STEM education should be grounded in our knowledge of how students think in STEM-focused learning environments. However, little is currently known regarding specific types of thinking in these contexts. We explore the theoretical notion of STEM Ways of Thinking (SWoT) in interdisciplinary learning situations. Our primary focus is not on the…

One of the factors associated with the less than positive mathematics performance of American students could be poorly designed textbooks that fail to facilitate the development of critical mathematical ideas. This study examined two reform-based textbooks (Go math! and Investigations) in reference to essential, mathematical big ideas emphasized…

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic…

For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

Interviews 120 children in kindergarten and grades 2, 4, and 6 with five Piagetian tasks to determine the grade level at which most have constructed transitive reasoning, unit iteration, and conservation of speed. Indicates that construction of the logic necessary to make sense of the measurement of time is generally not complete before sixth…

Articulates and operationalizes a framework for investigating the level of quantitative literacy in the United States. Uses data from the Third International Mathematics and Science Study (TIMSS) to document the level of quantitative literacy in the U.S. Indicates that students fall short in their understanding of the nature of mathematics and the…

The relationship between a student's stated preference for solving a problem and his/her actual problem methodology, concrete or abstract, was studied. Comparisons were made between formal and nonformal students. (MP)

Presents a study in which some students in grades 3-6 were taught scientific concepts using instructional analogies while others received expository texts not containing analogies. Indicates that students who received the analogical text demonstrated better inferential reasoning than students who received the non-analogical text. (Contains 57…

Discusses the level of knowledge, understanding, and ability relative to mathematics for the college graduate in the 21st century. Focuses on mathematical literacy and abstraction such as the definition of abstraction, difficulties in addressing abstraction, and one approach to helping students learn to address abstraction. (Contains 12…

Describes a study in which 383 children in grades 1 through 5 were individually interviewed to find out at what point they construct unit iteration out of transitive reasoning. Indicates that most children construct unit iteration out of transitive reasoning by fourth grade. Suggests a better approach to the teaching of measurement that presents…

Presents an alternative pedagogy implicit in Imre Lakatos's "Proofs and Refutations: The Logic of Mathematical Discovery." Lakatos reveals that learning mathematics is a discourse-laden activity in which it is acceptable, if not preferable, to refute conjecture. Provides examples of using a Lakatosian approach in an elementary classroom.…

This research study shows that it is possible to advance the use of proportional reasoning of many secondary school students by means of a well-designed teaching program. (MP)

When worthwhile mathematical tasks are used in classrooms, they should also become a crucial element of assessment. For teachers, using these tasks in classrooms requires a different way to analyze student thinking than the traditional assessment model. Looking carefully at students' written work on worthwhile mathematical tasks and listening…

Reported is a study involving six group administered tasks concerning proportional, probablistic, and correlational reasoning with 505 students aged 11.5 to 20.0 years. Investigated were the effectiveness of the tasks for assessing formal reasoning; categories of classification for students' responses and implications for teaching are suggested by…

This study investigated differences and shifts in learning and motivation constructs among male and female students in a nonmajors, yearlong structured inquiry college physics course and examined how these variables were related to physics understanding and course achievement. Tests and questionnaires measured students' learning approaches,…