Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

Teaching Statistics to Engineers: Learning from Experiential Data

The purpose of the work is to claim that engineers can be motivated to study statistical concepts by using the applications in their experience connected with Statistical ideas. The main idea is to choose a data from the manufacturing factility (for example, output from CMM machine) and explain that even if the parts used do not meet exact specifications they are used in production. By graphing the data one can show that the error is random but follows a distribution, that is, there is regularily in the data in statistical sense. As the error distribution is continuous, we advocate that the concept of randomness be introducted starting with continuous random variables with probabilities connected with areas under the density. The discrete random variables are then introduced in terms of decision connected with size of the errors before generalizing to abstract concept of probability. Using software, they can then be motivated to study statistical analysis of the data they encounter and the use of this analysis to make engineering and management decisions.

Bringing engineering education to life – an empirical approach to learning and teaching

Learning and teaching approaches to engineering are generally perceived to be difficult and academically challenging. Such challenges are reflected in high levels of student attrition and failure. In addressing this issue, a unique approach to engineering education has been developed by the paper authors. This approach, which is suitable for undergraduate and postgraduate levels, brings together pedagogic and engineering epistemologies in an empirically grounded framework. It is underpinned by three distinctive concepts: Relationships, Variety & Synergy. Based upon research, the R + V + S approach to Engineering Education provides a learning and teaching strategy, which in enhancing the student experience, increases retention and positively impacts student success [S2]. Based on the study findings, this paper shows how, by designing engineering education around the concepts of Relationships, Variety and Synergy, the student learning experience becomes one that is academically challenging yet beneficial to both students and engineering educators. The challenge is to widen and test the approach in other areas of engineering education, before going on to investigate the value of the approach in other disciplines.

A comparison of the effects of social constructivist and traditional approaches to teaching on students' attitude and achievement in high school chemistry

Current views of the nature of knowledge and of learning suggest that instructional approaches in science education pay closer attention to how students learn rather than on teaching. This study examined the use of approaches to teaching science based on two contrasting perspectives in learning, social constructivist and traditional, and the effects they have on students' attitudes and achievement. Four categories of attitudes were measured using the Upper Secondary Attitude Questionnaire: Attitude towards school, towards the importance of science, towards science as a career, and towards science as a subject in school. Achievement was measured by average class grades and also with a researcher/teacher constructed 30-item test that involved three sub-scales of items based on knowledge, and applications involving near-transfer and far-transfer of concepts. The sample consisted of 202 students in nine intact classrooms in chemistry at a large high school in Miami, Florida, and involved two teachers. Results were analyzed using a two-way analysis of covariance (ANCOVA) with a pretest in attitude as the covariate for attitudes and prior achievement as the covariate for achievement. A comparison of the adjusted mean scores was made between the two groups and between females and males. ^ With constructivist-based teaching, students showed more favorable attitude towards science as a subject, obtained significantly higher scores in class achievement, total achievement and achievement on the knowledge sub-scale of the knowledge and application test. Students in the traditional group showed more favorable attitude towards school. Females showed significantly more positive attitude towards the importance of science and obtained significantly higher scores in class achievement. No significant interaction effects were obtained for method of instruction by gender. ^ This study lends some support to the view that constructivist-based approaches to teaching science is a viable alternative to traditional modes of teaching. It is suggested that in science education, more consideration be given to those aspects of classroom teaching that foster closer coordination between social influences and individual learning. ^

An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

What Teaching Strategies Can I Employ to Improve Student Achievement in the Addition of Fractions with Different Denominators?

The purpose of this action research was to determine what instructional strategies could be used to improve student achievement in fraction addition. An eighth grade intensive math class practiced multiplication facts and hands-on applications of fractions concepts for 2 months. Pretests/posttests were used to measure improvement in computation and understanding.

Gaining insight into teaching: A phenomenological exploration of the lived experience of Teachers of the Year

What qualities, skills, and knowledge produce quality teachers? Many stake-holders in education argue that teacher quality should be measured by student achievement. This qualitative study shows that good teachers are multi-dimensional; their effectiveness cannot be represented by students' test scores alone. The purpose of this phenomenological study was to gain a deeper understanding of quality in teaching by examining the lived experiences of 10 winners or finalists of the Teacher of the Year (ToY) Award. Phenomenology describes individuals' daily experiences of phenomena, examines how these experiences are structured, and focuses analysis on the perspectives of the persons having the experience (Moustakas, 1994). This inquiry asked two questions: (a) How is teaching experienced by recognized as outstanding Teachers of the Year? and (b) How do ToYs feelings and perceptions about being good teachers provide insight, if any, about concepts such as pedagogical tact, teacher selfhood, and professional dispositions? Ten participants formed the purposive sample; the major data collection tool was semi-structured interviews (Patton, 1990; Seidman, 2006). Sixty to 90-minute interviews were conducted with each participant. Data also included the participants' ToY application essays. Data analysis included a three-phase process: description, reduction, interpretation. Findings revealed that the ToYs are dedicated, hard-working individuals. They exhibit behaviors, such as working beyond the school day, engaging in lifelong learning, and assisting colleagues to improve their practice. Working as teachers is their life's compass, guiding and wrapping them into meaningful and purposeful lives. Pedagogical tact, teacher selfhood, and professional dispositions were shown to be relevant, offering important insights into good teaching. Results indicate that for these ToYs, good teaching is experienced by getting through to students using effective and moral means; they are emotionally open, have a sense of the sacred, and they operate from a sense of intentionality. The essence of the ToYs teaching experience was their being properly engaged in their craft, embodying logical, psychological, and moral realms. Findings challenge current teacher effectiveness process-product orthodoxy which makes a causal connection between effective teaching and student test scores, and which assumes that effective teaching arises solely from and because of the actions of the teacher.

