The acquisition and transfer of knowledge of electrokinetic-hydrodynamics (EKHD) fundamentals: an introductory graduate-level course

Relevant engineering applications, such as bioseparation of proteins and DNA, soil-cleaning, motion of colloidal particles in different media, electrical field-based cancer treatments, and the cleaning of surfaces and coating flows, belongs to the family of ‘Applied Field Sensitive Process Technologies’ requiring an external field to move solutes in a fluid within a fibrous (or porous) domain. This field incorporates an additional variable that makes the analysis very challenging and can create for the student a number of new problems to solve. A graduate-level course, based on active-learning approaches and High Performance Learning Environments, where transfer of knowledge plays a key role, was designed by the Chemical Engineering Department at Tennessee Technological University. This course, where the fundamentals principles of EKHD were taught to science, engineering and technology students was designed by the Chemical Engineering Department at the Tennessee Technological University, Cookeville, TN. An important number of these students were able to grasp the tools required to advance their research projects that led to numerous technical presentations in professional society meetings and publications in peered-reviewed journals.     

Mathematical Modeling in the Elementary Grades: Developing and Testing an Assessment

Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed.

     

A blended learning approach for teaching computer programming: design for large classes in Sub-Saharan Africa

The challenge of teaching programming in higher education is complicated by problems associated with large class teaching, a prevalent situation in many developing countries. This paper reports on an investigation into the use of a blended learning approach to teaching and learning of programming in a class of more than 200 students. A course and learning environment was designed by integrating constructivist learning models of Constructive Alignment, Conversational Framework and the Three-Stage Learning Model. Design science research is used for the course redesign and development of the learning environment, and action research is integrated to undertake participatory evaluation of the intervention. The action research involved the Students’ Approach to Learning survey, a comparative analysis of students’ performance, and qualitative data analysis of data gathered from various sources. The paper makes a theoretical contribution in presenting a design of a blended learning solution for large class teaching of programming grounded in constructivist learning theory and use of free and open source technologies.     

Evidence of a Spiral Curriculum Using a Mathematical Problem-Solving Tool

Traditional mathematical problem-solving currently being implemented in schools in Britain uses the methods of controlling the variables, drawing up a table of cases and using differencing techniques to create a solution for n cases. However, Bruner advocates the use of a spiral curriculum whereby students are “scaffolded” to higher and higher levels of generalization by revisiting a problem on multiple occasions, each time with an increased understanding of the task at hand. Clearly this is impossible using current classroom techniques. This paper outlines the use of a mathematical programming language, Zeno, which facilitates such levels of generalization. For demonstration purposes, the transformational effect of a singular 2 × 2 matrix is considered. Each stage in the spiral is clearly reproduced visually for the reader and attention is paid to one method of assessing the students' work, namely through the “externalizations” stored in the time-stamped journal activated on entering the software.     

Weighing up the Influence of Context on Judgements of Mathematical Literacy

Mathematical literacy, viewed as a set of ideas involving applications of mathematics to real-world contexts, has recently featured in curricular discussions about the aims for mathematics education. This article explores the effect that differences in the way that a mathematical task is contextualised can have on students’ mathematical arguments and, therefore, on their perceived levels of mathematical literacy. Seventy-two students’ responses to three similar measurement tasks are described according to Kaiser and Willander’s levels of mathematical literacy. The arguments used for assigning each level of mathematical literacy are then investigated for the presence of specific macro- and micro-linguistic features. The context of the task affects what students perceive to be most relevant approaches to use, which are reflected in the arguments they give; this, in turn, affects external judgements of their level of mathematical literacy.     

关于在校园网中建立学习型SNS社区的思考

随着网络、社交网络的日益成熟发展,学校教育与网络相结合、师生学习社交关系圈形成的新型教育模式,将是成人学习的新型模式。在校园网中建立学习型SNS社区,可为教师与教师、教师与学生、学生与学生之间的交流提供更好的平台,可以为学生营造出自主、协作的学习氛围,更好地完成学习任务,为教师打造专业平台,快捷知识和观点分享。如何利用学生的网络活跃性和群居性为教学服务,是目前学校网络建设与发展的热点、创新点。在校园网中建立学习型的SNS社区网站就是一个新的探索。     

Beyond Motivation: Exploring Mathematical Modeling as A Context for Deepening Students' Understandings of Curricular Mathematics

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical modeling is treated more as a venue for learning other mathematics than as an instructional goal in its own right. From this perspective, we are compelled to ask how learning of mathematics beyond modeling may occur as students generate and validate mathematical models. We consider a diagrammatic model of mathematical modeling as a process that allows us to identify how mathematical understandings may develop or surface while learners engage in modeling tasks. Through examples from prospective teachers' mathematical modeling work, we illustrate how our diagrammatic model serves as a tool to unpack the intricacies of students’ mathematical experience while engaging in modeling tasks.     

Investigating the effect of imikode virtual reality game in enhancing object oriented programming concepts among university students in Nigeria

Education and Information Technologies - Learning object oriented programming (OOP) has been a daunting and challenging task for students across tertiary institutions in Nigeria. Various...     

