This study reports on the development, validation, and administration of a 48-item multiple-choice test to assess students' representational fluency of linear functions in a physics context (1D kinematics) and a mathematics context. The test includes three external representations: graphs, tables, and formulas, which result in six possible…

Data-driven inquiry as a science practice and instructional approach can provide a powerful context for project-based learning (PBL). Students engage in data-driven inquiry when they explore a rich data set and observe patterns, ask questions suggested by the data, and pursue answers about underlying phenomena. Krajcik (2015) describes five…

This paper presents a rule-based task-oriented dialogue system for second language learning and a knowledge extraction method which automatically extracts the training data for Natural Language Understanding (NLU) and dialogue rules for dialogue management from a Dialogue Map (DM). The DM consists of turn-by-turn utterances between the system and…

We create a continuous, nowhere monotone function, which would be more suitable for students. (Contains 3 figures.)

Four rather different scatterplots of two variables X and Y are given, which, after dichotomizing X and Y, result in identical fourfold-tables misleadingly showing no association. (Contains 1 table and 1 figure.)

This article draws on extensive experience working with secondary and tertiary teachers and educators using an applet to display rational polynomials (up to degree 7 in numerator and denominator), as support for the challenge to deduce as much as possible about the graph from the graphs of the numerator and the denominator. Pedagogical and design…

Visualization is commonly used in the interpretation of physical behavior (PB) data, either in conjunction with or as precursor to formal analysis. Effective representations of the data can enable the identification of patterns of behavior, and how they relate to the temporal context in a single day, or across multiple days. An understanding of…

This article advances the prerequisite network as a means to visualize the hidden structure in an academic curriculum. Networks have been used to represent a variety of complex systems ranging from social systems to biochemical pathways and protein interactions. Here, I treat the academic curriculum as a complex system with nodes representing…

The incorporation of engaging and meaningful learning experiences is essential for the enhancement of critical thinking and the development of scientific literacy. The study engaged several groups of students in activities designed to elicit their understanding of a graphical representation of motion, and to determine the kinesthetic effect of…

In most epistemologies, practical actions and speech are the consequences of thought. In this study, I provide three case studies of highly educated scientists producing aspects of graphs only to erase these as soon as they have been drawn. The case studies are consistent with an alternative approach, already formulated by L. S. Vygotsky and M.…

This paper explores a new tool for instructional designers. By calculating and graphing the Student Momentum Indicator (M) for 196 university-level online courses and by employing the constant comparative method within the grounded theory framework, eight distinct graph shapes emerged as meaningful categories of dropout behavior. Several of the…

Teaching and theorizing in psychology has long been torn between targeting general underlying principles by observing dynamics in the individual or focusing on average behavior. As dealing with group averages is common practice in psychology, it is important for students to understand how individual learning curves relate to group average curves.…

When working within a meaningful context quite young students are capable of working with sophisticated data. Year 3 students investigate thermal insulation and the transfer of heat in a STEM inquiry, developing skills in measuring temperature by conducting a statistical investigation, and using a stylised graph to interpret their data.

The present study considers the potential influence of first language (L1) in reading second language (L2) science text. University mixed proficiency Korean English language learners (n = 136) were asked to complete pre- and post-reading "sorting maps" in L1 or L2 (e.g., sort Korean, read text, sort English). All of the participants'…

Teachers must be proficient at using data to evaluate the effects of instructional strategies and interventions, and must be able to make, describe, justify, and validate their data-based instructional decisions to parents, students, and educational colleagues. An important related skill is the ability to accurately read and interpret…