This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

The National Council of Teachers of Mathematics (NCTM) has been emphasizing the importance of teachers' pedagogical communication as part of mathematical teaching and learning for decades. Specifically, NCTM has provided guidance on how teachers can foster mathematical communication that positively impacts student learning. A teacher may have…

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M[superscript 2]EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level…

In this study, the teacher candidates who learnt to find the algebraic equation corresponding to geometric structure of the ellipse in analytic geometry classes were requested to find the algebraic representations corresponding to the structures that contained ellipses in different positions. Thus, it would be possible to determine higher order…

In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

This research provides insight into one US state's effort to incorporate higher-order thinking on its Algebra I End-of-Course tests. To facilitate the inclusion of higher-order thinking, the state used "Dimensions of Thinking" (Marzano et al., 1988) and "Bloom's Taxonomy" (Bloom et al., 1956). An analysis of Algebra I test…

During several years of experimentation, we accumulated a large collection of data on the analysis of problems generally encountered in algebra and on the reasoning developed by students at different levels when confronted with these problems. Analysis of this data led us to a new way of looking at differences among word problems, and to the…