Science and drawing have been paired for hundreds of years, and this synergy is still prevalent in research investigating the role of drawing for developing and assessing understanding. However, despite research at the primary and secondary levels of education, there is limited research on whether drawing facilitates learning at the undergraduate…

This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…

Problem-solving activities have been studied from a diversity of epistemological perspectives. In problem-solving activities, the initial tensions of a problematic situation led to a cognitive dissonance between conflicting motives and instruments to reach the activity goal. We analyze problem-solving in the continuation of Sannino and Laitinen's…

A compelling demonstration of implicit learning is the human ability to unconsciously detect and internalize statistical patterns of complex environmental input. This ability, called statistical learning, has been investigated in people with dyslexia using various tasks in different orthographies. However, conclusions regarding impaired or intact…

Recent studies have found that infants show relational learning in the first year. Like older children, they can abstract relations such as "same" or "different" across a series of exemplars. For older children, language has a major impact on relational learning: labeling a shared relation facilitates learning, while labeling…

This paper uses evidence-centered assessment design (ECD) to structure and analyze a laboratory activity where students collect and represent titration curve data to determine acid strength in terms of molarity and dissociation constant. Following principles of multidimensional learning, the activity prompts students to demonstrate knowledge of…

In everyday life, people seek, evaluate, and use online sources to underpin opinions and make decisions. While education must promote the skills people need to critically question the sourcing of online information, it is important, more generally, to understand how to successfully promote the acquisition of any skills related to seeking online…

Retrieval practice is a learning strategy that has repeatedly been found to have positive effects on memory and learning. However, studies indicate that students rarely use retrieval practice on a voluntary basis. The objective of the present study was to examine students' self-regulated use of retrieval practice, and to determine whether sex and…

Scaffolds that support self-regulated learning (SRL) have been found to improve learning outcomes. The effects of scaffolds can differ depending on how learners use them and how specific scaffolds might influence learning processes differently. Personalized scaffolds have been proposed to be more beneficial for learning due to their adaptivity to…

The Topic Hypothesis posits that Chinese language learners progress through a developmental sequence comprising five stages (Gao, 2009; Wang, 2011), which includes the Object-Subject-Verb (OSV) structure at stage 4 and the ba-construct at stage 5. According to this hypothesis, learners typically master the OSV structure before acquiring the…

Iconicity, or the resemblance between form and meaning, is often ascribed to a special status and contrasted with default assumptions of arbitrariness in spoken language. But does iconicity in spoken language have a special status when it comes to learnability? A simple way to gauge learnability is to see how well something is retrieved from…

The benefits of technological and theoretical scaffolding were observed when pre-service teachers aiming to teach upper elementary grades were given three learning-based geometrical inquiry tasks involving inscribed circles. They were asked to collaboratively examine the accompanying geometrical illustration and data for some new or interesting…

Design Research (DR) has been used to develop means of supporting mathematical learning for typically-developing students. This study investigated the use of DR to develop context specific tools to support adults with intellectual disabilities (ID) to improve their numeracy capabilities and engagement in daily tasks. Using observation and…

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers': view prompts as important…

In this paper, we present parts of an online qualitative research project which lasted a whole semester about the understanding of real numbers by sixty first-year Greek mathematics undergraduate students during the COVID-19 pandemic. We focus on the distinction between rational and irrational numbers and their location on the number line using…