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…

Problem solving is a necessary component of developing a strong mathematics curriculum that will help all students achieve their life goals, regardless of their specific academic plans. What day-to-day instructional decisions do teachers need to make if they believe that problem solving is a vehicle for learning mathematical content? In this…

This study examined the effectiveness of two methods of increasing student learning from posterior probability lessons: diagrams and questioning while reading. Undergraduate students (N = 245) read a lesson in one of three diagram conditions and one of three questioning-while-reading conditions (embedded questions, elaboration interrogations, and…

Background: A number of studies report that few questions are asked in classrooms and that many of them are shallow questions. Aims: This study investigates the way in which reading goals determine questioning on scientific texts. Reading goals were manipulated through two different tasks: reading for understanding versus reading to solve a…

Scientific reasoning and scientific argumentation are highly valued outcomes of K-12 and higher education. In this article, we first review main topics and key findings of three different strands of research, namely research on the development of scientific reasoning, research on scientific argumentation, and research on approaches to support…

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students…

This study focuses on elucidating and explaining reasons for the stability of and interrelationships between students' conceptions about "Light Propagation" and "Visibility of Objects" using contextualized questions across 3 years of secondary schooling from Years 7 to 9. In a large-scale quantitative study involving 1,233…

The author explores concrete ways to help students learn more and have fun doing it while they support each other's learning. The article specifically shows the relationships between cooperative learning and deep learning. Readers will become familiar with the tenets of cooperative learning and its power to enhance learning--even more so when…

Science, technology, engineering, and mathematics (STEM) education is an emerging initiative in Australia, particularly in primary schools. This qualitative research aimed to understand Year 4 students' involvement in an integrated STEM education unit that focused on science concepts (e.g., states of matter, testing properties of materials) and…

In this article, we describe how using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics. In doing so, we characterize the nature of the predictions students made and the levels of sophistication in students' reasoning within a middle school algebra context. In this study, when…

Open-ended questions, as discussed in this article, are questions that can be solved or explained in a variety of ways, that focus on conceptual aspects of mathematics, and that have the potential to expose students' understanding and misconceptions. When working with teachers who are using open-ended questions with their students for the…

The aim of this study is to investigate the effects of solution methods and question prompts on generalization and justification of non-routine problem solving for Grade 9 students. The learning activities are based on the context of the frog jumping game. In addition, related computer tools were used to support generalization and justification of…

"A Framework for K-12 Science Education" identifies eight science and engineering practices for K-12 classrooms. These practices, along with core ideas and crosscutting concepts, define the nation's learning goals for science. The practices outlined in the framework are: (1) Asking questions and defining problems; (2) Developing and using models;…

This dissertation presents the results of an experiment that measured the learning outcomes associated with three different pedagogical approaches to introductory physics labs. These three pedagogical approaches presented students with the same apparatus and covered the same physics content, but used different lab manuals to guide students through…

During an informal, after-school, math program, a group of middle school students worked collaboratively on open-ended problems. The students co-constructed arguments, provided justifications for their solutions, and engaged in mathematical reasoning. This paper describes the specific teacher moves that promoted this phenomenon. The findings of…