The purpose of this research is to examine fourth grade students' ability to solve mathematical problems which have the same solutions but are given in three different formats as "symbolic, numerical and story (word) problem" and which require four operations. Within this frame, the students' solutions in different formats, their…

The More A-More B intuitive rule has become a research hotspot in the field of mathematical education in recent years. The intuitive rule of More A-More B is often reflected in students' responses to comparison tasks. In such tasks, students are asked to compare 2 objects that differ in a certain salient quantity A (where A[subscript 1] >…

Pronouns encouraging a second-person perspective (e.g., "you/your") affect peoples' mental representations constructed while reading and improve learning. The present study applied these insights to a domain in that such pronoun effects have yet been unexplored: mathematical word problem solving. Specifically, we encouraged a…

This paper explores misconceptions and errors (M/Es) of eighth-grade students in Nepal with a quasi-experimental design with nonequivalent control and experimental groups. The treatment was implemented with teaching episodes based on different remedial strategies of addressing students' M/Es. Students of control groups were taught under…

Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved learning outcomes. Most existing approaches for automated student solution analysis and feedback require manually…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

Hypothesis testing involves a complex stepwise procedure that is challenging for many students in introductory university statistics courses. In this paper we assess how feedback from an Intelligent Tutoring System can address the logic of hypothesis testing and whether such feedback contributes to first-year social sciences students' proficiency…

Problem solving, worked examples, and erroneous examples have proven to be effective learning activities in Intelligent Tutoring Systems (ITSs). However, it is generally unknown how to select learning activities adaptively in ITSs to maximize learning. In the previous work of A. Shareghi Najar and A. Mitrovic, alternating worked examples 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…

Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to…

Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers' (PSTs) errors and…

This qualitative study examines the gifted students' self-reflections about the mathematical problems in an elaborated way. The participants of the study were three gifted students in 10th grade and 10 problem solving sessions were carried out with these participants. According to findings, the gifted students did not take into account the…

Mistakes can be a source of frustration for teachers and students in mathematics classrooms because they reveal potential misunderstandings or a lack of learning. However, increasing evidence shows that making mistakes creates productive pathways for learning new ideas and building new concepts (Boaler 2016; Borasi 1996). Learning through…

Recent works on Intelligent Tutoring Systems have focused on more complicated knowledge domains, which pose challenges in automated assessment of student performance. In particular, while the system can log every user action and keep track of the student's solution state, it is unable to determine the hidden intermediate steps leading to such…

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs' faulty reasoning displayed in errors they make.…