A brief historical introduction to solitons and the inverse scattering transform–a vision of Scott Russell

The objective of this study was to evaluate biomathtutor by (i) investigating the impact of biomathtutor on the mathematics skills competencies of bioscience undergraduates, and (ii) assessing students’ and tutors’ reactions to biomathtutor, identifying whether and how tutors might integrate it into their curricula and blend it with more traditional teaching practices to enhance their students’ learning experiences. A multi-method approach was adopted in which a quasi-experiment and non-experimental evaluation of biomathtutor were used to collect both quantitative and qualitative data, using mathematics tests, questionnaires, tutor interviews and student focus groups. Eighty-nine bioscience undergraduates and eight tutors participated in the study. A comparison of student performance in the quasi-experiment, which adopted a pre-test-intervention-post-test methodology, revealed no significant difference between pre-test and post-test scores for either the ‘control’ group (no intervention) or for any of the mathematics learning support interventions used, including biomathtutor. Despite the limitations of the quasi-experiment which are discussed, tutors’ and their students’ reactions towards biomathtutor were very positive, with both groups agreeing that biomathtutor represents a very well designed and useful learning resource that has a valuable role to play in supporting mathematics learning within bioscience curricula. Students felt that using biomathtutor had helped them acquire new biological and mathematical knowledge and had increased their competence and confidence in mathematics, with many students confirming that they would use biomathtutor again. Tutors felt it would be useful to embed biomathtutor, where possible, into their curricula, perhaps linking it to assessment strategies or integrating it with their current more traditional teaching practices. Students indicated that they too would like to see biomathtutor embedded within their curricula, primarily because it would motivate them to use the resource. Modifications to biomathtutor, which may need to be considered in light of any potential further development of this resource, are discussed.     

Differential and integral calculus III through WebCT: analysis of results

In this paper a Calculus course for students of Engineering in the virtual environment is discussed. This course used WebCT course management software only, without traditional lessons. A feedback survey obtained by questionnaires and data concerning the progress of students are presented and analysed. Conclusions point out the need for further research into the use of the virtual universe within the teaching/learning process and the necessity of re-examining the work normally done in the classroom.     

Academic achievement with cooperative learning using homogeneous and heterogeneous groups

Cooperative learning is a proven teaching strategy that teachers have been using for over 40 years. Teachers often group students heterogeneously so that students who are lower achieving are learning with and from higher achieving students. The purpose of this study was to test homogeneous and heterogeneous grouping while using cooperative learning teaching structure. This study aimed to answer the question of whether students be grouped homogeneously or heterogeneously while participating in cooperative learning. The primary research design for this study was a quasi-experimental nonequivalent control-group design. A convenience sample of fifth-grade students was drawn from a Georgia elementary school in the 2017–2018 school year. The data were analyzed using analysis of covariance (ANCOVA) and paired samples t tests. The ANCOVA was run to compare the scores from the FOSS Survey/Posttest, and the analysis showed no significant difference between the homogeneous and heterogeneous group posttest scores. Both groups made significant gains (as shown by the results of the paired samples t-tests).     

Large sets of resolvable idempotent Latin squares

An idempotent Latin square of order v is called resolvable and denoted by RILS(v) if the v(v−1) off-diagonal cells can be resolved into v−1 disjoint transversals. A large set of resolvable idempotent Latin squares of order v, briefly LRILS(v), is a collection of v−2 RILS(v)s pairwise agreeing on only the main diagonal. In this paper we display some recursive and direct constructions for LRILSs.     

Choosing more mathematics: happiness through work?

This paper examines how A-level students construct relationships between work and happiness in their accounts of choosing mathematics and further mathematics A-level. I develop a theoretical framework that positions work and happiness as opposed, managed and working on the self and use this to examine students' dual engagement with individual practices of the self and institutional practices of school mathematics. Interviews with students acknowledge four imperatives that they use as discursive resources to position themselves as successful/unsuccessful students: you have to work, you have to not work, you have to be happy, you have to work at being happy. Tensions in these positions lead students to rework their identities or drop further mathematics. I then identify the practices of mathematics teaching that students use to explain un/happiness in work, and show how dependable mathematics and working together are constructed as ‘happy objects’ for students, who develop strategies for claiming control over these shapers of happiness.     

The Effects of Project‐Based Learning on Students' Academic Achievement,Attitude, and Retention of Knowledge: The Subject of “Electricity in Our Lives”

The aim of this study is to analyze the effects of project‐based learning on students' academic achievement, attitude, and retention of knowledge in relation to the subject of “Electricity in Our Lives” in a fourth‐grade science course. The study was conducted in a quasi‐experimental design as a “pre‐test, post‐test with control group.” In the experimental group, the unit was taught through the project‐based learning method. The measuring tools were administered to both groups before and after the applications. To perfectly analyze the “process” of the method, seven different learning assessment “forms” were administered to the students. The findings of the forms indicated that the students learn to construct their own learning and to evaluate changes in their own behavior through the application of the method. The application of different methods between both groups had a statistically significant effect in terms of academic achievement, (F(1,112) = 46.78, p = .000) and of retention of knowledge (F(1,112) = 35.24, p = .000). However, there were no statistically significant effects from being in different groups for the attitudes of students (F(1,112) = .99, p = .321). For the students, being in the project‐based learning groups resulted in better academic achievement and retention of knowledge than being in the traditional teaching group.     

