14,479 research outputs found
Multiple perspectives on the concept of conditional probability
Conditional probability is a key to the subjectivist theory of probability; however, it plays a subsidiary role in the usual conception of probability where its counterpart, namely independence is of basic importance. The paper investigates these concepts from various perspectives in order to shed light on their multi-faceted character. We will include the mathematical, philosophical, and educational perspectives. Furthermore, we will inspect conditional probability from the corners of competing ideas and solving strategies. For the comprehension of conditional probability, a wider approach is urgently needed to overcome the well-known problems in learning the concepts, which seem nearly unaffected by teaching
Drawing to learn in STEM
Scientists, mathematicians and engineers draw and model to create knowledge. This presentation will describe a guided inquiry approach to teaching and learning science that involves students actively creating visual and other representations to reason and explain as they explore the material world. The approach has been successfully used in a number of major professional learning initiatives in Victoria and NSW. Evidence will be presented of increased student engagement and quality learning flowing from the approach, which aligns classroom processes more authentically with processes of imaginative scientific discovery. Examples of activities and student drawings and model construction will be used to unpack the relationship between representation, reasoning and learning. Video evidence including that generated in the Science of Learning Research Centre (SLRC) classroom at the University of Melbourne, equipped with sophisticated video capture facilities, will be drawn on to explore ways in which drawing, gesture and talk are coordinated to imaginatively respond to material challenges. The presentation will explore the alignment of these sociocultural analyses to recent findings from neuroscience. Evidence will be presented that the creation of representations is central to quality learning across the STEM disciplines and for interdisciplinary STEM challenges
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Enactivism and ethnomethodological conversation analysis as tools for expanding Universal Design for Learning: the case of visually impaired mathematics students
Blind and visually impaired mathematics students must rely on accessible materials such as tactile diagrams to learn mathematics. However, these compensatory materials are frequently found to offer students inferior opportunities for engaging in mathematical practice and do not allow sensorily heterogenous students to collaborate. Such prevailing problems of access and interaction are central concerns of Universal Design for Learning (UDL), an engineering paradigm for inclusive participation in cultural praxis like mathematics. Rather than directly adapt existing artifacts for broader usage, UDL process begins by interrogating the praxis these artifacts serve and then radically re-imagining tools and ecologies to optimize usability for all learners. We argue for the utility of two additional frameworks to enhance UDL efforts: (a) enactivism, a cognitive-sciences view of learning, knowing, and reasoning as modal activity; and (b) ethnomethodological conversation analysis (EMCA), which investigates participants’ multimodal methods for coordinating action and meaning. Combined, these approaches help frame the design and evaluation of opportunities for heterogeneous students to learn mathematics collaboratively in inclusive classrooms by coordinating perceptuo-motor solutions to joint manipulation problems. We contextualize the thesis with a proposal for a pluralist design for proportions, in which a pair of students jointly operate an interactive technological device
A Comparative Analysis of the Supernova Legacy Survey Sample with {\Lambda}CDM and the Universe
The use of Type~Ia SNe has thus far produced the most reliable measurement of
the expansion history of the Universe, suggesting that CDM offers the
best explanation for the redshift--luminosity distribution observed in these
events. But the analysis of other kinds of source, such as cosmic chronometers,
gamma ray bursts, and high- quasars, conflicts with this conclusion,
indicating instead that the constant expansion rate implied by the Universe is a better fit to the data. The central difficulty with the
use of Type~Ia SNe as standard candles is that one must optimize three or four
nuisance parameters characterizing supernova luminosities simultaneously with
the parameters of an expansion model. Hence in comparing competing models, one
must reduce the data independently for each. We carry~out such a comparison of
CDM and the Universe, using the Supernova Legacy Survey
(SNLS) sample of 252 SN~events, and show that each model fits its individually
reduced data very well. But since has only one free parameter
(the Hubble constant), it follows from a standard model selection technique
that it is to be preferred over CDM, the minimalist version of which
has three (the Hubble constant, the scaled matter density and either the
spatial curvature constant or the dark-energy equation-of-state parameter). We
estimate by the Bayes Information Criterion that in a pairwise comparison, the
likelihood of is , compared with only for
a minimalist form of CDM, in which dark energy is simply a
cosmological constant. Compared to , versions of the standard
model with more elaborate parametrizations of dark energy are judged to be even
less likely.Comment: 31 Pages, 5 Figures, 1 Table. Accepted for publication in A
AN EXAMINATION OF THE IMPACT OF COMPUTER-BASED ANIMATIONS AND VISUALIZATION SEQUENCE ON LEARNERS' UNDERSTANDING OF HADLEY CELLS IN ATMOSPHERIC CIRCULATION
Research examining animation use for student learning has been conducted in the last two decades across a multitude of instructional environments and content areas. The extensive construction and implementation of animations in learning resulted from the availability of powerful computing systems and the perceived advantages the novel medium offered to deliver dynamic representations of complex systems beyond the human perceptual scale. Animations replaced or supplemented text and static diagrams of system functioning and were predicted to significantly improve learners' conceptual understanding of target systems. However, subsequent research has not consistently discovered affordances to understanding, and in some cases, has actually shown that animation use is detrimental to system understanding especially for content area novices (Lowe 2004; Mayer et al. 2005).
