Microteaching Lesson Study: Mentor interaction structure and its relation to elementary preservice mathematics teacher knowledge development

This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a southern urban university were part of the study. This included 72 participants who completed MLS across three different mentor interaction structures as part of their course requirements and 31 elementary preservice teachers who did not complete MLS as part of their methods course and served as a comparison group for a portion of the study. A sequential mixed-methods research design was used to analyze the relationship between MLS mentor interaction structure and growth in preservice teachers' mathematics teacher knowledge. Data sources included pre and post assessments, group developed lesson plans and final reports, a feedback survey with Likert-type and open-ended questions, and transcripts of audio-recorded debriefing sessions. The pre and post assessments were analyzed using Analysis of Variance (ANOVA) and descriptive statistics were used to analyze the Likert-type feedback survey questions. Group MLS lesson plans, final reports, and transcripts of debriefing sessions along with the open-ended questions from the feedback survey were coded in a three-step process as described by Miles and Huberman (1994). In alignment with findings from M. Fernandez (2005, 2010), elementary preservice teachers participating in MLS grew in content knowledge related to MLS topics taught by one another. Results from the analysis of pre and post content knowledge assessments revealed that participants grew in their understanding of the mathematics topics taught during MLS irrespective of their mentor interaction structure and when compared to the participants who did not complete MLS in their methods course. Findings from the analysis of lesson plans for growth in pedagogical content knowledge revealed the most growth in this area occurred for participants assigned to the interaction structure in which the MLS mentor participated in the first two debriefing sessions. Analysis of the transcripts of the discourse during the debriefing sessions and the feedback surveys support the finding that the elementary preservice teachers assigned to the interaction structure in which the MLS mentor participated in the first and second debriefing sessions benefited more from the MLS experience when compared to elementary preservice teachers assigned to the other two interaction structures (MLS mentor participated in only the first debriefing session and MLS mentor participated in only the last debriefing session).

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

Informe del seminari Library and Information Science Education in Europe: "Issues in joint curriculum development and Bologna perspectives" (Copenhaguen, Dinamarca, 11-12 d'agost de 2005)

Els dies 11 i 12 d'agost va tenir lloc a Copenhaguen, Dinamarca, el seminari de treball Library and Information Science Education in Europe: ¿Issues in joint curriculum development and Bologna perspectives¿. Aquest seminari, que va estar coordinat per la Royal School of Library and Information Science de Dinamarca, amb la col·laboració de l'European Association for Library and Information Education and Research (EUCLID), es va organitzar en el marc d'un projecte europeu subvencionat pel programa Sòcrates. La Facultat de Biblioteconomia i Documentació de la Universitat de Barcelona, present entre 2001 i 2005 en la Junta de Govern de l'EUCLID, va participar-hi com a soci del projecte. L'objectiu del seminari era aplegar una cinquantena d'experts europeus de l'àrea de Biblioteconomia i Documentació ¿tots ells professors d'escoles i de facultats d'universitats europees¿ per discutir qüestions relacionades amb els plans d'estudis dels ensenyaments des de la perspectiva del procés de Bolonya. El seminari consistí en dues conferències i en les reunions de treball de dotze grups formats per experts que examinaren dotze grans temes ¿prèviament acordats pels organitzadors de l'esdeveniment¿ relacionats amb els plans d'estudis d'aquells ensenyaments.

Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

Controversy between curriculum design and curriculum development of online "highly specialized" education in the field of construction

