Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about…

A news story claiming that the cream filling of a popular "double" cream sandwich cookie is not really "double" went viral in fall 2013. A high school mathematics teacher posted a blog entry describing how he and his students measured 20 cookies, analyzed the data, and concluded that the double cream cookies had only 1.86 times…

This paper describes students' perspectives of a one-off flipped lecture in a large undergraduate mathematics service course. The focus was on calculating matrix determinants and was designed specifically to introduce debate and argumentation into a mathematics lecture. The intention was to promote a deeper learning and understanding through…

Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

Estimation is an important skill that we rely on every day for simple tasks, such as providing food for a dinner party or arriving at an appointment on time. Despite its importance, most people have never been formally taught how to estimate. Estimation can also be a vital tool for scientific inquiry. We have created an activity designed to teach…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

In this article James Russo presents the Strategies, Understanding, Reading and Fast Facts Framework (SURF) for mental computation. He explains how this framework can be used to deepen mathematical understanding and build mental flexibility.

Computational Thinking is considered a universal competence, which should be added to every child's analytical ability as a vital ingredient of their school learning. In this article we further elaborate on what Computational Thinking is and present examples of what needs to be taught and how. First we position Computational Thinking in Papert's…

In this article, I (a) illustrate how the K-2 CCSSM reflect the major findings from research studies carried out over the last 30 years on early mathematical abilities that indicate these standards are developmentally appropriate for young children, and (b) offer insights into some types of instructional strategies (e.g., student-centered…

In this case study with Devin (pseudonym), which was part of a larger, constructivist teaching experiment with students identified as having learning difficulties in mathematics, we examine how a fourth grader constructed a dual anticipation involved in monitoring when to start and when to stop the simultaneous count of composite units (numbers…

Why is subsequent recall sometimes better for self-generated answers than for answers obtained from an external source (e.g., calculator)? In this study, we explore the relative contribution of 2 processes, recall attempts and self-computation, to this "generation effect" (i.e., enhanced answer recall relative to when problems are practiced with a…

A computational experiment investigating the [superscript 1]H and [superscript 13]C nuclear magnetic resonance (NMR) chemical shifts of molecules with unpaired electrons has been developed and implemented. This experiment is appropriate for an upper-level undergraduate laboratory course in computational, physical, or inorganic chemistry. The…

Place-value is an essential concept that is foundational for understanding our number system and for developing procedures for multidigit operations, but there has been limited research into the place-value understanding of students with learning disabilities. This research is a two-part mixed-methods study that links basic research to…

In classrooms today, teachers continue to strive to enhance student knowledge and application by designing learning environments which create experiences for students to interact collaboratively, solve problems, think critically, and learn by doing. Research has indicated that teacher knowledge of the experiential learning cycle has become…

This manuscript reviews the empirical literature of the TouchMath© instructional program. The TouchMath© program is a commercial mathematics series that uses a dot notation system to provide multisensory instruction of computation skills. Using the program, students are taught to solve computational tasks in a multisensory manner that does not…