We presented two empirical studies to assess the efficacy of two Deep Reinforcement Learning (DRL) frameworks on two distinct Intelligent Tutoring Systems (ITSs) to exploring the impact of Worked Example (WE) and Problem Solving (PS) on student learning. The first study was conducted on a probability tutor where we applied a classic DRL to induce…

This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

A key challenge in e-learning environments like Intelligent Tutoring Systems (ITSs) is to induce effective pedagogical policies efficiently. While Deep Reinforcement Learning (DRL) often suffers from "sample inefficiency" and "reward function" design difficulty, Apprenticeship Learning (AL) algorithms can overcome them.…

The purpose of this study is to gain understanding of how secondary teachers conceptualize the relationships between mathematical modeling and problem solving. Eight secondary teachers participated in semi-structured, think-aloud individual interviews. Some conceptualizations include (a) modeling and problem solving are two distinct processes; (b)…

Numerous studies (Anwar et al., 2016; Carpenter et al., 1980; Huang & Witz, 2013; Outhred & Mitchelmore, 1996; Machaba, 2016; Van de Walle, Karp & Bay-Williams, 2014; Winarti et al., 2012) have shown that students need help understanding the concept of area and perimeter. This study aimed to investigate what students know about finding…

This article elucidates a nuanced methodology to embed the Sustainable Development Goals (SDGs) within engineering curricula, grounded in the tenets of the CDIO Standard 3 framework. Given the heightened emphasis on sustainability within contemporary industrial contexts, there is an imperative demand for engineers endowed with sophisticated…

As digital technologies become a commonplace in mathematics classrooms, they transform the ways students and teachers interact with mathematics. Students learn to use a technological tool for solving mathematical tasks through a process known as instrumental genesis. Teachers' support for this process is known as instrumental orchestration. In…

A Prolog program consists of a set of facts and rules rather than imperative statements, commonly used in most other programming languages. Therefore, the Prolog language is used to encode logic, from which the inference engine deduces logical conclusions. In this article, we argue that the use of the Prolog language can be useful to help students…

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

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…

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…

This study posits mathematics as a fundamental methodological framework for navigating the complexities of multidisciplinary research. It argues that the increasing prevalence of real-world problems demands the integration of knowledge from diverse scientific fields, where mathematics, particularly through the method of analysis and synthesis,…

As problems become increasingly complex, science educators need to better understand how new knowledge is constructed and applied in heterogeneous team collaborations, and how to teach students to productively engage in these processes. We discuss the emergence of insights in collaborative sensemaking and suggest a model that articulates the…

In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic…

In this study, we sought to understand what might be learned about preservice teachers' mathematics learner and mathematics educator identities in the context of a problem-solving focused mathematics content course. Twenty-two preservice teachers participated in this study as part of their undergraduate teacher preparation program. We implemented…