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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 19651966

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 commut...
Show moreMax 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.
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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 19651966

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...
Show moreMax 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.
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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 19651966

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 ...
Show moreMax 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 newlylearned principles. Black and white picture with sound. Eastman Kodak edge code reads "square triangle," which correlates to 1965.
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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 19641965

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 pict...
Show moreMathematician 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.
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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 19651966

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 ...
Show moreMax 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.
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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 19651966

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 ...
Show moreMax 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.
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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 19651966

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 w...
Show moreMathematician 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.
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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 19651966

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 ...
Show moreMathematician 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.
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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 19651966

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...
Show moreMathematician 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.
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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 19641965

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...
Show moreMathematician 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.
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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 19651966

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....
Show moreMax 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.
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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 19651966

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 easilysolved root. Beberman introduces the Uniqueness Principle for Addition and its converse, the Cancellation Principle for Addition. ...
Show moreMathematician Max Beberman discusses how to solve an equation when it must be simplified in order to create a more easilysolved 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.
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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 19651966

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 constr...
Show moreMathematician 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.
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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 19651966

Resource

Max Beberman film collection

Description

Mathematician Max Beberman leads students to the discover and proof of the The ZeroProduct Theorem the Concept of Contrapositive Negation of a Conjunction Double Negation. Students indicated what information is needed about y and v with the constricti...
Show moreMathematician Max Beberman leads students to the discover and proof of the The ZeroProduct 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.
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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 19651966

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 searc...
Show moreMathematician 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.
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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 19651966

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 num...
Show moreMathematician 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.
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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 19641965

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 166lesson course for secondary school students, using Beberman's meth...
Show moreMathematician Max Beberman teaches students from the Mathematics Institute the many ways beginning math students may misinterpret math problems. Instructor Herbert Wills initiates a 166lesson 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.
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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 19651966

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 166lesson course for secondary school students, using Beberman's met...
Show moreMathematician 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. 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.
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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 19651966

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 l...
Show moreMax 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.
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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 19651966

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 f...
Show moreMathematician 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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