Algebraic thinking of grade 8 students in solving word problems with a spreadsheet

This paper describes and discusses the activity of grade 8 students on two word problems, using a spreadsheet. We look at particular uses of the spreadsheet, namely at the students’ representations, as ways of eliciting forms of algebraic thinking involved in solving the problems. We aim to see how the spreadsheet allows the solution of formally impracticable problems at students’ level of algebra knowledge, by making them treatable through the computational logic that is intrinsic to the operating modes of the spreadsheet. The protocols of the problem solving sessions provided ways to describe and interpret the relationships that students established between the variables in the problems and their representations in the spreadsheet

Developing algebraic and didactical knowledge in pre-service primary teacher education

This study analyzes the contribution of a teaching experiment for the development of prospective primary teachers regarding knowledge of algebra and of algebra teaching as well as their professional identity. The case study of a prospective teachersuggests that an exploratory approach combining content and pedagogy supports this development, especially in the need to propose challenging tasks, to provide opportunity for students’ autonomous work and collective discussions and to be attentive to children’s representations and strategies in order to promote algebraic thinking

From quasi-variable thinking to algebraic thinking: A study with grade 4 students

This communication presents a study that is part of a broader teaching experiment research that focus on the development students’ algebraic thinking in one grade 4 class. The particular goal of this communication is to analyze students’ algebraic thinking when they explore numerical equalities with two unknown quantities. Data collection focuses on the students’ work on one task in the classroom, and is based on participant observation and on the analyses of students’ worksheets. We conclude that students are starting to evidence the emergence of algebraic thinking by expressing the generalization of the numerical relationships in different representations.FCT - Fundação para a Ciência e Tecnologi

Errors in algebraic statements translation during the creation of an algebraic domino

We present a research study which main objective is to inquire into secondary school students´ ability to translate and relate algebraic statements which are presented in the symbolic and verbal representation systems. Data collection was performed with 26 14-15 years old students to whom we proposed the creation of an algebraic domino, designed for this research, and its subsequent use in a tournament. Here we present an analysis of the errors made in such translations. Among the obtained results, we note that the students found easier to translate statements from the symbolic to the verbal representation and that most errors in translating from verbal to symbolic expressions where derived from the particular characteristics of algebraic language. Other types of errors are also identified. KEYWORDS: Algebraic language, domino, errors, translation between representation systems, verbal representation