ChatGPT and Excel -- trust, but verify

This paper adopts a critical approach to ChatGPT, showing how its huge reach makes it a useful tool for people with simple requirements but a bad, even misleading guide to those with more complex problems which are more rarely present in the training data and even more rarely have straightforward solutions. It works through four exercises in creating lookup formulas using chatbots, showing the need to test the offered solutions. They are a simple lookup, a lookup to the left, a match of two values at the same time, and intentionally confusing the models by using common language with technical meaning in Excel. It concludes with a practical guide for how to add an Excelscript button, with system and user prompts, to the ChatGPT API into the Excel desktop environment, supported by a blog post giving the technical details for those interested.Comment: 15 pages, 3 figure

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

The mathematics curriculum and pupils' Thinking processes: Learning to solve algebraic problems in year 7 and year 8 in England and Thailand

Previous studies of pupils' learning of algebra have been inclined to study errors in given answers. The present study attempts to investigate pupils' thinking processes in the early stages of learning algebra by examining and comparing responses made by English and Thai pupils to the researcher's algebra test. The research was conducted among pupils during their "normal" lessons in secondary school algebra. Pupil participants were in the first two years of secondary education. Data collection included lesson observations, interviews, and the researcher's algebra test. The thinking processes were first categorised from the interview data to provide a framework for analysing pupils' written responses to the researcher's test. Later, a codebook was kept in which pupils' responses to the researcher’s test were coded. The study goes on to analyse the outcomes from this coding procedure. The research indicates that the differences in the way pupils think appear to be closely related to the teaching and curriculum provided. In both countries, success in algebra is dependent on having good arithmetic skills. Also the reluctance of pupils to use algebra to solve easy problems results in algebraic skills being inadequately developed to solve more difficult problems. An implication for practice is that the Thai school should consider the bearing which the understanding of simplification of like terms has upon a pupil's ability to solve linear equations. Both schools could consider ways of making effective use of patterns and sequences to develop algebraic thinking. The codebook developed in this research could serve as a tool for mathematics teachers in helping them to understand the complexity of their pupils thinking processes in solving algebraic problems. An investigation involving more schools in other settings could follow this

Modelling human teaching tactics and strategies for tutoring systems

One of the promises of ITSs and ILEs is that they will teach and assist learning in an intelligent manner. Historically this has tended to mean concentrating on the interface, on the representation of the domain and on the representation of the student’s knowledge. So systems have attempted to provide students with reifications both of what is to be learned and of the learning process, as well as optimally sequencing and adjusting activities, problems and feedback to best help them learn that domain. We now have embodied (and disembodied) teaching agents and computer-based peers, and the field demonstrates a much greater interest in metacognition and in collaborative activities and tools to support that collaboration. Nevertheless the issue of the teaching competence of ITSs and ILEs is still important, as well as the more specific question as to whether systems can and should mimic human teachers. Indeed increasing interest in embodied agents has thrown the spotlight back on how such agents should behave with respect to learners. In the mid 1980s Ohlsson and others offered critiques of ITSs and ILEs in terms of the limited range and adaptability of their teaching actions as compared to the wealth of tactics and strategies employed by human expert teachers. So are we in any better position in modelling teaching than we were in the 80s? Are these criticisms still as valid today as they were then? This paper reviews progress in understanding certain aspects of human expert teaching and in developing tutoring systems that implement those human teaching strategies and tactics. It concentrates particularly on how systems have dealt with student answers and how they have dealt with motivational issues, referring particularly to work carried out at Sussex: for example, on responding effectively to the student’s motivational state, on contingent and Vygotskian inspired teaching strategies and on the plausibility problem. This latter is concerned with whether tactics that are effectively applied by human teachers can be as effective when embodied in machine teachers

The development of multiplicative thinking and proportional reasoning: Models of conceptual learning and transfer

This thesis considers the development of multiplicative thinking and proportional reasoning from two perspectives. Firstly, it examines the research literature on progressions in conceptual understanding to create a Hypothetical Learning Trajectory (HLT). Secondly, it surveys modern views of how transfer by learners occurs in and between situations, contrasting object views of abstraction with knowledge in pieces views. Case studies of six students aged 11-13 years illustrate conceptual changes that occur during the course of a school year. The students are involved in a design experiment in which I (the researcher) co-teach with the classroom teacher. The students represent a mix of gender, ethnicity and level of achievement. Comparison of the HLT with the actual learning trajectory for each student establishes its validity as a generic growth path. Examination of the data suggests that two models of learning and by inference, transfer, describe the conceptual development of the students. There is consideration of students’ use of anticipated actions on physical and imaged embodiments as objects of thought with a focus on the significance of object creation for conceptual growth, and the encapsulation, completeness and contextual detachment of objects. There is broad consistency in students’ progress through the phases of the HTL within each sub-construct though the developmental patterns of individual are variable and temporal alignment across the sub-constructs does not uniformly hold. Some consistency of order effect in concept development is noted. Discussion on the limitations of the HTL includes the difference between knowledge types from a pedagogical perspective, absence of significant model-representation-situation transfer, and order relations in conceptual development. Considerable situational variation occurs as students solve problems that involve applications of the same concepts. Partial construction of concepts is common. This was true of all learners, irrespective of level of achievement. High-achieving students more readily anticipate actions and trust these anticipations as objects of thought than middle and low achievers. The data supports knowledge in pieces views of conceptual development. Complexity for learners in observing affordances in situations, and in co-ordinating the fine-grained knowledge required, explains the difficulty of transfer. While supporting the anticipation of action as significant from a learning perspective the research suggests that expertise in applying concepts involves a process of noticing similarity across contextually bound situations and cueing appropriate knowledge resources

