This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

How does early feedback change the programming problem solving in an online environment and help students choose correct approaches? This study was conducted in a sample of students learning programming in an online course entitled Introduction to C++ and OOP (Object Oriented Programming) using the ANGEL learning management system platform. My…

Learning about linear relationship with one unknown, middle school students may often demonstrate a certain degree of proficiency manipulating algebraic symbols. When encouraged, they can verbalize and explain the steps they perform, thereby demonstrating awareness of the procedures with symbols according to fixed rules. It is well known that…

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then…

A solution to the Rubik's Cube was introduced to an eighth grade mathematics class. The purpose of this study was to determine if an introduction to a solution to the Rubik's Cube could enhance students' problem-solving abilities, increase their general interest in mathematics, and enhance students' problem solving self-efficacy. Pre and Post…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

The greatest benefit of including leap year in the calculation is not to increase precision, but to show students that a problem can be solved without such presumption. A birthday problem is analyzed showing that calculating a leap-year birthday probability is not a frivolous computation.

Problem-based learning (PBL), initiated when learners meet the problem scenarios, develops learners' skills and subject matter content to make the transition from beginner to more expert problem solver. Beginning students might benefit from simple, well-structured problems, in which the understanding of sets of rules and principles results in a…

The study describes students' patterns of thinking for statistical problems set in two different contexts. Fifteen students representing a wide range of experiences with high school mathematics participated in problem-solving clinical interview sessions. At one point during the interviews, each solved a problem that involved determining the…

Norms govern the criteria by which students decide what is good and what is not good, and align their learning trajectories accordingly.We found that the high-school students' norm is to produce working, but not necessarily error-free, programs and to argue for their correctness solely on the basis of a few executions. Therefore, they prefer…