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…

This work addresses the importance of innovation in entrepreneurial and business education to ensure that students develop the ability to make complex decisions and solve complex challenges. The intention was to incorporate the complexity theory in decision-making and problem-solving in business and entrepreneurship. To achieve this, we present…

In this paper, we report on the pedagogical actions of one teacher in eliciting and developing students' mathematical reasoning during one mathematics lesson. The findings illustrate that through the careful design and planning of a contextually relevant task (the construction of a manu tukutuku), and the implementation of specific teacher…

Mathematical reasoning is foundational to making sense of mathematics. Yet assessing mathematical reasoning can be challenging for teachers. This paper reports on a project where teachers taught two lessons with a specific focus on reasoning and came together with other teachers at their school to attempt to assess the reasoning of their students.…

This paper articulates a stance on the study of students' meaningful mathematics understanding with multiple representations. We integrate Thompson's theory of quantitative reasoning and Dreyfus' theory of multiple representations in our approach to frame and conduct empirical investigations of the study of meaningful understanding of function. We…

Logical reasoning is very important in the child's development, increasing their performance in learning as a whole, improving their concentration and decision-making when solving problems. The introduction of this tool and stimulus from the first years of education is necessary for children to grow up with a broad and more critical view, being…

We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive…

Probability and independence are difficult concepts, as they require the coordination of multiple ideas. This qualitative research study used clinical interviews to understand how three undergraduate students conceptualize probability and probabilistic independence within the theoretical framework of APOS theory. One student's reasoning was…

The purpose of this paper is to investigate students' engagement in computational thinking (CT) and programming with MATLAB when solving a mathematical task in a programming course at the undergraduate level. The data collection method is participant observation of three groups of three students presented with a mathematical task to solve. The…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

The current Australian Curriculum mandates that technology be utilised to support students to "investigate, create and communicate mathematical ideas and concepts" (ACARA, 2018). However, research reports suggest that use of digital technologies in Australian primary mathematics often focuses on the lower-order drilling of algorithms and…

In this exploratory study we considered how one teacher's understanding of proportional reasoning related to his teaching. We relied on Knowledge in Pieces as a lens for considering the teacher's knowledge organization as a way to make sense of his understanding. We did so by collecting data from two instruments and using Epistemic Network…

To investigate the effects that experiences of programming have on parents' concerns about programming education in primary schools, a survey was carried out before and after a programming seminar for children and their parents. Participation in the programming seminar seemed to boost parents' expectations and decrease their anxieties about…

This research targets children's informal strategies and knowledge of fractions by examining their ability to create, interpret, and connect representations in doing and communicating mathematics when solving fractions tasks. Our research group followed a constant comparative method to analyze clinical interviews of children in grades 2-6 solving…

The aim of the paper is to provide a process model to evaluate mathematical problem solving by analogy, in order to better determine at which point and under what conditions a learner is prompted to use analogies. The model is a theoretical construct. Qualitative results of an empirical study are used to underline and illustrate core aspects of…