This article builds upon a systematic review of 53 articles in international research journals and makes three main contributions. First, it develops a method for identifying motives, values, and assumptions in research by analysing segments of text in journal articles. Second, it represents a reflective account of research within the field of mathematics education. Third, it captures the ongoing directions of intentionalities inherent in the diverse field of special education mathematics and, thereby, some of the characteristics of the core issues in this field. Three directions of intentionalities were identified: towards teachers and teaching competence, towards enhanced mathematical achievement, and towards every student's learning. The results indicate that each direction has specific limitations and potentials. In order to improve special education mathematics, we recommend that researchers and practitioners remain broadly informed and involved in all three directions of intentionalities.
The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.
This conceptual research framework addresses the problem of rote learn- ing by characterising key aspects of the dominating imitative reasoning and the lack of creative mathematical reasoning found in empirical data. By relating reasoning to thinking processes, student competencies, and the learning milieu it explains origins and consequences of different reasoning types
An earlier study (Lithner 1998) treated the question “what are the main characteristics and background of undergraduate students’ difficulties when trying to solve mathematical tasks?” This paper will focus on, and extend, the part of the earlier study that concerns task solving strategies. The results indicate that focusing on what is familiar and remembered at a superficial level is dominant over reasoning based on mathematical properties of the components involved, even when the latter could lead to considerable progress.
Video recordings of three undergraduate students’ textbook-based home- work are analysed. A focus is on the ways their exercise reasoning is mathematically well- founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive reasoning attempts are made.
Mathematics-specific learning difficulties and disabilities (MLD) have received increasing attention in scholarly research. In this study, we place MLD research in its wider context of risk societies by discussing the manufacturing of MLD as a risk. This framing of MLD builds on a certain idea of hope in how research could provide the means to better understand and support learners with MLD. We conduct a Foucault-informed analysis to understand how scholarly knowledge about MLD has been produced through discourses of risk and hope. Our material consists of 30 influential journal articles published in the three fields of MLD research: cognitive sciences, special education and mathematics education. Our study indicates that MLD has been predominantly conceptualised through a technico-scientific risk discourse that frames MLD as harmful for learners and societies alike; such risk discourse relies on a discourse of hope in scientific methods. We also analyse a social risk discourse that identifies risks in social exclusion and marginalisation of students with MLD, finding hope in inclusive learning environments. Based on our analysis, we propose that the mere conceptualisation of MLD has thoroughly revolved around discourses of current liminalities (risk) and enunciations of better futures (hope). However, what has been unexplored is the politics of such risk and hope discourses themselves. We propose a socio-politically oriented discourse of risk/hope as a way to reframe scientific knowledge production about MLD. This discourse identifies risks not in MLD itself but in how research manufactures MLD as a threat to both economic growth and student identities. Instead of asking research communities to mitigate the risk of MLD, we call for them to embrace it.
In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties.
Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students' attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.
This paper examines the views of proof held by university level mathematics students and teachers. A framework is developed for characterizing people's views of proof, based on a distinction between public and private aspects of proof and the key ideas which link these two domains.
It is well-known that a key to promoting students’ mathematics learning is to provide opportunities for problem solving and reasoning, but also that maintaining such opportunities in student–teacher interaction is challenging for teachers. In particular, teachers need support for identifying students’ specific difficulties, in order to select appropriate feedback that supports students’ mathematically founded reasoning without reducing students’ responsibility for solving the task. The aim of this study was to develop a diagnostic framework that is functional for identifying, characterising, and communicating about the difficulties students encounter when trying to solve a problem and needing help from the teacher to continue the construction of mathematically founded reasoning. We describe how we reached this aim by devising iterations of design experiments, including 285 examples of students’ difficulties from grades 1–12, related to 110 tasks, successively increasing the empirical grounding and theoretical refinement of the framework. The resulting framework includes diagnostic questions, definitions, and indicators for each diagnosis and structures the diagnostic process in two simpler steps with guidelines for difficult cases. The framework therefore has the potential to support teachers both in eliciting evidence about students’ reasoning during problem solving and in interpreting this evidence.