A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…

In this set of tips, parents and caregivers will learn how to: (1) support children's understanding of fractions at home with activities on dividing objects (recommended for grades K-5); (2) support children's understanding of fractions at home with measurement activities (recommended for grades K-4); (3) support children's understanding of…

STEM Pathways aims to increase youths' long-term interest, learning, and achievement in STEM through a deliberate and interconnected system of STEM learning opportunities. In fall 2014 and spring 2015, a survey was administered to fourth- and fifth-grade students at the six STEM Pathways schools in Minneapolis Public Schools (MPS). Most of the…

Presents a divisibility problem and how a class of students discussed the problem and determined a plan to solve it. (ASK)

The Palos Heights School District, Illinois, eliminated neighborhood elementary schools in favor of a primary (K-2), intermediate (3-5), and middle school (6-8) configuration. Details the strategies for handling public opposition. (MLF)

In traditional North American Indian societies, decisions are made by consensus rather than by authorities. Americans for Indian Opportunity (AIO), an organization concerned with the issue of tribal governance, considers poor communication and disagreements about issues of power, resources, and recognition to be among the causes for conflict…