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Title: Teaching High School Mathematics; First Course; Adding Real Numbers, Teaching High School Mathematics; First Course; Adding Real Numbers
Identifier: e_mb_0003
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 1964-1965
Resource: Max Beberman film collection
Description: Max Beberman teaches schoolchildren the 4th lesson of a 166-lesson 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.

Title: Teaching High School Mathematics; First Course; Advent of Awareness, Teaching High School Mathematics; First Course; Advent of Awareness
Identifier: e_mb_0004
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (instructor), Hendrix, Gertrude (content director), Orvedahl, Jesse (asst. content director), Sims, Byrl (film director), Guide Dogs for the Blind, Inc. (cooperation), Mark Anderson (narrator)
Dates: circa 1964-1965
Resource: Max Beberman film collection
Description: 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 seeing-eye guide dogs. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Bound Variables: Matching Language with Awareness, Teaching High School Mathematics; First Course; Bound Variables: Matching Language with Awareness
Identifier: e_mb_0021
Creator: University of Illinois Committee on School Mathematics (producer)
Contributor: Beberman, Max (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 1964-1965
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches a class of instructors at the Mathematics Institute how to use language creatively to formulate generalizations. He discusses the use of open sentences to instruct both older and younger students. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1965.

Title: Teaching High School Mathematics; First Course; Equivalent Equations: Developing the Concept, Teaching High School Mathematics; First Course; Equivalent Equations: Developing the Concept
Identifier: e_mb_0039
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 guides students in finding different names for the same set of numbers. He proposes what happens when the problem changes from recognizing descriptions of the same set to recognizing equations with the same roots?What happens when these students encounter an equation they cannot solve by inspection? This film is a precursor to solving easier, equivalent equation with the same roots. Black and white picture with sound. Eastman Kodak edge code reads "triangle square" which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Isomorphism: Developing the Concept Part 1, Teaching High School Mathematics; First Course; Isomorphism: Developing the Concept Part 1
Identifier: e_mb_0005
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 1964-1965
Resource: Max Beberman film collection
Description: Mathematician Max Beberman instructs students from the Mathematics Institute how to teach the concept of isomorphism to their pupils. He shows that when students are first introduced to real numbers they find that the numbers of arithmetic are sometimes inadequate for situations that require knowing both magnitude and direction. Beberman addresses these questions: Are the nonnegative real numbers different from the numbers of arithmetic? Why can we sometimes find the answer to one problem by solving another one instead? This is part one of a two-part lesson. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Isomorphism: Developing the Concept Part 2, Teaching High School Mathematics; First Course; Isomorphism: Developing the Concept Part 2
Identifier: e_mb_0006
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 1964-1965
Resource: Max Beberman film collection
Description: In this film, mathematician Max Beberman continues to teach students from the Mathematics Institute how to teach the concept of isomorphism to their pupils. He shows that when students are first introduced to real numbers they discover that the numbers of arithmetic may be inadequate for situations that require knowing both magnitude and direction. Beberman addresses these questions: How can a teacher emphasize that the operation used with the first set may be different from the one used with the second set? In what respect do the nonnegative reals act more like the numbers of arithmetic than do the nonpositive reals? This is part two of a two-part lesson. Black and white picture with sound. Eastman Kodak edge code reads "triangle square," which correlates to 1964.

Title: Teaching High School Mathematics; First Course; Numbers and Numerals Part 1, Teaching High School Mathematics; First Course; Numbers and Numerals Part 1
Identifier: e_mb_0046
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 1964-1965
Resource: Max Beberman film collection
Description: Mathematician Max Beberman teaches students from the Mathematics Institute the many ways beginning math students may misinterpret math problems. Instructor Herbert Wills initiates a 166-lesson course for secondary school students, using Beberman's methods, with a class on numbers and numerals. Black and white picture with sound. Eastman Kodak edge code reads "triangle, square" which correlates to 1964.

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; 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; 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.

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