This study investigated the performance of 790 fourth graders from Taiwan for judging the reasonableness of a computational result by using corresponding methods pertaining to whole numbers. A number-sense web-based two-tier diagnostic test was used to assess the number-sense performance of the fourth graders who participated in this study. The…

Literature has established that some learners encountered difficulties solving first order ordinary differential equations (ODEs). The use of error analysis in teaching ODEs is believed to make essential contribution towards calculus knowledge development. This paper therefore focuses on analyzing pre-service teachers' (PSTs) errors and…

Mathematics is full of mystery. We illuminate the myth to expose two conflicting senses of mystery at work in mathematics and its education practices. There is a sense of boundlessness with mathematics--the idea that we never fully know. There is also a practice of concealment, in which an answer or solution is known by special people who may…

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the…

The purpose of this study was to 1) help novice students scaffold problem-solving and engage safely in the deliberate practice of diagnostic reasoning and medical decision-making in real time; 2) assess how accurately students gather and apply data in medical reasoning and treatment during high-fidelity patient simulations (HFPSs); 3) identify…

Halloween provides an opportunity to teach public administration and nonprofit management concepts in a fun way, which increases student retention and understanding. Teaching cases are an evidence-based pedagogical tool that facilitates active learning and brings together perspective-taking, critical thinking, and problem-solving. This article…

This study describes the use of worksheet activities based on alternative concepts from a two-tiered diagnostic assessment on chemical phenomena to remediate 37 first year non-major chemistry pre-service teachers' alternative conceptions about word chemical equations. The instruments for data collection were tiered assessments and group learning…

Background: Pre-service teachers (PSTs) training does not equip students with adequate skills and knowledge of geometry to enable them to teach this section of mathematics competently. Inadequate teacher knowledge of transformation geometry, in particular, requires intervention that targets PSTs' faulty reasoning displayed in errors they make.…

The authors describe activities designed to teach the concept of weight to five and six year old children, using the imaginary 'Measureland' and its brand-new ride 'The Zipline Balancer'. They explore how they addressed misconceptions and insights are provided into the evolving measurement understandings of young children.

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

This study focuses on proportional division, a specific problem type of proportions and proportional relationships, which embeds a part-part-whole relationship. We investigated how students in grades 6 to 9 solved and perceived three proportional division problems. Analysis of the students' performance on the tasks revealed three types of…

Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true--they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths…

Student learning in simple electric circuits has been extensively studied, which has revealed a large number of persistent misunderstandings. This study applies the conceptual framework model to investigate student difficulties in the knowledge integration perspective. The results are used to guide the design of a concept test that targets the…

The article deals with mathematical literacy in relation to mathematical knowledge and mathematical problems, and presents the Slovenian project NA-MA POTI, which aims to develop mathematical literacy at the national level, from kindergarten to secondary education. All of the topics treated represent starting points for our research, in which we…

The current study examined the effectiveness of self-explanation prompts, visual signaling cues, and a combination of the two features on middle school students' (N = 202) algebra learning. Also explored were the differential effects of features for students with faulty conceptual knowledge (evidenced by a higher prevalence of making errors during…