For the last four years, Soenderholm School, near the town of Aalborg, Northjutland, Denmark, has had an optional subject in the seventh grade called First "Lego" League (FLL). FLL is an international contest which aims to advance pupils' scientific interest. The task is for participants to build and program a "Lego" robot able…

One way of providing middle-school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. Students are expected to learn serious, substantive mathematics in classrooms in which the emphasis is on thoughtful…

Understanding students' conceptual deficiencies of fractions is an essential step toward effective teaching. The authors proposed a novel 2-component multidimensional item response theory (MIRT) model to analyze students' conceptual deficiencies of fractions in a group-wise fashion. They identified 5 latent classes for the 5th and 6th graders in…

Connections between science and mathematics seem natural. First, mathematics can be used in science to organize and analyze data in tables and graphs. Second, mathematics can help represent scientific phenomena and understand scientific concepts. Student learning should benefit when teachers make the connections between science and mathematics…

Mathematics is both a beautiful language and the simplest systematic discipline men ever created. The simplicity of mathematical concepts almost guarantees that the facts it establishes about those concepts will also be elemental. Despite this simplicity, most people complain about the difficulty of mastering the subject and shun the study of…

The production and operations management class offered at California State University, Fresno underwent a transformation from being a four-unit, face-to-face course to a hybrid course. This hybrid course, which is required for all students in the Craig School of Business, includes two units of face-to-face instruction each week, with some coverage…

Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Research, from all around the world, has shown that teachers' actions are informed by a variety of factors, including long-held and frequently unarticulated traditions about teaching and learning, systemic expectations of the processes of schooling, available textbooks, traditions of teacher education, school cultures, assessment traditions and…

Played in university classes for preservice teachers as well as in middle and high schools, the River Crossing Game depends on the sum of tosses of two fair dice. This paper describes the game as well as some lines of thinking about winning strategies, which are not obvious even with an understanding of the overall distribution for the sum of two…

Because of the educational importance of mathematics and science, IEA's (International Association for the Evaluation of Educational Achievement) Trends in International Mathematics and Science Study, widely known as TIMSS, is dedicated to providing countries with information to improve teaching and learning in these curriculum areas. Conducted…

Teacher educators use children's thinking activities as a means to prepare prospective teachers to teach mathematics. Research in methods courses and student teaching practica has shown these types of activities help prospective teachers deepen their own mathematical knowledge as well as better understand how children think. This study…

Teaching is a complex endeavour that requires teachers to meld knowledge about the nature of learners, pedagogical strategies and discipline content. In recent years an increasing variety of educational technologies are finding their way into the school classroom, including the widespread acceptance of interactive whiteboards (IWBs). The emerging…

Students have difficulty learning fractions, and problems in understanding fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision-making. Remediation of student misconceptions is hampered by deficiencies in teachers' knowledge of the discipline and pedagogical content knowledge. We theorized…

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…