Umeå universitets logga

Curricula in many countries include mathematical reasoning as an aim, a competence or proficiency that students should acquire. This inclusion has been supported by wide dissemination of frameworks advocating reform that have arisen from the research community. We present the first part of a project aiming to investigate how ideas about reasoning originating in these frameworks are recontextualised in curricula, textbooks and classrooms. We analyse discourses about reasoning in three such frameworks, identifying how each characterises the nature of mathematical reasoning and the ways students are expected to relate to it. We also examine the extent to which reasoning is construed as a goal of mathematics education or as a means to achieving other goals. In this paper, we explain the methods used for analysing reasoning discourse and identify key findings from the analysis.

In mathematics, students’ abilities to make transformations between mathematical representations are fundamental. The recent implementation of digital technologies, such as Dynamic Geometry Environments (DGEs), have changed students’ access to mathematical representations by providing a variety of different representations, available just by pressing a button. Students use of a DGE may change their mathematical communication to become more dynamic and active. However, it is not clear how the use of DGEs and the change in communication style relate to more epistemological aspects of students’ mathematical work. This study, therefore, investigates the interplay between students’ dynamic mathematical communication and their transformations of mathematical representations when using a DGE from a competency perspective. Based on analyses of instances of lower secondary school students’ dynamic mathematical communication, findings indicate that students’ mathematical communication reflect the new ways of engaging with mathematical representations when using a DGE. Hence, the communication becomes dynamic. Theoretically, the complexity of having “continuous” transformations of mathematical representations may reduce the readiness of the mathematical communication competency. The “continuous” transformation may in fact cause students to unintentionally ascribe dynamic properties to mathematical representation.

A reader of mathematical text must often switch between reading mathematical symbols and reading words. In this study, five different categories of structural connections between symbols and language, which invite such switches, are presented in a framework. The framework was applied in a study of Swedish mathematics textbooks, where 180 randomly selected pages from different educational stages were analyzed. The results showed a significant change in communication patterns as students progress through school. From a predomination of connections based on proximity found in year two, there is a gradual change to a predomination of symbols interwoven in sentences in year eight. Furthermore, more qualitative investigations of the different connections complemented the quantification, both through further explanations of the quantitative results, and through more examples of differences in communication patterns. The implications for readers of mathematics texts are discussed.

When mathematics tasks are used in multilanguage assessments, it is necessary that the task versions in the different languages are equivalent. The purpose of this study is to deepen the knowledge on different aspects of equivalence for mathematics tasks in multilanguage assessment. We analyze mathematics tasks from PISA 2012 given to students in English, German and Swedish. To measure formal equivalence, we examine three linguistic features of the task texts and compare between language versions. To measure functional equivalence, a Differential item functioning (DIF) analysis is conducted. In addition, we examine statistically if there is a relation between DIF and the differences regarding linguistic features. The results show that there is both DIF and differences regarding the linguistic features between different language versions for several PISA tasks. However, we found no statistical relation between the two phenomena.

There is much research on the role of theory in mathematics education research, at least from more overarching or theoretical perspectives. Micro analyses of the role of theory in particular research studies are rarer. We contribute by analysing one empirical study to allow for in-depth analyses and discussions around the role of theory in a specific case, concerning relationships between mathematics and reading. Our results show that studies that do not use an explicit theoretical model can still be strongly influenced by implicit theoretical assumptions. We conclude that it is important to identify existing theoretical assumptions in an empirical research study and try to convey them as clearly as possible, and we discuss specific issues concerning research on relationships between mathematics and reading.

When using a dynamic geometry environment, students’ mathematical communication may becomemore dynamic, shown by adverbs and verbs indicating activity or change. In this paper, three examples of students’ answers when using a DGE template are analysed through Duval’s (2017) semiotic register approach as well as the concept of dynamic mathematical communication. Results exemplify how students’ mathematical communication when using DGE may have a dynamic character (using words such as ‘drag’). Results also indicate that coordinating representations across four different registers is challenging, and students may focus on only performing treatments in one register. Furthermore, the students’ insightful readiness to communicate mathematically may be challenged in DGE settings.

In mathematical text and talk, natural language is a constant companion to mathematical symbols. The purpose of this study is to identify different types of relations between natural language and symbolic language in mathematics textbooks. Here we focus on the level of integration. We have identified examples of high integration (e.g., when symbols are part of a sentence), medium integration (e.g., when the shifts between natural and symbolic language occurs when switching to a new line), and low integration (e.g., when symbols and written words are connected by the layout).

In this study, we examine how the use of natural language varies, considering the symbolic language in procedural and conceptual aspects of mathematics.