Spurred by Kilpatrick's (1987) "Where do good problems come from?", this study explores problem-posing triggers of experienced problem posers for mathematics competitions. Triggers are conceived as instances of noticing, where an impulse draws a poser's attention and "triggers off" a mathematical re-action, one of the outcomes…

Through the historical analysis of Dienes' works and through the suggestions of activities, the objective of this text is to understand the movement of systematization of knowledge for teaching and to teach classification, ranking, and ordination through the use of logical blocks during the Modern Mathematics Movement (1960-1980), a time of…

This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

When public schooling was first introduced in the United States, early proponents emphasized the need for mathematics as critical for an informed citizenry in a democracy. Half a century later, this purpose of mathematics has been almost entirely overshadowed by the push for mathematics to maintain technological and economic advantages. The belief…

Suppose you were an alien trying to understand how people in the United States feel about the Common Core School Standards for Mathematics (CCSSM). You could look at the Internet, mass media, YouTube and all of the other venues available. Walking away from them, you would be very confused about whether the U.S. loves or hates the CCSSM, whether…

Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the…

Concern about students' math achievement is nothing new, and debates about the mathematical training of the nation's youth date back a century or more. In the early 20th century, American high-school students were starkly divided, with rigorous math courses restricted to a college-bound elite. At midcentury, the "new math" movement sought,…

One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

The media's response to the release of "Math Instruction that Makes Sense" (2011), a research report by the Frontier Centre for Public Policy (FCPP), helped spark a public controversy and spur the Saskatchewan government to reexamine the Ministry of Education's math curriculum. The purpose of this article is to examine the CBC's…

This study examined the effects of a computer game on students' mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skill, and English language skill on their achievement and motivation as they played the game. A total of 193 students and 10 teachers participated in this study. The teachers were randomly…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

The purpose of this study was to obtain the attitudes and beliefs of mathematics teachers in the School District of Philadelphia regarding an eighth grade middle school mathematics core curriculum. This study explored the attitudes and beliefs of teachers in the reform of an eighth grade math "Core Curriculum, Math In Context" (School…

The "Building Blocks PreK Math Curriculum" (Clements & Sarama, 2007) was designed to facilitate children's engagement in math and talk about math. Much research investigates the effect of curriculum on classrooms or teacher practices. This study used a mediational model to look at a curriculum's effect on children's achievement gain, operating…

This study investigated the level of concern in teachers and administrators regarding the adoption of a new math curriculum in the adoption's second year of implementation. Utilizing the Stages of Concern Questionnaire, based upon the Concerns-Based Adoption's Model as the instrumentation for the study, the findings of the study revealed that…