The present study aimed to examine the opinions of in-and preservice middle school mathematics teachers about teaching four operations with integers through "number line" and/or "counters". Participants were 42 middle school mathematics teachers and 51 pre-service mathematics teachers. The data were collected through open-ended…

This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. The understanding and use of algorithms is informed by two…

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)…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

This paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks…

Reported are the findings of a study of over seven hundred fourth-, sixth-, and eighth-grade pupils' ability to understand division involving zero. Implications for the classroom are discussed, including suggested teaching strategies. (JP)

Early experience with grouping objects is valuable for later understanding of and work with place value, division, and multiplication. Examples are drawn from the Developing Mathematical Processes Curriculum Project at the Wisconsin Research and Development Center for Cognitive Learning. (RS)

Argues for the rich development of mathematical ideas that can flow from considering the apparently simple question of finding a divisibility test for the number six. Presents approaches to teaching this topic that could be interesting to teachers. (ASK)

Utilizes two interpretations for the positive and negative signs to demonstrate how multiplication and division involving negative numbers can be represented and their inverse nature illustrated. (RP)

Computational algorithms appearing in early American arithmetic text are discussed. (SD)