The Science Teaching Self‐Efficacy of Prospective Elementary Education Majors Enrolled in Introductory Geology Lab Sections

This study examined prospective elementary education majors' science teaching self‐efficacy while they were enrolled in an introductory geology lab course for elementary education majors. The Science Teaching Efficacy Belief Instrument Form B (STEBI‐B) was administered during the first and last lab class sessions. Additionally, students were asked an open‐ended question to describe their experience in the education majors' geology lab. The results of the STEBI‐B were analyzed using paired t‐tests to determine whether the students changed their personal science teaching efficacy (PSTE) and science teaching outcome expectancy (STOE). Results of this study indicate a significant increase in PSTE. No significant differences were found in STOE. This study suggests that science content courses designed for education majors may lead to a positive change in science teaching self‐efficacy and has implications for teacher educators in preparing science content courses for their teacher preparation program.     

A Collaborative Effort to Improve University Engineering Instruction

This study focused on the instructional development of an assistant professor of environmental engineering in collaboration with science education and higher education faculty members. One semester of data was collected in the assistant professor's environmental engineering laboratory class as he endeavored to address his teaching goals. Data collection included pre and post interviews with the assistant professor, students, and program coordinator, and collection of course documents, such as the course syllabus and assignments. In addition, all of the classroom sessions were observed and videotaped, and a midsemester video stimulated‐recall interview was conducted. Results show the assistant professor made growth in the areas of questioning strategies, “think time” for students, increased class participation, and the implementation of a student‐designed field research project. Implications include that new professors can benefit from peer faculty support, and they and their students can benefit when the new professors recognize the complementary nature of research and teaching.     

Active learning: a case study of student engagement in college Calculus

This paper presents a case study for strategic engagement of students in a Calculus course in order to produce increased learning in the classroom. Since it has been shown that active learning can promote greater comprehension for students in science, technology, engineering, and mathematics (STEM) courses, the researcher utilized many types of active learning techniques to enhance classroom instruction. The key components implemented are presented as a model of enhanced learning through developed classroom engagement. This course redesign model entitled, Strategic Engagement for Increased Learning (SEIL), has the potential to (1) contribute to the body of knowledge on ways to improve mathematics skills for college students, (2) identify successful teaching strategies and technologies that will promote the retention of STEM students, (3) increase the success rate of students taking Calculus, and (4) help produce more STEM graduates needed for the STEM workforce in the United States of America.     

Instructors’ use of technology in post-secondary undergraduate mathematics teaching: a local study

In this study, instructors of undergraduate mathematics from post-secondary institutions in Newfoundland were surveyed (N = 13) and interviewed (N = 8) about their use of, experiences with, and views on, technologically assisted teaching. It was found that the majority of them regularly use technologies for organizational and communication purposes. However, the use of math-specific technology such as computer algebra systems, or dynamic geometry software for instructional, exploratory, and creative activities with students takes place mostly on an individual basis, only occasionally, and is very much topic specific. This was even the case for those instructors who use technology proficiently in their research. The data also suggested that familiarity with and discussions of examples of technology implementation in teaching at regular and field-oriented professional development seminars within mathematics departments could potentially increase the use of math-specific technology by instructors.     

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group.     

Nonlinear homogeneous retarded differential equations and population dynamics via translation semigroups

In this paper nonlinear homogeneous retarded differential equations and models from population dynamics and epidemiology are considered and studied by the use of translation semigroup theory. We show that the corresponding solution semigroups are equivalent to appropriate translation semigroups. Existence results for the retarded equations are established by taking the space of initial functions of the form W ^1,p ((-r,0),F) where F is a Banach space, 1≤ p<∈fty and 0<r\le∈fty . June 28, 1999     

The Effects on Students' Cognitive Achievement When Using the Cooperative Learning Method in Earth Science Classrooms

This study investigated the effects of cooperative learning instruction versus traditional teaching methods on students' earth science achievement in secondary schools. A total of 770 ninth-grade students enrolled in 20 sections of a required earth science course participated in this nonequivalent control group quasi-experiment. The control groups (n= 10) received a traditional approach, while the experimental groups (n= 10) used cooperative strategies. Study results include (a) no significant differences were found between the experimental groups and the control groups when overall achievement (F= 0.13, p > .05), knowledge-level (F= 0.12, p > .05), and comprehension-level (F= 0.34, p > .05) test items were considered; and (b) students who worked cooperatively performed significantly better than students who worked alone on the application-level test items (F= 4.63, p < .05). These findings suggest that cooperative-learning strategies favor students' earth science performance at higher but not lower levels of cognitive domains in the secondary schools.     

