Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…

KenKen® is the new Sudoku. Like Sudoku, KenKen requires extensive use of logical reasoning. Unlike Sudoku, KenKen requires significant reasoning with numbers and operations and helps develop number sense. The creator of KenKen puzzles, Tetsuya Miyamoto, believed that "if you give children good learning materials, they will think and learn and…

Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

Faced with a chronic shortage of single-subject mathematics teachers and a directive from the federal legislation "No Child Left Behind" that all students are taught by highly qualified teachers, California instituted a new subject-matter competency exam, the California Subject Exam for Teachers for Mathematics (CSET), and created a new…

In this study, we investigated the effects of a group approach versus a non-group approach on the mathematics performance of learners. A group approach refers to an arrangement in which learners sit together to discuss and solve mathematics tasks. We studied a convenience sample of low-performing Grade 10 mathematics learners using a…

The study investigated teachers' pedagogical content knowledge of common students' errors and misconceptions in sets. Five mathematics teachers from one Lesotho secondary school were the sample of the study. Questionnaires and interviews were used for data collection. The results show that teachers were able to identify the following students'…

The difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

When using time series accountability data to evaluate system-wide education policies, concurrent changes often pose threats to internal validity. The standard difference-in-differences (DID) method resorts to a non-equivalent comparison group whose average outcome change is due to such confounding. This strategy relies on the strong assumption…

Algebra is typically the gatekeeper for higher-level math coursework. Low math performance on standardized assessments impedes access to these higher-level math classes. Limited math progress in high school affects future career opportunities and quality of life. High school students who have historically struggled with math need interventions…

This paper examines correspondences and disjunctions within a national curriculum and between various aspects of its delivery, and how these align with the mathematical needs of the workplace. This is investigated in the context of the New Zealand school mathematics curriculum; the Numeracy Development Project; the senior school assessment regime,…

Vocabulary is vital for success in secondary content area curricula and students with learning disabilities often have limited vocabulary knowledge which inhibits their success in secondary-level content area classes. Therefore, the purpose of this study was to examine the effects of an explicit algebra vocabulary intervention with graphic…

Mathematical proof is a strange concept; it is ironical that there is no precise definition of what constitutes a mathematical proof since without definitions there can be no proof--Dreyfus, 1999. Proof can be divided into many different categories. In this article, the author discusses these categories. She looks first at the background of proof…

The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world…

The purpose of this study is to apply the Rasch model to investigate both the Van Hiele theory for geometric development and an associated test. In terms of the test, the objective is to investigate the functioning of a classic 25-item instrument designed to identify levels of geometric proficiency. The dataset of responses by 244 students (106…

At a time when Australia's international competitiveness is compromised by a shortage of skilled workers in Science, Technology, Engineering and Mathematics (STEM) related careers, reports suggest a decline in Australian secondary school students' performances in international tests of mathematics. This study focuses on the mathematics performance…