The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Financial analysts generally create static formulas for the computation of NPV. When they do so, however, it is not readily apparent how sensitive the value of NPV is to changes in multiple interdependent and interrelated variables. It is the aim of this paper to analyze this variability by employing a dynamic, visually graphic presentation using…

We examined faulty strategies with possible underlying misconceptions, as well as execution mistakes, among middle schoolers with and without mathematics disabilities when estimating fractions on number lines. Fifty-one middle schoolers participated in this study, including 27 students with mathematics disabilities. Participants were asked to…

Background: This study aimed to identify the mathematical domains affected in adults with neurofibromatosis 1 (NF1) and the impact of the numerical difficulties on the patients' activities of daily living. Methods: We assessed 28 adult patients with NF1 and 28 healthy control participants. All participants completed the standardised battery of…

Throughout the general chemistry lab curriculum, a common shortcoming is the way in which students measure, record, and manipulate quantitative data. From initial measurements with different digital and analog instruments to proper conversions, calculations, and comparisons, students are often expected to be experts before they have been taught…

This study examined differences in cognitive processing between 4th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or…

This paper is part of a wider action research project taking place at a secondary school in South Wales, UK. The overarching aim of the project is to examine the potential for aspects of literacy and computational thinking to be developed using extensible 'build your own block' programming activities. This paper examines classroom talk at an…

The focus of the current proposal is to examine the effect of two dynamic simulations on the participants' conceptions of rate of change. Conceptions of rate of change were measured according to Carlson et al.'s (2002) Mental Actions framework and how the participants related the physical simulations to the graphical representations (Heid, et al.,…

This paper is part of a wider action research project taking place at a secondary school in South Wales, UK. The overarching aim of the project is to examine the potential for aspects of literacy and computational thinking to be developed using extensible 'build your own block' programming activities. This paper examines classroom talk at an…

Though proficiency with computation is highly emphasized in national mathematics standards, students with mathematics difficulty (MD) continue to struggle with computation. To learn more about the differences in computation error patterns between typically achieving students and students with MD, we assessed 478 3rd-grade students on a measure of…

High School graduation rates are key indicators of accountability for high schools and school districts in Oregon. Beginning with the 2008-09 school year, the Oregon Department of Education (ODE) implemented the cohort method of calculating graduation rates. The cohort method identifies the year the student entered high school for the first time…

This study examined differences in cognitive processing between 4th-grade students who respond adequately, as opposed to inadequately, to intervention on 3 fraction outcomes: number-line estimation, calculation, and word problems. Students were assessed on 7 cognitive processes and on the 3 fraction outcomes. Students were grouped as adequate or…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Purpose: Computational modeling was used to examine the consequences of 5 different laryngeal asymmetries on acoustic and perceptual measures of vocal function. Method: A kinematic vocal fold model was used to impose 5 laryngeal asymmetries: adduction, edge bulging, nodal point ratio, amplitude of vibration, and starting phase. Thirty /a/ and /?/…

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead…