Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by…

In the context of scholarly and scientific discourse, students often have to deal with graphic-visual modes of communication, which requires their ability to comprehend and utilize inscriptions, that is, scientific visual representations, to convey information effectively--what we call graphical literacy. Despite its pivotal role for training…

In this study, we developed a classification system of programming errors based on the historical data of 680,540 programming records collected on the Online Judge platform. The classification system described six types of programming errors (i.e., syntax, logical, type, writing, misunderstanding, and runtime errors) and their connections with…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

This paper proposes a novel application of knowledge space theory for identifying discrepancies between the knowledge structure that experts expect students to have and the real knowledge structure that students demonstrate on tests. The proposed approach combines two methods of constructing knowledge spaces. The expected knowledge space is…

In this study, we investigate students' ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14-16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise…

This paper is about the development of a task sequence to help overcome the fragmented understanding of the "function" concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students' use of functions more flexible in certain respects, for example when functions are…

Summary writing is an important skill that students use throughout their academic careers, writing supports reading and vocabulary skills as well as the acquisition of content knowledge. This exploratory and development-oriented investigation appraises the recently released online writing system, "Graphical Interface of Knowledge…

Gesturally controlled information and communication technologies, such as tablet devices, are becoming increasingly popular tools for teaching and learning. Based on the theoretical frameworks of cognitive load and embodied cognition, this study investigated the impact of explicit instructions to trace out elements of tablet-based worked examples…

This article reports on a study of six Grade 11 learners' levels of understanding of concepts related to the function definition and representation. Task-based clinical interviews were used to elicit the learners' interpretations and reasoning when working with these function-related concepts. Indicators for Action-Process-Object-Schema (APOS)…

Algebra has been explicit in many school curriculum programs from the early years but there are competing views on what content and approaches are appropriate for different levels of schooling. This study investigated 12-13-year-old Australian students' algebraic thinking in a hybrid environment of functional and equation-based approaches to…

This study examined prospective middle school mathematics teachers' problem-posing skills by investigating their ability to associate linear graphs with daily life situations. Prospective teachers were given linear graphs and asked to pose problems that could potentially be represented by the graphs. Their answers were analyzed in two stages. In…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

Our paper focuses on the relationship between spatial and geometrical knowledge in problem solving situations at primary school. We have created tasks that involve three different spaces: physical space, graphical space and geometrical space. We aim to study the specific role of graphical space as a bridge between the other two spaces using paper…

Rapid cognitive diagnosis allows measuring current levels of learner domain-specific knowledge in online learning environments. Such measures are required for individualizing instructional support in real time, as students progress through a learning session. This article describes 2 experiments designed to validate a rapid online diagnostic…