An Historical Phenomenology of Mean and Median

Using Freudenthal’s method of historical phenomenology, the history of statistics was investigated as a source of inspiration for instructional design. Based on systematically selected historical examples, hypotheses were formulated about how students could be supported in learning to reason with particular statistical concepts and graphs. Such a historical study helped to distinguish different aspects and levels of understanding of concepts and helped us as instructional designers to look through the eyes of students. In this paper, we focus on an historical phenomenology of mean and median, and give examples of how hypotheses stemming from the historical phenomenology led to the design of instructional activities used for teaching experiments in grades 7 and 8 (12–14-years old).     

Neuropsychological intervention in kindergarten children with subtyped risks of reading retardation

Kindergarten children at risk of developing language problems were administered the Florida Kindergarten Screening Battery. A principal components analysis revealed a verbal and a visual-spatial component and subsequent discriminant function analyses a high verbal/low visual-spatial group (LAL: Latent L) and a high visual-spatial/low verbal group (LAP: Latent P). LAL- and LAP-children were considered at risk for developing an L- or P-type of dyslexia, respectively. As is common practice with children suffering from manifest L- or P- dyslexia, the LAL- and LAP-kindergartners received right and left hemisphere stimulation, respectively. The outcomes were compared with those of bilateral hemispheric stimulation and no intervention. Reading tests were administered in primary school Grades 1 and 5/6; teachers’ evaluation of reading took place in Grade 5/6. Overall, the LAL- and LAP- groups showed significant backwardness in word and text reading, both at early and late primary school. Types of intervention made a difference though: not significantly backward in early word, late word, and late text reading were the LAL-children who had received right hemisphere stimulation. Nonintervened LAP-children did not show significant backwardness in early word reading and late text reading, nor did LAP-children who had received left hemisphere or bilateral stimulation. Early text reading was not affected by any treatment. Teacher’s evaluations were in support of these findings.     

Effects of Instruction on Verbal Interactions During Collaborative Problem Solving

During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving.     

Designing for learning in the Yellow House: a comparison of instructional and learning design origins and practices

ABSTRACT

For the past two decades, there has been persistent debate around whether there is a difference between the fields of instructional design (ID) and learning design (LD). While differences in the two approaches are certainly apparent, there are cross-over points that can provide ID and LD researchers and practitioners with opportunities for dialogue about the purposes and remit of research-based practices for optimal design. Though potentially disruptive, initiating dialogues among learning and instructional designers could lead to more thorough and critical analyses of both ID and LD repertoires. Should boundary crossings occur, there is a potential for a third space for the contemplation, research, and practice of design. A goal of this article is to use the notion of Van Gogh’s Yellow House as an anchoring metaphor for the third space – a location for shared discourse, inspiration, collaboration, and challenge for a community of designers of/for learning. Using the impressionist and expressionist terminology to help elucidate the ways of thinking of designers of both traditions, this article examines the history, underlying philosophical approaches, methodologies, and design goals of ID and LD. We conclude that the emergence of a third space for design can help us move beyond the LD and ID dichotomies. We suggest that a socio-materialist perspective alleviates issues of incommensurability by acknowledging ontological multiplicity.     

A description model of the genesis of guidance and its application

Based on a review of literature, developments in guidance and counseling (further: guidance) in Dutch general secondary education are described with a three phase model, originating from an analysis of the developmental histories of guidance in the United States, Great-Britain, and West-Germany. This article begins with the clarification of the developmental model. Before this is applied to the Dutch situation, some basic information about secondary (general)eduction in the Netherlands is supplied. Besides offering an overview of developments, an attempt is made to assess some of the more recent characteristics and developments of guidance in Holland.     

The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning

Previous research has shown that – due to the extensive attention spent to proportional reasoning in mathematics education – many students have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. This phenomenon is sometimes referred to as the ‘illusion of linearity’. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too. In this article, the empirical evidence for this phenomenon is expanded to the domain of probabilistic reasoning. First, we elaborate on the notion of chance and provide some reasons for expecting the over generalization of linear models in the domain of probability too. Afterwards, a number of well-known and less-known probabilistic misconceptions are described and analysed, showing that they have one remarkable characteristic in common: they can be interpreted in terms oft he improper application of linear relations. Finally, we report on an empirical investigation aimed at identifying the ability of 10^th and12^th grade students to compare the probabilities of two binomial chance situations. It appears that before instruction in probability, students have a good capability of comparing two events qualitatively, but at the same time they incorrectly quantify this qualitative insight as if the variables in the problem were linked by a linear relationship. Remarkably, these errors persist after instruction in probability. The potential of this study for improving the teaching and learning of probability, as well as suggestions for further research, are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Writing reviews: perspectives from the editors of Educational Studies in Mathematics

Educational Studies in Mathematics -     

Trends in gender differences in mathematics and science (TIMSS 1995–2003)

This article investigates changes in gender differences evident in the performance of grade 8th grade students participating in the Trends in International Mathematics and Science Study (TIMSS) between 1995 and 2003. Gender specific results and patterns found in TIMSS 1995 were compared with later cycles of the study in order to address the question of how far the mathematics and science gender gap has narrowed over time. Using a regression approach to compare the trend data, the findings indicated no major changes for mathematics but it appears that the gap in science may be closing, especially in the previously male dominated content areas of chemistry and physics.     

Two new readability predictors for the professional writer: pilot trials

A combination of two new, but very different, approaches to the prediction of readability could be particularly valuable in evaluating English texts written for native and non-native speakers. One approach develops the concept of lexical density, whereas the other is a novel measurement of two mechanical variables of text. The paper first outlines the traditional approach to readability. Next, it explains the concept of lexical density, and presents the results of a pilot study into reader preferences for different levels of density in text. It then offers an alternative approach to readability that uses sentence and ‘packet’ lengths. Finally, it indicates how the two approaches have been combined into a computer software program, and suggests the direction of future work. Our conclusions are threefold. Firstly, the lexical density of text is a better indicator of its readability than the scores given by many of the more common readability formulae. Secondly, the effective breaking up of sentences into ‘packets’ is as important to readability as sentence length. Finally, in looking at the mechanical variables of texts, we should not only be concerned with averages, but with distributions and most frequently occurring values.     

Initial foot contact and related kinematics affect impact loading rate in running

This study assessed kinematic differences between different foot strike patterns and their relationship with peak vertical instantaneous loading rate (VILR) of the ground reaction force (GRF). Fifty-two runners ran at 3.2 m · s^?1 while we recorded GRF and lower limb kinematics and determined foot strike pattern: Typical or Atypical rearfoot strike (RFS), midfoot strike (MFS) of forefoot strike (FFS). Typical RFS had longer contact times and a lower leg stiffness than Atypical RFS and MFS. Typical RFS showed a dorsiflexed ankle (7.2 ± 3.5°) and positive foot angle (20.4 ± 4.8°) at initial contact while MFS showed a plantar flexed ankle (?10.4 ± 6.3°) and more horizontal foot (1.6 ± 3.1°). Atypical RFS showed a plantar flexed ankle (?3.1 ± 4.4°) and a small foot angle (7.0 ± 5.1°) at initial contact and had the highest VILR. For the RFS (Typical and Atypical RFS), foot angle at initial contact showed the highest correlation with VILR (r = ?0.68). The observed higher VILR in Atypical RFS could be related to both ankle and foot kinematics and global running style that indicate a limited use of known kinematic impact absorbing “strategies” such as initial ankle dorsiflexion in MFS or initial ankle plantar flexion in Typical RFS.