Graphical representations appear everywhere in modern society. Their ubiquity has, in part, justified graph literacy as a core competency in education. Graph literacy - the capacity to read and interpret graphs - consists of understanding features, identifying variables, interpreting trends, and forming real-world connections. Experts and novices…

Comprehensive and evidence-based, Structured Literacy (SL) approaches place a high value on explicit, systematic, and sequential instruction. This book brings together leading experts on key components of literacy to help K-6 teachers design and target SL interventions for particular student profiles. Chapters identify effective features of…

We tested a specific theoretical assumption of a learning trajectories (LTs) approach to curriculum and teaching in the domain of early length measurement. Participating kindergartners (n = 189) were assigned to one of three conditions: LT, reverse-order (REV), or business-as-usual (BAU). LT and REV students received one-on-one instruction using…

This research integrates context-based learning and modelling. It presents a teaching-learning sequence (TLS) about the dissolution of gases in liquids using carbonated drinks as the context. The impact of the TLS is analysed in a longitudinal short-term study involving two groups of learners aged 13-14 years old (n=53). The results led us to…

One way to reduce the cognitive load students feel during instruction is to change the way content is delivered. This can be achieved by optimising the instructional sequence and providing sufficient instructional support during problem-solving. However, the literature is unclear regarding whether an inductive or a deductive instructional sequence…

Although hypothetical learning trajectories (HLTs) are often viewed as a valuable instructional tool, little research has directly evaluated their value. A basic assumption of HLTs is that ordering instructional activities by developmental difficulty enhances learning. A randomized control trial (RCT) served to evaluate this assumption with a…

We discuss the importance of bringing teaching to the forefront of instructional design. We do so by describing the process of developing an instructional sequence for early number, using design research. The instructional sequence was developed with the specific aim of supporting teaching, conceived as a complex and demanding job, not reducible…

An introductory physics course may be run like a video game, where students have an almost unlimited number of attempts to demonstrate their competencies through a sequence of zero-penalty assessments until the end of a semester. Each checkpoint is conducted as a 10-minute, one-on-one oral interview with the instructor, and students are not…

In the current conceptualisations of Problem Based Learning and how we practice it, the students are expected to possess the necessary academic competencies in order to study through PBL. However, a desk research reveals that students in many cases don't have the necessary understanding or conceptual comprehension of disciplines such as problem…

This study investigates the capacity of elementary-level Chinese second language learners to memorize serial verb sentences based on the results of a questionnaire. Our findings show that adult second language learners employ the concept of temporal sequence in language learning, consciously or unconsciously, whether or not the chronological…

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 study aims to examine the changes in students' mental constructions of function transformation based on the designed activities, classroom discussions, exercises (ACE) teaching cycle in the light of the action, process, object, schema (APOS) theoretical framework. The study was conducted by seven volunteer students who were enrolled in…

Background and Context: We explored how learning trajectories (LTs) might be used to design variables instruction. Objective: We aimed to develop an LT for variables and use it to guide curriculum development for fourth graders working in Scratch in an integrated mathematics+CS curriculum. Method: We synthesized learning goals (LGs) and levels of…

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…