For the past two decades, both pros and cons of calculus reform have been discussed. A question often asked is, “Has the calculus reform project improved students’ understanding of mathematics?” The advocates of the reform movement claim that reform-based calculus may help students gain an intuitive understanding of mathematical propositions and have a better grasp of the real-world applications. Nonetheless, many still question its effect and argue that calculus reform purges calculus of its mathematical rigor and poorly prepares students for advanced mathematical training. East Asian students often rank in the top 10 of TIMSS and PISA. However, out-performing others in an international comparison may not guarantee their success in the learning of calculus. Taiwanese college students usually have a high failure rate in calculus. The National Science Council of Taiwan therefore initiated several projects in 2008 for improving students’ learning in calculus. This paper provides a preliminary report on one of the projects, PLEASE, and discusses how it was planned to respond to the tenets of calculus reform movement.

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本研究主要目的在瞭解透過動態評量回饋系統輔助教學對提升國中數學學習成效及數學學習態度的影響。本研究針對新北市某國中八年級兩班學生共38人，每週進行五節，總計為六週之數學教學實驗。本研究採準實驗研究設計，自變項為教學模式，在實驗組以動態評量回饋系統融入學習之數學教學課程而在對照組使用一般傳統教學方法進行數學評量及回饋課程。依變項為「數學學習成效測驗」、「數學學習態度量表」，共變項為八上三次段考平均。以單因子共變數分析與二因子重複量數混合設計變異數分析進行統計分析，研究結果如下: 一、在數學科學習成效方面：以動態評量回饋系統輔助數學教學，能提升數學科學習成效。 二、在數學學習態度方面：在數學學習態度分向度之「外在動機」向度上，實驗組與對照組有顯著差異，證實以動態評量回饋系統輔助數學教學，能提升數學學習態度之外在動機。在數學學習態度整體面向並未有顯著差異，證實以動態評量回饋系統輔助教學並未能提升數學整體學習態度。 三、學生對動態評量回饋系統輔助教學的回饋： 1、學生普遍具有正向、積極的反應。 2、學生願意多花時間來加強數學的學習。 綜上所述，本研究針對結果提出具體建議，以提供教學設計、數學教學及未來相關研究之參考。 / The purpose of this study was to investigate junior high school students’ mathematics learning achievement by using a Dynamic Assessment and Feedback (DAF) system. The overall investigation process is designed as a quasi-experiment, where two classes of eighth-grade junior high school students in New Taipei County were randomly assigned to either the experimental(n=18) or the control groups(n=20). It took totally six weeks, and there were five classes per week to perform the instructional experiments. In the experiments, the independent variables were instructional strategies and the dependent variables were Mathematics Achievement Test and Mathematics Learning Attitude. The measurement instruments include Questionnaire for Mathematics Learning Attitude, Mathematics Achievement Test, and Questionnaire for Students’ Perception of Mathematics Instruction with DAF system. According to the students’ Mathematics Achievement Test, the statistical analysis was performed by one-way ANCOVA. By conducting t-test for the scores of the math learning attitude measurement, the analysis of math learning attitude was carried out by the two-way Mixed ANOVA. After analyzing the data, the findings of this study are summarized below: 1.Mathematics Achievement: The experimental group scored higher in the Mathematics achievement test than the control group did. 2.Mathematics Learning Attitude: No significant interaction between the teaching methods was found in attitude for learning Mathematics. A significant difference was found between the experimental group and the control group in their extrinsic motivation for Mathematics Learning Attitude. 3.The students’ feedback after the (DAF) system mode: I.Most students in the experimental group did enjoy the DAF system. II.Most students were willing to spend more time using the DAF system to practice Mathematics. Finally, based on these findings, this study proposes several suggestions for school administrators, teachers in junior high school math curriculum and future research are also discussed.