This study sought to determine whether animation inclusion in an authentic learning context improved student understanding for an introductory earth science concept, Hadley Cell circulation. In addition, the study sought to determine whether the timing of animation examination improved conceptual understanding. A quasi-experimental pretest posttest design administered in an undergraduate science lecture and laboratory course compared four different learning conditions: text and static diagrams with no animation use, animation use prior to the examination of text and static diagrams, animation use following the examination of text and static diagrams, and animation use during the examination of text and static diagrams. Additionally, procedural data for a sample of three students in each condition were recorded and analyzed through the lens of self regulated learning (SRL) behaviors. The aim was to determine whether qualitative differences existed between cognitive processes employed. Results indicated that animation use did not improve understanding across all conditions. However learners able to employ animations while reading and examining the static diagrams and to a lesser extent, after reading the system description, showed evidence of higher levels of system understanding on posttest assessments. Procedural data found few differences between groups with one exception---learners given access to animations during the learning episode chose to examine and coordinate the representations more frequently. These results indicated a new finding from the use of animation, a sequence effect to improve understanding of Hadley Cells in atmospheric circulation
Student and AI responses to physics problems examined through the lenses of sensemaking and mechanistic reasoning
Several reports in education have called for transforming physics learning
environments by promoting sensemaking of real-world scenarios in light of
curricular ideas. Recent advancements in Generative-Artificial Intelligence has
garnered increasing traction in educators' community by virtue of its potential
in transforming STEM learning. In this exploratory study, we adopt a
mixed-methods approach in comparatively examining student- and AI-generated
responses to two different formats of a physics problem through the cognitive
lenses of sensemaking and mechanistic reasoning. The student data is derived
from think-aloud interviews of introductory students and the AI data comes from
ChatGPT's solutions collected using Zero shot approach. The results highlight
AI responses to evidence most features of the two processes through
well-structured solutions and student responses to effectively leverage
representations in their solutions through iterative refinement of arguments.
In other words, while AI responses reflect how physics is talked about, the
student responses reflect how physics is practiced. Implications of these
results in light of development and deployment of AI systems in physics
pedagogy are discussed
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Exploring the episodic structure of algebra story problem solving
This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem-solving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses of written protocols compare the strategic, tactical, and conceptual content of solution attampts, looking within these attempts at the interplay between problem comprehension and solution. Comprehension and solution of algebra story problems are complimentary activities, giving rise to a succession of problem solving episodes. While direct algebraic problem solving is sometimes effective, results suggest that the algebraic formalism may be of little help in comprehending the quantitative constraints posed in a problem text. Instead, competent problem solvers often reason within the situational context presented by a story problem, using various forms of "model-based reasoning" to identify, pursue, and verify quantitative constraints required for solution. The paper concludes by discussing the implications of these findings for acquiring mathematical concepts (e.g., related linear functions) and for supporting their acquisition through instruction
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