Make a drawing. Effects of strategic knowledge,drawing accuracy,and type of drawing on students’ mathematical modelling performance

Drawing strategies are widely used as a powerful tool for promoting students’ learning and problem solving. In this article, we report the results of an inferential mediation analysis that was applied to investigate the roles that strategic knowledge about drawing and the accuracy of different types of drawings play in mathematical modelling performance. Sixty-one students were asked to create a drawing of the situation described in a task (situational drawing) and a drawing of the mathematical model described in the task (mathematical drawing) before solving modelling problems. A path analysis showed that strategic knowledge about drawing was positively related to students’ modelling performance. This relation was mediated by the type and accuracy of the drawings that were generated. The accuracy of situational drawing was related only indirectly to performance. The accuracy of mathematical drawings, however, was strongly related to students’ performance. We complemented the quantitative approach with a qualitative in-depth analysis of students’ drawings in order to explain the relations found in our study. Implications for teaching practices and future research are discussed.     

An Introduction to Servo Pneumatic Positioning: An Interactive Multimedia Program Development Supporting Outcome-driven Engineering Assessment

Servo pneumatics retains the advantages of standard pneumatics and adds the opportunity for closed-loop controlled, programmable positioning to within fractions of a millimeter in systems in which positions can be approached rapidly and without overshoot, stability under variable loads and conditions, and adaptive control for optimized positioning. Our challenge was to create an interactive multimedia program that could communicate exciting technical material to interested parties, including students and academia, professional design, industrial and manufacturing systems engineers, marketing and sales engineers and managers in a non-linear, enjoyable fashion. Our approach was that of interactive multimedia on CD-ROM, allowing the integration of text, color images, videos and animation for the purpose of following an engineering problem-solving approach, both when modeling, as well as when illustrating real-world solutions with interactive digital videos. Furthermore, this article introduces outcome-driven assessment principles ( as defined by the American Accreditation Board of Engineering Education) as the key to our educational multimedia design objectives. It illustrates open-loop controlled pneumatic and closed-loop controlled servo pneumatic positioning systems, their components, their programming and some of their applications.     

The philosophical and pedagogical underpinnings of Active Learning in Engineering Education

ABSTRACT

In this paper the authors draw on three sequential keynote addresses that they gave at Active Learning in Engineering Education (ALE) workshops in Copenhagen (2012), Caxias do Sol (2014) and San Sebastian (2015). Active Learning in Engineering Education is an informal international network of engineering educators dedicated to improving engineering education through active learning (http://www.ale-net.org/). The paper reiterates themes from those keynotes, namely, the philosophical and pedagogical underpinnings of Active Learning in Engineering Education, the scholarly questions that inspire engineering educators to go on improving their practice and exemplary models designed to activate the learning of engineering students. This paper aims to uncover the bedrock of established educational philosophies and theories that define and support active learning. The paper does not claim to present any new or innovative educational theory. There is already a surfeit of them. Rather, the aim is to assist Engineering Educators who wish to research how they can best activate the learning of their students by providing a readable, reasonable and solid underpinning for best practice in this field.     

Exploring a complex gender wage gap dataset: an introductory activity in identifying issues and data visualization

In this paper, we provide instructors with an approach for a classroom activity for students in an introductory data science or statistics course who have little or no statistical programming experience. We designed this activity to help students improve their statistical literacy while exploring a social justice problem-the gender wage gap. To minimize the challenges of developing statistical literacy in students who lack programming skills, we developed a web-based data visualization application that does not require users to have any prior programming knowledge. The data in this visualization application comes from the March 2018 Current Population Uniform Extracts detailed by the Center for Economic Policy Research. Students can use the visualization application to create tables and plots to explore data on factors such as earnings and gender. Instructors can also use the application for other wage-related variables, such as race, occupation and family size.     

Flowery math: a case for heterodiscoursia in mathematics problems solving in recognition of students’ authorial agency

In an innovative, progressive school, students were asked to solve a fairly routine mathematical problem using real money in a “real-world” scenario. Even though the school values students’ ideas, the reaction of the teacher to one student’s alternative modelling of the problem suggests that he was expecting a particular answer to be provided using routine mathematical models and thinking while not being interested in exploring the student’s unexpected alternative. We place his reasoning for doing so within broad pedagogical discourses that we think define the “allowable” responses of teachers and students in ways that inhibit meaning-making for both. These broad discourses are defined as the progressive constructivist approach, the scaffolding discursive approach, the situation modelling approach and the dialogic approach. We consider the advantages and the potential consequences each might bring to the case. We suggest that extensive consideration of pedagogical discourses in mathematics classes must be reconsidered both for how we understand students’ mathematical meaning-making and how we construct student agency in relationship to culture, whether as apprentices or authors.     

