Introduction to Discrete Mathematics with ISETL

Fenton, William E.; Dubinsky, Ed

doi:10.1007/978-1-4612-4052-5

Cited by 10 publications

(6 citation statements)

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“…As an example of work that is exploring relationships between combinatorics and computational thinking and activity in particular, some researchers have investigated ways in which combinatorial thinking may be well-suited for fostering computational thinking and activity, as well as how computational settings might reinforce and enrich students' reasoning about combinatorics problems (e.g., Fenton & Dubinsky, 1996;Lockwood & De Chenne, 2019;De Chenne & Lockwood, 2020;Lockwood, Valdes-Fernandez, & De Chenne, 2019). For instance, in their book Introduction to Discrete Mathematics with ISETL, Fenton and Dubinsky (1996) proposed a new programming language (ISETL) that would explicitly help to reinforce topics of discrete mathematics in a computational setting. As another example, Lockwood & De Chenne (2019) report on two students' exploration of tasks in which they solved counting problems in a computational setting of programming involving coding in Python.…”

Section: -Combinatorics Is a Natural Domain In Which To Examine (And Develop) Computational Thinking And Activitymentioning

confidence: 99%

A case for combinatorics: A research commentary

Lockwood

Wasserman²,

Tillema

2020

The Journal of Mathematical Behavior

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In this commentary, we aim to make a case for the explicit inclusion of combinatorial topics in the curriculum -both in K-12 classrooms and in introductory postsecondary mathematics courses -where it is currently essentially absent. To do so, we suggest ways in which researchers might inform the field's understanding of combinatorics and its potential role in curricula. We reflect on five decades of research that has been conducted since a call by Kapur (1970) for a greater focus on combinatorics in mathematics curricula. We offer five assertions about combinatorics, including three existing assertions and two new assertions that relate to increasingly relevant trends in mathematics education. Specifically, we discuss the following in making our case for combinatorics: 1) Combinatorics is accessible, 2) Combinatorics problems provide opportunities for rich mathematical thinking, 3) Combinatorics fosters desirable mathematical practices, 4) Combinatorics can contribute positively to issues of equity in mathematics education, and 5) Combinatorics is a natural domain in which to examine (and develop) computational thinking and activity. As we discuss each of these ideas, we summarize and synthesize existing research and offer new ideas for research. Ultimately, we hope to make a case for the valuable and unique ways in which combinatorics might effectively be leveraged within K-16 curricula, and we hope to elevate its status in the mathematics education research community.

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Section: -Combinatorics Is a Natural Domain In Which To Examine (And Develop) Computational Thinking And Activitymentioning

confidence: 99%

A case for combinatorics: A research commentary

Lockwood

Wasserman²,

Tillema

2020

The Journal of Mathematical Behavior

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“…Çünkü "func" yapısının ikinci kısmında incelenen özelliğe ait matematiksel tanım ya da ilişki yazılmaktadır. Diğer matematiksel kavramların programlanma sürecinde de geçerli olan bu durum öğrencilerin kavramları zihinlerinde yapılandırmalarında, en etkili yollardan biri olarak görülmektedir (Fenton & Dubinsky, 1996). Bu bağlamda bu çalışmada, APOS teorisinin önerdiği zihinsel yapıların oluşturulması sürecinde ACE döngüsü içinde yer alan ISETL aktivitelerinin etkililiği araştırılmıştır.…”

Section: Isetl Programlama Diliunclassified

The Impact of Computer-Assisted Abstract Algebra Instruction on Achievement and Attitudes Toward Mathematics: The Case of ISETL

Yorgancı¹

2019

Turkish Journal of Computer and Mathematics Education (TURCOMAT)

