Our work focuses on the transition from high school to university in the field of calculus. In France, recursive sequences are studied as one of the classical exercises in both institutions. Their studies use different theorems and notions, such as functions, convergence, monotonicity, induction, etc. The work expected at this transition requires…

This work presents the result of the application of a didactic sequence designed to understand the concept of the Cavalieri's Principle, supported by the GeoGebra application in its version for mobile phones -- 3D Calculator. For this study, the Theory of Categories of Intuitive Reasoning, by Efraim Fischbein, was used as a conceptual basis. The…

The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

This case study of one small urban California high school enrolling predominantly low-socioeconomic status (SES) Latinx youth and many emergent bilinguals found that a college-for-all school culture, guided by leadership and school vision, was enacted in classrooms as caring, safe, productive spaces promoting college-going comportment. However,…

Example-based learning often uses a design in which learners first receive basic instructional explanations of new principles and concepts and then examples thereof. In this sequence, it is crucial that learners self-explain by using the content of the basic instructional explanations to elaborate on the examples. Typically, learners are not…

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

Sequence of contextual information refers to the order of descriptions involved in the context component of items, such as sequence of events, sequence of intention and action, and sequence of effect and cause. To build on prior findings on how different sequences of contextual information could influence student test scores, we used eye tracking…

According to Geary's evolutionary approach, humans are able to easily acquire primary knowledge and, with more efforts, secondary knowledge. The present study investigates how primary knowledge contents can facilitate the learning of formal logical rules, i.e., secondary knowledge. Framing formal logical problems in evolutionary salient contexts…

Career and technical education (CTE) courses, including agricultural education courses, are home to a disproportionately large number of students with learning disabilities. Agricultural education has been sought as a potential solution to teaching abstract STEM concepts through experiential learning methods. Abstract concepts are noted in the…

This article examines the process of shifting to a "Physics First" sequence in science course offerings in three school districts in the United States. This curricular sequence reverses the more common U.S. high school sequence of biology/chemistry/physics, and has gained substantial support in the physics education community over the…

The purpose of the report is to explore some of the mechanisms involved in the writing process. In particular, we examine students' process data (keystroke log analysis) to uncover how students approach a knowledge-telling task using 2 different task types. In the first task, students were asked to list as many words as possible related to a…

This study focuses on the design of a learning program to introduce complexometric titration as a method for determining water hardness in a high school chemistry laboratory. Students are introduced to the different properties and reactions of hard water in a stepwise manner so that they gain the necessary chemical knowledge and conceptual…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

This study used a multiple probe across participants design to examine the effects of concrete-representational-abstract sequence of instruction on solving equations using inverse operations with high school students with mild intellectual disability. Results demonstrated a functional relation between the Abstract sequence of instruction and…