Uso de crisis, realimentación y desvanecimiento para el diseño de tareas en línea

A recent discussion involves the elaboration on possible design principles for sequences of tasks. This paper builds on three principles, as described by Bokhove and Drijvers (2012a). A model with ingredients of crises, feedback and fading of sequences with near-similar tasks can be used to address both procedural fluency and conceptual understanding in an online environment. Apart from theoretical underpinnings, this is demonstrated by analyzing a case example from a study conducted in nine schools in the Netherlands. Together with quantitative results of the underlying study, it is showed that the model described could be a fruitful addition to the task design repertoire.Una discusión reciente implica la elaboración de posibles principios para el diseño de secuencias de tareas. Este documento se basa en tres principios, descritos en Bokhove y Drijvers (2012a). Un modelo que comprende las componentes de crisis, realimentación y desvanecimiento de secuencias con tareas muy similares puede ser utilizado para abordar tanto la fluidez procedimental como la comprensión conceptual en un entorno en línea. Además de estar fundamentado teóricamente, esto se demuestra mediante el análisis de un ejemplo de caso de un estudio realizado en nueve centros educativos de los Países Bajos. Junto con los resultados cuantitativos del estudio subyacente, se muestra que el modelo descrito podría ser una incorporación útil en el repertorio del diseño de tareas

Using crises, feedback and fading for online task design

A recent discussion involves the elaboration on possible design principles for sequences of tasks. This paper builds on three principles, as described by Bokhove and Drijvers (2012a). A model with ingredients of crises, feedback and fading of sequences with near-similar tasks can be used to address both procedural fluency and conceptual understanding in an online environment. Apart from theoretical underpinnings, this is demonstrated by analyzing a case example from a study conducted in nine schools in the Netherlands. Together with quantitative results of the underlying study, it is showed that the model described could be a fruitful addition to the task design repertoire

How can we engage mathematics ITE students with research?

In the Erasmus+ Research in Teacher Education (RiTE) project, student teachers are stimulated to use evidence from educational and scientific research to experiment and innovate their teaching and learning processes. In two case studies we use Engestrom’s expansive learning cycle. The first case study reports on the design and implementation of materials designed to enhance student teachers’ critical review of literature in the context of the post-graduate study that is incorporated within their teacher education. The second case study presents the design of collaborative lesson research that aims to foster authentic connections between school-based learning (teaching practice) and research that informs mathematics teaching and learning. We discuss the aims of research-informed mathematics teacher education at each site, demonstrate some of the approaches used and discuss tensions within the design and early implementation of the projects

Mathematics textbook use in England: mining Ofsted reports for views on textbooks

According to TIMSS data, the use of textbook in mathematics classrooms in England is relatively low in comparison to other countries. Although the reasons for this might be varied, the pronouncements of Ofsted, the official body for inspecting schools in England, might have an influence. This paper reports on a text analysis of almost 10,000 publicly-available Ofsted secondary school inspection reports and mathematics- specific commentaries from the year 2000 until now. The analysis focused on what Ofsted said over this period about textbook use in general and about the use of mathematics textbooks in particular. The analysis was conducted by first ‘scraping’ the reports from the Ofsted website and then utilising basic text mining and analysis methods to extract information on these documents. While the analyses showed that the occurrence of comments by Ofsted on textbooks appeared to be relatively minor, interpreting these findings from text mining alone was not straightforward. A further qualitative analysis of a sample of Ofsted publications found mention of ‘over-reliance’ on textbooks. Such allusion to ‘over-reliance’ on textbooks might have negative connotations and may have contributed to the relatively low use of textbook in mathematics classrooms in England

Authoring your own creative, electronic book for mathematics: the MC-squared project

The EU-funded ‘MC-squared’ project is working with a number of European communities to develop digital, interactive, creative, mathematics ‘textbooks’ that the project calls ‘cBooks’. The cBooks are authored in a Digital Mathematics Environment in which participants can construct books with various interactive ‘widgets’. This paper provides an outline of the MC-squared project illustrating an interactive storyboard of the Digital Mathematics Environment architecture. This includes examples of how authoring by cBook designers of interactive ‘widgets’ is possible. The workshop that relates to this paper is augmented, of course, by suitable ‘hands-on’ materials aimed at two possible cBooks: one focusing on aspects of geometric and spatial thinking using building blocks, the other on aspects of number and fractions

MathPen: identifying and solving the problems of online collaborative learning for mathematics

Combining the interactive communication power of Web 2.0 and social-constructivist theory in education research, online collaborative learning (OCL) has now become an area of intensive research and has generated many favourable results. Yet, the term online collaborative learning, or any other related terms, are seldom seen in mathematics education journals. This paper will, after a brief overview of OCL theory, describe the problems associated with OCL in mathematics education and offer MathPen (an online handwriting recognition system) as a potential solution

Use of ICT for acquiring, practicing and assessing algebraic expertise

For several years the skill level of students leaving secondary education in the Netherlands has been discussed. Lecturers in higher education –for example– complain about their freshmen’s apparent lack of algebraic skills. Another development in recent years is the advent of the use of technology in mathematics education. Combining algebraic expertise and ICT use, the aim of this study is to design an online environment for learning supported by formative assessment of both procedural skills and conceptual understanding in algebra, to investigate the effects of the environment, and to identify decisive factors that influence the outcome. The central research question, therefore, is: in what way can the use of ICT support acquiring, practicing and assessing algebraic expertise? This general question leads to several sub-questions, each related to an appropriate cycle in the study. The theoretical framework is based on the three key perspectives n ICT tool use, algebraic expertise, assessment and feedback. As we aim to design an intervention in several iterations, the research method is based on the principles of design research. Research takes place in one preparatory cycle and three subsequent cycles. The preliminary cycle concerns the design of criteria for an evaluation instrument for digital algebra tools. The instrument was used to choose an appropriate algebra tool for the remainder of the study, and design prototypical digital activities. In the first research cycle one-to-one think-aloud sessions were conducted with five 12th grade students. The results were used to examine the interplay between ICT and the acquisition of algebra, and determine what feedback could be added to the intervention. Based on the initial characteristics, the digital activities and feedback, the intervention was redesigned in an iterative fashion. The revised intervention was field tested in a second cycle for two classes (12th grade, wiskunde B, N=31), after which we made the final improvements based on three design principles all focusing on feedback. The final intervention was field tested in the third and last cycle in nine different schools (N=324). The use of the intervention for an average of five hours has a large effect on improving algebraic expertise, as post-test score is significantly higher than the pretest score. Furthermore, previous knowledge, time spent in self-test and summative test mode, and general attitude towards mathematics are the largest predictors for a high posttest outcome. The fact that these variables have nothing to do with ICT may indicate that indeed conventional pen-and-paper techniques and ICT techniques are reconciled. In line with this, the variables overall quality of the school (operationalized by trend exam grades), total practice time and the home work – school work ratio did not significantly predict the outcome. Discussion points for the study concern the interplay between acquiring skills and understanding, the extrapolation of the findings for a small sub-domain of algebraic knowledge to algebra as a whole and the methodology of the study