Lockwood has argued that taking a set-oriented perspective is critical for successful combinatorial enumeration. To date, however, the research literature has not yet captured the cognitive processes involved in taking such a perspective. In this theoretical paper, we elaborate the constructs of spatial structuring and spatial-numerical linked…

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead…

Background & Aims: Cognitive load theory assumes that the higher the learner's prior knowledge (i.e., the more expert the learner), the lower the intrinsic cognitive load (complexity) experienced for a given problem. While this is the case in many scenarios, there can be cases in which the converse is also true, resulting in more expert…

Geometric habits of mind (GHoM) are the approaches that individuals use to solve geometry problems. This study aimed to determine the effect of dynamic geometry software (DGS) in activating the GHoM of pre-service mathematics teachers. The study was conducted with six teacher candidates who were enrolled in a semester-long course titled…

Mathematical modeling and applications are an important part of curriculum and considered to be important for students' current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the…

Arithmetic word problems are a staple in mathematical curricula yet give individuals of all ages difficulty. Successful word problem solving requires translating the problem into a symbolic arithmetic format. However, the linguistic component may make problem solving more complex and increase cognitive load, specifically the processes that…

In light of the known visuoperceptual strengths and altered language skills in autism, we investigated the impact of problem content (semantic/visuospatial) combined with complexity and presence of lures on fluid reasoning in 43 autistic and 41 typical children (6-13 years old). Increased complexity and presence of lures diminished performance,…

Eye tracking technology enables the visualisation of a problem solver's eye movement while working on a problem. The eye movement of experts has been used to draw attention to expert problem solving processes in a bid to teach procedural skills to learners. Such affordances appear as eye movement modelling examples (EMME) in the literature. This…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

Combinatorial proof is an important topic both for combinatorics education and proof education researchers, but relatively little has been studied about the teaching and learning of combinatorial proof. In this paper, we focus on one specific phenomenon that emerged during interviews with mathematicians and students who were experienced provers as…

The response process of problem-solving items contains rich information about respondents' behaviours and cognitive process in the digital tasks, while the information extraction is a big challenge. The aim of the study is to use a data-driven approach to explore the latent states and state transitions underlying problem-solving process to reflect…

Many empirical studies about STEM (science, technology, engineering, and mathematics) curriculum present problems for students to solve. This paper draws upon the data collected from the enactment of an integrated STEM curriculum to discuss problems as constitutive of problem spaces where four Grade 5 Singapore students engage with the…

The current examined the roles of cognitive strategies using Chi's framework in mobile learning. Three conditions (active, constructive, and interactive) were created for a college statistics I course where students were randomly assigned to each condition. The results indicate constructive and interactive support students' problem solving and…

Effective learning in chemistry education requires students to understand visual representations across multiple conceptual levels. Essential to this process are visuospatial skills which enable students to interpret and manipulate these representations effectively. These abilities allow students to construct mental models that support problem…

Learning interaction patterns is key to the explanation of learning outcomes. Different studies have reported the relationship between classroom process variables and learning outcomes in a traditional classroom setting. However, the advent of robotics and its attendant student-robot interaction moderated by students' mathematical ability is yet…