teachers of the experimental school. The reliability coefficients for AAT and AII were 0.87 and 0.81 respectively showing that the instruments were reliable and could be used for the study. The results revealed that Form 2 students performed better in Algebraic concepts of directed numbers and simplification of algebraic expressions when taught using the CRA Instructional Strategy compared to those taught using the Conventional Abstract Instruction (CAI). In addition, CRA instructional strategy arouses students’ interests in algebra. The recommendations for the study were: The Concrete Representational Abstract (CRA) instructional strategy should be adopted in the teaching and learning of algebra in particular and Mathematics in general in Cameroon schools. Also, teachers should be trained on how to teach Algebra in particular using the CRA Instructional Strategy and CRA should be incorporated into teacher training education programmes to equip potential teachers with the skills of CRA instructional strategy.

At Teachers College, Columbia University, from July 7th to August 14th, in addition to the major course on the teaching and supervision of mathematics and one on the teaching of algebra given by Professor Reeve, the following courses will be offered. By Miss Sutherland: Teaching arithmetic in primary grades, teaching arithmetic in intermediate grades, and professionalized subject matter in junior high school mathematics. By Professor Shuster: Modern business arithmetic and field work in mathematics. By Dr. Sanford: Teaching algebra in junior high schools, and the history of mathematics. By Mr. Smith: Teaching geometry in secondary schools and a demonstration class in plane geometry. By Dr. Swenson: Professionalized subject matter in senior high school mathematics, and a demonstration class in eleventh year mathematics. By Dr. Wolff, visiting professor from Germany: Teaching mathematics in the secondary schools of Germany and the correlation of secondary school mathematics with science and art.

Since the virtual abolition of the double-track system, secondary school education worldwide has carried a double task: to continue to provide general education for qualified students after they finish elementary schooling and to train mid-level professional personnel and technically skilled workers. These will continue to be the tasks of secondary school education until the realization of universalization of higher education. Secondary school education is the intermediate link in the whole school system. The state of secondary school education influences the quality of higher education and affects the development of the national economy and the co-ordination of social life. Therefore, we should pay special attention to the reform of secondary school education in order to make it suitable to the rapid development of scientific technology and the national economy and to the changes in social life. The reform of secondary school education concerns many areas, but the key point is to set up a proper structure. How, then, can the structure of secondary school education be made effective? First, let us look at the present state of structural reform in secondary school education in various countries. In Bulgaria, vocational education takes precedence in the various schools at the secondary level. After finishing a compulsory eightyear education, 90 percent of the students go on studying in one of the following three types of secondary schools: 48.3 percent in secondary vocational-technical school (three years); 27.3 percent in general comprehensive technical school, that is, general high school (four years); 16.1 percent in secondary vocational school (four years). Thus the students in secondary technical schools and secondary vocational schools represent 64.4 percent of all the students in secondary schools. In Romania, measures were taken in 1977 to reform the structure of secondary school education. Vocational-technical education in the high school was strengthened and the high school program was divided into many vocational courses including industry, agriculture, law, administration, mathematics, teacher training, history, medicine, art, and language. Besides learning a basic knowledge of culture and science according to a study plan, students are now required to master some skills in a profession. Research has shown the variation in some developed countries in the proportion of students in vocational schools to those in general middle schools: in the United States of America, the ratio is 4:6; in Japan, 4:6; in the Federal Republic of Germany, 6:4; in Italy, 3:1; and in the USSR, 4:6 (Li, L., 1984).

What Does Globalization Mean for Educational Change? A Comparative Approach

Uspostavljanje modela filmske edukacije u srednjoj školi

Education reform and the pursuit of quality education are common concerns among stakeholders showing their concern to educational development. In recent years, Teacher Professional Development (TPD) has emerged as a pivotal component for advancing education reform efforts and bolstering educational quality. This article attempts at describing the existing TPD status of the secondary level schools in Nepal. In the study, the headmasters of the four selected secondary level schools were the informants; and a survey checklist was used as the research tool to collect required data. The data were analyzed and interpreted using descriptive statistics. The study found that the secondary schools were quite poor regarding their performance of TPD related activities, most of them had weak TPD status. This finding led to conclude that the concerned authorities need to be more responsible to make improvements in the existing TPD situation at the secondary schools in Nepal.

