Multiple models of the gene are used to explore genetic phenomena in scientific practices and in the classroom. In genetics curricula, the classical and molecular models are presented in disconnected domains. Research demonstrates that, without explicit connections, students have difficulty developing an understanding of the gene that spans…

This paper analyses pre-service secondary mathematics teachers' responses to a hypothetical situation concerning a student's struggle to determine the area of an irregular hexagon. The analysis focuses on individuals' Knowledge at the Mathematical Horizon, as it relates to philosophical notions of inner and outer horizons. Specifically, the paper…

This study expands contemporary theorising about students' conceptions of equality. A nationally representative sample of New Zealand students' were asked to provide a spoken numerical response and an explanation as they solved an arithmetic additive missing number problem. Students' responses were conceptualised as acts of communication and…

This paper identifies the strategies Singaporean and Australian students (n = 1,187) employed to solve a 24-item mathematics test. A mathematics-processing framework is proposed, which describes the way primary-aged students successfully process graphic and non-graphic mathematics tasks. There were distinct differences in the way in which the…

The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

While previous work in the domain of proportional reasoning has primarily focused on the coordination of integer quantities, this study investigates how students coordinate fractional quantities. Fine-grained analysis of two seventh graders' responses to a set of systematically designed proportional tasks, shows how their knowledge of…

This study used a multiple probe across participants design to examine the effects of concrete-representational-abstract sequence of instruction on solving equations using inverse operations with high school students with mild intellectual disability. Results demonstrated a functional relation between the Abstract sequence of instruction and…

School-based psychological interventions which require students and pupils to think of counter-stereotypic individuals (e.g., a female mechanic, a Black President) have been shown to reduce stereotyping and prejudice. But while these interventions are increasingly popular, no one has tested whether tasks like this can have benefits beyond…

We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

Innovation is central to modern industry. It can and should be taught in schools. Not only does providing students a background in innovation benefit them later in life and industry, but it also promotes and further develops their critical thinking and collaboration skills. Despite the need for innovation, many have struggled with how to teach it.…

In this article, the author applies Makiguchi Tsunesaburo's (1871-1944) perspectives to language policy and planning (LPP). One theoretical question in LPP theory is why individuals opt to use particular languages and varieties of languages in certain contexts. The author contends that Makiguchi's theory of value can be used to systematically…

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs…

The goal of this research was to investigate the extent to which young children use the past reliability of another person's statements to make inferences about the accuracy of that person's claims about a hidden toy. When children interacted with a previously reliable speaker, both 30- and 36-month-olds searched in the new location of the toy, in…

Classification problems ("find the odd-one-out") are frequently used as tests of inductive reasoning to evaluate human or animal intelligence. This paper introduces a systematic method for building the set of all possible classification problems, followed by a simple algorithm for solving the problems of the R-ASCM, a psychometric test derived…