Measurement of Student Perceptions and Attitudes in Mathematics

As in other subjects, student perceptions of and attitudes towards mathematics play a role in their motivation and approaches to learning. This is of special concern in mathematics as so many students take terminal math courses at the post-secondary level as part of other programs. Ultimately, we are interested in how these attitudes influence further math course choices and student performance in the courses they do take, as well as instructional choices that can promote more expert-like attitudes.This academic year, our research group adapted an existing survey for Physics (the CLASS developed at U. Colorado), a measure of student orientation towards expert attitudes about the subject, which including perceptions of math as a field and (self-perceived) dispositions in math problem solving. We surveyed UBC students at the beginning and end of a range of early Math courses (primarily first-year calculus courses), as well as a variety of experts in our department (faculty, graduate students and post-docs). This has allowed us to assess student attitudes and perceptions, and to track how they shift over time, relative to an expert response. Similar adaptations of this survey exist for other science disciplines (see http://www.colorado.edu/sei/class/).In this presentation, I will discuss some existing tools in math and other disciplines for assessing student attitudes, review the development process we are following, and show highlights from our preliminary results

PROARTIS: Probabilistically analyzable real-time systems

Static timing analysis is the state-of-the-art practice of ascertaining the timing behavior of currentgeneration real-time embedded systems. The adoption of more complex hardware to respond to the increasing demand for computing power in next-generation systems exacerbates some of the limitations of static timing analysis. In particular, the effort of acquiring (1) detailed information on the hardware to develop an accurate model of its execution latency as well as (2) knowledge of the timing behavior of the program in the presence of varying hardware conditions, such as those dependent on the history of previously executed instructions. We call these problems the timing analysis walls. In this vision-statement article, we present probabilistic timing analysis, a novel approach to the analysis of the timing behavior of next-generation real-time embedded systems. We show how probabilistic timing analysis attacks the timing analysis walls; we then illustrate the mathematical foundations on which this method is based and the challenges we face in the effort of efficiently implementing it. We also present experimental evidence that shows how probabilistic timing analysis reduces the extent of knowledge about the execution platform required to produce probabilistically accurate WCET estimations. © 2013 ACM.Peer Reviewe

Improving Measurement-Based Timing Analysis through Randomisation and Probabilistic Analysis

The use of increasingly complex hardware and software platforms in response to the ever rising performance demands of modern real-time systems complicates the verification and validation of their timing behaviour, which form a time-and-effort-intensive step of system qualification or certification. In this paper we relate the current state of practice in measurement-based timing analysis, the predominant choice for industrial developers, to the proceedings of the PROXIMA project in that very field. We recall the difficulties that the shift towards more complex computing platforms causes in that regard. Then we discuss the probabilistic approach proposed by PROXIMA to overcome some of those limitations. We present the main principles behind the PROXIMA approach as well as the changes it requires at hardware or software level underneath the application. We also present the current status of the project against its overall goals, and highlight some of the principal confidence-building results achieved so far

A Mechanistic Approach to Understanding the Factors Affecting Drug Absorption: A Review of Fundamentals

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97203/1/00970002042006005.pd

Astronomical Distance Determination in the Space Age: Secondary Distance Indicators

The formal division of the distance indicators into primary and secondary leads to difficulties in description of methods which can actually be used in two ways: with, and without the support of the other methods for scaling. Thus instead of concentrating on the scaling requirement we concentrate on all methods of distance determination to extragalactic sources which are designated, at least formally, to use for individual sources. Among those, the Supernovae Ia is clearly the leader due to its enormous success in determination of the expansion rate of the Universe. However, new methods are rapidly developing, and there is also a progress in more traditional methods. We give a general overview of the methods but we mostly concentrate on the most recent developments in each field, and future expectations. © 2018, The Author(s)

Measuring student beliefs, attitudes and dispositions relative to experts in science and mathematics: the C-LASS survey and its derivatives.

As part of the Science Education Initiatives under the directorship of Carl Wieman at the University of British Columbia (CWSEI) and the University of Colorado at Boulder (CUSEI), a suite of survey instruments has been developed to measure student orientation to expert-like attitudes and dispositions in each of Physics, Chemistry, Biology, Earth Sciences, Mathematics, Statistics and Computer Science. The surveys, usually administered online, consist of 35-50 statements each, with a 5-point Likert scale, and may be completed quickly as opinions are measured rather than content knowledge or skills (e.g. To learn biology, I only need to memorize facts and definitions , Nearly everyone is capable of understanding math if they work at it. ). Students are scored relative to the expert response for each statement (i.e. the one chosen by a strong majority of instructors and researchers in the discipline); some early validation found that students were able to identify the expert response choice but would respond with their own opinion as instructed. The result is a quick assessment of attitudes, including motivation and understanding of the nature of the discipline, which are known to be related to learning. We will present the development process, involving iteration between survey data and statement validation stages with students and experts, as well as findings from the different disciplines in (primarily early) university courses. These include common trends, such as a tendency to see a decrease in overall expert orientation in the first year and alignment of expert attitudes with course performance, as well as some unique disciplinary outcomes. We hope to further discuss the implications for instruction with those who attend

The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students\u27 perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students\u27 overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education

Measurement-Based Probabilistic Timing Analysis for Multi-path Programs

The rigorous application of static timing analysis requires a large and costly amount of detail knowledge on the hardware and software components of the system. Probabilistic Timing Analysis has potential for reducing the weight of that demand. In this paper, we present a sound measurement-based probabilistic timing analysis technique based on Extreme Value Theory. In all the experiments made as part of this work, the timing bounds determined by our technique were less than 15% pessimistic in comparison with the tightest possible bounds obtainable with any probabilistic timing analysis technique. As a point of interest to industrial users, our technique also requires a comparatively low number of measurement runs of the program under analysis, less than 650 runs were needed for the benchmarks presented in this paper.Peer Reviewe