Ben Zunica describes a lesson in which computational thinking has been successful in assisting students to understand the process of simplifying surds. The strengths and limitations of this approach are discussed. The author concludes that computational thinking can assist in solidifying understanding of a range of mathematical processes for…

It was a quest that began over three decades ago when the author began teaching at the Owen Sound Collegiate and Vocational Institute (OSCVI) in 1984. The school had a long, storied history dating back to 1856 when it first opened its doors to students from Owen Sound and the surrounding area. As a teacher of a survey course in Canadian history…

Learning to respond to a computer program that is not working as intended is often characterized as finding a singular bug causing a singular problem. This framing underemphasizes the wide range of ways that students and teachers could notice discrepancies from their intention, propose causes of those discrepancies, and implement interventions.…

The National Council of Teachers of Mathematics (NCTM, 2014) highlights that effective teaching practices promote students' reasoning and sense making through various problem-solving strategies. Rather than telling students what to do and how to solve problems, teachers are expected to engage learners in accessible real-life problem situations…

When Katrina Lindo taught Integrated Mathematics 1 to ninth- and tenth-grade students, she encountered some students who appeared initially resistant to doing mathematics. Lindo wanted her students to see themselves as capable of making sense of mathematics. Lindo said that being a mathematician is "the process of taking what you know and…

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 Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

This article describes the use of project-based instruction in activities and labs intended to develop higher-order thinking skills with high school students and pre-service teachers through the use of soap making.

Prior research suggests that students' understanding of scientific concepts is pre-determined by their reasoning ability. Other efforts suggest that American students' scientific literacy is in decline. One difficulty Bybee (2009) acknowledges is that there are two divergent philosophical models of scientific literacy. The first describes the…

"Reasoning and sense making should occur in every classroom every day," states "Focus in High School Mathematics: Reasoning and Sense Making" (NCTM 2009, p. 5). As this book suggests, reasoning can take many forms, including explorations and conjectures as well as explanations and justifications of student thinking. Sense making, on the other…

The goal of this article is to present a sketch of what, following the German social theorist Arnold Gehlen, may be termed "sensuous cognition." The starting point of this alternative approach to classical mental-oriented views of cognition is a multimodal "material" conception of thinking. The very texture of thinking, it is suggested, cannot be…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Benchmarks and standards have become an important part of the teachers' instructional focus since the No Child Left Behind Act of 2001. As educators they all recognize the importance of having high expectations of their students. Standards help schools articulate these expectations clearly to students, their parents, and the community. Yet, there…

Students must be encouraged to think for themselves by tapping into their imaginations. Only when mathematical concepts are presented in an imaginative way will students fully benefit from their experience. Both teachers and students must engage themselves in this creative realm of thinking, where imagination plays a vital part in learning and…