Situating graphs as workplace knowledge

We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use, and more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the notion of transparency to characterise instances of graph use by highly educated scientists in cases where the context was familiar: the scientists were able to read the situation "through" the graph. This paper explores the limits of the validity of the transparency metaphor. We present two vignettes of actual graph use by a factory worker, and contrast his actions and knowledge with that of a highly-qualified process engineer working on the same production line. We note that in neither case were the graphs transparent. We argue that a fuller account that describes a spectrum of transparency is needed, and we seek to achieve this by adopting some elements of a semiotic approach that enhance a strictly activity-theoretical view

Improving work processes by making the invisible visible

Increasingly, companies are taking part in process improvement programmes, which brings about a growing need for employees to interpret and act on data representations. We have carried out case studies in a range of companies to identify the existence and need of what we call Techno-mathematical Literacies (TmL): functional mathematical knowledge mediated by tools and grounded in the context of specific work situations. Based on data gathered from a large biscuit manufacturing and packaging company, we focus our analysis here on semiotic mediation within activity systems and identify two sets of related TmL: the first concerns rendering some invisible aspects visible through the production of mathematical signs; the second concerns developing meanings for action from an interpretation of these signs. We conclude with some more general observations concerning the role that mathematical signs play in the workplace. The nee

Attributing meanings to representations of data: the case of statistical process control

This article is concerned with the meanings that employees in industry attribute to representations of data and the contingencies of these meanings upon context. Our primary concern is to characterise more precisely how the context of the industrial process is constitutive of the meaning of graphs of data derived from this process. We draw on data from a variety of sources including ethnographic studies of workplaces and reflections on the design of prototype learning activities supplemented by insights obtained from trying out these activities with a range of employees. The core of this article addresses how different groups of employees react to graphs used as part of statistical process control, focussing in particular on the meanings they ascribe to mean, variation, target, specification, trend and scale as depicted in the graphs. Using the notion of boundary crossing we try to characterise a method that helps employees to communicate about graphs and come to data-informed decisions

Techno-mathematical literacies in the workplace: a critical skills gap

There has been a radical shift in the mathematical skills required in modern workplaces. With the ubiquity of IT, employees now require Techno-mathematical Literacies, the mastery of new kinds of mathematical knowledge shaped by the systems that govern their work. The education system does not fully recognise these skills, employees often lack them, and companies struggle to improve them. This project has developed prototype learning resources to train a variety of employees in the mathematical awareness and knowledge that today’s employment require

Characterizing the use of mathematical knowledge in boundary crossing situations at work

The first aim of this paper is to present a characterisation of techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory, specifically to the notions of boundary object and boundary crossing. In this paper we draw on ethnographic research in a pensions company and focus on data derived from detailed analysis of the diverse perspectives that exist with respect to one symbolic artefact, the annual pension statement. This statement is designed to facilitate boundary crossing between company and customers. Our study showed that the statement routinely failed in this communicative role, largely due to the invisible factors of the mathematical-financial models underlying the statement that are not made visible to customers, or to the customer enquiry team whose task is to communicate with customers. By focusing on this artefact in boundary-crossing situations, we identify and elaborate the nature of the techno-mathematical knowledge required for effective communication between different communities in one financial services workplace, and suggest the implications of our findings for workplaces more generally

Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic framework to answer the question of how students learned the concept of "distribution" in a statistics course by "diagrammatic reasoning" and by developing "hypostatic abstractions," that is by forming new mathematical objects which can be used as means for communication and further reasoning. Peirce's semiotic terminology is used as an alternative for notions such as modeling, symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning and of communication in mathematics classroo

Designing an instrument to measure the development of techno-mathematical literacies in an innovative mathematics course for future engineers in STEM education

