When Robert Moses first began to teach algebra at the King Open school, he taught algebra using the regular method. After he worked with a couple of students, several of whom had difficulty understanding algebraic concepts, he realized that he needed to find a new way to teach algebra. He drew upon some of the ideas being taught by his professor at Harvard W. Quine and the teachings of Piaget on learning which were being taught at Wheelock College. Quine emphasized that the abstract language of mathematics could only be first learned when put into everyday language. Piaget emphasized that learning comes from the experiences that an individual has, reflects upon, improves upon the experience, and tries the updated idea again.

Moses developed a curriculum which would make it easier for the children to make a switch from arithmetic to algebra. Together the children would share experiences from their everyday life, which they would study and relate to algebra. Moses's curriculum is comprised of five important steps: 1.) Physical events 2.) Pictorial Representation/Modeling 3.) Intuitive Language/"People Talk" 4.) Structured Language/ "Feature Talk" 5.) Symbolic Representation. In other words the children would share a common experience, which through a series of steps they would gradually express in more abstract language until their experience was finally expressed in a mathematical statement.

Bill Crombie, a teacher, in 1990 said, "The mathematics questions were not formulated mathematically. He was pointing to the issues at the root of every mathematics question, encouraging a kind of a general thinking about the issue there,' as if he was saying, 'We can talk about that fundamental issue first and then specialize the results we get to the mathematics formulation'. ...'What this means is that, from the first instance, everybody has a voice at the mathematical table."

For example, Moses took the class on a subway trip from Central Square in Cambridge to Park Street in downtown Boston and then back from Park Street to Harvard Square in Cambridge. Back at the King school the children drew pictures, wrote stories and talked with one another about the trip. A key part of this process was having the children asking questions such as "How many"? and "Which way?". They would then try and discover the answers pn thier own. Already the children had completed three of the steps of Moses' process. Proceeding to step four the children were instructed to examine their trip for four fundamental mathematical features of trips: start, finish, direction and distance, features that are present in all trips. Finally the students make symbols to represent these features. Initially each student or groups of students may use symbols whose meaning is evident only to them. Later the class works to convert these symbols in standard symbols of algebra. The subway line represented a math number line containing positive and negative integers. It helped students to look at numbers in terms of how many and which way. This type of trip exercise can be applied to all sorts of situations, walking around neighborhoods, and bus rides.

This exercise is part of Moses's sixth grade "transistion curriculum". It is not specific to one section of the country. Students all over the country can study these lessons and learn the concepts of integers, displacements, and addition and subtraction of integers.










See how the process of asking questions helped in the context of Civil Rights