The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

The combination of new instructional methods and new accountability pressures puts many in a quandary in evaluating math instruction. There is much for principals to learn about how and under what conditions new instructional methods work in math classrooms, how to support teachers as they develop new instructional skills, and how to integrate a…

The "word problem" is stated for a given collection. Facts regarding Dehn's Algorithm, definition of Thue systems, a rewriting system, lemmas and corollaries are provided. The situation is examined where the monoid presented by a finite Thue system is a group. (DC)

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

Cites Mandelbrot as an example of one who learned the language of mathematics, biding his time until he could employ his knowledge both as a means of creative expression and as a tool for comprehending the intricacies of the world around us. (KHR)

In everyday interactions with children, there are many things that parents can do--and do without lecturing or applying pressure--to help children learn to solve problems, to communicate mathematically and to demonstrate reasoning abilities. These skills are fundamental to learning mathematics. The major portion of this booklet is made up of…

This publication contains reference materials and activities for teachers in a staff development program in New York City, teaching grades 3 and 6. The program combines content and methodology. Sections in the publication include: (1) Student Verbalization Resources; (2) Manipulative Resources; (3) Probability, Statistics, and Graph Resources; (4)…