The impact of the pre-instructional cognitive profile on learning gain and final exam of physics courses: a case study

The case study described in this paper investigates the relationship among some pre-instructional knowledge, the learning gain and the final physics performance of computing engineering students in the introductory physics course. The results of the entrance engineering test (EET) have been used as a measurement of reading comprehension, logic and mathematics skills and basic physics knowledge of a sample of 47 Computing Engineering freshmen at the University of Palermo (Italy). These data give a significant picture of the initial knowledge status of a student choosing engineering studies. The students' physics learning gain has been calculated using a standardized tool in mechanics: the force concept inventory (FCI). The analysis shows that mathematical and physical background contribute to achieve a good final preparation in physics courses of engineering faculties; however the students' learning gain in physics is independent of students' initial level of mathematics skills and physics knowledge. Initial logic skills and reading comprehension abilities are not significant factors for the learning physics gain and the performance on physics courses.     

Self-efficacy,mathematics’ anxiety and perceived importance: an empirical study with Portuguese engineering students

The accomplishment in mathematics has gained attention from educators and arises as an emerging field of study, including in engineering education. However, in Portugal, there is still incipient research in the area; so it is high time to explore factors that might enlighten the gap in the study of the relationship between Portuguese engineering students and the learning of mathematics. The main purpose of this study is to explore three factors identified in the literature as influencing the learning of mathematical concepts – self-efficacy, anxiety towards mathematics and perceived importance of mathematics – and search for differences by gender and by type of engineering course, a dimension not much reported in the literature but which was revealed as important in the team's previous research. Based on a sample of 140 undergraduate students of different engineering courses from University of Minho, results only identify differences in the type of course and not in gender. These results constitute a contribution and open new paths for future research in the engineering education.     

A systematic approach to embedding academic numeracy at university

This paper argues that academic numeracy is an important, but undervalued and under-researched, area in tertiary education. Academic numeracy is first defined in terms of students' competence, confidence and critical awareness of their own mathematical knowledge and the mathematics needed in context. The development of academic numeracy is then discussed in terms of obuchenie (teaching/learning) and the metaknowledge around the mathematics in context needed by key staff. The paper presents a systematic approach to develop academic numeracy at the university, program, course and individual student and teacher level. Finally, it provides examples of how to embed academic numeracy. This paper provides a framework for future studies in this under-researched area.     

Programming and Mathematics in an Upper-Level University Problem-Solving Course

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions.     

工程数学教学模式的改革——数学理论与专业应用相结合

工程数学是工科专业一门重要的专业基础课,针对教学中容易出现数学理论和专业应用脱节,学生学习兴趣不高的情况,从教师队伍、教学内容、与专业应用的结合等方面。对工程数学教学模式进行了改革与实践。     

The role of a children's mathematical thinking experience in the preparation of prospective elementary school teachers

Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics.     

Self-regulated learning: the role of motivation,emotion, and use of learning strategies in students’ learning experiences in a self-paced online mathematics course

Enrollment in online remedial mathematics courses has increased in popularity in institutions of higher learning; however, students unskilled in self-regulated learning (SRL) find online remedial mathematics courses particularly challenging. We investigated the role of SRL, specifically motivation, emotion, and learning strategies, in students’ learning experiences in a remedial online mathematics course. With an online survey of 229 college students, we found that student motivation explained a small portion of variance in achievement; whereas student motivation and emotion explained a significant portion of variance in satisfaction. In addition, significant differences in motivation and emotion were found in passing and nonpassing students; however, learning strategies did not influence student achievement and satisfaction. Implications for teaching and learning in self-paced online remedial mathematics courses are discussed.     

Linking Mathematics and Psychological Science

Abstract

We describe a successful collaboration between mathematics and psychological science faculty members to create a learning community for our students that linked sections of introductory mathematical reasoning and psychological science courses. The students in our learning community were in their second or third semester. The learning community is designed so that, throughout the semester, students regularly move across the border between the two linked disciplines by completing common assignments, including a group project. We modified our existing course topics and frameworks to be intentional about building connections between the courses.     

Design of learning objects for concept learning: effects of multimedia learning principles and an instructional approach

Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching techniques – (a) variation theory and (b) representations of subject matter – on the design of learning objects for secondary school algebra concept learning. The results of this study showed that the experimental group performed significantly better than the control group on algebra learning achievement. The results also showed that only the experimental design with the addition of the instructional approach resulted in higher-order mathematical thinking skills and improved procedural skills of the students. Further analysis reveals that concept learning was simplified when multimedia learning principles were applied and the information was presented by the instructional approach.     

Linking mathematics with engineering applications at an early stage – implementation,experimental set-up and evaluation of a pilot project

Too difficult, too abstract, too theoretical – many first-year engineering students complain about their mathematics courses. The project MathePraxis aims to resolve this disaffection. It links mathematical methods as they are taught in the first semesters with practical problems from engineering applications – and thereby shall give first-year engineering students a vivid and convincing impression of where they will need mathematics in their later working life. But since real applications usually require more than basic mathematics and first-year engineering students typically are not experienced with construction, mensuration and the use of engineering software, such an approach is hard to realise. In this article, we show that it is possible. We report on the implementation of MathePraxis at Ruhr-Universität Bochum. We describe the set-up and the implementation of a course on designing a mass damper which combines basic mathematical techniques with an impressive experiment. In an accompanying evaluation, we have examined the students' motivation relating to mathematics. This opens up new perspectives how to address the need for a more practically oriented mathematical education in engineering sciences.     

数学建模的专业教学实践与认识

开设数学建模课,一方面可以培养学生的数学建模能力,提高学生把专业理论知识运用于实践的能力;另一方面,数学建模课的学习却在一定程度上影响了专业课的学习。因而如何将数学建模思想和方法融入到大学专业主干课程的教学中,是当前数学和专业教学体系、内容、方法改革面临的一个新课题。     

Teaching Students to Formulate Questions

Abstract

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a variety of freshman and sophomore mathematics courses (and above). In particular, in this model the students read the textbook before class and formulate questions, submitted prior to class via a learning management system, about the material to be covered in class the next day. During class they solve problems about that topic, and solutions are presented and discussed before the end of the period. After class, students complete standard homework about the topic, and are encouraged to bring any unresolved homework, worksheet, or reading questions for the next class period. This paper will discuss this method of engaging students, focusing on how student questions evolve during the semester, and student feedback.     

Teaching neuroanatomy using computer‐aided learning: What makes for successful outcomes?

Computer‐aided learning (CAL) is an integral part of many medical courses. The neuroscience course at Oxford University for medical students includes CAL course of neuroanatomy. CAL is particularly suited to this since neuroanatomy requires much detailed three‐dimensional visualization, which can be presented on screen. The CAL course was evaluated using the concept of approach to learning. The aims of university teaching are congruent with the deep approach—seeking meaning and relating new information to previous knowledge—rather than to the surface approach of concentrating on rote learning of detail. Seven cohorts of medical students (N = 869) filled in approach to learning scale and a questionnaire investigating their engagement with the CAL course. The students' scores on CAL‐course‐based neuroanatomy assessment and later university examinations were obtained. Although the students reported less use of the deep approach for the neuroanatomy CAL course than for the rest of their neuroanatomy course (mean = 24.99 vs. 31.49, P < 0.001), deep approach for CAL was positively correlated with neuroanatomy assessment performance (r = 0.12, P < 0.001). Time spent on the CAL course, enjoyment of it, the amount of CAL videos watched and quizzes completed were each significantly positively related to deep approach. The relationship between deep approach and enjoyment was particularly notable (25.5% shared variance). Reported relationships between deep approach and academic performance support the desirability of deep approach in university students. It is proposed that enjoyment of the course and the deep approach could be increased by incorporation of more clinical material which is what the students liked most. Anat Sci Educ 10: 560–569. © 2017 American Association of Anatomists.     

Learning mechanisms in multidisciplinary teamwork with real customers and open-ended problems

Recently, there has been a trend towards adding a multidisciplinary or multicultural element to traditional monodisciplinary project courses in computing and engineering. In this article, we examine the implications of multidisciplinarity for students' learning experiences during a one-semester project course for real customers. We use a qualitative research approach and base our analysis on students' learning reports on three instances of a project course titled Multidisciplinary working life project. The main contribution of this article is the unified theoretical picture of the learning mechanisms stemming from multidisciplinarity. Our main conclusions are that (1) students generally have a positive view of multidisciplinarity; (2) multidisciplinary teams enable students to better identify their own expertise, which leads to increased occupational identity; and (3) learning experiences are not fixed, as team spirit and student attitude play an important role in how students react to challenging situations arising from introduction of the multidisciplinarity.     