Demography for actuarial students

One purpose of this paper is to draw attention to several ideas from demography, which could be useful to an actuary. An actuarial course of study might not have considered these concepts at great length. The ideas are: (1) stable populations and pension applications; (2) population statistics and their uses; (3) analytic expressions for P(t), the population at time t; (4) probabilistic models in demography; (5) population projections; and (6) finding probabilities from observed rates.A second purpose is to focus on several excellent demography-based papers which could serve an actuary. They are illustrative of works which could strengthen the professional work of an actuary.A third purpose is to provide a list of references for study by actuarial students.     

Gender Differences in Learning Constructs,Shifts in Learning Constructs,and Their Relationship to Course Achievement in a Structured Inquiry,Yearlong College Physics Course for Life Science Majors

This study investigated differences and shifts in learning and motivation constructs among male and female students in a nonmajors, yearlong structured inquiry college physics course and examined how these variables were related to physics understanding and course achievement. Tests and questionnaires measured students' learning approaches, motivational goals, self‐efficacy, epistemological beliefs, scientific reasoning abilities, and understanding of central physics concepts at the beginning and end of the course. Course achievement scores were also obtained. The findings showed that male students had significantly higher self‐efficacy, performance goals, and physics understanding compared to females, which persisted throughout the course. Differential shifts were found in students' meaningful learning approaches, with females tending to use less meaningful learning from beginning to end of the course; and males using more meaningful learning over this time period. For both males and females, self‐efficacy significantly predicted physics understanding and course achievement. For females, higher reasoning ability was also a significant predictor of understanding and achievement; whereas for males, learning goals and rote learning were significant predictors, but in a negative direction. The findings reveal that different variables of learning and motivation may be important for females' success in inquiry physics compared to males. Instructors should be cognizant of those needs in order to best help all students learn and achieve in college physics.     

On the reconstruction of rayless infinite forests

A graph G is called strongly p-reconstructible if it is (up to isomorphism) uniquely determined by the collection of its pairwise nonisomorphic subgraphs G – v where v is a pendent vertex of G. Using previous results of the second author concerning the structure of infinite rayless graphs it is shown that every rayless forest with an infinite edge-set is strongly p-reconstructible. This result is applied to the classical reconstruction problem to find that every infinite rayless forest G with a finite number of components is reconstructible; i.e., G is (up to isomorphism) uniquely determined by its collection of vertex-deleted subgraphs. Furthermore, an example is given which shows that nonreconstructible rayless forests with a countable number of components exist.     

From Individuals to Populations: A Symbolic Process Algebra Approach to Epidemiology

Is it possible to symbolically express and analyse an individual-based model of disease spread, including realistic population dynamics? This problem is addressed through the use of process algebra and a novel method for transforming process algebra into Mean Field Equations. A number of stochastic models of population growth are presented, exploring different representations based on alternative views of individual behaviour. The overall population dynamics in terms of mean field equations are derived using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. The utility of our approach for epidemiology is confirmed by constructing a model combining population growth with disease spread and fitting it to data on HIV in the UK population. This work was supported by EPSRC through a Doctoral Training Grant (CM, from 2004–2007), and through System Dynamics from Individual Interactions: A process algebra approach to epidemiology (EP/E006280/1, all authors, 2007–2010).     

The Relationship Between Various Filter Notions on aGL-Monoid

The notion of a generalised filter is extended to the setting of aGL-monoid. It is shown that there exists a one-to-one correspondence between the collection of generalised filters on a setXand the collection of strongly stratifiedL-filters onX. Specialising to the case whereLis the closed unit interval [0, c] viewed as a Heyting algebra, we show that any strongly stratified [0, c]-filter onXcan be uniquely identified with a saturated filter onI^Xwith characteristic valuec. In this way, the notion of a generalised filter unifies various filter notions. In particular, necessity measures and finitely additive probability measures are specific examples of generalised filters.     

Reports: Vanderbilt's New Change School

Abstract

In my experience, students of all races are hungering to be heard, to listen to others, and to have honest conversations about race and racism. I recently taught one course that brought out particularly clearly the challenges of teaching racially volatile material, of integrating personal experience and academic learning, and of negotiating the minefields of identity politics. It taught me the satisfactions of helping students cross racial barriers and of learning from one another.

The class—“Race and Racism”— met once a week. A master's-level course with a few doctoral students, it raised pedagogical issues similar to those I'd found teaching undergraduates. The class consisted of nine black students, of whom one was African (from Ethiopia), one Jamaican (but had spent most of her life in the United States), the rest African American; in addition, it included one Cuban American, one Filipino American, one Russian Jewish immigrant (seven years in this country), and one Japanese student who had only recently arrived in the United States. The remaining 13 students were white and non-Hispanic.