We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

A continuous representation of a hybrid method with three "off-step" points is developed via interpolation and collocation procedures, and used to obtain initial value methods (IVMs) for solving initial value problems. The IVMs are assembled into a single block matrix equation which is convergent and A-stable. We note that accuracy is improved by…

Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)

This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

This article is concerned with how computer science, and more exactly computational complexity theory, can inform cognitive science. In particular, we suggest factors to be taken into account when investigating how people deal with computational hardness. This discussion will address the two upper levels of Marr's Level Theory: the computational…

This study investigated the role of broad cognitive processes in the development of mathematics skills among children and adolescents. Four hundred and forty-seven students (age mean [M] = 10.23 years, 73% boys and 27% girls) from an elementary school district in the US southwest participated. Structural equation modelling tests indicated that…

The purpose of this study was to extend the literature regarding elementary teachers' beliefs about mathematics instruction to include special education teachers by surveying special education and general education teachers' mathematics teaching efficacy. In addition, the researchers' surveyed teachers' mathematics skills. The participants (n =…

Number sense is critical to the development of higher order mathematic abilities. However, some children have difficulty acquiring these fundamental skills and the knowledge base of effective interventions/remediation is relatively limited. Based on emerging neuro-scientific research which has identified the association between finger…

The purpose of this study was to provide preliminary evidence of the criterion-related validity of curriculum-based measurement (CBM) for reading, mathematics, and written expression with postsecondary students with intellectual and developmental disabilities (ID). The participants included 41 postsecondary students with ID enrolled in a 2-year…

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

"Classroom Discussions: Seeing Math Discourse in Action, Grades K-6" provides preservice and inservice instructors, coaches and facilitators with real, classroom-based video examples that illustrate the principles and practices covered in the authors' best-selling book, "Classroom Discussions: Using Math Talk to Help Students Learn, Grade K-6,…

The presented strategy of chemistry calculation is based on mole-concept, but it uses only one fundamental relationship of the amounts of substance as a basic panel. The name of LEGO-method comes from the famous toy of LEGO[R] because solving equations by grouping formulas is similar to that. The relations of mole and the molar amounts, as small…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study the electric potential of a uniformly charged square sheet on its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of the square sheet. The…

We propose a simple and straightforward method based on Wronskians for the calculation of bound-state energies and wavefunctions of one-dimensional quantum-mechanical problems. We explicitly discuss the asymptotic behaviour of the wavefunction and show that the allowed energies make the divergent part vanish. As illustrative examples we consider…

The investigation monitored the digital game-playing behaviours of 428 primary-aged students (aged 10-12 years). Chi-square analysis revealed that boys tend to spend more time playing digital games than girls while boys and girls play quite different game genres. Subsequent analysis revealed statistically significant gender differences in terms of…