The pass rate in mathematics is unsatisfactory both in South Africa and internationally. Historically disadvantaged students tend to underachieve even more due to a variety of hampering factors. An investigation into the reasons for underachievement in mathematics prompted the researcher to launch a study through which she wanted to remediate some of these identified problems. The research project took place at Technikon Northern Gauteng (TNG), and comprised of the implementation of tutorial sessions. The study was conducted by means of a quasi-experimental design using action research. The primary goal of this dissertation is to report on the process, outcomes and recommendations in order to facilitate improvement in practice. The researcher's overarching hypothesis was that tutorials in mathematics would have a positive effect on the achievement of first year mathematics students at TNG. The following questions were focussed on during the course of the study: ¨ What is the impact of mathematics tutorials on problem-solving abilities and critical thinking? ¨ What is the impact of tutorials on the self-image of the students, with reference to mathematics and mathematics achievement? ¨ What is the impact of tutorials on mathematics achievement? ¨ Which role could tutors play in the creation of role models? ¨ Do students have the need to communicate mathematically in their mother tongue? ¨ How successfully could portfolio assessment be implemented? Quantitative and qualitative data were gathered through a standardised questionnaire, the SOM, a specifically designed, structured questionnaire, observations, focus group interviews, reflective diaries and student records. Some of the findings include: ¨ Historically disadvantaged students § often possess a unsatisfactory study orientation; § apply inefficient time management; § suffer from mathematics anxiety; § do not show a correlation in terms of grade 12 symbols and success at tertiary level § often experience milieu deficit; § do not achieve according to their expectations; and § do not have a learning culture (COLT) at their disposal. ¨ Students generally perceived the tutorials as positive and contributing towards success. The students § did not often speak in their mother tongues; § appreciated the relaxed work tempo; and § utilise the support system of the smaller group. ¨ During the focus group interviews students recognised the following success factors: § regular class attendance; § completion of homework § planning and revision according to a study timetable. ¨ Students shared some personal experiences with the researcher, namely that § the tutorials boosted their self-image and make them willing to ask questions during lectures; § some tutors acted as positive role models; and § the consistent involvement of the lecturer motivated students. The statistical procedures revealed that the students in the experimental group did not perform significantly better than those in the control group, yet that does not diminish the value of the study in any way. The researcher recommends further research in the tertiary mathematics environment in order to empower students. / Dissertation (MEd (Curriculum Studies))--University of Pretoria, 2005. / Curriculum Studies / unrestricted

Mathematics learning seems to be a demanding and time-consuming task for many learners. Information and communication technology (ICT) is an attractive tool of learning for students at any level and it can provide an effective atmosphere for understanding mathematics. The question is how to combine mathematics teaching contents, approaches, curricula, and syllabus with new media. The key issue in European educational policy (and other countries as well) is exchange and sharing digital learning resources (learning objects) among countries. In order to accumulate the practice of various countries and use the best digital resources created by different countries, it is necessary to localize learning objects (LO). The paper deals with some problems connected with localization of LO, developed for mathematics education, and presents some solution. Software localization is mainly referred to as language translation (e.g., translation of user interface texts and help documents). However, there are many other important elements depending on the country and people who will use the localized software. In this paper, the main attention is paid to localization of learning objects used for teaching and learning mathematics.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is the product of an investigation that is part of the LP1: Research, Training, Knowledge and Professional Development Line of the Graduate Program in Education of the Federal University of Santa Maria / RS, focused on broadening the discussions in The initial training of teachers of mathematics and their first years of teaching. The aim of this research is to identify the constituent elements of the initial formation of teachers of mathematics that contribute to the first years of teaching, verifying the approximation and distances of the initial formation course and the reality experienced in the schools, through the gaze of the beginning teacher who teaches mathematics. The research theme came from the experience of the researcher as a teacher who teaches mathematics in her early years of teaching, given the emergence of problems, challenges, uncertainties and difficulties to be faced in the classroom, and that often the beginner teacher Is not prepared to face them. The theoretical references that base this writing that refer to the initial formation are Charlot (2000), Tardif (2002), Mizukami (2006), Imbérnon (2011), Vaillant; Garcia (2012), in the initial formation of teachers of mathematics are Ponte (1998), Moura (2001, 2002), Libâneo (2004), Lorenzato (2010), among others. In relation to the first years of teaching, the main references were Huberman (1992), Garcia (2009), Vaillant and Tardif (2002). For that, the investigation was carried out with teachers who teach mathematics in the state public network of the municipality of Ijuí / RS, the dialogue was recorded and occurred through semistructured interviews with seven teachers. Through their narratives we have been able to know them from the choice of the mathematics course, the first ones counted with the teaching in the initial formation and the entrance in the teaching career. With the transcribed dialogue the interpretation and understanding of the data was based on the narrative analysis of Galvão (2005) with the contribution of the hermeneutic experience, for understanding to happen, Gadamer (1997) argues that the interpreter moves from a projected meaning of the whole to the parts, and then returns to the whole, Called by the author of the hermeneutic circle, in this way the knowledge of the completeness of the text allows the interpreter to question between what is not familiar and what is being shared. The results allow us to share that the teachers understand that initial training is a necessary support for future practices, motivating and encouraging future teachers to think about mathematics teaching, however, during the training, there were difficult situations in the stages that marked The identity of these teachers. They concluded that the entry into the career was a moment of expectation but that feelings of insecurity, uncertainty, fears were greater and emphasized that the main deficiency in this initial period was in the organization of pedagogical practice and that the lack of support is Remarkable, end up resorting to experienced teachers. We conclude that the initial training course left some gaps strongly felt by the teachers at the beginning of the career, so they understand that the training course needs to provide more classroom practices, believe that they learn in practice, and could thus face with greater Clarity in classroom situations. / Este trabalho é produto de uma investigação que insere-se na LP1: Linha de Pesquisa Formação, Saberes e Desenvolvimento Profissional, do Programa de Pós-graduação em Educação da Universidade Federal de Santa Maria/RS, tem seu foco voltado a ampliação das discussões no âmbito da formação inicial de professores que ensinam matemática e seus primeiros anos de atuação docente. O objetivo desta pesquisa é identificar elementos constituintes da formação inicial de professores que ensinam matemática que contribuem para os primeiros anos da docência, verificando a aproximação e os distanciamentos do curso de formação inicial e a realidade vivenciada nas escolas, através do olhar do professor iniciante que ensina matemática. A temática da investigação surgiu a partir da vivência da pesquisadora como professora que ensina matemática em seus primeiros anos de atuação docente, visto o surgimento de problemas, desafios, incertezas e dificuldades a serem enfrentadas em sala de aula, e que muitas vezes o professor principiante não está preparado para enfrentá-los. O referenciais teóricos que embasaram esta escrita que referem-se a formação inicial são Charlot (2000), Tardif (2002), Mizukami (2006), Imbérnon (2011), Vaillant; Garcia (2012), na formação inicial de professores que ensinam matemática são Ponte (1998), Moura (2001; 2002), Libâneo (2004), Lorenzato (2010), dentre outros. Em relação aos primeiros anos de atuação docente os principais referenciais foram Huberman (1992), Garcia (2009), Vaillant e Tardif (2002). Para tanto, a investigação foi realizada com professores que ensinam matemática na rede pública estadual do município de Ijuí/RS, o diálogo foi gravado e ocorreu através de entrevistas semiestruturadas com sete professoras. Através das suas narrativas pudemos conhecê-las desde a escolha pelo curso de matemática, os primeiros contados com a docência na formação inicial e a entrada na carreira docente. Com o diálogo transcrito a interpretação e compreensão dos dados baseou-se na análise narrativa de Galvão (2005) com a contribuição da experiência hermenêutica, para que a compreensão aconteça, Gadamer (1997) argumenta que o intérprete se move de um significado projetado do todo para as partes, e então volta para o todo, denominado pelo autor de círculo hermenêutico, dessa forma o conhecimento da completude do texto permite que o intérprete questione entre aquilo que não lhe é familiar e o que está sendo compartilhado. Os resultados nos permitem compartilhar que as professoras entendem que a formação inicial é um suporte necessário para as futuras práticas, motivando e incentivando os futuros professores a pensar o ensino de matemática, no entanto, durante a formação, nos estágios houveram situações difíceis o que marcou a identidade dessas professoras. Completam que a entrada na carreira, foi um momento de expectativas, mas que os sentimentos de insegurança, incertezas, medos, foram maiores e enfatizaram que a principal deficiência, nesse período inicial, foi na organização da prática pedagógica e que a falta de apoio é notável, acabam recorrendo aos professores experientes. Concluímos que o curso de formação inicial deixou algumas lacunas fortemente sentidas pelas professoras na entrada na carreira, assim, elas entendem que o curso de formação precisa fornecer mais práticas em sala de aula, acreditam que aprendem na prática, sendo assim, poderiam enfrentar com maior clareza as situações em sala de aula.