Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

Various domains require practitioners to encounter and resolve ill-structured problems using collaborative problem-solving. As such, problem-solving is an essential skill that educators must emphasize to prepare learners for practice. One potential way to support problem-solving is through further investigation of instructional design methods that…

How better to begin the study of linear equations in an algebra class than to determine what students already know about the subject? A seventh-grade algebra class in a suburban school undertook a project early in the school year that was completed before they began studying linear relations and functions. The project, which might have been…

The current study explores the perceptions of a group of Academic English (AE) lecturers on their views on critical thinking in teaching English for academic purposes and the ways they believe this can be developed, if at all. The findings suggest that the majority of teachers believe in the importance of touching upon critical thinking in their…

This paper reports the learning analytics on the initial stages of a large-scale, government-funded project which inducts university students in Hong Kong into consideration of academic integrity and ethics through mobile Augmented Reality (AR) learning trails--Trails of Integrity and Ethics (TIEs)--accessed on smart devices. The trails immerse…

The ability to innovate is an important requirement in many organisations. Despite this pressing need, few selection systems in healthcare focus on identifying the potential for creativity and innovation and so this area has been vastly under-researched. As a first step towards understanding how we might select for creativity and innovation, this…

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers'…

We describe a case study of a problem-solving section, using the "Harkness" discussion method, of an honors multivariable calculus course. Students in the problem-solving section had equivalent outcomes on exams, reported higher ratings in self-assessments of skills, and took more math classes in the following year, compared with…

Interactive whiteboard offers a high-potential innovative tool in mathematical educational environments, in which teachers' modeling processes and students' exploring activities can easily be executed. Nevertheless, these affordances are not self-evident. There is a gap between the potential claims of the tool and its actual use in the classrooms.…

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class…

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

NCTM's "Principles to Actions: Ensuring Mathematical Success for All" (2014), outlines eight teaching practices for effective teaching and learning mathematics. One of them, facilitate meaningful mathematical discourse, states, "Effective teaching of mathematics facilitates discourse among students to build shared understanding of…

This article looks at a simple geometry problem that also involves some reasoning about number combinations, and show how it was used in a Year 7 classroom. The problem is accessible to students with a wide range of abilities, and provides scope for stimulating extensive discussion and reasoning in the classroom, as well as an opportunity for…

Student learning communities (SLCs) are more than just a different way of doing group work. Like the professional learning communities they resemble, SLCs provide students with a structured way to solve problems, share insight, and help one another continually develop new skills and expertise. With the right planning and support, dynamic…

Rehearsal is an increasingly important teacher education pedagogy. We explore how 3 science teacher educators thought about and used pauses within rehearsals to support secondary science teacher candidates in learning to facilitate sense-making discussions. Video data indicated that the most common purposes for pausing a rehearsal were to provide…