Data rules schools and ignorance is far from bliss. From assessment results to questioning educational claims, there is a growing need to understand the numbers used in education. Education data blogger and teacher Richard Selfridge (aka Jack Marwood) unravels the complexities of dealing with educational data and explains statistics in an…

In this short thought-piece, I attempt to capture the type of freewheeling discussions I had with our late colleague, Mika Seppälä, a research mathematician from Helsinki. Mika, not being a psychometrician or learning scientist, was blissfully free from the design constraints that experts sometimes ingest, unwittingly. I also draw on delightful…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

The floor function maps a real number to the largest previous integer. More precisely, floor(x)=[x] is the largest integer not greater than x. The square bracket notation [x] for the floor function was introduced by Gauss in his third proof of quadratic reciprocity in 1808. The floor function is also called the greatest integer or entier (French…

Motivating middle school students to learn can be challenging. One proven method for doing so is through an integrated curriculum. Educational philosophers and curriculum theorists have long noted the benefits of an integrated curriculum, which recognizes that the subject areas within the curriculum are connected to one another and to the real…

Math is everywhere! Mathematics is "a way of describing the world--a way of thinking, knowing, and problem-solving" (Virginia's Early Childhood Development Alignment Project 2008, 83). Infants and toddlers are natural mathematicians. Even without adult support, infants and toddlers use math concepts to make sense of their world. An important role…

Expanded to include connections to Common Core State Standards, as well as National Council of Teachers of Mathematics (NCTM) standards, this critically acclaimed book will help every teacher and coach to meet the challenges of differentiating mathematics instruction in the K-8 classroom. In this bestseller, math education expert Marian Small…

Teachers are using technological innovations--including interactive whiteboards--in pre-K-grade 3 classrooms across the country. An IWB is a wall-mounted, touch-sensitive flat screen. When connected to a computer (or another electronic device) and a projector, it displays enlarged instructional content (such as a math word problem, pictures or…

We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."

How can teachers encourage their geography students to make sense of big numbers? The key math skills geography students need to apply are ones they learned long ago in fifth grade: estimation and place value. However, in order to recognize the size of a city, or strength of a country's per capita income, or value of a birth rate, they need…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Tables and charts are efficient tools for organizing numbers, but many people give little consideration to the order in which they present the data. This article illustrates the strengths and weaknesses of four criteria for organizing data--empirical, theoretical, alphabetical and a standardized reporting scheme.

I describe how data pooling and data visualization can be employed in the first-semester general chemistry laboratory to introduce core statistical concepts such as central tendency and dispersion of a data set. The pooled data are plotted as a 1-D scatterplot, a purpose-designed number line through which statistical features of the data are…

The inertial balance is one device that can help students to quantify the quality of inertia--a body's resistance to a change in movement--in more generally understood terms of mass. In this hands-on activity, students use the inertial balance to develop a more quantitative idea of what mass means in an inertial sense. The activity also helps…