Little research in the field of Mathematics Education is directed towards emotions of students beyond their emotions in problem-solving. In particular, the daily emotions of students in a mathematics class have been sparsely studied in the field of mathematics education. In order to fill this gap, this qualitative research aims to identify high…

The aim of this qualitative research is to identify Mexican high school students' emotional experiences in mathematics classes. In order to obtain the data, focus group interviews were carried out with 22 students. The data analysis is based on the theory of the cognitive structure of emotions (Ortony, Clore & Collins, 1988) that specifies the…

This research questions were "how do the characteristics of learning model of logic & algorithm according to APOS theory" and "whether or not these learning model can improve students learning outcomes". This research was conducted by exploration, and quantitative approach. Exploration used in constructing theory about the…

The aim of this qualitative research is to identify Mexican high school students' emotional experiences in mathematics classes. In order to obtain the data, focus group interviews were carried out with 22 students. The data analysis is based on the theory of the cognitive structure of emotions, which specifies the eliciting conditions for each…

This article explores theoretical and methodological issues associated with task-based interviews conducted with pairs of children. We explore different approaches to interviews from sociological, psychological and subject-based perspectives. Our interviews, concerning mathematical questions and carried out with pairs of 10 and 11-year-olds, are…

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct…

Explores the development of understanding of the concept of average with students from grades 3 to 9 through interviews. Observed six levels of response based on an hierarchical model of cognitive functioning. Documents usage of ideas associated with the three standard measures of central tendency and representation as strategies for problem…

This paper presented various issues about pedagogical and cognitive aspects of problem solving and explored ways to lessen the heavy cognitive load of a problem solving task. It established a problem type schema for students at different levels. It recognizes the role of modern technology as a cognitive tool that promotes learning mathematics with…

Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

A mathematician who has been teaching for 58 years discusses 3 types of knowledge that are subjects for teaching or learning (what, how, and why) and why teaching must include problem solving or the use of the Socratic, Moore, or discovery method. (MKR)

Presents evidence indicating that spontaneously generated analogies can play a significant role in expert problem solving. Focuses on an evaluation strategy known as bridging that has been observed in solutions to both science and mathematics problems. Contains 23 references. (DDR)

This paper outlines a theoretical perspective for studying student understandings of the concept of addition. The notion of operational sense is defined as a way to describe the notion of addition as a mathematical object, paving the way for an application of the theory of reification at this level. Previous frameworks relative to problem solving…

To examine how conceptual knowledge about fraction magnitudes changes as students' learning progresses, 5th and 7th-grade students were asked to solve fraction magnitude problems that entailed finding a fraction between two given fractions and then to evaluate solutions for similar problems that were modeled for them. When the given fractions…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…