College physics textbooks (algebra based) tend to shy away from topics that are usually thought to require calculus. I suspect that most students are just as happy to avoid these topics. Occasionally, I encounter students who are not so easily satisfied, and have found it useful to maintain a storehouse of non-calculus solutions for some common…

The development of multiple solutions for a given problem is important for learning mathematics. In the present intervention study, we analyzed whether prompting students to construct multiple solutions (more precisely: prompting them to apply multiple mathematical procedures to real-world problems) and prior self-efficacy influenced students'…

To reach their goals, companies are on a never-ending search to find new methods for innovation. In order to tackle the complex problems, which cannot be solved by a single person, the implementation of teamwork is assumed to be applicable. With this paper, we propose a framework for Collaboration Support Systems, which aims to enhance team…

The idea of using fingers as a key component in arithmetic development has received a great deal of support, much of which is based on neuroscientific evidence. However, this body of work pays limited attention to how fingers are used and possible different outcomes in arithmetic problem solving. The aim of our paper, based on an analysis of 126…

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

One of the main goals of gamification in educational settings is to increase student motivation and engagement. To facilitate the design of gamified educational systems, in recent years, studies have proposed various approaches (e.g., methodologies, frameworks and models). One of the main problems, however, is that most of these approaches are…

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers' solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers' (PSTs) reasoning about proportional…

Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…

With the inclusion of engineering disciplinary core ideas (DCIs), the Next Generation Science Standards (NGSS) position engineering as a new priority in K-12 science classrooms. This paper reports findings from the implementation of SLIDER, a problem-based learning 8th grade physical science curriculum that integrates engineering and physical…

Assessment is fundamental to school psychology, but its purpose has shifted from making predictions about children to improving outcomes for children. This commentary on the special issue focuses on screening and progress-monitoring decisions that can be used to solve student problems. We outline several psychometric and practical issues that…

This study examined the effects of two training methods (interest-based and traditional) used to improve math word problem performance of middle school students with and without learning disabilities, as measured by the Herr Scale of Mathematical Word Problem Solving Situations. Students were randomly assigned to one of the two treatment groups:…

Spearman concluded that performance on any test of mental ability could be explained by several cognitive factors organized hierarchically as one general factor and several subordinate specific factors (Spearman, 1904, 1927). The general factor accounted for the significant amount of inter-correlation between all ability tests for any one…

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…