Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance

BACKGROUND : Demands by engineering faculties of mathematics departments have traditionally been for teaching computational skills while also expecting analytic and creative knowledge-based skills. We report on a project between two institutions, one in South Africa and one in Sweden, that investigated whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than the traditional more procedurally oriented way of teaching. PURPOSE (HYPOTHESIS) : We focus on how second-year engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between Swedish and South African groups of students in answering conceptual and procedural mathematics problems. We also compare these students’ conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. DESIGN/METHOD : An instrument consisting of procedural and conceptual items as well as items on student opinions on the roles of the different types of knowledge in their studies was conducted with groups of second-year engineering students at two universities, one in each country. RESULTS : Although differences between the two countries are small, Swedish students see procedural items to be more common in their mathematics studies while the South African students find both conceptual and procedural items common; the latter group see the conceptually oriented items as more common in their studies outside the mathematics courses. CONCLUSIONS : Students view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics. The use of mathematics in other subjects within engineering education can be experienced differently by students from different institutions, indicating that the same type of education can handle the application of mathematics in different ways in different institutions.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2168-9830hb201

Reform-Based Mathematics Teaching in the United States

This chapter examined the trends in reform-based mathematics teaching practices in the United States classrooms. The authors systematically analyzed the journal articles in the Mathematics Teacher: Learning and Teaching PK-12 (MTLT) in order to reveal the current practices that practitioners and experts in mathematics education deem significant and worthy. They found that the most trending reform practices were mathematical discourse, conceptual understanding, task selection, and real-life applications. They discussed each trending practice through sample strategies and provided examples from the reviewed articles. They also identified the least trending reform practices that need attention and discussed associated challenges

Relating procedural and conceptual knowledge

Relating procedural and conceptual mathematical knowledge is a very important educational goal that is difficult to attain. However, research has evidenced that some progress towards achieving this goal can be made. This contribution briefly reviews some of the main outcomes of research in this area, focusing on relating these knowledge types with technology, particularly that based upon a computer algebra system

Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

On the Development of Early Algebraic Thinking

This article deals with the question of the development of algebraic thinking in young students. In contrast to mental approaches to cognition, we argue that thinking is made up of material and ideational components such as (inner and outer) speech, forms of sensuous imagination, gestures, tactility, and actual actions with signs and cultural artifacts. Drawing on data from a longitudinal classroom-based research program where 8-year old students were followed as they moved from Grade 2 to Grade 3 to Grade 4, our developmental research question is investigated in terms of the manner in which new relationships between embodiment, perception, and symbol-use emerge and evolve as students engage in patterning activities

Instructional Leadership, Teaching Quality, and Student Achievement: Suggestive Evidence from Three Urban School Districts

Does providing instruction-related professional development to school principals set in motion a chain of events that can improve teaching and learning in their schools? This report examines professional development efforts by the University of Pittsburgh's Institute for Learning in elementary schools in Austin, St. Paul, and New York City

Using Concept Inventories to Measure Understanding

Measuring understanding is notoriously difficult. Indeed, in formulating learning outcomes the word “understanding” is usually avoided, but in the sciences, developing understanding is one of the main aims of instruction. Scientific knowledge is factual, having been tested against empirical observation and experimentation, but knowledge of facts alone is not enough. There are also models and theories containing complex ideas and inter-relationships that must be understood, and considerable attention has been devoted across a range of scientific disciplines to measuring understanding. This case study will focus on one of the main tools employed: the concept inventory and in particular the Force Concept Inventory. The success of concept inventories in physics has spawned concept inventories in chemistry, biology, astronomy, materials science and maths, to name a few. We focus here on the FCI, ask how useful concept inventories are for evaluating learning gains. Finally, we report on recent work by the authors to extend conceptual testing beyond the multiple-choice format

Creation, Coordination, and Activation of Resources in Physics and Mathematics Learning

This project seeks to study introductory college level courses in physics, mechanics, and mathematics. The research questions involve the processes by which students become able to use resources across contexts (such as between mathematics and physics), how ideas in math and physics form a resource network, and what mechanisms trigger individual resources or coordinated networks. The researcher will conduct clinical interviews, small group interviews, and statistical analysis of survey questions as well as videos from classroom and help sessions. The data being collected would be analyzed for purpose of describing the development of students as they refine skills in mathematics and physical reasoning. A small group of students (15) at the University of Maine will be the subject of the study.The outcome of this project is expected to be a better model of student reasoning and learning . The reviewers were particularly interested in the possibly useful observations about the connections between mathematics and physics learning. Papers would be prepared for all education research associations, including physics

An investigation into supporting the teaching of calculus-based senior mathematics in Queensland

David Chinofunga investigated student participation in calculus-based senior secondary mathematics in Queensland and pedagogical resources that enhance teaching of mathematics. Trend analysis reveal a high dropout rate. David also found that pedagogical resources that comprise procedural flowcharts and concept maps can enrich mathematics teaching and promote student participation and engagement

UTILIZING SEMIOTIC PERSPECTIVE TO INVESTIGATE ALGEBRA II STUDENTS’ EXPOSURE TO AND USE OF MULTIPLE REPRESENTATIONS IN UNDERSTANDING ALGEBRAIC CONCEPTS

The study employed Ernest (2006) Theory of Semiotic Systems to investigate the use of and exposure to multiple representations in a 10th grade algebra II suburban high school class located in the southeastern region of the United States. The purpose of this exploratory case study (Yin, 2014) was to investigate the role of multiple representations in influencing and facilitating algebra II students’ conceptual understanding of piece-wise function, absolute-value functions, and quadratic functions. This study attempted to answer the following question: How does the use of and exposure to multiple representations influence algebra II students’ understanding and transfer of algebraic concepts? Furthermore, the following sub-questions assisted in developing a deeper understanding of the question: a) how does exposure to and use of multiple representations influence students’ identification of their pseudo-conceptual understanding of algebraic concepts?; b) how does exposure to and use of multiple representations influence students’ transition from pseudo-conceptual to conceptual understanding?; c) how does exposure to and use of multiple representations influence students’ transfer of their conceptual understanding to other related concepts? Understanding the notion of pseudo-conceptual understanding in algebra is significant in providing a tool for examining the veracity of algebra students’ conceptual understanding, where teachers have to consistently examine if students accurately understand the meanings of the mathematical signs that they are constantly using. The following data collection techniques were utilized: a) classroom observation, b) task based interviews, and c) study of documents. The unit of analysis was students’ verbal and written responses to task questions. Three themes emerged from the analysis of in this study: (a) re-imaging of conceptual understanding; (b) reflective approach to understanding and using mathematical signs; and (c) representational versatility in the use of mathematical signs. Findings from this study will contribute to the body of knowledge needed in research on understanding and assessing algebra students’ conceptual understanding of mathematics. In particular the findings from the study will contribute to the literature on understanding; the process of algebraic concepts knowledge acquisition, and the challenges that algebra students have with comprehension of algebraic concepts (Knuth, 2000: Zaslavsky et al., 2002)