STEM education in elementary school is guided by the understanding that engineering represents the application of science and math concepts to make life better for people. The Engineering Design Process (EDP) guides the application of creative solutions to problems. Helping teachers understand how to apply the EDP to create lessons develops a…

This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers'…

This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of…

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…

This paper describes a proportional reasoning problem set within a real-life context and a complete analysis of one small group discussion of this problem over the course of a 90-minute block. The seventh-grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some…

This paper defines correlation, describes the Mix It Up program, discusses the teachers' beliefs about the value of correlating mathematics and science prior to program participation, and identifies problems teachers associated with correlation before and during the program. Teachers' beliefs about the value of correlation and about the problems…

Discusses the role of teacher questioning in the development of a child's concepts of and about mathematics. Proposes the development of mathematical concepts and procedures in problem-solving situations through questioning that engages student thinking and decision making. (MDH)

Examines 250 sixth-grade students' understanding of arithmetic average by assessing their understanding of the computational algorithm. Results indicate that the majority of the students knew the "add-them-all-up-and-divide" averaging algorithm, but only half of the students were able to correctly apply the algorithm to solve a…

Discusses potential pedagogical difficulties arising from using physics-related contexts in high-school mathematics problems. Suggests that such problems should not require any external knowledge of physics by the students; meanwhile, the problems should not contradict the physics knowledge that the students may already have. Presents several…

An example is discussed in which a drill exercise, initially involving whole number addition, can be used to develop concepts in equations of many variables. (MP)

The objective were to explore some of the ways in which the calculator can be used and to determine the effects. Areas covered are: computation, mathematics readiness, problem solving, and discovery learning. (MP)

Describes a study, involving 120 first grade children, which supports the hypothesis that the rate of attainment of conservation skills is significantly enhanced by experiences made possible by the first grade program of SCIS. Describes the six conservation tasks used for pre-tests and post-tests: number, liquid amount, solid amount, length,…

Children may perform computational operations readily when dealing with physical materials, but may have difficulty dealing with representational stimuli (pictures of objects) or symbolic stimuli. Describes and illustrates the function of mediators in moving from physical to representational or symbolic stimuli. (PR)

Presents correct solutions to an osmosis problem of two high school science students who relied on inaccurate and inappropriate conceptual knowledge. Identifies characteristics of the problem solvers, salient properties of the problem that could contribute to the problem misrepresentation, and spurious correct answers. (27 references) (Author/MKR)