Mathematical "funds of knowledge" (Civil 2007) that students bring from their community and home lives can offer entry points for concepts such as functions and rate of change, which are important "big ideas" across all grade levels (NCTM 2000). The Common Core State Standards (CCSSI 2010) ask high school students to…

The temperature dependence of the Gibbs energy and important quantities such as Henry's law constants, activity coefficients, and chemical equilibrium constants is usually calculated by using the Gibbs-Helmholtz equation. Although, this is a well-known approach and traditionally covered as part of any physical chemistry course, the required…

This case study describes the ways in which problems involving additive differences with unknown starting quantities, constrain the problem solver in articulating the inherent quantitative relationship. It gives empirical evidence to show how numerical reasoning takes over as a Grade 6 student instantiates the quantitative relation by resorting to…

Molenaar (2003, 2011) showed that a common factor model could be transformed into an equivalent model without factors, involving only observed variables and residual errors. He called this invertible transformation the Houdini transformation. His derivation involved concepts from time series and state space theory. This article verifies the…

An important open issue in Functional Measurement is whether the three most important models of cognitive algebra are sufficient to describe the great majority of possible response behaviors. Generally speaking, the individual response "R" is a function of the subjective scale values "s[subscript k]" and can be imagined as a continuous manifold.…

The NCTM Algebra Standard suggests that students use technology to explore the effects of varying the parameters in y = ax2 + bx + c. This article discusses an extension of this task that incorporates dynamic geometry software to engage students in generating, testing, and proving mathematical conjectures.

Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

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…

Reducing problem complexity by isolating elements has been shown to be an effective instructional strategy. Novices, in particular, benefit from learning from worked examples that contain partially interacting elements rather than worked examples that provide full interacting elements. This study investigated whether the isolating-elements…

New networking and social interaction technologies offer new media for learning and teaching both inside and outside the classroom. How and what kind of learning may take place in these new media is the main focus of this paper. An integrative theoretical framework for investigating these questions is posed based on the Didactic Tetrahedron (Olive…

Blended learning has caught the attention of an increasing number of educators and policymakers who see it as one of the most promising means of catering to students with a wide variety of learning styles and abilities. Alliance Tennenbaum Family Technology High School, a charter school on L.A.'s eastside, which opened in 2011, is one of its…

The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different "whys" and "hows" of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

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…

The complex nature of multiplicative thinking can be challenging for students and teachers to navigate. We report on the impact on student learning of school-based professional learning that targeted teachers' pedagogical content knowledge related to Multiplicative Thinking. Analysis of Year 4 students' longitudinal data indicated greater growth…