Nowadays, on a global level, the Higher Education System has a complex and broad horizon of curricular tools to use in the teaching and learning process. In addition to these new educational instruments, full of possibilities, we face specific socio-economic conditions that affect in a significantly way the Curriculum Development in certain knowledge areas (areas traditionally built on a methodology based on a physical presence of students in the classroom). Some areas such as Restoration, Rehabilitation or Construction Pathologies, and the construction sector in general, require very defined and particular knowledge that only a small number of experts claim as specialized training. All these aspects condition the teaching methodology performed in a physical classroom at a university campus (the only option used until recent years) and made us consider the integration of online teaching in these areas too. The present work shows the teaching methodology used for the development of two online courses, where we offer distance learning for "highly specialized" formation in the Edification area (an area where traditionally there was only classroom training). At the beginning, both courses were designed by classroom training, but got a really small number of applications due to the specialized topic proposed. Later, we proposed a "Curriculum Redesign" of the contents, offering an online modality, which implied a significant demand both within and outside the university area. A notable feature of this educational experience is the great spectrum opened for attendees of both courses in the online version. This situation improved significantly the "Curriculum Development" for the student and implied an interesting new proposal on the offered contents and materials (what would have been really difficult to get in a face to face classroom). In conclusion, the absence of certain types of specialized contents in the academic university curricula makes essential to raise new methodologies to save the gap in this area through additional training courses as those analyzed in this paper. Thus, our experience opens a debate on the appropriateness of implementing online training in relation to the face to face training in constructive content subjects and, especially, presents a new scheme, not without controversy, for the curriculum design.

A methodology for discipline-specific curriculum development

A methodology and framework for discipline-specific curriculum development in a local context is described. These activities, as part of the Thailand-Australia Science and Engineering Assistance Project, were in response to a needs analysis for curriculum assistance to a number of publicly-funded Thai universities in the engineering priority area of Materials Processing and Manufacturing. The paper outlines a strategy for the delivery of a centralised curriculum development workshop for academic staff follow-up visits and local curriculum activities with participating universities, and the presentation of technical short courses as guidance for such activity in other settings and/or discipline areas. This paper is part of a process of documentation so that others can apply the developed methodology and framework for curriculum development. While the paper is a report on curriculum activities in a particular setting, it is written in a manner that allows application of the methodology to other settings. The reader is advised that each curriculum activity needs to adopt a methodology and strategy to fit the particular circumstances being considered To assist in applying this approach elsewhere, a description of the various steps in the curriculum process, and typical responses to some of the more global issues, have been presented. Full details are available in the various TASEAP reports prepared by the authors. Specific detail has been omitted where this detail does not provide any information for generalized consumption.

Building a Social Education curriculum based on Professional Competences : the experience of University of Girona

This article describes the process of adapting Social Education studies to the European Higher Education Area undertaken by a team of the teaching staff at the University of Girona (Spain). The aim of the experience is to build a curriculum based on thecompetencies recognized as such by professionals in the field of social education in our region. The article specifies the development of the various phases, each involving the active participation of professionals and teaching staff from the universities. To conclude, main characteristics of the curriculum are highlighted

Creating a global consciousness throught the driver model of curriculum development

The purpose of this study was to investigate the effect a human link through the One World Youth Project has on a global education program, if a human connection through the program enhances a student's ability to develop a critical consciousness of global issues, and the etTectiveness of thc constructivist-based Driver Model of Curriculum Development, which served as the curriculum model in this study. An action based research cycle was chosen as this study's research methodology and incorporated 5 qualitative data collection instruments: a) interviews and questionnaires, b) artifacts, c) teacher journal, d) critical friend's observation forms, and e) my critical friend's postobservation interviews. The data were conected from 4 student participants and my critical friend during all stages of the action research cycle. The results of this study provide educators with data on the impact of human connections in a global education program, the effects these connections have on students, and the effectiveness of the Driver Model of Curriculum Development. This study also provides practical activities and strategies that could be used by educators to develop their own global education programs. The United Nations drafted the Millennium Development Goals in an effort to improve the lives of billions of people across the globe. The eight goals were developed with the support of all member nations since all human beings are global citizens who have a responsibility to make the world a better place. Students need to develop a critical consciousness of global issues so that they can work with others to eliminate them. Students who are taught to restate the opinions of others win not be prepared to inherit a world full of challenges that will require new innovative ideas to foster positive change.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Handbook of curriculum development. 'Manual de desarrollo curricular'.

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