Applying an Error Taxonomy to Examine Inexperienced Spreadsheet Users’ Planning and Execution Errors

This paper presents preliminary findings of an application of the Panko-Aurigemma (2010) error taxonomy to errors generated in a spreadsheet training task. Data from 11 inexperienced trainees were obtained on two spreadsheet training tasks of different complexity and scored by two judges. High levels of inter-rater reliability were obtained for a refined planning and execution error classification. Preliminary findings relating to the likely processes underlying task completion indicate that trainees make more execution than planning errors on easy tasks. Negative associations were found between the frequency of execution and planning errors and task performance when completing easy tasks. For hard tasks, we found a negative association between task performance and frequency of execution errors; however, the association between the number of planning errors and performance was positive. These findings point to the utility of examining error types in IS training strategy research

Monitoring Handbook 6: Analyzing and interpreting monitoring data

The basic purpose of data analysis is to identify patterns of change in your indicator over time, and to evaluate these changes. Without doing some kind of analysis, it will be difficult for you to know the effect your project is actually having. The data analysis techniques presented in this handbook are not difficult. Most of them can be easily done using little more than a calculator and scratch paper. If necessary, there are resources listed in the handbook for additional assistance analyzing your data

Role of an artefact of Dynamic algebra in the conceptualisation of the algebraic equality

In this contribution, we explore the impact of Alnuset, an artefact of dynamic algebra, on the conceptualisation of algebraic equality. Many research works report about obstacles to conceptualise this notion due to interference of the previous arithmetic knowledge. New meanings need to be assigned to the equal sign and to letters used in algebraic expressions. Based on the hypothesis that Alnuset can be effectively used to mediate the conceptual development necessary to master the algebraic equality notion, two experiments have been designed and implemented in Italy and in France. They are reported in the second part of this pape

Processing mathematical thinking through digital pedagogical media: the spreadsheet

Abstract This study is concerned with the ways mathematical understanding emerges when mathematical phenomena are encountered through digital pedagogical media, the spreadsheet, in particular. Central to this, was an examination of the affordances digital technologies offer, and how the affordances associated with investigating mathematical tasks in the spreadsheet environment, shaped the learning trajectories of the participants. Two categories of participating students were involved, ten-year-old primary school pupils, and pre-service teachers. An eclectic approach to data collection, including qualitative and quantitative methods, was initially undertaken, but as my research perspective evolved, a moderate hermeneutic frame emerged as the most productive way in which to examine the research questions. A hermeneutic process transformed the research methodology, as well as the manner in which the data were interpreted. The initial analysis and evolving methodology not only informed this transition to a moderate hermeneutic lens, they were constitutive of the ongoing research perspectives and their associated interpretations. The data, and some that was subsequently collected, were then reconsidered from this modified position. The findings indicated that engaging mathematical tasks through the pedagogical medium of the spreadsheet, influenced the nature of the investigative process in particular ways. As a consequence, the interpretations of the interactions, and the understandings this evoked, also differed. The students created and made connections between alternative models of the situations, while the visual, tabular structuring of the environment, in conjunction with its propensity to instantly manage large amounts of output accurately, facilitated their observation of patterns. They frequently investigated the visual nature of these patterns, and used visual referents in their interpretations and explanations. It also allowed them to pose and test their informal conjectures and generalisations in non-threatening circumstances, to reset investigative sub-goals easily, hence fostering risk taking in their approach. At times, the learning trajectory evolved in unexpected ways, and the data illustrated various alternative ways in which unexpected, visual output stimulated discussion and extended the boundaries of, or reorganised, their interaction and mathematical thinking. An examination of the visual perturbations, and other elements of learning as hermeneutic processes also revealed alternative understandings and explanations. Viewing the data and the research process through hermeneutic filters enhanced the connectivity between the emergence of individual mathematical understanding, and the cultural formation of mathematics. It permitted consideration of the ways this process influences the evolution of mathematics education research. While interpretive approaches are inevitably imbued with the researcher perspective in the analysis of what gets noticed, the research gave fresh insights into the ways learning emerges through digital pedagogical media, and the potential of this engagement to change the nature of mathematics education

