The Common Core State Standards (CCSS) for Mathematics are organized by grade level in Grades K-8. At the high school level, the standards are organized by conceptual category (number and quantity, algebra, functions, geometry, modeling and probability and statistics), showing the body of knowledge students should learn in each category to be…

This study examined High School Geometry standards from recent individual states' and the Common Core Standards (CCSSM) featuring reasoning and proof. We examined specificity of content and use of proof or reasoning as a process in the language of standards. Results indicated standards with proof as its primary process are more likely to have…

To implement current reforms regarding proof and reasoning in secondary school mathematics successfully, pre-service secondary mathematics teachers must have adequate understandings of concepts across mathematical domains for their future teaching. This paper examined the strategies that pre-service secondary mathematics teachers had for…

In high school geometry courses, students are often given a prepackaged statement that they are asked to prove. In these situations, the process of writing proofs is being abridged, if not misrepresented. To provide her students with a more authentic experience in writing a proof, the author provided them with a summative project for which they…

Although not all children may enjoy eating them, it is fairly safe to assume that most students will at least know what ring doughnuts are, and what they look like. Familiarity with these intriguingly-shaped items of patisserie means that students will not immediately be daunted at the thought of doing some mathematics with the relatively…

Assigning activities based on current or past events allows students to explore mathematics in a social context. Using social justice events in the mathematics classroom is a way for teachers to provide contextual problems that will reach all students and promote equity. Learning mathematics in an environment in which social issues are explored…

In mathematics education, a vast amount of research has shown that students of different ages have a strong tendency to apply linear or proportional models anywhere, even in situations where they are not applicable. For example, in geometry it is known that many students believe that if the sides of a figure are doubled, the area is doubled too.…

Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…

Imagine two classfuls of American high school students, separated by 1,500 miles and profound differences in local cultures (East Coast urban and Midwestern rural) as they correspond and collaborate in writing between their geometry classes. Reading the students' observations, one sees authentic voice, specific detail, precise language, what…

The purpose of this study was to determine the metaphors used by students to describe mathematical problem solving. This study focused on identifying how students interpret and perceive mathematical problem solving via conceptual metaphors (Lakoff and Johnson, 2003). These perceptions and interpretations were coded and analyzed qualitatively and…

This paper examines the effect of the use of dynamic geometry environments on children's thinking about angle. Using a driving angle model in Sketchpad, kindergarten children were able to develop an understanding of angle as "turn," that is, of angle as describing an amount of turn. Gestures and motion played an important role in their…

The "High Schools That Work" school improvement initiative is the nation's largest comprehensive school reform model with over a thousand schools adopting its framework. The initiative's premise is that all students can meet the demands of a college preparatory curriculum if provided the right supports. Analyzing over a decade of data on student…

Many students at all levels--from middle school to graduate programs for in-service teachers--struggle with visualizing three-dimensional shapes. Many also are challenged to locate appropriate centers of rotation, placement of lines of symmetry, and translation vectors for transformations on the plane. Hands-on experience helps with these…

Statements conveying a degree of certainty or doubt, in the form of hedging, have been linked with logical inference in students' talk (Rowland, 2000). Considering the current emphasis on increasing student autonomy for effective mathematical discourse, I posit a relationship between hedging and student autonomy. In the current study, high school…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…