This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They…

This study analyzed the relative importance of different cognitive abilities for solving complex mathematical word problems (CWPs)--a demanding task of high relevance for diverse fields and contexts. We investigated the effects of spatial, verbal, numerical, and general reasoning abilities as well as gender on CWP performance among N = 1282…

We investigated the impact of assistance on learning and affect during problem-solving activities with a computer tutor we built using the Cognitive Tutor Authoring Tools framework. The tutor delivered its primary form of assistance in the form of worked-out examples. We manipulated the level of assistance the examples in the tutor provided, by…

This study investigated the development of problem-solving strategies demonstrated by 42 elementary pre-service mathematics teachers in problem-solving mathematics classes. The study used a mixed methods approach of quantitative and qualitative research by analyzing the collected data.. The quantitative portion calculates the frequencies and…

Productive struggle--expending effort to make sense of something beyond one's current level of understanding--aids in learning mathematics concepts and procedures. In this study, we surveyed 197 parents with children in the 1st to the 5th grade on their beliefs about productive struggle. Beliefs were assessed via questionnaire and rating of a…

This study investigated the mediating roles of self-efficacy and anxiety on the effects of teacher-student relationship on mathematical problem-solving ability. A total of 1667 fifth graders from central China participated in the large-scale survey. The findings indicated that (1) teacher-student relationship had a direct and positive effect on…

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.

We analyzed the solution pathways and errors found in the written responses of 469 prospective teachers solving an equation containing fractions. The majority (332, or 70%) used an algebraic method; 141 of the 332 (42%) were correct, and 22% of the algebraic methods were abandoned before a solution was obtained. We identified the steps in the…

The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed…

In this note, I present an 'easy-to-be-remembered' shortcut for promptly solving the ubiquitous integral [line integral] x[superscript n] e[superscript alpha x] dx for any integer n>0 using only the successive derivatives of x[superscript n]. Some interesting applications are indicated. The shortcut is so simple that it could well be included…

In this paper we consider how the integration of mobile technology apps into classroom practice can form an alternative pedagogical medium that influences the learning process in mathematics. We give an account of one aspect of a research project that examined the use of tablets and apps in primary school mathematics programmes and report teacher…

Pattern recognition is an important skill in computational thinking. In this study, an equation puzzle game was developed by combining pattern recognition with algebraic reasoning, and scaffolding was designed to support learners' learning. Sixty participants were enrolled in this study, divided into a control group and an experimental group to…

Mathematical literacy has an important role in solving students' real-life problems in supporting literacy skills, teachers can use real contexts as outlined in tasks in-class learning. The Bengkulu context can be used because it is closely related to the environment and students' daily live. This study aims to produce math literacy tasks in the…

The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

In the literature in recent years, a number of developmental studies have demonstrated the importance of children entering the school environment with a solid foundation of mathematical content knowledge and argued that problem solving, as an important mathematical process, should be acknowledged in early childhood mathematical education. However,…