Sometimes, in the teaching and learning of mathematics, open-ended problems posed by teachers or students can lead to a fuller understanding of mathematical concepts--a depth of understanding that no one could have anticipated. Interesting solutions and ideas emerged unexpectedly when the authors asked prospective and in-service teachers an "old"…

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

The purpose of this study was to explore pre-service and in-service mathematics teachers' analyses of student learning in a video case of mathematics instruction via an online learning forum. The study was conducted in the context of three different mathematics methods courses in a 4-year college in the Midwestern United States. Twenty-six…

This study compared data related to National Board Certification (NBC) of mathematics teachers in a South Florida school district. Data included 1,162 student scores on the 2014 AP Calculus AB exam, student gender, student grade level, and eligibility for free or reduced price lunch (FRL) status. Teachers completed the Standards' Beliefs…

An exciting event had occurred for the grade 3 classes at Woodlands State School. A new play space designated for the older grades had now been opened to the third graders. In sharing their excitement over this "real treat, real privilege," the teachers invited the children to find out more about playgrounds and, in particular, their new…

Some people recognize a palindrome when they see one, however fewer realize that a palindrome is a special case of a pattern and that these patterns are all around. Palindromes frequently occur in names, both of vehicles and people, and in music. The traditional mathematical curriculum has often left palindromes out of the common vernacular. Where…

The National Council of Teachers of Mathematics (NCTM, 1989, 2000) and the new "Australian Curriculum: Mathematics" for senior secondary (ACARA, 2010) highlight the importance of teaching spatial reasoning as early as preschool when mathematics is introduced. Studies have shown that there is a relationship between spatial abilities and…

Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students' everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the…

Students are more likely to develop a deep conceptual understanding of mathematics when they interact with and discuss their thoughts with others. The National Council of Teachers of Mathematics (NCTM) (1989, 2000) has recommended that students be active learners--communicating with one another, conjecturing, exploring, and justifying claims by…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

In this paper, the author discusses the major components of a junior level pedagogy course for elementary education majors learning to teach mathematics. The course reviews content and knowledge of the teacher candidates and introduces methods and materials for teaching elementary mathematics using the Standards or benchmarks from the National…

The Sliding along a Side task was presented at a National Council of Teachers of Mathematics (NCTM) conference session for high school teachers. According to the authors, while exploring this task with this group of experienced mathematics educators and classroom teachers, they shared a "gasp!" moment. With the aid of the dynamic mathematics…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Measurement is an integral component of the PK-12 mathematics curriculum. At various grade levels, much attention is given to the areas of geometric shapes. However, there is research evidence that measurement is problematic for US students. In this paper, the merits and demerits of two possible sequences (conventional and alternative) in teaching…

Mathematics teachers face a myriad of instructional obstacles. Since the early 1990s, mathematics education researchers have proposed the use of constructivist practices to counteract these ever-prevalent obstacles. While we do give credit to the choices of instructional activities the constructivist paradigm promotes, there are problems with its…