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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.

Title: Teaching High School Mathematics; First Course; Prelude to Deduction, Teaching High School Mathematics; First Course; Prelude to Deduction
Identifier: e_mb_0023
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 that idea that if students accept the Communitive Principle for addition, then they must accept the mathematical consequences (instances) of the principle. He then demonstrates that each instance is a consequence, but not every consequence is an instance. When students acquire the concept of instance and consequence, they can begin to distinguish between deduction and experiment. This film is the students' first experience with formal proofs. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Prerequisite to Communication, Teaching High School Mathematics; First Course; Prerequisite to Communication
Identifier: e_mb_0019
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 1964-1965
Resource: Max Beberman film collection
Description: What conditions are necessary for effective communication? Nonverbal communication occurs even when students learn without us telling them what we want them to know. The film explores this idea and raises other issues that arise from this study, including the need to distinguish between what one understands from one's own inferences, and what one interprets from messages sent by others. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Principles and Discovery in Algebraic Manipulation Part II: Simplification, Teaching High School Mathematics; First Course; Principles and Discovery in Algebraic Manipulation Part II: Simplification
Identifier: e_mb_0029
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 high school students how to simplify complex mathematical equations in order to prove or disprove the equivalency-to-example expressions. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Principles and Discovery in Algebraic Manipulation Part IV: Some Common Cases, Teaching High School Mathematics; First Course; Principles and Discovery in Algebraic Manipulation Part IV: Some Common Cases
Identifier: e_mb_0030
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 shows high school students methods and shortcuts to simplify equations and equivalency tests. The students learn how to simplify equations that contain fractions and expressions that include radical signs, and how to remove parentheses preceded by a minus sign. In addition, Beberman teaches them how to find the roots of complex equations and to construct theorems based on the findings. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Proving Generalizations Part I: Test Pattern Principle, Teaching High School Mathematics; First Course; Proving Generalizations Part I: Test Pattern Principle
Identifier: e_mb_0026
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 students to a pattern for testing any instance. The test pattern is a proof for different generalizations and the generalizations are consequences of the test pattern. Black and white picture with sound. Eastman Kodak edge code reads " square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Proving Generalizations Part II: Classroom Examples, Teaching High School Mathematics; First Course; Proving Generalizations Part II: Classroom Examples
Identifier: e_mb_0027
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 continues his lesson Proving Generalization by showing examples of his methods. He begins with proving the Principle for Multiplying by 0, which forms the 0-sum theorem. The students next discuss if oppositing distributes over addition. This is done by searching for counter-examples of the theorem. Black and white picture with sound. Eastman Kodak edge code reads " square triangle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Punctuation and Conventions in Mathematics Part 1: Punctuation, Teaching High School Mathematics; First Course; Punctuation and Conventions in Mathematics Part 1: Punctuation
Identifier: e_mb_0007
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 explores various mathematical expressions that have become ambiguous from inadequate mathematical punctuation. He introduces the idea of rules for order of operations in order to remove punctuation without introducing ambiguity. These conventions are discussed further in the next film within this series: Punctuation and Conventions in Mathematics Part II: Conventions [e_mb_0008]. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Punctuation and Conventions in Mathematics Part 2, Teaching High School Mathematics; First Course; Punctuation and Conventions in Mathematics Part 2
Identifier: e_mb_0008
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 expands on the idea of conventions for order of operations in order to remove punctuation without introducing ambiguity, which he explored in the last film (Punctuation and Conventions in Mathematics, Part I; e_mb_000). These conventions include left to right convention, multiplication first - addition second convention, and division first - subtraction second convention. Black and white picture with sound. Eastman Kodak edge code reads square circle which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Real Numbers: Developing the Concept, Teaching High School Mathematics; First Course; Real Numbers: Developing the Concept
Identifier: e_mb_0002
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: In this film, Max Beberman focuses on real numbers. He discusses the concept with a class of schoolchildren, first explaining the differences between basic numbers of arithmetic and real numbers, and then tying the idea of positive and negative directionality to real numbers and to zero. Beberman also addresses the topic with students from the Mathematics Institute. Black and white picture with sound. Eastman Kodak edge code reads "square circle," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Sentences and Solution Sets, Teaching High School Mathematics; First Course; Sentences and Solution Sets
Identifier: e_mb_0031
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 1964-1965
Resource: Max Beberman film collection
Description: In this film, building on students' knowledge of using open statements to generate sentences, mathematician Max Beberman considers how open sentences partition the set of all real numbers into those that work and those that do not work within the generated sentences. By the end of the lesson, students can provide solution sets and compose verbal descriptions of the sets. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Solving Equations: Informal Approach, Teaching High School Mathematics; First Course; Solving Equations: Informal Approach
Identifier: e_mb_0034
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 1963-1964
Resource: Max Beberman film collection
Description: Mathematician Max Beberman discusses the process of helping pupils to find solution set sentences and solve equations with a class from the Mathematics Institute. He suggests they make a game of finding solutions to open sentences so that students may understand the process of solving equations. Teaching students to use the natural discovery process to solve equation sequences is the reason Max Beberman created this film course. Mathematician Eleanor McCoy demonstrates Beberman's method when she leads a class in solving equations. Black and white picture with sound. Eastman Kodak edge code reads "circle triangle," which correlates to 1963.

