As students have struggled to use the "chip model" (i.e., red and yellow chips representing positive and negative numbers) to model integer addition and subtraction and have found it confusing, the authors developed a series of activities based on adding and removing opposite objects to and from a boat to better help students in this…

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Building upon the blockbuster success of "Building Thinking Classrooms in Mathematics," Peter Liljedahl has joined forces with co-author Maegan Giroux to bring the Building Thinking Classrooms (BTC) framework to life in this new book, "Mathematics Tasks for the Thinking Classroom, Grades K-5." But this book is so much more than…

In typical school mathematics, students experience problem solving in different ways. Sometimes students learn about problem solving by being introduced to different strategies, such as making a table or drawing a picture. Other times, problem solving is presented as a context for applying previously learned mathematics skills and concepts.…

Infinite series are known to be challenging for Calculus II students, perhaps because they lack intellectual need for the content. In their analysis of Calculus textbooks found few instances of potential intellectual needs for infinite series. This study combines a textbook analysis with interviews of four professors and observations of their…

This article draws on the simple context of a two animal farm to create an engaging and mathematically meaningful problem solving task for students. It aims to encourage students to think systematically and to present their findings methodically. The task is structured sequentially, making it suitable for primary school students from Year 1 to…

Effective teaching requires enjoyable classroom tasks aimed at promoting students' learning of mathematics meaningfully, and previous research has demonstrated that the use of origami activities in mathematics classrooms can help achieve that goal. In this article, the authors describe their "LOVE MATH" one-straight-cut letter origami…

In this article, the authors discuss two ways of improving the rigour and integrity of mathematics in STEM programs drawing on examples from their research. The authors examine how mathematics can be made a stronger part of a STEM unit using examples from two pairs of teachers engaged in a STEM teacher professional development program, conducted…

This article dives into the importance of engaging students in investigating the mathematics of businesses that pressure their members to recruit new members as a basis for success, also referred to as multi-level marketing (MLM). The mathematics behind these businesses are discussed, and a sample student task is given.

Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. "Figuring Out Fluency in Mathematics Teaching and Learning" offers educators the inspiration to develop a deeper understanding of procedural fluency, along with…

This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.

This article presents examples of how early childhood educators (prek-2nd grade) might use their daily read alouds as a vehicle for increasing mathematical talk and mathematical connections for their students.

An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.