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…

One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

When presented with a problem in mathematics class, students often function as problem performers rather than problem solvers (Rigelman 2007). That is, rather than understanding the problem, students focus on using an operation to complete it. Students' tendencies to act as problem performers can prevent them from suggesting problem-solving…

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…

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…

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…

In the first years of life, as children observe, imitate, and interact with people and their environment, the brain is structuring a foundation for vocabulary, values, cognitive processes, and social skills. Educators, you can help influence that development by teaching the skills and dispositions of intelligent, creative, effective decision…

Learn how to design history lessons that foster students' knowledge, skills, and dispositions for civic engagement. Each section of this practical resource introduces a key element of civic engagement, such as defending the rights of others, advocating for change, taking action when problems are observed, compromising to promote reform, and…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

This article suggests the introduction of the concepts of areas bounded by plane curves and the volumes of solids of revolution in Pre-calculus. It builds on the basic knowledge that students bring to a pre-calculus class, derives a few more formulas, and gives examples of some problems on plane areas and the volumes of solids of revolution that…

Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…

The teaching of science, especially at pre-college and teacher education levels has undergone tremendous transformation over the years: from teacher-centred transmission to student-centred approaches rooted in constructivism. Whereas constructivism has been charged with all manner of shortfalls, it still can be of benefit to the way physics…

This study explores the mathematical problem-solving process of trainee teachers in a teachers' training institute. This research adopts a constructivist perspective that views learning mathematics as a process of constructing meaningful representation and knowledge as being constructed by the individual. The research methodology employs the case…

The author recently read a research paper by Padberg (2002), in which the development of understanding associated with decimal fractions was studied. Padberg (2002) outlined the situation that existed in Germany, where students were introduced to decimal fractions in the sixth year of school. He claimed that it was assumed students would have a…

The curriculum for eleven-year old students in the United Kingdom, currently adopted by most schools, includes solving linear equations with the unknown on one side only before moving onto those with the unknown on both sides in later years. School textbooks struggle with the balance between developing algebraic understanding and training…