This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

Introducing challenging tasks in such a way that makes them accessible, rather than daunting, to students is a challenge for teachers. Solving challenging tasks involves students having to grapple with the problem. The role of the teacher is to motivate and clarify the problem rather than showing students how to solve the problem.

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

Developing students' 21st century skills, including creativity, critical thinking, and problem solving, has been a prevailing concern in our globalized and hyper-connected society. One of the key components for students to accomplish this is to take part in today's participatory culture, which involves becoming creators of knowledge rather than…

In this paper, we describe a framework for data analysis that can be embedded into a base application. Since it is important to analyze the data directly inside the application where the data is entered, a tool that allows the scientists to easily work with their data, supports and motivates the execution of further analysis of their data, which…

Youth with juvenile justice (JJ) interactions and/or adjudications face a number of challenges as they transition back into their community, including college and career readiness needs. In addition to the typical concerns of adolescents facing postsecondary decisions, these youths' decisions are complicated by a myriad of other factors, often…

The social studies curriculum travels through time and space and is bigger on the inside than it is on the outside. To an outsider, the social studies curriculum is a single line on a program of studies, 45 minutes of a student's school day. Those on the inside, however, know that the field covers history, geography, civics, economics, and much…

How do we preserve our civil society and dynamic political system and prepare students to be active citizens in a democratic society? The need for civic education is more essential now than ever before, and students deserve access to powerful civic lessons that actively engage them in learning about our democracy. The ultimate goal would be for…

Humans have become the most dominant animal on the planet. They have adaptations providing advantages over other animals. They have even out competed other species in their own genus. Humans have opposable forefingers and thumbs for superior dexterity, very large brains for intelligence, walk upright with bipedal locomotion to cover distances more…

The first author's initial attempts at a whole-class mathematics discussion were woefully dysfunctional. Ten second graders showing their answers to a missing addend question about the number of children left riding a school bus did not result in the mathematical epiphany that the textbook promised. She did not give up on using mathematical…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…

The National Council of Teachers of Mathematics (NCTM) has called on teachers to create supportive and equitable classroom environments, to steadfastly advocate that all students can learn mathematics, to hold high expectations for all students and to adopt practices that offer students the opportunity to excel (NCTM 2014). The overarching aim of…

Organic chemistry students at two universities, one in Canada and the other in the United States, connected using video conferencing software as learning partners for six online collaborative assignments. Mixed-methods analysis of interviews, surveys, and student-written reflections was used to identify barriers that students encountered during…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Special educators can play an essential role in the development of students' understanding of and capacity to do mathematics. Whether a special education teacher's goal is to help kindergartners develop counting skills or to support 10th graders in constructing geometric proofs and whether instruction will occur in co teaching, consulting, or…