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Title: Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part II Distributive Principles for Numbers of Arithmetic; Discovery and Use, Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part II Distributive Principles for Numbers of Arithmetic; Discovery and Use
Identifier: e_mb_0015
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches mathematics instructors how to help students to recognize the distributive principle for multiplication over addition. He discusses constructing exercises that allow children to determine whether subtraction and division are commutative or associative operations. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part III: Principles of Arithmetic for Real Numbers, Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part III: Principles of Arithmetic for Real Numbers
Identifier: e_mb_0016
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman leads students on an investigation to find and prove various mathematical principles, including the Communitive Principle for Multiplication of Real Numbers, the Associative Property for Addition of Real Numbers, the Communitive Principles for Addition of Real Numbers, and the Principle for Adding the Real Number Zero. The students learn to check their findings and develop a working acquaintance with all of the principles. They also begin to use letters as variables to indicate patterns and to generate terms and sentences. In addition, Beberman introduces the pupils to using letters as indices to modify a sentence to indicate generalizations, which is discussed in future films. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part IV Discovery and Patterns, Teaching High School Mathematics; First Course; Basic Principles for Real Numbers Part IV Discovery and Patterns
Identifier: e_mb_0017
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches mathematics instructors how to lead students to discover various principles/generalizations of real numbers. He then shows them how to challenge students' assumptions of real numbers and discusses the classroom activities that are appropriate for practicing these newly-learned principles. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Comparing Real Numbers: The Number Line, Teaching High School Mathematics; First Course; Comparing Real Numbers: The Number Line
Identifier: e_mb_0018
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches students how to compare real numbers. He explores whether the concept of "less than" comes from the number line or must the student have the set or real numbers ordered before lining up makes sense. He and the class then establish a test for comparing real numbers. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Dividing Real Numbers, Teaching High School Mathematics; First Course; Dividing Real Numbers
Identifier: e_mb_0014
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches mathematics instructors how help pupils produce a formal definition of division. Rather than allow them to watch someone solve a division problem and imitate the procedures, he teaches students to use real discovery. Beberman also develops the idea that division reverses what multiplication accomplishes. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Equation Transformation Principles in Practice Part I, Teaching High School Mathematics; First Course; Equation Transformation Principles in Practice Part I
Identifier: e_mb_0041
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman guides students through practice exercises for the Equation Transformation Principles. They use the knowledge they have gained up to this point to solve equations that require principles they have not yet learned. Black and white picture with sound. Eastman Kodak edge code reads "square circle" which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Equation Transformation Principles in Practice Part II, Teaching High School Mathematics; First Course; Equation Transformation Principles in Practice Part II
Identifier: e_mb_0042
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman asks students if the following equations are equivalent: 3(x + 2) = 6 + 3x and 6 = 6. Beberman previously introduced students to the Equation Transformation Principles. In this film, students practice using this principle on equations that transform to a closed set. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Equivalent Equations and Transformation Principles, Teaching High School Mathematics; First Course; Equivalent Equations and Transformation Principles
Identifier: e_mb_0040
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman introduces and proves the Equation Transformation Principles, but does not show the the principle in practice. He also explores what happens when students encounter an equation they cannot solve by inspection. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Functions: Foreshadowing the Concept, Teaching High School Mathematics; First Course; Functions: Foreshadowing the Concept
Identifier: e_mb_0012
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches mathematics instructors how to use the concepts he has covered in previous films (binary and singulary operations and inverses of operations) to ease children into working with functions in a way that will seem logical and natural. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Inverses of Operations, Teaching High School Mathematics; First Course; Inverses of Operations
Identifier: e_mb_0011
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman addresses several questions concerning inverse operations: Does the binary operation of addition have an inverse? Is there any quick way of looking at a list of pairs for one operation that will tell you if the operation has an inverse? Inverse operations allow children to quickly find pairs in a new operation by altering the pairs that are already listed for a different operation. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part I, Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part I
Identifier: e_mb_0035