Meta-assessment in a project-based systems engineering course

Project-based learning (PBL) facilitates significant learning, but it poses a major assessment challenge for assessing individual content knowledge. We developed and implemented an assessment approach and tool for a mandatory undergraduate systems engineering PBL-based course. We call this type of assessment student-oriented meta-assessment. Research participants included 131 undergraduate engineering students who carried out team projects requiring conceptual modelling of complex systems. Next, individual students assessed their peer team projects. Finally, the course staff assessed students individually, based on the content knowledge that was reflected in students’ comments to their peers, by using the new meta-assessment tool. The research findings validated the meta-assessment tool which can serve for assessing various PBL courses. Our contribution is twofold: a new approach for assessing project-based undergraduate engineering courses, and classification of meta-assessment methods into three types, where a student-oriented meta-assessment as one of the three meta-assessment methods is our newly introduced and validated method.     

A time sequence-oriented concept map approach to developing educational computer games for history courses

Concept maps have been recognized as an effective tool for students to organize their knowledge; however, in history courses, it is important for students to learn and organize historical events according to the time of their occurrence. Therefore, in this study, a time sequence-oriented concept map approach is proposed for developing a game-based environment to facilitate students' learning of historical events and their organization during the gaming process. With this approach, students can easily learn the precedence relationships among the historical events that occurred in different time periods with the time sequence-oriented concept map. To evaluate the effectiveness of the proposed approach, a historical role-playing game has been developed for an elementary school history course to examine the students' performance in terms of learning motivation, self-efficacy and learning achievements. A subject unit, the “Siege of Fort Zeelandia by Zheng Cheng-Gong,” was chosen as the history topic. The results show that the proposed approach can significantly enhance the students' learning achievement, but did not affect their learning motivation or self-efficacy for the history course. As a consequence, it is concluded that students can benefit from concept maps in terms of enhancing their learning achievement, but they do not necessarily enjoy using concept maps in game-based learning activities.     

Using argumentation as a learning strategy to improve student performance in engineering Statics

ABSTRACT

Research suggests that a significant reason that a large number of students earn low grades in the fundamental engineering science course Statics is that they may be entering the course with incorrect conceptual knowledge of mathematics and physics. The self-explanation learning approach called collective argumentation helps k-12 students to understand their misconceptions of mathematical principles that often appear abstract to them. This study investigated collective argumentation as an instructional approach that helps engineering students identify and correct their misconceptions of topics taught in Statics. Results suggest that argumentation improves student performance as measured by grades earned on semester exams. Survey and focus group results suggest that students did not understand the argumentation process. Therefore, the students did not like using it as a learning approach.     

融合现代教育技术的工科数理类基础课程教学模式改革

数理类基础课是工科院校各专业的重要公共基础课,其特点是学时数多、授课面广,是后续课程学习的基础.由于学生对这些课程的认识不够,导致其对课程学习的动力不足、兴趣不高,学习效果不佳.鉴于此,以"数理基础课概论"为切入点,深度融合基础课和专业课教学内容;以"混合式教学模式"为抓手,深度融合基础课和现代教育技术;以"成绩统计分...     

From Parental Involvement to Children's Mathematical Performance: The Role of Mathematics Anxiety

This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping several domains of parental involvement, and children were assessed on mathematics anxiety, whole number arithmetic, word problems, and algebraic reasoning. Research Findings: The results indicated that parents influence children's mathematics achievement by reducing mathematics anxiety, particularly for more difficult kinds of mathematics. Specifically, the mediation analyses demonstrated that parental home support and expectations influenced children's performance on word problems and algebraic reasoning by reducing children's mathematics anxiety. Mathematics anxiety did not mediate the relationship between home support and expectations and whole number arithmetic. Practice or Policy: Policies and programs targeting parental involvement in mathematics should focus on home-based practices that do not require technical mathematical skills. Parents should receive training, resources, and support on culturally appropriate ways to create home learning environments that foster high expectations for children's success in mathematics.