An Innovative Approach to Teaching Structural Induction for Computer Science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

Laboratory focussed learning of core electronic engineering concepts in the first year of an honours degree programme

In common with most universities teaching electronic engineering in the UK, Aston University has seen a shift in the profile of its incoming students in recent years. The educational background of students has moved away from traditional Alevel maths and science and if anything this variation is set to increase with the introduction of engineering diplomas. Another major change to the circumstances of undergraduate students relates to the introduction of tuition fees in 1998 which has resulted in an increased likelihood of them working during term time. This may have resulted in students tending to concentrate on elements of the course that directly provide marks contributing to the degree classification. In the light of these factors a root and branch rethink of the electronic engineering degree programme structures at Aston was required. The factors taken into account during the course revision were:. Changes to the qualifications of incoming students. Changes to the background and experience of incoming students. Increase in overseas students, some with very limited practical experience. Student focus on work directly leading to marks. Modular compartmentalisation of knowledge. The need for provision of continuous feedback on performance We discuss these issues with specific reference to a 40 credit first year electronic engineering course and detail the new course structure and evaluate the effectiveness of the changes. The new approach appears to have been successful both educationally and with regards to student satisfaction. The first cohort of students from the new course will graduate in 2010 and results from student surveys relating particularly to project and design work will be presented at the conference. © 2009 K Sugden, D J Webb and R P Reeves.

Engineering the future! Innovation in learning & teaching:an empirical approach

Learning and teaching approaches to engineering are generally perceived to be difficult and academically challenging. Such challenges are reflected in high levels of student attrition and failure. In addressing this issue, a unique approach to engineering education has been developed by one of the paper authors. This approach, which is suitable for undergraduate and postgraduate levels, brings together pedagogic and engineering epistemologies in an empirically grounded framework. It is underpinned by three distinctive concepts: Relationships, Variety & Alignment. Based upon research, the R + V + A approach to engineering education provides a learning and teaching strategy which in enhancing the student experience increases retention and positively impacts student success. In discussing the emergent findings of a study into the pedagogical value of the approach the paper makes a significant contribution to academic theory and practice in this area.

The Visual Arts as a Canvas for Teaching Computer Programming

We explore the relationships between the construction of a work of art and the crafting of a computer program in Java and suggest that the structure of paintings and drawings may be used to teach the fundamental concepts of computer programming. This movement "from Art to Science", using art to drive computing, complements the common use of computing to inform art. We report on initial experiences using this approach with undergraduate and postgraduate students. An embryonic theory of the correspondence between art and computing is presented and a methodology proposed to develop this project further.

Sociocultural context as a facilitator of student learning of function concepts in mathematics

In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its  applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP) Official Program.  Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.

Understanding Notional Machines through Traditional Teaching with Conceptual Contraposition and Program Memory Tracing

A correct understanding about how computers run code is mandatory in order to effectively learn to program. Lectures have historically been used in programming courses to teach how computers execute code, and students are assessed through traditional evaluation methods, such as exams. Constructivism learning theory objects to students’ passiveness during lessons, and traditional quantitative methods for evaluating a complex cognitive process such as understanding. Constructivism proposes complimentary techniques, such as conceptual contraposition and colloquies. We enriched lectures of a “Programming II” (CS2) course combining conceptual contraposition with program memory tracing, then we evaluated students’ understanding of programming concepts through colloquies. Results revealed that these techniques applied to the lecture are insufficient to help students develop satisfactory mental models of the C++ notional machine, and colloquies behaved as the most comprehensive traditional evaluations conducted in the course.

Teaching by chat

This paper discusses some didactical aspects of chat usage for instructional purposes. Areas covered range from the choice of course type and student group for using chats, to the preparation and moderation of chats, and discussing how to manage both troublemaking students and systems. In February 1998 I was the chair of a committee at my previous university that was authoring a recommendation list about the Internet to the president of the school. One of our recommendations was to eliminate the IRC server (Internet Relay Chat), since it was only causing traffic and was just being used for games. We stated that we could not envision a use for chatting either for research or for instructional purposes. Five years later here I am: teaching 4 of my 5 courses by way of chat. There has been an enormous growth in the use of chat-based instruction, but also quite a lot of problems encountered. Much of the available literature addresses technical problems, or discusses chats from an educational psychology perspective. This paper will address ten of the didactical issues in chat-based instruction, summarizing the experiences that I have made in many years of chat experience (DIPF/Orig.)

Technical and Didactical Scenarios of Student-centered Teaching and Learning

In this paper we envision didactical concepts for university education based on self-responsible and project-based learning and outline principles of adequate technical support. We use the scenario technique describing how a fictive student named Anna organizes her studies of informatics at a fictive university from the first days of her studies to make a career for herself.(DIPF/Orig.)