BKT and other classical student models are designed for binary environments where actions are either correct or incorrect. These models face limitations in open-ended and data-driven environments where actions may be correct but non-ideal or where there may even be degrees of error. In this paper we present BKT-SR and RKT-SR: extensions of the…

Reporting on a Grade 4 teaching and learning sequence, we highlight foundational constructs of measurement and data modelling which are fundamental to competence development in both science and mathematics. The sequence involved students generating and representing measures of their teacher's arm-span, with a focus on the invention and refinement…

K-12 students are expected to acquire competence in data display as part of developing statistical literacy. To support research, assessment design, and instruction, we developed a hypothesized learning progression (LP) using existing empirical literature in the fields of mathematics and statistics education. The data display LP posits a…

To determine factors that influence faculty engagement and success in faculty learning communities focused on collaborative Scholarship of Teaching and Learning (SoTL), our project gathered information on (1) faculty motivation to engage with SoTL; (2) structures that support collaboration; (3) the perceived impact of SoTL on teaching,…

This study designed a decision-making learning module to engage students in collective decision-making in a collaborative learning environment. The purpose of this study was to explore the interplay of students' regulation learning in groups and their collective decision-making about a socioscientific issue. Thirty-eight 10th-grade students…

We present the results of a qualitative research study designed to explore differences in the types of reasoning triggered by information presented to chemistry students in two different formats. One group of students was asked to analyze a sequence of images designed to represent critical elements in the explanation of a target phenomenon.…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

Children in a first-grade class who were taking their first steps in formal mathematical knowledge were given a sequence of five modelling tasks during their regular mathematics lessons. These tasks were different in nature from the problems they encountered in their textbooks. They are more complex and challenging, requiring analysis of the…

This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…

Instructional technologies critically depend on systematic design, and learning hierarchies are a commonly advocated tool for designing instructional sequences. But hierarchies routinely allow numerous sequences and choosing an optimal sequence remains an unsolved problem. This study explores a simulation-based approach to modeling learning…

Purpose: The purpose of this paper is to review the variation in methods used to analyse lessons in order to improve teaching and learning. Design/methodology/approach: It addresses the question of how observations of lessons can be analysed, and what approaches and methods are applicable in the analysis of collected data in lesson and learning…

This paper reports on results of applying process discovery mining and sequence classification mining techniques to a data set of semi-structured learning activities. The main research objective is to advance educational data mining to model and support self-regulated learning in heterogeneous environments of learning content, activities, and…

Diagnostic assessments are intended to support teachers' instructional decision making by providing instructionally relevant information. In this article, we propose that using cognitive theories of learning to design diagnostic assessments can provide teachers with two diagnostic outcomes: (a) the location of a student's thinking within the…

In a MOOC environment, each student's interaction with the course content is a crucial clue for learning analytics, which offers an opportunity to record learner activity of unprecedented scale. In online learning, the educators and the administrators need to get informed with students' learning states since the performance of unsupervised…

The concept of variability is central to statistics. In this research report, we review mathematics education research on variability and, based on that review and on feedback from an expert panel, propose a learning progression (LP) for variability. The structure of the proposed LP consists of 5 levels of sophistication in understanding…