The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting students' postsecondary success as STEM majors. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. In the present study, the connections…

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

The network externality function plays a very important role in the study of economic network industries. Moreover, the consumer group dynamic interactions coupled with network externality concept is going to play a dominant role in the network goods in the 21st century. The existing literature is stemmed on a choice of externality function with…

Automated theorem proving (ATP) for Propositional Classical Logic is an algorithm to check the validity of a formula. It is a very well-known problem which is decidable but co-NP-complete. There are many algorithms for this problem. In this paper, an educationally oriented implementation of Semantic Tableaux method is described. The program has…

In this paper, we examine the ways the history of mathematics is integrated in the national textbooks of Cyprus and Greece. Our data-driven analyses suggest that the references identified can be clustered in four categories: (a) biographical references about mathematicians or historical references regarding the origins of a mathematical concept…

Preservice teachers in six sections (n = 87) of a sequenced, methodological and process-integrated elementary mathematics/science methods course were able to reconcile an issue centered on a similar area of epistemology. Preservice teachers participated in a science inquiry lesson on biological classification and a mathematics problem-solving…

This white paper considers the affordability of four-year public institutions for an average Pell Grant recipient who receives the average amount of grant aid, takes out the average amount of federal loans, and collects reasonable work wages to contribute to an education. An astounding 75 percent of residential four-year institutions--including 90…

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of…

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

A critical numeracy examination of Benford's Law suggests that our understanding of the integers is faulty. We think of them as equally likely to turn up as the first digit of a random real world number. For many real world data sets this is not true. In many cases, ranging from eBay auction prices to six digit numbers in Google to the…

We compute closed forms for some parametric integrals. The tools used are MacLaurin developments and other infinite series. Finally, Stirling numbers appear. (Contains 1 figure.)

Finding methods for generating Pythagorean triples have been of great interest to Mathematicians since the Babylonians (from 1900 to 1600 BC). One of these methods is the less known two-fraction method which works for any two fractions whose product is 2. In this work, we analyse the method and show that it can be obtained from the fact that the…

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

The purpose of this article was to summarize results from 5 randomized control trials assessing the effects of intervention to improve the fraction performance of 4th-grade students at-risk for difficulty in learning about fractions. We begin by explaining the importance of competence with fractions and why an instructional focus on fractions…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…