MODERN CHINESE MEDICAL EDUCATION HAS RECENTLY UNdergone 3 distinct periods of development—before, during, and after the 1966-1976 Cultural Revolution—driven largely by extra-academic political forces. In 1965 in China, there were 298 secondary medicalpharmaceutical schools with a 3to 4-year curriculum, which admitted students with a junior high (9-year) education; 92 medical-pharmaceutical universities, usually with a 5-year curriculum, which admitted students after high school; and 21 colleges of traditional Chinese medicine. The curriculum of the secondary medical schools at the time often included general education in language, literature, mathematics, and science, as well as specific vocational training in medicine. The medical university curriculum included 3 years of basic science lectures, 1 year of clinical didactics, and a 1-year practicum (similar to an internship year in the United States). University graduates were eligible to practice with no further training, whereas secondary school graduates were usually required to complete a practical internship first. With the onset of the Cultural Revolution, medical education essentially ceased; between 1966 and 1970, no new students were admitted and no formal instruction was given to those already enrolled. In 1970, Chinese medical schools and universities were reopened but with a new philosophy of training peer-chosen “worker-peasant-soldier” students in a curriculum emphasizing political ideology and practical training over basic science. Entrance examinations, as well as degrees and diplomas, were abolished, and a limited 3-year curriculum was instituted, even at the upperlevel medical universities. Approximately one fourth of the curriculum was devoted to political science, and students were required to complete several weeks of agricultural and factory labor each year. Priority for admission was given to peasants, factory workers, or those in the liberation army, and students were not required to have finished high school. In fact, because of the disruptions during the initial period of the Cultural Revolution, many students began medical school with no more than a junior high education. Universities themselves had limited input, and, while in theory students were chosen by communities and coworkers whom they would return to serve, in practice they were also often chosen by Communist party officials. The end of the Cultural Revolution brought the reinstitution of a national entrance examination in 1977, and by 1980, university admission was highly competitive, with an admission rate of less than 10%. Many graduates of the 1970s were recalled from their jobs for remedial coursework. The 1980s also brought attempts to reform extrauniversity medical education, such as that of the “barefoot doctors.” Begun decades prior to and expanded during the Cultural Revolution, this program gave young agricultural or factory workers a few weeks to a year of training in preventive and practical medicine. They then provided medical care in the countryside, in factories, or in urban health stations and usually continued to work alongside those they treated. They numbered in the millions, and in all, fewer than 10% of “doctors” in 1972 China were college-educated in medicine. Similar to the way that many of the worker-peasantsoldier graduates were recalled in the post-Revolution period, so were many of the barefoot doctors: most took a written examination in 1980, and by 1984, one third had been retrained to secondary school level. Overall, though, the restored university curriculum looked much like the pre-Revolution curriculum, with some expansion of the time spent in clinical clerkships and the practicum. In 1988, a national conference sponsored by the World Bank and the World Health Organization suggested several reforms, including the introduction of problem-based, less didactic learning and a focus on prevention and rural health needs. Then as now, the majority of physicians in China were educated within secondary schools rather than universities, and further reform of 3-year secondary medical education and barefoot doctor programs were discussed as a means of meeting the needs of the increasingly elderly rural Chinese population. As of 1996, there were 550 secondary medicalpharmaceutical schools, 123 medical-pharmaceutical universities, and 30 colleges of traditional Chinese medicine in China. Medical curricula vary greatly, from 3 years at secondary schools to 5 to 8 years at universities. The most common course of study is 5 years and has changed little since the late 1970s. Students are placed based on the results of national entrance examinations, but there is still no national exit examination, nor is there a central accreditation body for medical schools and universities. It remains to be seen whether recent regional and global attempts to set universal standards for medical education will be incorporated in China.

There is a great searching of heart among the teachers of algebra. The idea is abroad that algebra is the barren fig tree. Our association has a committee at work revising the old or devising a new algebra syllabus. Only about a year ago the Central Association published the report of its committee on algebra in the secondary schools, which report constitutes an algebra syllabus with many suggestions as to method of treatment.

Concurrent enrollment refers to partnerships between postsecondary institutions and schools through which secondary school students can complete a university class taught by a qualifying secondary school teacher at their secondary school. We propose that concurrent enrollment programs are an under-recognized tool for extending the impact of Universal Design for Learning (UDL). The context of our study is an equity-focused university course in algebraic mathematical modeling that is also offered through concurrent enrollment in over 30 secondary schools to over 800 secondary students annually in our state of Minnesota, U.S.A. This paper presents a qualitative analysis of secondary school teachers’ experiences implementing the inquiry pedagogy and the equity goals of the course. Several results are important for UDL. Teachers (1) describe equity in social terms of race, ethnicity, income, immigration, and language status in addition to measures of academic success; (2) perceive improvements in students’ attitudes towards mathematics, school, and university education; (3) perceive student academic growth through mathematical writing; and (4) report close relationships with students. If higher education faculty design their on-campus classes to incorporate UDL principles, concurrent enrollment offers the potential to improve inclusive pathways from secondary schools to universities.