To learn mathematics, historically students had no choice but to memorize fundamental facts and apply memorized algorithms. Since 1995 in the US, all states have adopted standards to govern K-12 mathematics instruction, and in most, standards have de-emphasized memorization and emphasized reasoning based on concepts. This change assumed the brain…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

According to the design principle of progressive schematization, learning trajectories towards procedural rules can be organized as independent discoveries when the learning arrangement invites the students first to develop models for mathematical concepts and model-based informal strategies; then to explore the strategies and to discover pattern…

The purpose of this article is to study and analyse how a teacher implements an outdoor realistic problem situation for children aged 4-5 in a Swedish preschool. By an "outdoor realistic problem situation", I mean a situation initiated by a teacher in which children come into contact with mathematical concepts and in which the outside…

Many rules taught in mathematics classrooms "expire" when students develop knowledge that is more sophisticated, such as using new number systems. For example, in elementary grades, students are sometimes taught that "addition makes bigger" or "subtraction makes smaller" when learning to compute with whole numbers,…

This study is an exploration of teachers' engagement with concepts embedded in the normal distribution. The participants were a group of 290 in-service teachers enrolled in a teacher development program. The research instrument was an assessment task that can be described as an "unknown percentage" problem, which required the application…

Teachers typically teach subjects separately, but integrated science, technology, engineering, and mathematics (STEM) curriculums that focus on real-world practices are gaining momentum (NAE and NRC 2009). Before release of the "Next Generation of Science Standards" ("NGSS") (NGSS Lead States 2013), 36 states already had a…

Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations…

This protocol guided the review of research that informed the recommendations contained in the What Works Clearinghouse (WWC) practice guide "Improving Mathematical Problem Solving in Grades 4 through 8," published in May 2012. The research review involved the following steps: (1) The research staff searched the professional literature…

This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…

Proposes using the reform documents from the National Council of Teachers of Mathematics (NCTM), a theory-based multidimensional assessment framework, to help expand the scope of assessment in mathematics. Presents a framework using a context based on mathematical reasoning and components that comprise mathematical concepts, procedures,…

This book reinforces the outstanding work done by the National Council of Teachers of Mathematics (NCTM) in developing curriculum standards for students in kindergarten through fourth grade by discussing the 13 strands of mathematics and their implications for teachers and parents who work with students. It also provides some suggested resources…

This book contains activities designed to help teachers enrich the mathematical experiences of all children and reach toward fulfillment of the National Council of Teachers of Mathematics (NCTM) Standards. Chapters include: (1) "Prenumber, Number, Non-Number"; (2) "Place Value"; (3) "Addition, Subtraction"; (4)…

Ways in which the standards of problem solving, communication, reasoning, and connections can be incorporated into the elementary geometry curriculum are identified. Visualization of figures, conservation of area, shape and space, and multicultural study are discussed. (KR)

Presents an activity in which students were required to develop their own house plans, including finding the perimeter of the lot and house and calculating the total area of the house. (ASK)