After studying the Common Core State Standards for Mathematics (CCSSM) and brain-based learning research, James Olsen believes mental math instruction in secondary school mathematics (grades 7-12) and in teacher education programs needs increased attention. The purpose of this article is to share some keys for teaching mental math. Olsen also…

The Transcontinental Railroad began laying track east from Sacramento, California, in 1863 and west from Omaha, Nebraska, in 1865; the two lines eventually met in Promontory Summit, Utah, in 1869. One of the train towns, Ogallala, Nebraska, consisted of only a section house and water tank alongside newly laid track. Over the next few years, train…

We describe two metaphors that we hope can be used to better understand the contemporary mathematics curriculum context in U.S. middle schools, to see how this new context is both similar to and different from prior curriculum contexts. We explain the role and positioning of middle school mathematics curriculum materials over the last century or…

One of the primary goals of teacher education is to aid preservice candidates in formulating a personal philosophy of teaching that is research-based. Teacher candidates should recognize that their philosophy of teaching and learning must be grounded in research-affirmed theory, certain dimensions of which (e.g., motivation) are critical to…

In spring 2015 Mississippi began testing the college readiness of all grade 11 public high school students and found that approximately 18 percent were ready for college math, a percentage that had changed little by 2017/18. This study examined: (1) the sequences of math courses that Mississippi students took in grades 6-11; (2) the math…

Debates in education policy draw on different theories about how to raise children's achievement. The "school competition" theory holds that achievement rises when families can choose among competing schools. The school resource theory holds that achievement rises with school spending and resources that spending can buy. The "family…

In this article, we derive a number of identities involving both Pell numbers and binomial coefficients. We also consider briefly the potential for obtaining Pell identities involving trinomial coefficients and beyond. A key point is the simplicity of the derivations, and indeed this work can lead on to a number of interesting explorations for…

Retaining mathematical knowledge is difficult for many students, especially for those who learn facts and procedures without understanding the meanings underlying the symbols and operations. Repeated practice may be necessary for developing skills but is unlikely to make conceptual ideas stick. An idea is more likely to stick if students are…

Like many commodities, the price of gasoline continues to rise, and these price changes are readily observed in gas stations' signage. Moreover, algebraic methods are well suited to model price change and answer the student's question. Over the course of one ninety-minute block or two forty-five-minute classes, students build functions…

The Gale-Shapley stable marriage theorem is a fascinating piece of twentieth-century mathematics that has many practical applications--from labor markets to school admissions--yet is accessible to secondary school mathematics students. David Gale and Lloyd Shapley were both mathematicians and economists who published their work on the Stable…

This paper deals with the ancient origin of matrices, and the system of linear equations. Included are algebraic properties of matrices, determinants, linear transformations, and Cramer's Rule for solving the system of algebraic equations. Special attention is given to some special matrices, including matrices in graph theory and electrical…

This study focuses on potentially misleading information (PMI) and potentially helpful information (PHI) embedded in the 2-D sketch of a 3-D geometric object. Our quest was to discover whether and how PHI and PMI capture visual obstacles, for high-school students, to desirable comprehension of the sketches used in teaching spatial geometry. We…

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Pre-service secondary mathematics teachers' (PSMTs) understanding and ability of constructing a proof is not only important for their own learning process, but also important for these PSMTs to help their future students learn how to do proofs. Therefore, this study is focused on and explains PSMTs' behaviors that they revealed throughout the…

This article comments on mathematics textbooks for lower secondary schools. Authors do not focus on texts in the books but on the nonverbal elements instead. A possible system of categories which enables mapping and classifying of such elements is suggested in this article. As a result of that, it is possible to evaluate and compare the textbooks…