In an interplay between the Fundamental Theorem of Arithmetic and topology, this paper presents material for a capstone seminar that expands on ideas from number theory, analysis, and linear algebra. It is designed to generate an immersive way of learning in which students discover new connections between familiar concepts, create definitions, and…

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

The transition from arithmetic to algebra in middle school can be critical for students having persistent difficulties in mathematics. The leading perception in our project is that holistic relational thinking is an effective problem-solving tool in both arithmetic and algebra. We worked in collaboration with two teachers of special classes to…

Math consists of many components such as arithmetic, algebra, geometry, trigonometry, statistics, where each component holds its importance in the field of math. Students of Grades 11 and 12 are at an important stage in their career, where the attitude and performance in math determines their future choices. Therefore, the aim of this study was to…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

This item bank was compiled by the Australian Council for Educational research (ACER) to help teachers at the secondary school level construct objective tests in arithmetic and algebra. The multiple-choice items were written by teachers who attended ACER writing workshops. The questions are classified according to their subject content and the…

Laboratory experiments by Steele and Aronson (1995) found that African-American subjects' performance on difficult verbal items, described as a verbal problem-solving task, was adversely affected when they were asked about their ethnicity just before working on the items. These results were attributed to stereotype threat. Asking about ethnicity…

The Calculators and Mathematics Project, Los Angeles (CAMP-LA), funded by the National Science Foundation for developing use of technology in the classroom, developed curriculum materials focused solely on the use of calculators in three stages. The first stage studied the mathematics curricula from different states and identified topics that are…