Basic Principles for Real Numbers
Parts 2, 3, and 4 of this lesson. In Part 2, Max Beberman teaches mathematics instructors how to help students to recognize the distributive principle for multiplication over addition. Beberman leads students on an investigation to find and prove various mathematical principles, including the Communitive Principle for Multiplication of Real Numbers in Part 3 and, in Part 4, he teaches mathematics instructors how to lead students to discover various principles/generalizations of real numbers. 
 Equation Transformation Principles in Practice
Parts 1 and 2 of this lesson. In Part 1, Max Beberman guides students through practice exercises for the Equation Transformation Principles. In Part 2, students practice using the Equation Transformation Principles on equations that transform to a closed set. 

Isomorphism: Developing the Concept
Parts 1 and 2 of this lesson. In Part 1, Max Beberman instructs students from the Mathematics Institute how to teach the concept of isomorphism to their pupils. He continues the lesson in Part 2, asking questions such as “How can a teacher emphasize that the operation used with the first set may be different from the one used with the second set?” 
 Logical Basis for Equation Transformation Principles
Parts 1, 2, and 3 of this lesson. In Part 1, Max Beberman discusses how to solve an equation when it must be simplified in order to create a more easilysolved root. In Part 2, he guides students through the formulation and proof for the Uniqueness Principle for Multiplication, the Cancellation Principle for Multiplication, and the Logical Principle Modus Ponens. Beberman leads students to the discover and proof of the The ZeroProduct Theorem the Concept of Contrapositive Negation of a Conjunction Double Negation in Part 3. 

Numbers and Numerals
Parts 1 and 2 of this lesson. In Part 1, Max Beberman teaches students from the Mathematics Institute how to introduce the concept of symbols and abbreviations for numbers. Instructor Herbert Wills initiates a 166lesson course for secondary school students, using Beberman's methods, with a class on numbers and numerals. In Part 2, Beberman teaches the students how beginning math students may misinterpret math problems. 
 Principles and Discovery in Algebraic Manipulation
Parts 2 and 4 of this lesson. In Part 2, Max Beberman teaches high school students how to simplify complex mathematical equations in order to prove or disprove the equivalencytoexample expressions. In Part 4, he shows how to simplify equations that contain fractions and expressions that include radical signs, and how to remove parentheses preceded by a minus sign. 

Proving Generalizations
Parts 1 and 2 of this lesson. In Part 1, Max Beberman introduces students to a pattern for testing any instance. In Part 2, he continues the lesson by showing examples of his methods. 
 Punctuation and Conventions in Mathematics
Parts 1 and 2 of this lesson. In Part 1, Max Beberman explores various mathematical expressions that have become ambiguous from inadequate mathematical punctuation. In Part 2, he expands on the idea of conventions for order of operations in order to remove punctuation without introducing ambiguity. 

Teaching High School Mathematics; First Course; Adding Real Numbers
Source:Beberman (Max) Film Collection Max Beberman teaches schoolchildren the 4th lesson of a 166lesson course. He covers the addition of real numbers and the rules
associated with the interactions between positive and negative numbers and zero. Beberman also discusses with the students from the Mathematics Institute the proper methods to teach their
pupils to solve problems using mathematical operations. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964. From the original reel,
optical audio track loses synchronization with picture from 19:18 to 24:35. 
 Teaching High School Mathematics; First Course; Advent of Awareness
Source:Beberman (Max) Film Collection This film addresses the perception many instructors hold that if students cannot express the answer they do not know the answer.
The narrator introduces Beberman's idea of the Advent of Awareness. He uses examples from previous films, as well as the training methods of seeingeye guide dogs. Black and white picture
with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964. 