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman discusses how to solve an equation when it must be simplified in order to create a more easily-solved root. Beberman introduces the Uniqueness Principle for Addition and its converse, the Cancellation Principle for Addition. These two principles form the Addition Transformation Principle. The students learn clear distinctions between a logical principle and a mathematical principle, and how to interpret conditional sentences. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part II, Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part II
Identifier: e_mb_0036
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman guides students through the formulation and proof for the Uniqueness Principle for Multiplication, the Cancellation Principle for Multiplication, and the Logical Principle Modus Ponens. He also teaches the class how to construct Truth Values for Conditional Sentences. Students also name instances for the converse of a condition and a contrapositive of a conditional based on the Rule of Contraposition. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part III, Teaching High School Mathematics; First Course; Logical Basis for Equation Transformation Principles Part III
Identifier: e_mb_0037
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), McCoy, Eleanor (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman leads students to the discover and proof of the The Zero-Product Theorem the Concept of Contrapositive Negation of a Conjunction Double Negation. Students indicated what information is needed about y and v with the constriction y times v is not equal to 0 in order to guarantee that the product of y and v is not 0. Black and white picture with sound. Eastman Kodak edge code reads " square circle " which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Naming Sets: The Set Abstractor, Teaching High School Mathematics; First Course; Naming Sets: The Set Abstractor
Identifier: e_mb_0032
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches students the standard method of naming solution sets of real numbers, which they then describe in sentences. The pupils also learn to abbreviate solution sets and to interpret the new abbreviation symbol as they search for solution sets. Black and white picture with sound. Eastman Kodak edge code reads " square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Number Line Graphs of Solution Sets, Teaching High School Mathematics; First Course; Number Line Graphs of Solution Sets
Identifier: e_mb_0033
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Hart, Alice (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman and Alice Hart instruct students on how to create a visual representations of a solution sets. This representation is known as a number graph. They go on to explore special circumstances that would cause exceptions on teh number graph such as a sentence with an empty solution set. The film concludes with students beginning a lesson on solution subsets and their graphs. Black and white picture with sound. Eastman Kodak edge code reads " square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Numbers and Numerals Part 2, Teaching High School Mathematics; First Course; Numbers and Numerals Part 2
Identifier: e_mb_0001
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Wills, Herbert (instructor), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches students from the Mathematics Institute how to introduce the concept of symbols and abbreviations for numbers. Instructor Herbert Wills initiates a 166-lesson course for secondary school students, using Beberman's methods, with a class on numbers and numerals. Beberman elaborates on the lesson with examples of common mistakes pupils make when asked to name numbers and numerals and to use abbreviations and symbols for numerals in basic math lessons. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Numerical Variables: Developing the Concept Part II, Teaching High School Mathematics; First Course; Numerical Variables: Developing the Concept Part II
Identifier: e_mb_0020
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches high school students basic mathematical concepts that will lead to working with equations. He has them produce numerical substitutions within mathematical sentences that will make the sentences either true or false. Students also learn to compose open sentences from which each of a given set of sentences can be generated. Black and white picture with sound. Eastman Kodak edge code reads " square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Operation Machines, Teaching High School Mathematics; First Course; Operation Machines
Identifier: e_mb_0010
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman shows a Mathematics Institute class how to teach students singulary operations by introducing them to a make-believe machine that transforms numbers just as mathematical operations do. This idea easily eases children into solving equations. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Operations: Binary, Singulary, Teaching High School Mathematics; First Course; Operations: Binary, Singulary
Identifier: e_mb_0009
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Max Beberman teaches schoolchildren and students from the Mathematics Institute. The lesson first discusses how children understand the concepts of binary and singulary operations. Beberman uses clips from a 166-lesson course as examples of problems children associate with the differences and similarities between various mathematical operations. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Organizing Knowledge by Deduction, Teaching High School Mathematics; First Course; Organizing Knowledge by Deduction
Identifier: e_mb_0028
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Anderson, Mark (narrator), National Science Foundation (funding), U.S. Office of Education (funding), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director)
Dates: circa 1965-1966
Resource: Max Beberman film collection
Description: Mathematician Max Beberman instructs students at the Mathematics Institute on the best ways to give high school students experience organizing a large body of subject matter deductively. He pushes them to discover what other principles can be deduced from known principles. Beberman spends significant time performing principle proofs and producing predictions based on what the class already knows from previous lessons. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

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