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 COVID-19 pandemic has affected student learning; according to the National Assessment of Educational Progress (2022), scores for students in the United States have shown a decline in mathematics. . One way educators can strengthen students' current mathematical knowledge and bridge to new content is through Number Talks. Number Talks are brief…

Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

A highly distinctive and structured approach to teacher development, Lesson Study emerged in Japan but has since been adopted much more widely and now sees growing interest in the UK. Tony McConnell, Davinia Daley, Rebecca Levy, Lisa Waddell and Richard Waddington describe the process by which their school first investigated and then adopted…

According to the authors, we live in a society that is deeply influenced by technology, and social studies classrooms are ideal places for students to conduct inquiries into timely and relevant technological issues. In this article, the authors describe an approach that can be used across many situations to teach students to think critically about…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Students come to class with ideas about science content and the practices used to generate knowledge. Their lived experience provides them with basic ideas about how the world works. Tapping into their innate understandings and testing their ideas allows them to construct a more accurate understanding. Research shows that all students are ready to…

This article is prepared as part of a "Practice Teaching in Science" course of a teacher education program aiming for developing prospective science teachers' teaching through inquiry-based instruction involving practices of science and active learning strategies. During the semester, student teachers are required to prepare four…

As with all learners, English learners (ELs) require more than basic reading and writing skills to successfully engage with rigorous academic content, progress through school, and be fully prepared for postsecondary education and careers. ELs must be able to access grade-level content while simultaneously developing proficiency and autonomy in…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Despite the numerous benefits that stem from a coherent mathematical understanding, it is uncommon for teachers to encourage students to form a developed web of mathematical connections (Mousley, 1999). Additionally, when students explain their thinking, they frequently do not state how their reasoning connects to prior knowledge. This obscures…

The Puppy Love problem asked fifth and sixth grade students to use their prior knowledge of measures of central tendency to determine a data set when given the mean, mode, median, and range of the set. The problem discussed in this article is a task with a higher level of cognitive demand because it requires that students (1) explore and…

The art classroom is abundant with opportunities to develop meaningful questions, including one that constantly drives the author's own teaching practice: How might she best engage middle school students in a generative process of inquiry when interpreting and producing creative visual culture? In 2009, Chris Grodowski began translating research…

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…

How better to begin the study of linear equations in an algebra class than to determine what students already know about the subject? A seventh-grade algebra class in a suburban school undertook a project early in the school year that was completed before they began studying linear relations and functions. The project, which might have been…