This study described the mathematical depth in a mathematical activity carried out in a village in Turkey's Eastern Anatolia Region. This activity presented in the context of the game reflects a cultural situation of doing mathematics over time. In this context, it can identify as a study of ethnomathematics. Therefore, the cultural game was…

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

This pilot case study of two teachers and their learner groups from Adult and Community settings, investigates how numeracy teachers, working with adult learners in discrete numeracy classes, motivate and enable learners to build on their informal skills and apply new learning to their own real-life contexts. Teachers used a range of abstract and…

Because of the impact that mathematical beliefs have on an individual's behaviour, they are generally well researched. However, little mathematical belief research has taken place in the field of adult education. This paper presents preliminary results from a study conducted in this field in Switzerland. It is based on Ernest's (1989) description…

What if Stephen Douglas instead of Abraham Lincoln had won the U.S. presidential election of 1860? What if John F. Kennedy had not carried some of the eight states he won by 2 percentage points or fewer in 1960? What if six hundred more people in Florida had voted for Al Gore in 2000? And what if, in that same year, the U.S. House of…

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

This paper describes an action research project that investigated a range of activities to improve learners' mathematical communication skills. It also gives details of a subsequent case study that illustrates how technology can provide a means of overcoming some of the difficulties learners and tutors face in communicating about numeracy, while…

Recent studies have highlighted the potential importance of informal inferential reasoning (IIR) in supporting learners' general statistical reasoning. This paper presents a framework based on a retrospective analysis of design research in the context of technology-rich statistical professional learning experiences for high school mathematics…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

In applied mathematics particularly, one is interested in modeling real life situations; that is why, one tries to express some actual phenomenon mathematically, and then uses mathematics to determine future outcomes. It may be that one actually wishes to change the future outcome. Mathematics will not do this, but at least it tells one what to…

A common view seems to be emerging in the mathematics education world at the moment that the development and use of "rich tasks" is a good thing; a "right thing" to do. There are many examples of these "rich tasks" and teachers are encouraged to use them whenever they can. Professional learners don't just accept this uncritically, but question…

"Going Further" presents a roadmap to the works of the ACCLAIM (Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics) Research Initiative, the research effort of one the Centers for Learning and Teaching (CLTs) created with a grant (2001-2005) from the National Science Foundation. The Center began…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

The author drew the 2008 Easter conference to a close. During the final address, the author chose to focus on the domain of perimeter and area both because it is a topic accessible to teachers of all ages and because learners display considerable confusion between them. The core difficulty seems to lie in the necessity to attend either to the…

Filling the knowledge gap in the limited research on professional development leaders is an urgent issue if teacher learning is to be improved. This research and development project is studying how leaders learn to cultivate mathematically rich professional development environments. The authors adapted two frameworks from classroom-based…