Building on the work of Jean Piaget and other cognitive psychologists, Herbert Ginsburg -- TC’s Jacob H. Schiff Foundations Professor of Psychology and Education -- has devoted his career to debunking the common American misconception that very young children are unable to think mathematically. Ginsburg has spent countless hours interviewing and videotaping toddlers and preschoolers in the classroom and capturing examples of their “everyday mathematical thinking”—awareness of shape, number and other concepts employed in play, eating and other informal situations.
Similarly, TC pre-service teaching students in Ginsburg’s course “the Development of Mathematical Thinking” analyze video clips of young children in various situations, from free play to focused interviews to instruction, in order to identify and shed new light on their mathematical behaviors. The video clips are stored in an online learning environment called VITAL (Video Interactions for Teaching and Learning) that Ginsburg conceived and developed in collaboration with the Columbia University’s Center for New Media Teaching and Learning (CCNMTL). VITAL enables users to insert video clips into their electronic papers as clickable multimedia citations—viewable evidence that buttresses their analyses and interpretations.
“I don’t like my students to talk in vague ideological terms, like ‘it’s great to let kids construct knowledge,’” Ginsburg says. “I want them to integrate what they learn about kids from observation with what they read and with their own skills of teaching.”
Ginsburg’s findings are reflected in a preschool curriculum, “Big Math for Little Kids,” which he co-authored researchers at Arizona State University and Johns Hopkins, as well as in a 2009 National Academy of Sciences study, to which he was a major contributor. But he has also taken the lead in applying his own ideas. Working with commercial software developers, he has created several powerful new assessment and teaching technologies for use with young children, including:
- mCLASS:Math, marketed by Wireless Generation -- software that enables educators using handheld or laptop computers to assess and understand their students’ mathematical performance and thinking in order to guide teaching. Used by some 1,500 teachers in 15 states, mCLASS:Math prompts teachers with questions to ask that probe students’ mathematical understanding. They can record students’ answers under pre-determined category headings for different problem-solving strategies. And they can also use the mCLASS handheld device to upload such information onto a Web site maintained by Wireless Generation where they can view assessment results and analyses. The reports graph students’ progress and milestones over the course of a year and recommend new instructional activities targeted to what each individual student can do and how he or she thinks mathematically.
- MathemAntics, a sequence of educational computer games for teaching mathematics to children ages three through third grade. Currently in development by Educational Network Services, the program employs graphics of farmyard animals and other child-friendly scenarios that incorporate educational goals and standards for early math learning established by the National Governors Association Center for Best Practices. MathemAntics covers the concepts of “how many,” which includes counting, cardinality and subitizing (the ability to instantly recognize a small number of items, without counting); addition and subtraction; equivalence; symbolism; using a base-10 system to understand column addition; multiplication; and negative numbers. Each area is loosely geared to a different age level, yet allows for a wide range in comprehension and proficiency.
- The Birthday Party Project, an assessment system designed to determine what very young children understand about math. There’s no pencil or paper, no multiple choice questions. In fact, the kids involved (preschoolers ages three to five) don’t know they’re being evaluated; instead, they’ve been told they’re going to a make-believe birthday party. They play games, including activities such as counting presents and adding candies, and identifying shapes and patterns. Then the grown-ups running things ask them questions about how they arrived at their answers.
“Kids love to be tested if you can do it well and make it enjoyable,” says Ginsburg. “That means making assessment fun but still something that yields valuable information. Ultimately, he says, ”we’re not doing intelligence testing. That’s essentially irrelevant for teaching math. The goal is to help teachers understand each kid’s thinking so that they can teach better, and in a more personalized and effective way.”previous page