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Öz: Araştırma, bilgisayar destekli soyut cebir öğretiminin, ilköğretim matematik öğretmeni adaylarının akademik başarılarına ve matematiğe karşı tutumları üzerine etkisini belirlemeyi amaçlamaktadır. Çalışmanın örneklemini, bir devlet üniversitesinin eğitim fakültesi ilköğretim matematik öğretmenliği lisans programında öğrenim gören toplam 30 öğrenci oluşturmaktadır. Eşit olmayan kontrol gruplu ön test-son test deneysel desenin benimsendiği çalışmada kontrol grubunda geleneksel öğretim yöntemi, deney grubunda ise APOS teorisine dayalı olarak geliştirilen ACE (activities, class discussion, exercices) öğretim döngüsü kullanılmıştır. Bu çerçevede deney grubunda ACE döngüsünün ilk adımı olan bilgisayar aktivitelerinde ISETL programlama dili kullanılmıştır. Araştırmanın verileri akademik başarı testi, matematik tutum ölçeği ve görüşmeler yoluyla elde edilmiştir. Elde edilen sonuçlar, deney ve kontrol grubunun başarı ve tutum puanları arasında deney grubu lehine anlamlı farklar olduğunu göstermiştir. Görüşmelerden elde edilen bulgular; deney grubu öğrencilerinin normal alt grup ve bölüm grubu kavramlarına ilişkin anlamalarının, kontrol grubu öğrencilerine göre daha ileri düzeyde olduğunu göstermiştir.

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“…Other works (Siller and Greefrath, 2009) share with us a focus on mathematical modelling but most of them use software tools as Computer Algebra systems (CAS), Dynamic Geometry Software (DGS) or Spredsheet programs (SP). Our approach is very closed from (Fenton and Dubinsky, 1996). We adopt their APO model of concept formation together with a computer-supported approach The main differences are (1) that we use a lightweight formal method while they use a programming language, (2) that our approach doesn't restrict to mathematics but is cross-disciplinary.…”

Section: Related Workmentioning

confidence: 99%

“…In this section, we will explain how Alloy allows a pedagogy based on the Action-Process-Object model (Fenton and Dubinsky, 1996) which is considered today as the central model of concept formation. According to this model, three successive mental constructions are needed in order to develop an understanding of a mathematical concept.…”

Section: A Constructivist Approachmentioning

confidence: 99%

“…with the help of Alloy (Jackson, 2006) (Alloy, 2007), a lightweight formal method dedicated to rapid software modelling created by Daniel Jackson's, group at MIT. This tool allows us to elaborate a pedagogy based on the Actions-Process-Object model (Fenton and Dubinsky, 1996) which is considered today as the central model of concept formation.…”

Section: Introductionmentioning

confidence: 99%

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TEACHING ABSTRACTION IN MATHEMATICS AND COMPUTER SCIENCE - A Computer-supported Approach with Alloy

Simonot¹,

Homps²,

Bonnot³

2012

Proceedings of the 4th International Conference on Computer Supported Education

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ion skill is difficult but essential when learning computer science and mathematics. In this paper, we present an experience from the Computer Science Department of IUT de Montreuil in which mathematics and computing teaching work together in order to provide abstract thinking skills to students. Our approach is to connect mathematics and software engineering through a computer-supported approach which uses-in mathematics and software engineering undergraduate courses-Alloy, a lightweight formal method from MIT. Alloy serves as a continuum from micro-modelling activities-used to enforce an abstract understanding of basic mathematic concepts-to real software modelling practice. It enables us to elaborate a kind of exploratory learning where students are actively engaged.

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Introduction to Discrete Mathematics with ISETL

Abstract: Fenton, William (William E.) Introduction to discrete mathematics with ISETL I by William Fenton & Ed Dubinsky. p. cm. Includes bibliographical references (p. -) and index.

Cited by 10 publications

References 0 publications

A case for combinatorics: A research commentary

A case for combinatorics: A research commentary

The Impact of Computer-Assisted Abstract Algebra Instruction on Achievement and Attitudes Toward Mathematics: The Case of ISETL

TEACHING ABSTRACTION IN MATHEMATICS AND COMPUTER SCIENCE - A Computer-supported Approach with Alloy

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