The Cell Phone modeling task centers on a Fermi real-world estimation question. The task and rubric can be used at different grade levels to focus on the modeling process and classroom community. Finding time and space to engage students, especially novice modelers, in mathematical modeling can be a challenge, yet the benefits of modeling are…

There is a substantial amount of literature focusing on the importance of culturally relevant teaching that emphasizes connecting the school's curriculum with the culture of students. This approach can be accomplished through the concept of ethnomathematics. Ethnomathematics studies how cultural groups practice and use math in daily activities…

Deliberation and inquiry can go hand-in-hand. Inquiry-based learning calls on teachers to facilitate student-led discovery, something that can only happen when students ask questions and weigh possible answers before settling on a plausible and evidentiary answer. Teaching through inquiry is about setting students up to wrestle with the issue at…

Searching for sources of inspiration is central to creative design; however, we have limited knowledge of individual inspiration search strategies in response to varying levels of task constraints. We studied 39 high-school students' inspiration search strategies using Google Images. Low task constrainedness led to "divergent search"…

We implemented a STEM task that highlights the engineering cycle and engages students in productive struggle. Students problem solved in productive ways and saw tangible benefits of revising their work to achieve mathematical goals.

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Patterning tasks engage students in a core aspect of algebraic thinking-generalization (Kaput 2008). The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that students in grades 9-12 should "generalize patterns using explicitly defined and recursively defined functions" (NCTM 2000, p. 296). Although educators…

This article addresses the problem of how to best design authentic writing assessments in history that support learners in demonstrating the types of higher order thinking skills needed for effective citizenship. Recent research has primarily focused on curriculum interventions intended to build disciplinary literacies through various types of…

The ideas students bring to class and their perspectives on what is happening in the classroom change constantly. Keeping track of these changes is useful for adapting lessons, nurturing student self-reflection, increasing student ownership of learning, and building a teaching practice responsive to learners' needs. In this article, the authors…

A mysterious conflict of solutions emerged when a group of tenth- and eleventh-grade students were studying a seemingly ordinary problem on combination and probability. By investigating the mysterious "conflicts" caused by multiple randomization procedures, students will gain a deeper understanding of what it means to perform a task…

Complex Instruction is a multifaceted instructional model designed to provide highly challenging learning opportunities for students in heterogeneous classrooms. The model provides a rationale for and philosophy of creating equity of access to excellent curriculum and instruction for a broad range of learners, guidance for preparing students for…

Context is what makes mathematical modeling tasks different from more traditional textbook word problems. Math problems are sometimes stripped of context as they are worked on. For modeling problems, however, context is important for making sense of the mathematics. The task should be brought back to its real-world context as often as possible. In…

The Industrial Revolution is the subject of one of the high school inquiries of the New York State Toolkit. Social Education presents the following excerpts from the inquiry as an example of a typical Toolkit lesson. The supporting questions include: (1) Where did people move to and from during the Industrial Revolution?; (2) How did daily life…