"What's the unit?" The answer to this question makes all the difference. A young child who is asked to count shoes needs to know if the unit to be counted is "pairs" of shoes or individual shoes. A middle school student who is asked for the length of a table will want to know if the number should be in inches, feet, or…

John Dewey discussed the dry school curriculum a century ago. One of the "evils" was a simplified curriculum having an outward appearance of mathematics. Dewey posited that such a simplified curriculum deprived students of opportunities to experience the thought-provoking character of the accumulated wisdom found in human knowledge. Dewey's…

Spatial abilities help students identify features of various shapes and the relationship that exists among these features. Being able to mentally manipulate images and tell what those images represent are important spatial skills. Research has highlighted the relationship between mathematics performance and spatial abilities. This article's…

In education, it is common to set aside older curriculum documents when newer ones are released. In fact, some instructional leaders have encouraged the "out with the old, in with the new" process by asking teachers to turn in all copies of the older document. Doing so makes sense when the old curriculum document is incompatible with the new.…

When learning the order of operations, students are instructed to adhere to a directive when determining the numerical value of an arithmetic expression. A more typical approach is the use of a popular mnemonic called PEDMAS (parentheses, exponents, division, multiplication, addition, subtraction). The literature is scant on conceptual approaches…

To promote math and science, this author designed an activity to show students that biomedical fields are within their reach. The activity has three distinct goals: (1) To introduce the field of biomedical engineering to students and encourage them in these career pursuits; (2) To give them hands-on experience conducting a biomechanical test; and…

To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and…

Story problems either bring students to a screeching halt or send them into a frenzied search for numbers and operations. They cause greater anxiety, still, in English language learners. These problems are often the nemesis of many a math teacher. This author grappled with this challenge in the context of teaching a series of lessons on integers…

This article focuses on the Thinking Through a Lesson Protocol (TTLP) that is intended to facilitate the design of lessons based on cognitively challenging mathematics tasks. Included is a discussion of the key features of the TTLP, suggestions on ways in which the protocol can be used as a tool for collaborative lesson planning, and a discussion…

This article introduces prediction as a useful tool to promote mathematical reasoning. First, the article addresses prediction expectations in state standards and gives examples. It also provides a classroom example and activities to illustrate what prediction can look like and how it can serve as a building block for the development of students'…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

This article discusses two sequences of activities that were developed to support middle school students' and preservice teachers' construction of algorithms for dividing fractions. One sequence is intended to promote understanding of the common-denominator algorithm; the other sequence is intended to promote understanding of the…

This article describes a mathematics and literature interdisciplinary project for preservice elementary teachers that was implemented in several urban middle school classrooms. This project, based on the novel Chasing Vermeer by Balliett (2004), involved a dramatization of one of the chapters from the book and a follow-up mathematical exploration.

This article describes a joint effort between a mathematics educator and a middle school art teacher who wanted their students to experience first hand how construction works in the real world. It starts with students designing and building scale models for a large inflatable item in which they display their art and extends to building the…

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…