Search results for "Algebraic reasoning"
showing 5 items of 5 documents
Teaching and Learning of Algebra
2015
Topic Study Group 9 aimed to bring together researchers, developers and teachers who investigate and develop theoretical accounts of the teaching and learning of algebra. The group sought both empirically grounded contributions focussing on the learning and teaching of algebra in diverse classrooms settings, the evolution of algebraic reasoning from elementary through university schooling as well as theoretical contributions throwing light on the complexities involved in teaching and learning of algebra. Prospective contributors were requested to address one or more of the following themes: early algebra, use of ICT in algebra classrooms, proof and proving in algebra, problem solving, semio…
Domain Specific Knowledge Representation for an Intelligent Tutoring System to Teach Algebraic Reasoning
2012
Translation of word problems into symbolic notation is one of the most challenging steps in learning the algebraic method. This paper describes a domain-specific knowledge representation mechanism to support Intelligent Tutoring Systems (ITS) which focus on this stage of the problem solving process. The description language proposed is based on the concept of a hypergraph and makes it possible to simultaneously a) represent all potential algebraic solutions to a given word problem; b) keep track of the student's actions; c) provide automatic remediation; and d) unequivocally determine the current state of the resolution process. An experimental evaluation with students at a public school su…
Designed Examples as Mediating Tools: Introductory Algebra in Two Norwegian Grade 8 Classrooms
2019
A critical element in the introduction of algebra is to focus student attention on the basic ideas of algebraic reasoning including the use of concepts such as variable and algebraic expression. In the Norwegian classrooms, representing a student-centered instructional philosophy, the teachers utilized examples and problems that they themselves had designed, and the examples involved resources such as concrete objects and body movements in order to make algebra accessible to students. When designing these examples, teachers thus used their own previous experiences of teaching algebra in an attempt to articulate the passage from arithmetic to algebra.
A Hypergraph Based Framework for Intelligent Tutoring of Algebraic Reasoning
2013
The translation of word problems into equations is one of the major difficulties for students regarding problem solving. This paper describes both a domain-specific knowledge representation and an inference engine based on hypergraphs that permits intelligent student supervision of this stage of the solving process. The framework presented makes it possible to simultaneously: a) represent all potential algebraic solutions to a given word problem; b) keep track of the student’s actions; c) provide automatic remediation; and d) determine the current state of the resolution process univocally. Starting from these ideas, we have designed an intelligent tutoring system (ITS). An experimental eva…
Missing Curious Fraction Problems
2018
In this paper we present a study of one of the best-known types of descriptive word fraction problems. These problems have disappeared from today’s textbooks but are hugely important for developing arithmetic thinking. The aim of this paper is to examine the historical solution methods for these problems and discuss the analytical readings suggested by the authors. On the basis of this analysis we have conducted a preliminary study of the performance of 35 Spanish students who are highly trained in mathematics. Our results show that these students have a preference for algebraic reasoning, are reluctant to use arithmetic methods, and have reading comprehension difficulties that are reflecte…