We conducted a collective case study investigating two college algebra students' graph reasoning and selection on an online assessment. Students completed the assessment during individual, semi-structured interviews, as part of a broader validation study. The assessment contained six items; students selected Cartesian graphs to represent…

In this report, we present how one prospective elementary teacher (PT) engaged in the Ant Farm Task, which we designed to investigate PTs' reasoning about coordinate systems. We highlight the cognitive resources the PT drew upon in solving the task via the establishment of a Cartesian coordination and consider educational implications. [For the…

Reading comprehension is key to knowledge acquisition and to reinforcing memory for previous information. While reading, a mental representation is constructed in the reader's mind. The mental model comprises the words in the text, the relations between the words, and inferences linking to concepts in prior knowledge. The automated model of…

The body of research examining students' graphing understandings across STEM fields indicates students are not developing productive meanings for graphs. We conjecture such failings may, in part, be explainable by features of students' use of coordinate systems and graphing activity that are under examined. In this theoretical report, we present a…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

In this study I investigate Saldanha and Thompson's (1998) claim that conceptualizing a coordinate pair in the Cartesian coordinate system as a multiplicative object, a way to unite two quantities' values, supports students in conceptualizing graphs as emergent representations of how two quantities' values change together. I presented three…

This study investigates cognitive difficulties and mathematical ideas that are related to making connections among representations. A three-week intervention was designed and implemented to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to connection of representations in algebra. This study…

Hammond's Cognitive Continuum theory posits that certain task features induce distinct processing modes (e.g., intuitive or analytic) and thus result in qualitatively different decision performance. Although the theory suggests the relation between task features and performance characteristics a priori, the validity of these predictions requires…

This paper discusses a research study that focused on middle grades students' abilities to read and to move between different graphical representations before and after instruction. The data analyzed were collected from a group of 76 sixth grade students who were in 3 different mathematics classes in a middle school located in central North…

This paper reports on a study that investigated the interpretation of media graphs developed by student teachers. The analyses of interviews indicate that cognitive, affective and contextual, aspects might constitute important components of the interpretation of graph such as those that we can find in print media. Particularly we discuss Critical…

This paper reports on the development and evaluation of cognitive tools used by learners to interpret graphs and tables. The development of these tools was informed by research about how learners interpreted graphs and tables. A prototype of the cognitive tools was trialed with a small sample of preservice teachers. This prototype was then…

Starting from a situated cognition perspective, this paper reports on the activity of 9th grade students who are interpreting the shape of a graph arising from the motion of a bouncing ball. In an unfamiliar context, informed by previous knowledge of similar experiments, the obstacle of understanding why the graph does not start from the origin is…

The eight articles and two commentaries of this theme issue indicate the main lines of thinking represented at a symposium on the comprehension of graphics in text. The common assumption is that graphics per se do not have a direct effect on learning results but are effective only when processed adequately. (SLD)

The purpose of this exploratory, descriptive study was to examine how children process different tasks of comprehension presented in graphical form. During the Spring 1981, 8 fourth graders and 9 seventh graders were interviewed. The children were presented with graphs accompanied by six questions reflecting three levels of comprehension:…

Discusses current use of psychological theory in software science and reviews recent developments in cognitive psychology relevant to programing (human information processing, expert-novice differences). Critique of Maurice Halstead's model of cognitive aspects of programing and a structured data flow perspective (control flow and data flow…