We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

Research has shown that the ways in which teachers engage in professional development activities vary widely. identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that…

Teaching math is more than just numbers. It's about shaping future-ready students who are not only academically strong but thrive socially and emotionally. Research shows that learning both intrapersonal and interpersonal skills helps students academically, and teachers play a crucial role in providing social-emotional support. "The…

Sequences are an important topic--not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns…

To support teachers in implementing ambitious reform efforts, professional developers and teacher educators need to know more about teachers' thinking about argumentation. Specifically, there is a need to understand more about teachers' views and evaluations of "students'" mathematical arguments as they play out "in practice."…

Offering secondary math educators an innovative holistic and process-orientated approach for implementing nonroutine problems into their curriculum, this book defines and establishes practical strategies to develop students' problem-solving skills. The text focuses on the process skills necessary to solve nonroutine problems in mathematics and…

Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this…

In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…

Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…

At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

Embedding mathematics in a relatable context has changed the way Christie Henderson's elementary students view the subject. In this article, Henderson discusses how presenting mathematics through a relatable context enables students to visualize the math and make a pictorial representation to aid them in solving it. When relevant and relatable…

Arithmetic is a major mathematical focus in elementary school curriculum, and researchers such as Mason (2008) claim that "algebraic thinking is required in order to make sense of arithmetic" (p. 58). When adding, subtracting, multiplying, and dividing, learners must rely on a small set of fundamental properties also important for the…

Although traditional textbooks may not guide students through explorations or encourage group work, as many standards-based curricula do, virtually all textbooks contain mathematically accurate information and problems that, with adjustment, can be leveraged to support mathematical curiosity, reasoning, and discussion. Teachers who recognize rich…

In education, "dialogue protocols," or "protocols," are structured guidelines that were developed to promote meaningful and efficient communication and learning. They are "vehicles for building the skills--and culture-- necessary for collaborative work. The authors share protocols that were found to transform practices…

If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…