Mathematical modeling in the high school classroom

Mathematical modeling is the procedure whereby students apply mathematical concepts learned in class to new and unfamiliar situations. A modeling task is a mathematically-rich problem that engages students in mathematical thinking, drawing upon their previously learned knowledge and supporting their understanding of the mathematical concepts currently being covered. Modeling requires students to assign meaning to the mathematical concepts and to extend the concepts beyond rote learning. In order for students to be successful in a classroom that is centered around the idea of mathematical modeling, the students must be taught how to collaborate with other students, persevere through challenging problems, and become aware of their own thinking. In this thesis, I focus on a professional development workshop designed to train high school teachers on how to successfully use mathematical modeling in their classroom by providing them with guidelines on how to use modeling tasks effectively, sample tasks that can be used, and instruction on how to develop modeling tasks for their classroom. The goal is to affect change in the daily routines of high school mathematics classrooms by providing teachers with compelling reasons why changes are necessary, steps on how to make the necessary changes, and good examples of problems to be used in class

Information technology as an aid to teaching algebra

This project was concerned-with teaching algebra novices, all girls aged 13 or 14 years, to solve algebra word problems using an electronic spreadsheet. It was based on the realisation that a spreadsheet cell provides a suitable cognitive model for an algebraic variable and that the manipulation of a spreadsheet is essentially based on the construction of algebraic expressions. The main objectives were to test the effectiveness of spreadsheet use on the ability to construct algebraic expressions and to examine the effect of manipulating problem contexts (abstract vs. concrete) on this ability. Other objectives were to determine the relationship between general numerical ability, attitude to mathematics, attitude to computers and the experimental treatments. The particular skill taught was the construction of algebraic expressions to represent relational propositions from verbally stated problems. Problems from current textbooks and examination papers (Intermediate Certificate Syllabus B) were used in the instruction. A pretest - posttest control group design was used. Seventy three volunteers were recruited and received approximately eight hours of Instruction in a reasonably natural school setting. There were two treatment groups. One group worked on abstract (numerical) problems and the other group worked on mathematically identical problems set in concrete contexts which were familiar and relevant. Both treatment groups made considerable gains between pretest and posttest. The abstract group performed significantly better than the concrete group on the total posttest (p < .01), on its abstract subsection (p < .01) and on its concrete subsection (p < .05). Attitude to mathematics was also found to have a significant Interaction with the treatment (p <. 05). Those with a positive attitude to mathematics learned more from abstract problems, but the difference was much less for those with a negative attitude. Neither numerical ability or attitude to computers had any significant effect

College student novice spreadsheet reasoning and errors

The spreadsheet has become a common technology tool and is now a predominant form of end-user programming. Some of the same features that make spreadsheets excellent tools for ad-hoc development can introduce errors into the final product. Although a variety of research has been performed investigating methods to detect errors in spreadsheets, little has been done to investigate initial reasoning errors. The spreadsheet error taxonomy developed by Rajalingham, Chadwick, and Knight (2001) includes categories for reasoning errors that have not yet been investigated. Previous studies have categorized errors in existing spreadsheets, but have not analyzed the source of the error. This study investigates the reasoning of college students while developing spreadsheets and examines the reasoning associated with errors generated in spreadsheet development. For this study, a phenomenological qualitative design incorporated a think-aloud protocol, interviews, and recordings of spreadsheet development of three purposefully-selected students. Data sources were analyzed to determine their reasoning, the types of errors produced based on the taxonomy, and associations between reasoning and errors. The findings indicated that students used different types of reasoning in the mathematical phases of spreadsheet development than they do in the spreadsheet implementation phase. As novice spreadsheet developers, the students had significant difficulties translating problems into mathematical representations. Spreadsheet skills and concepts improved with practice through the course, but mathematical representations remained problematic. The students enjoyed using the spreadsheet as a tool for doing mathematical reasoning. Several themes emerged as the study progressed: Reasoning differences during mathematical and spreadsheet phases of development; using icons for functions affected conceptualization of the functions; copy operations were perceived as ―painting‖ rather than applying a formula to a series; and the effectiveness of the taxonomy for categorizing reasoning errors . The results suggested modifications to student learning experiences leading to more accurate spreadsheet development: Integrate spreadsheets into mathematics courses; increase education in spreadsheet development; integrate formal design and testing components to the spreadsheet curriculum; include spreadsheet errors in the curriculumKeywords: Reasoning, Spreadsheet, Errors, Educatio