Exploring grade 11 learner routines on function from a commognitive perspective

A thesis submitted to the Faculty of Humanities, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy September 2015This study explores the mathematical discourse of Grade 11 learners on the topic function through their routines. From a commognitive perspective, it describes routines in terms of exploration and ritual. Data was collected through in-depth interviews with 18 pairs of learners, from six South African secondary schools, capturing a landscape of public schooling, where poor performance in Mathematics predominates. The questions pursued became: why does poor performance persist and what might a commognitive lens bring into view? With the discursive turn in education research, commognition provides an alternate view of learning mathematics. With the emphasis on participation and not on constraints from inherited mental ability, the study explored the nature of learner discourse on the object, function. Function was chosen as it holds significant time and weight in the secondary school curriculum. Examining learners’ mathematical routines with the object was a way to look at their discourse development: what were the signifiers related to the object and what these made possible for learners to realise. Within learners’ routines, I was able to characterise these realisations, which were described and categorised. This enabled a description of learner thinking over three signifiers of function in school Mathematics: the algebraic expression, table and graph. In each school, Grade 11 learners were separated into three groups according to the levels at which they were performing, from summative scores of grade 11 assessments, so as to enable a description of discourse related to performance. Interviews were conducted in pairs, and designed to provoke discussion on aspects of function and its signifiers between learners in each pair. This communication between learners and with the interviewer provided data for description and analysis of rituals and explorations. Zooming in and out again on these routines made a characterisation of the discourse of failure possible, which is seldom done. It became apparent early in the study that learners talked of the object function, without a formal mathematical narrative, a definition in other words, of the object. The object was thus vested in its signifiers. The absence of an individualised formal narrative of the object impacts directly what is made possible for learners to realise, hence to learn. The study makes the following contributions: first, it describes learners’ discursive routines as they work with the object function. Second, it characterises the discourse of learners at different levels of performance. Third, it starts exploration of commognition as an alternate means to look at poor performance. The strengths and limitations of the theory as it pertains to this study, are discussed later in the concluding chapter. Keywords commognition, discourse, communication, participation, routines, exploration, ritual, learners, learning, narratives, endorsed narratives, visual mediators

Modellus: Learning Physics with Mathematical Modelling

Tese de doutoramento em Ciências da Educação, área de Teoria Curricular e Ensino das CiênciasComputers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge

Remediation of first-year mathematics students' algebra difficulties.

Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.The pass rate of first-year university mathematics students at the University of KwaZulu-Natal (Pietermaritzburg Campus) has been low for many years. One cause may be weak algebra skills. At the time of this study, revision of high school algebra was not part of the major first year mathematics course. This study set out to investigate if it would be worthwhile to spend tutorial time on basic algebra when there is already an overcrowded calculus syllabus, or if students refresh their algebra skills sufficiently as they study first year mathematics. Since it was expected that remediation of algebra skills would be found to be worthwhile, two other questions were also investigated: Which remediation strategy is best? Which errors are the hardest to remediate? Five tutorial groups for Math 130 were randomly assigned one of four remediation strategies, or no remediation. Three variations of using cognitive conflict to change students’ misconceptions were used, as well as the strategy of practice. Pre- and post-tests in the form of multiple choice questionnaires with spaces for free responses were analysed. Comparisons between the remediated and non-remediated groups were made based on pre- and post-test results and Math 130 results. The most persistent errors were determined using an 8-category error classification developed for this purpose. The best improvement from pre- to post-test was 12.1% for the group remediated with cognitive conflict over 5 weeks with explanations from the tutor. Drill and practice gave the next-best improvement of 8.1%, followed by self-guided cognitive conflict over 5 weeks (7.8% improvement). A once-off intervention using cognitive conflict gave a 5.9% improvement. The group with no remediation improved by 2.3%. The results showed that the use of tutorintensive interventions more than doubled the improvement between pre-and post-tests but even after remediation, the highest group average was 80%, an unsatisfactory level for basic skills. The three most persistent errors were those involving technical or careless errors, errors from over-generalising and errors from applying a distorted algorithm, definition or theorem