The profound advancements in technology have rendered novel forms of data and data visualisation increasingly accessible to individuals within society, thereby influencing daily decision-making processes. To address this change, this study sets out to review recent research on data-driven inquiries at the K-12 level from two perspectives:…

Many studies use instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) to support students' development of reasoning about covarying quantities. While students' forms of covariational reasoning and the designs are often the focus of these studies, the way students' interactions and transitions between…

In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of…

This study aimed to cluster learners based on the structures of the knowledge maps they created. Learners drew their own knowledge maps to reflect their learning activities. Our system collected individual knowledge maps from many learners and clustered them to generate an integrated version of the knowledge maps of each cluster. We applied the…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

Conventional coordinate systems are often considered representational tools for reasoning about mathematical concepts. However, researchers have shown that students experience persistent difficulties as they engage in graphing activity. Using examples from research and textbooks, we present a framework based on a conceptual analysis of the use of…

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

This study investigates relationships between differences in students' achievement and differences obtained by a technique held to yield a reasonably valid representation of students' memory structures of a particular subject matter. Also investigated was the nature of the flow of information between curriculum materials, teachers, and students.…

This paper has two goals. The first is to present a model of the acquisition of a concept image of function. Theories describing the objectification of function are outlined through two different but related paths, and both stem from the conception of function as a process. The first path to objectification involves the generalization of the…

This paper describes the possible effects of feedback on learning (associations) using a connectionist tool, the delta rule. Feedback in instruction can be described in terms of the interaction of stimulus inputs and response outputs, an associationist perspective. Here the delta rule is applied to each instance that an input and an output likely…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

This paper reports the results of an experiment with 21 Italian children (age 2;8-5;11) and 29 U.S. children (age 2;7-5;9) who were tested on their knowledge of verb raising to C in main WH-questions, an obligatory movement process in adult Italian and English. Along the lines of recent movement and feature checking theories, it is proposed that,…

This study compared the effects of instructor-provided vs. learner-generated analyses of semantic relationships between major concepts on structural knowledge acquisition in an introductory psychology course. One group explained the relationships on instructor-provided graphic organizers; the other group classified relationships between concepts…

Assuming that dynamic features of Dynamic Geometry Software may provide a basic representation of both variation and functional dependency, and taking Vygotskian perspective of semiotic mediation, a teaching experiment has been designed with the aim of introducing pupils to the idea of function. First data coming from the observations in Italian…

This paper discussed the use of structured observations as a research strategy in two recently completed studies that investigated students thought processes and behaviors in a microcomputer-based laboratory (MBL) environment and in other instrument-based laboratory environments. In the first study, students' behaviors and thought processes were…