This study investigates an exploratory teaching style used in an undergraduate geometry course to help students identify an ellipse. We attempt to probe beneath the surface of exploration to understand how the actions of teachers can contribute to developing students' competence in justifying an ellipse. We analyse the complex interactions between…

According to the Cognitive Theory of Multimedia Learning (Mayer, 2009) learning with multimedia requires the integration of verbal and visual information (e.g., printed text and static images, narrated animation). Studies exploring the effects of dynamic versus static presentations yield mixed results. Few studies explore comparing dynamic versus…

Virtual reality has the potential to revolutionize education because it immerses students in their learning, blocking out visual and auditory distractions and letting learners focus intensely on a structured learning experience. The authors describe how using virtual reality headsets helped 5th graders at Gavin Cochran Elementary School in…

Curriculum materials are integral to the mathematics classroom, yet little is known about how teachers read curriculum in order to envision enactment. Through an assignment involving an approximation of actual teaching practice, we investigated prospective teachers' documentational genesis (Pepin et al. in ZDM 45:929-943, 2013) from curriculum…

Problem posing in mathematics education is one of the most important skills. Since mathematics teachers are one of the most important parts of mathematics education and teaching, this research was conducted to evaluate their views on this important skill and the implementation process. The research was carried out by 56 mathematics teachers…

We present a model for describing the growth of students' understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important…

This study aimed to identify the different types of factual, conceptual and procedural errors among the six-years-old preschool children. The data were collected from 45 children from 3 kindergartens. The children responded to a Math worksheet which had 20 addition problems based on the early numeracy curriculum. The worksheet was validated by two…

There is rising concern in research and practice to improve early years mathematics education as initial mathematical mastery sets the foundation for future academic success. In response to these concerns, this study used observational data from 20 kindergarten classrooms to understand current pedagogies teachers use for mathematics. In…

Recognizing identity not only as an important educational outcome but also as being inter-related to students' knowledge and practice, this paper explores an affordance of proof scripts; exploring students' identities. Specifically, drawing on data from teaching experiments and the construct of perceptual ambiguity, this paper presents an analysis…

A central issue in the mathematics curriculum is that we want students to make connections. This issue has been analysed in a series of curricula and instruction design and analysis studies. Moving towards mathematics connections--and away from treating mathematics as a body of isolated concepts and procedures--is an important goal of mathematics…

Whole Number Arithmetic (WNA) appears as the very first topic in school mathematics and establishes the foundation for later mathematical content. Without solid mastery of WNA, students may experience difficulties in learning fractions, ratio and proportion, and algebra. The challenge of students' learning and mastery of fractions, decimals, ratio…

Prospective elementary school teachers (PTs) come to their mathematics courses fluent in using procedures for adding and subtracting multidigit whole numbers, but many are unaware of the essential features inherent in understanding the base-ten place-value system (i.e., grouping, place value, base). Understanding these features is crucial to…

Research has documented that mathematics teachers rarely use communicative activities; activities that allow for the sharing of ideas and clarification of understandings (NCTM, 2000). Teacher metacognitive awareness provides a possible framework for understanding the difficulties secondary mathematics teachers face when attempting to incorporate…

This paper shares how fourth grade students solved a unique type of number line task. Instead of giving students the unit and asking them to locate a fraction on the number line, students were given two points on the number line and asked to either find 1, or another number on the number line. This type of task is called "reconstructing the…

The right types of technology can create new opportunities for students to demonstrate mathematical understandings and can strengthen existing formative assessment practices. The authors write that they frequently use the Math Learning Center apps--covering the range of manipulatives and models--to empower students to explain their thinking. The…