The Common Core State Standards (CCSSI 2010) and NCTM's (2014) "Principles to Actions" agree that "for meaningful learning of mathematics, tools and technology must be indispensable features of the classroom . . . that support students in exploring mathematics as well as in making sense of concepts and procedures and engaging in…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

This article examines the impact of programming robots on sequencing ability in early childhood. Thirty-four children (ages 4.5-6.5 years) participated in computer programming activities with a developmentally appropriate tool, CHERP, specifically designed to program a robot's behaviors. The children learned to build and program robots over three…

This work is an attempt to see how physics undergraduates view the basic ideas of general relativity when they are exposed to the topic in a standard introductory course. Since the subject is conceptually and technically difficult, we adopted a "case studies" approach, focusing in depth on about six students who had just finished a one semester…

The Physics First movement--teaching a true physics course to ninth-grade students--is gaining popularity in high schools. There are several different rhetorical arguments for and against this movement, and it is quite controversial in physics education. However, there is no actual evidence to assess the success, or failure, of this substantial…

This article presents a case study in which researcher-practitioner collaboration took place to promote effective use of technology in an urban elementary school mathematics classroom. Data were primarily gathered through classroom observations and interviews. The aim of this study was twofold. First, to increase our understanding of the effects…

The aim of this study was to elicit students' conceptions about big bubbles in boiling liquids (water, ethanol and aqueous CuSO[subscript 4] solution). The study is based on twenty-four students at different ages and grades. The clinical interviews technique was conducted to solicit students' conceptions and the interviews were analyzed to…

In order to develop successful teaching approaches to transformations of matter, we need to know more about how young students develop an understanding of these processes. In this longitudinal study, we followed 25 students from 7 to 13 years of age in their reasoning about transformations of matter. The questions addressed included how the…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

The phenomenon of using progress monitoring data to inform literacy instruction was explored in the context of four schools during their 2nd year of Reading First implementation. Open-ended interviews and surveys from 10 teachers, purposefully selected for maximum variation in effectiveness and skills and resistance to using data to inform…

Although researchers in higher education propose alternatives to traditional approaches to assessment, traditional methods are commonly used in college or university science courses. The purpose of this study was to explore the feasibility and validity of Prospective Science Teachers' (PSTs) concept maps as authentic assessment tools in a…

Interviews with fourth, fifth, and sixth graders found that they thought about the concept of average as mode, median, and/or a procedure. Presents approaches to develop the concept of average. (MKR)

Because second grade students had difficulty in explaining what they knew about the number 15, it was suspected that they did not understand place value. Realizing every number has a place value and its place provides facility for calculation, a teacher attempted to ascertain second grade students' (N=18) knowledge of place value. Results of…

Considers what college students think reasoning about physics involves. Discusses whether it is possible to identify students' general conceptions of physics and the effects of a course on students' concepts. Data indicated that students' understandings had an effect on problem solving, qualitative problems, and misconceptions. (YP)

The focus of this document is on students' understanding of symbolization processes in algebra, and specifically their understanding of semantically laden letters. In the first four sections, four inappropriate ways in which many college students use semantically laden letters are described. Evidence from clinical interview protocols demonstrate…