It has been over thirty years since the nuclear reactor meltdown at the Chernobyl nuclear power plant, but why there is still an officially designated exclusion zone? The Chernobyl Disaster Task combines the learning of exponential functions with properties of radioactive substances to help students understand the ongoing effects of the meltdown.…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

Generalizing, conjecturing, representing, justifying, and refuting are integral parts of algebraic thinking and mathematical thinking in general (Lannin et al., 2011). The activity described in this article makes a case for generalizing as an overall mindset for any introductory algebra or geometry class by illustrating how generalization problems…

Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where the…

During professional development, the authors learned about strings--a powerful instructional routine used in elementary classrooms to elicit students' mental mathematics strategies and use those strategies to build conceptual understanding. Strings provided the authors with a way to make relatively small changes to guided notes in algebra 1,…

One does not have to teach for very long to see students applying the wrong formula in the wrong situation (e.g., Kirshner and Awtry 2004; Tan-Sisman and Aksu 2016). Students can become overreliant on the power of the formula instead of thinking about the relationships it describes. It is not surprising that students can see formulas as a way to…

Children see and describe patterns in the primary grades when they develop the meaning of numbers by composing and decomposing. During their early years, they use patterns to learn properties of operations (Common Core Standards Writing Team 2011). While describing the intent of the third-grade standards for multiplication, the CCSS writers…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…