Techno-mathematical Literacies (TmL), which are defined as a combination of mathematical, workplace and ICT knowledge, and communicative skills, are acknowledged as important learning goals in STEM education. Still, much remains unknown about ways to address them in teaching and to assess their development. To investigate this, we designed and implemented an innovative course in applied mathematics with a focus on Techno-mathematical Literacies for 1st-year engineering students, and we set out to measure the learning effect of the course. Because measuring TmL is an uncharted terrain, we designed tests that could serve as pre- or posttests. To prevent a test learning effect, we aimed to design two different but equally difficult tests A and B. These were assigned randomly to 68 chemistry students, as a pretest, with the other one serving as posttest after the course. A significant development in TmL was found in the B-pre group, but not in the A-pre group. Therefore, as a follow-up analysis we investigated whether the two tests were equally difficult and searched for possible explanations. We found that test B was indeed perceived as more difficult than test A, but also that students who were assigned B (pre) were previously higher achieving than A (pre), and a sound mastery level of basic skills that ground the higher-order TmL seemed necessary. Furthermore, as TmL are very heterogenous by nature, some of them are easier learned and measured than others. Based on the results, we propose ways of testing TmL, which should be validated in future research

The Multidimensional Structure of Interest

There is increasing attention for interest as a powerful, complex, and integrative construct, ranging in appearance from entirely momentary states of interest to longer-term interest pursuits. Developmental models have shown how these situational interests can develop into individual interests over time. As such, these models have helped to integrate more or less separate research traditions and focus the attention of the field more on the developmental dynamics. This, however, also raises subsequent questions, one being how development can be understood in terms of interest structure. The developmental models seem to suggest that development occurs roughly along the line of six dimensions, which we summarize as the dimensions of historicity, value, agency, frequency, intensity, and mastery. Using an experience sampling method that was implemented in a smartphone application, we prompted 94 adolescents aged 13 to 16 (60% female) to rate each interest they experienced during two weeks on these six dimensions. A latent profile analysis on 1247 interests showed six distinct multidimensional patterns, indicating both a homogeneous and heterogeneous structure of interest. Four homogeneous patterns were indicated by more or less equal levels on all six dimensions in varying degrees, and contained 86% of the interests. Two heterogeneous patterns were found, describing variations of interest that are interpreted and discussed. These results endorse the complexity of the construct of interest and provide suggestions for identifying different manifestations of interest

Word problems versus image-rich problems: an analysis of effects of task characteristics on students’ performance on contextual mathematics problems

This article reports on a post hoc study using a randomised controlled trial with 31,842 students in the Netherlands and an instrument consisting of 21 paired problems. The trial showed a variability in the differences of students’ results in solving contextual mathematical problems with either a descriptive or a depictive representation of the problem situation. In this study the relation between this variability and two task characteristics is investigated: (1) complexity of the task representation; and (2) the content domain of the task. We found indications that differences in performance on descriptive and depictive representations of the problem situation are related to the content domain of the problems. One of the tentative conclusions is that for depicted problems in the domain of measurement and geometry the inferential step from representation of the problem situation to the mathematical problem to be solved is smaller than for word problems

Assessing Students’ Interpretations of Histograms Before and After Interpreting Dotplots: A Gaze-Based Machine Learning Analysis

Many students persistently misinterpret histograms. Literature suggests that having students solve dotplot items may prepare for interpreting histograms, as interpreting dotplots can help students realize that the statistical variable is presented on the horizontal axis. In this study, we explore a special case of this suggestion, namely, how students’ histogram interpretations alter during an assessment. The research question is: In what way do secondary school students’ histogram interpretations change after solving dotplot items? Two histogram items were solved before solving dotplot items and two after. Students were asked to estimate or compare arithmetic means. Students’ gaze data, answers, and cued retrospective verbal reports were collected. We used students’ gaze data on four histogram items as inputs for a machine learning algorithm (MLA; random forest). Results show that the MLA can quite accurately classify whether students’ gaze data belonged to an item solved before or after the dotplot items. Moreover, the direction (e.g., almost vertical) and length of students’ saccades were different on the before and after items. These changes can indicate a change in strategies. A plausible explanation is that solving dotplot items creates readiness for learning and that reflecting on the solution strategy during recall then brings new insights. This study has implications for assessments and homework. Novel in the study is its use of spatial gaze data and its use of an MLA for finding differences in gazes that are relevant for changes in students’ task-specific strategies