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Chapter and Conference Paper
PEM4PPM: A Cognitive Perspective on the Process of Process Mining
During the last decades, process mining (PM) has matured and rapidly increased in its adoption. Making sense of data is a main part of the work of PM analysts, which involves cognitive processes. Recent work h...
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Chapter and Conference Paper
Investigating the Under-Usage of Code Decomposition and Reuse Among High School Students: The Case of Functions
Functions can provide substantial benefits for programmers. They offer ways that can be used to simplify a given programming task through decomposition, reusability and abstraction. As observed by the first a...
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Chapter
Revisiting the Medical Diagnosis Problem: Reconciling Intuitive and Analytical Thinking
A recurrent concern in mathematics education—both theory and practice—is a family of mathematical tasks which elicit from most people strong immediate (“intuitive”) responses, which on further reflection turn ...
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Article
Intuitive vs analytical thinking: four perspectives
This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psy...
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Article
The Rationality Debate: Application of Cognitive Psychology to Mathematics Education
Research in mathematics education usually attempts to look into students’ learning and other mental processes. It could therefore be expected to build on knowledge acquired within the academic discipline of co...
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Article
The Emergence of Mathematical Collaboration in an Interactive Computer Environment
We present a case study of two students engaged in an investigation of number theory concepts in the computer environment, Geoboard. The two students struggle with significant problems to communicate mathematics,...
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Article
Being sloppy about slope: The effect of changing the scale
What is the slope of a(linear) function? Due to the ubiquitous use of mathematical software, this seemingly simple question is shown to lead to some subtle issues that are not usually addressed in the school cur...
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Chapter
Computers and applied constructivism
In this paper we discuss and demonstrate the nature of computational learning environments which support and encourage learners’ constructions in a way which is compatible with constructivist learning theory. ...
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Article
A Reaction to Burn's “What Are The Fundemental Concepts of Group Theory?”
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Article
The World According to Johnny; A Co** Perspective in Mathematics Education
Students in mathematical problem-solving situations often experience confusion and loss of meaning. In these situations, affective and social factors are as much part of the student's thinking and behavior as ...
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Article
Just give me a computer and i will move the earth: Programming as a catalyst of a cultural revolution in the mathematics classroom
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Article
Learning group isomorphism: A crossroads of many concepts
This article is concerned with how undergraduate students in their first abstract algebra course learn the concept of group isomorphism. To probe the students' thinking, we interviewed them while they were wor...
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Article
On learning fundamental concepts of group theory
The research reported in this paper explores the nature of student knowledge about group theory, and how an individual may develop an understanding of certain topics in this domain. As part of a long-term rese...
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Book
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Chapter
Subgroups
Edit your proc name_group to obtain a new proc group_table which will define the same names G, o, e, i as name_group, but where o and i will be maps rather than funcs. For example, o will be the set of all pai...
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Chapter
Rings
In arithmetic, there is the distributive law involving addition and multiplication: for all numbers a, b,c $$\begin{array}{*{20}{c}} {a(b + c) = ab ...
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Chapter
Mathematical Constructions in ISETL
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Chapter
Subgroups
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Chapter
Rings
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Chapter
Groups
Following is a list of some funcs that you worked with in the first chapter.
