Interpreting statistical graphs and making inferences based on the graphs are a precursor for formal statistical inferences. To support student inferences, both teachers and future teachers should have adequate knowledge regarding students' thinking on graphs as well as their potential misinterpretations and difficulties in interpreting graphs. In…

In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative…

In the subject matter of functional relationships, a student's ability to translate from one form of representation to another is seen as a central competence. In the course of the HEUREKO project (heuristic work with representations of functional relationships and the diagnosis of mathematical competencies of students), a theoretical competence…

If a teacher asked their students what thinking looks like, what would they say? Would they just look at the teacher quizzically? The question is challenging because thinking is largely an invisible endeavor, and developing thoughtful students can be a daunting task. However, the job of mathematics teachers is to develop students who think about…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

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…

Linear models are frequently inappropriately applied to various situations. When misapplied, linearity is traditionally referred to as a tendency, a misconception, or an error. Cognitive linguistic, situated cognition, and sociocultural or cultural-historical activity theory, on the other hand, suggest that linear models are adopted by learners…

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…

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.…

A study determined the abilities of students to interpret and represent graphs by asking 15-year-old female students (n=10) to write stories to accompany any 3 of 12 graphs presented. Results indicated that the students were not able to accurately relate real life situations to graphical forms. (MDH)

Research in this project studied cognitive processes involved in understanding and solving problems used in instruction in the domain of mathematics, and explored implications of these cognitive analyses for the design of instruction. Three general issues were addressed: knowledge required for understanding problems, knowledge of the conditions…

Promotes the use of computers in teaching not only to solve problems but also to help students be better at analyzing problems and developing procedures for their solution. Outlines several problems where a computer-assisted analysis can help give students a thorough understanding of the topic. (TW)

Describes a study which measured how ninth-grade students integrated information about mathematical concepts when working with Triple Representation Model software. Tables, graphs, and algebraic functions were linked, allowing students to manipulate several representations of the same concept. Examples of mathematical problems and student case…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…