Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

In this paper we frame our observations in enactivism, specifically problem posing, to propose the notion of problem drift as a method to analyze the curriculum generating actions of small group learning systems in relation to teacher interventions intended to trigger specific content goals. Teacher attentiveness to problem drift is suggested to…

The success of online learning depends on interaction, pedagogical approaches and active participation. Garrison, Anderson and Archer (2000) introduced interactive learning through the community of inquiry model (COI). This study used the lens of social, cognitive and teaching presence (Garrison, Anderson & Archer, 2009) to examine the…

The use of case-based learning (CBL) provides students with diverse experiences in the classroom, including problem-solving, knowledge co-construction, communication, and group collaboration. Through these activities, students can explore and develop new knowledge, and acquire relevant skills that have application both in the classroom and beyond.…

In this paper, we finish describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools. ROAR is composed of three teaching units addressed to grades 10, 11, and 12, respectively. To improve students'…

Teaching advanced programming can be a challenge, especially when the students are pursuing different majors with diverse analytical and problem-solving capabilities. The purpose of this paper is to explore the efficacy of using a particular problem as a vehicle for imparting a broad set of programming concepts and problem-solving techniques. We…

Our research programme, a part of which is presented in this paper, looked at four year old children's ability to use manipulatives in the construction of cube models. We looked at how pre-school children managed the creation of cube nets as a mathematical problem and whether graphical representations of solutions could become a useful tool in a…

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Our students will continue to be confronted with many environment and sustainability issues during their lifetimes because they are unpredictable, serious and complex by nature. These issues challenge not just our technologies but our universities and educational institutions, values and way of living and interaction. Competency-based education…

In this paper, we frame mathematics classrooms as heterogeneous spaces wherein students draw on multiple storylines based on different notions of schooling and school mathematics to both communicate mathematical ideas and position themselves and one another. We focus on a fourth grade (age range 9.4-10.8 years) mathematics classroom discussion in…

The skillset that students acquire during college is not always well-aligned and/or well-developed relative to the skills needed to be successful in the business world. Employers have complained for many years that graduating students often lack adequate critical thinking and communication skills, in particular. In the marketing field (and other…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…