Supporting Programming and Learning-to-Program with an Integrated CAD and Scaffolding Workbench*

Programming is a complex cognitive task for students, because of the difficulty of finding the appropriate elements (the “decomposition” problem) and integrating them correctly into a whole (the “composition” problem). Programming is also hard to learn, because so much of the thinking behind a program is implicit and the process of programming is long and complicated. Our approach is to integrate a computer-aided design tool (CAD) with scaffolding to create a single, cohesive, and coherent workbench for the entire process. Our workbench is called the GPCeditor. We have evaluated its use by high-school students. Our results suggest that students program well in the GPCeditor, they learn good programming practices, and that the learning is occurring through use of the GPCeditor.     

对"工科数学"教学改革的探讨

"工科数学"是工科院校重要的基础课.一个人的数学素质的高低已成为衡量其综合素质的重要因素.因此,工科院校因根据社会对人才需求的多样化和对人才规格的不断变化,利用先进的教学理念、教学内容、教学手段,对传统教学内容进行改革,以培养学生的定量思维、数学建模及计算能力.     

A STEM extended learning project to raise awareness of social justice in a Year 3 primary classroom

Governments worldwide are advocating for STEM curricula as essential to economic viability but the opportunity for STEM to create a re-envisioned world where there is equal access to wealth, opportunities, and privileges is less prominent. The literature has also not clearly articulated how the combination of the individual disciplines areas: science, technology, engineering and maths should be structured to form a cohesive paradigm within a contextual real-world problem. This paper details one example of a STEM unit had with an equity and social justice agenda. The teacher orchestrated a range of learning experiences to develop student intellectual and emotional engagement with the learning experience sequence, which was to design a pair of shoes for students in a refugee camp using resources that might be available there. Her teaching approach involved the choreography of student attention to the different dimensions of STEM. While all were in play particular disciplinary concepts and practices were foregrounded at different times. We propose that teaching STEM involves a choreography of focus on the different disciplines of Science, Technology, Engineering and Maths, with the relative weight at any one time and overall depending on the nature of the task that is to be accomplished.     

How to Make a Math Modeling Class from Scratch in Six (Not-So) Easy Steps

The recent introduction of a new course in mathematical modeling at Manhattan College has provided students with a valuable opportunity to gain practical experience utilizing tools in applying their mathematical abilities to a real-world problem. This paper describes the steps taken to create this class, from obtaining a real-world partner (client) to designing the assessment plan, as well as mentoring the student participants, so as to provide a road map to any instructor looking to initiate such a course on their own. Although the first two iterations focused on data analytics, the course presented here easily translates to projects utilizing differential equations, optimization, stochastic modeling, and simulation. Discussions included reflect on what elements of the course have proven successful and what may be open to improvement; responses from students are also included.     

Software‐Realized Scaffolding to Facilitate Programming for Science Learning

Abstract

Programming is an activity through which students can learn about other domains, but the difficulty of programming diminishes its usefulness as a learning activity. One approach to facilitate the use of programming for learning is to view programming as a skill like those taught through apprenticeships, and to use the apprenticeship concept of scaffolding to facilitate doing and learning through programming. Scaffolding means providing modifiable support (through fading) that communicates process, coaches, and elicits articulation. Software‐realized scaffolding embeds scaffolding in a computer‐based environment. Emile implements software‐realized scaffolding to facilitate student learning of physics by facilitating students building computer‐based models and simulations. In this article, I present Emile's features as examples of software‐realized scaffolding, and I present the results of an evaluation of Emile's effectiveness. Students were able to use Emile to create fairly sophisticated programs and gained a qualitative understanding of kinematics in the process.     

Developing Students’ Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the practitioners in the extra-mathematical domain. For students to experience the significance of different scientific practices and cultures for the function and status of mathematical modeling in other sciences, students need to be placed in didactical situations where such differences are exposed and made into explicit objects of their reflections. It can be difficult to create such situations in the teaching of contemporary science in which modeling is part of the culture. In this paper we show how history can serve as a means for students to be engaged in situations in which they can experience and be challenged to reflect upon and criticize, the use of modeling and the significance of the context for the function and status of modeling and models in scientific practices. We present Nicolas Rashevsky’s model of cell division from the 1930s together with a discussion of disagreement between him and some biologists as one such episode from the past. We illustrate how a group of science students at Roskilde University, through their work with this historical case, experienced that different scientific cultures have different opinions of the value of a model as an instrument for gaining scientific knowledge; that the explanatory power of a model is linked not only to the context of its use, but also to the underlying philosophical and theoretical position held by the modeler(s) and the scientists discussing the model and its use. The episode’s potential to challenge students to reflect upon and criticize the modeling process and the function of models in an extra mathematical domain is discussed with respect to the notions of internal and external reflections.     

《化工CAD》课程网络化教学模式探讨

根据《化工CAD》课程的实际教学需求,结合CAD技术发展的特点和趋势,自主研发了集课程讨论、作业提交、课程管理、网上答疑、下载中心、模拟练习和在线考试等功能为一体的的网络教学平台。体现了学生主体、教师主导的教学理念。实践证明教学效率提高,师生互动明显改善。网上问卷调查结果表明学生对网络化教学模式的满意率达85%以上。