Title: Teaching High School Mathematics; First Course; Solving Worded Problems, Teaching High School Mathematics; First Course; Solving Worded Problems
Identifier: e_mb_0045
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 helps students solve word problems using the principles that they have learned so far in the course. Students solve simple worded problems without formal education on these methods by solving the equations that these problems create. They first learn to solve equations systematically by using what they know. Black and white picture with sound. Eastman Kodak edge code reads "square circle" which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Subset of a Set: Developing the Concept, Teaching High School Mathematics; First Course; Subset of a Set: Developing the Concept
Identifier: e_mb_0038
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 1964-1965
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches students that they can solve some equations simply by inspection but some are harder to solve. Easier equations must be solved first. Beberman introduces the idea that if you can prove that equation 1 is equal to equation 2 and equation 2 is equal to equation 3 then you can be sure that 1 and 3 are int he same solution set. Students are given homework to select equations that will have the same solution set. Black and white picture with sound. Eastman Kodak edge code reads " triangle square " which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Substitution and the Linking Rule, Teaching High School Mathematics; First Course; Substitution and the Linking Rule
Identifier: e_mb_0024
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 1964-1965
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches students substitution, an important step on the way to formal deduction. The pupils become acquainted with some of the rules governing this action. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Subtracting Real Numbers, Teaching High School Mathematics; First Course; Subtracting Real Numbers
Identifier: e_mb_0013
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 shows mathematics teachers how to help students produce a formal definition of subtraction. Rather than allow them to watch someone solve a division problem and imitate the procedures, he teaches students to use real discovery. He then develops the concept of adding negative 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; Teaching High School Mathematics; First Course; Prelude to Deduction, Teaching High School Mathematics; First Course; Teaching High School Mathematics; First Course; Prelude to Deduction
Identifier: e_mb_0025
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 1966-1967
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches a Mathematics Institute class that the distinction between instance and consequence is subtle, but definite and sharp, and that an understanding of this distinction is necessary for constructing deductive proofs. Black and white picture with sound. Eastman Kodak edge code reads "triangle circle," which correlates to 1966.

Title: Teaching High School Mathematics; First Course; Transformation Principles for Inequations Part I, Teaching High School Mathematics; First Course; Transformation Principles for Inequations Part I
Identifier: e_mb_0043
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 math teachers on how to lead their students to formally justify and solve inequations via the Transformation Principles for Inequations. Black and white picture with sound. Eastman Kodak edge code reads "square circle" which correlates to 1965.

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