“Almost everyone who has tried to make a crowd estimate has a vested interest in what the outcome of the estimate is”

–Charles Seife, Professor of Journalism and Mathematician at NYU.

4th Graders use the Jacob’s Method of Crowd Counting to Estimate the Protest Crowd at Washington Square Park on Wednesday, January 25th, 2017. 

On Wednesday evening, January 25th, 2017, a protest crowd gathered at Washington Square Park in response to President Trump’s executive orders on immigration that he signed earlier that day. The New York Post reported that “Hundreds Gathered” (Marino & Perez, 1/25/17). The New York Observer (Toure, 1/25/17), called it a “Massive Demonstration”. Vogue (Codinha, 1/26/17), reported that “Thousands of New Yorkers Gathered”. So just how many people showed up for this rally? LREI fourth graders wanted to find out.

The Jacob’s Method of Crowd Counting

Herbert Jacobs, a University of California journalism professor in the 1960’s, devised a basic density rule that has been widely accepted. Watching students protesting the Vietnam War from his office window, Jacobs saw that they had gathered on a plaza that was arranged in a grid. He counted those in a few squares to get an average number per square and multiplied that by the total number of squares. He also came up with a basic density rule that states a “light crowd” has one person per square meter, and doubled that for a “dense crowd”. A “heavy crowd” would have as many as four people per square meter, according to this method.

A Summary of LREI’s Math Philosophy Written by Teachers from Lower, Middle, and High School: 

Children at every developmental level deeply engage in the discovery of mathematics through the inquiry and investigation of interesting problems. LREI students collaborate on solving worthwhile problems that have rich mathematical underpinnings. Problems can be solved on a variety of levels, have multiple entry points, and therefore provide both accessibility and challenge to the abilities of all students in a class.

A good problem is also defined as not having a predetermined solution pathway that is known in advance. A worthwhile task, or problem, will often open the door to other interesting conjectures and theories that students have, and support an emerging mathematical habit of mind.

Throughout each unit of study, students develop and maintain computational fluency. Students are instilled with an enthusiasm for mathematical challenges and the open-endedness of mathematical inquiry. Our students develop perseverance and a sense of ownership of mathematics. Students achieve genuine understanding when they actively construct knowledge rather than passively absorb; when they use it to solve problems rather than memorize facts and formulae.

Students throughout the divisions learn through inquiry and collaboration. Emphasis is placed on the presentation and communication of mathematics in written, oral, graphic and symbolic forms. Students are encouraged to clearly describe, explain and support their findings with valid evidence.

In the Lower School, students display their work using a document camera and engage their peers in the discussion of a problem. In the Middle School, students can share their thinking by reflecting work done on an iPad or graphing calculator to a Smartboard. Working in small groups is a commonly used practice across the grades. In High School, students put their mathematical ideas on small whiteboards and then each group presents to the rest of the class, and the classmates ask questions.

Consistent with LREI’s philosophy, the mathematics department values creativity and critical thinking, as well as risk-taking when problem solving as a means to confront life’s challenges and variables. Our students understand that mathematics has the power to model the world around us on multiple levels. Projects and problems, offered in math classes, have relevance to students and their lives.