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Bostonian

Dolciani/Houghton Mifflin math sequence

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Mary P. Dolciani co-authored several books in the Houghton Mifflin Modern Mathematics Series, starting in the 1960s, and the books were used widely. I think a sequence that could be used from grades 7 on are

 

Pre-Algebra: An Accelerated Course (1996)

by Mary P. Dolciani

 

Modern Algebra Structure and Method (Book 1), revised ed. (1973),

by Mary P. Dolciani and William Wooton

 

Modern Algebra and Trigonometry: Structure and Method (Book 2) (1963)

by Mary P. Dolciani, Simon L. Berman, and William Wooton

 

Modern Geometry: Structure and Method (1965)

by Ray C. Jurgensen, Alfred J. Donnelly, and Mary P. Dolciani

 

Modern introductory analysis (1964),

by Mary P. Dolciani, Edwin F. Beckenbach, Alfred J. Donnelly, Ray C. Jurgensen, and William Wooton

 

A calculus book in the series, not co-authored by Dolciani, is

 

Limits; a transition to calculus (1966)

by O. Lexton Buchanan

 

I have used the publication dates of the books I own -- there have been several editions of many of the books. I wonder what experiences have had with the Dolciani series. The books have good reviews on Amazon, and I think they are especially suitable for strong math students. The books have many problems, divided in A (basic), B (intermediate), and C (challenging) categories.

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I wonder what experiences have had with the Dolciani series.

 

Do you see the Dolciani tag on this thread that someone put there? Click on it, and it will take you to many Dolciani threads. Many here are fans of the old Dolciani books. Esp. Jane in NC. :D

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Do you see the Dolciani tag on this thread that someone put there? Click on it, and it will take you to many Dolciani threads. Many here are fans of the old Dolciani books. Esp. Jane in NC. :D

 

Fan? I am the self proclaimed WTM Dolciani proselytizer.

 

Jane (who apparently needs a title :D)

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I've found that Roxbury Latin, a prestigious private boys school in Boston, uses "Dolciani" texts until calculus, as described at http://www.roxburylatin.org/school_life/math.aspx and http://www.stanford.edu/~meehan/xyz/rls.html . An excerpt of the Roxbury Latin site is below.

Pre-Algebra is designed to give boys a strong background in basic mathematical concepts and skills. Students study arithmetic operations with fractions, decimals, and signed numbers before examining percents, ratio, proportion, and divisibility rules. The course also covers fundamental geometric concepts including perimeter, area, and volume. Basic probability and statistics are taught as well. Finally, in preparation for Algebra 1, students learn to solve elementary equations and word problems. The text for the course is Dolciani, Pre-Algebra, An Accelerated Course, supplemented by Bridgess, Exercises in Basic Mathematics.

Algebra 1 Algebra 1 presents a comprehensive overview of the fundamentals of algebra. The course emphasizes algebraic techniques, particularly factoring, solving equations, and analyzing linear functions. Strategies for solving problems form an important component of the course, and an assortment of word problems are taught throughout the year. Other topics covered include real numbers, operations with polynomials and algebraic fractions, variation, inequalities, systems of equations, radical expressions, and quadratic functions. The text for the course is Brown, Dolciani, Sorgenfrey, and Cole, Algebra Book 1.

Algebra 2 extends the foundation in algebra begun in Algebra 1. Students explore the classic elementary functions, namely polynomial, rational, exponential, and logarithmic functions. Other topics studied include conics, sequences and series, and triangle trigonometry. Students also become much more adept at using the numerical and graphing capabilities of their calculators. The text for the course is Brown, Dolciani, Sorgenfrey, and Kane, Algebra Book 2.

Geometry provides an introduction to geometric techniques and ideas. Though different sections approach the subject in different ways, all sections develop results involving lines, planes, inequalities, triangles, circles, polygons, perpendicularity, congruence, similarity, area, and volume. Algebraic techniques are revisited through topics such as inequalities, proportions, and coordinate geometry. Mathematical writing and axiomatic reasoning form a natural component of the curriculum. Further topics may include vectors, constructions, and similarity transformations. The text for all sections is Brown, Jurgenson, and Jurgenson, Geometry. Teachers also rely on problem sets developed both internally and externally.

Trigonometry has its roots in the relationships between the sides and angles of a triangle. Students derive equations involving the sine, cosine, and tangent functions, and then investigate a wide array of real world applications. Further study focuses on identities, analytic properties of the trigonometric functions, and features of their graphs such as periodicity, symmetry, amplitude, and phase shift. The text consists of relevant chapters from Brown, Advanced Mathematics.

Analysis continues the development of topics studied in Algebra 2. Exponential, logarithmic, polynomial, and rational functions are revisited in greater depth. Students have by now become proficient with their calculators, which aid them in their study of these functions and their graphs. Other topics include sequences and series, probability, conic sections, and polar coordinates. The text is relevant chapters from Brown, Advanced Mathematics. Upon completion of this course, students will be prepared to take the Mathematics Level 2 SAT Subject Test.

Statistics is the science of collecting, analyzing, and drawing conclusions from data. Both the Advanced Placement and regular Statistics courses cover four major topics: exploratory data analysis—students use graphs and numbers to describe and analyze data; experimental and sampling design—students discover the proper ways to collect data via sampling and controlled experiments; probability—students learn fundamental principles of random variables and sampling distributions; and statistical inference—students draw conclusions from data using confidence intervals and tests of significance. The text is Bock, Velleman, and Deveaux, Stats: Modeling the World.

Calculus is one of the masterpieces of mathematics. In this course students extend the concepts of slope and area to all the non-linear functions they have studied. This Advanced Placement course is offered at two levels: AB and BC Calculus. Both sections study the derivative and integral in depth, covering topics such as tangent lines, curve sketching, related rates, implicit differentiation, slope fields, optimization problems, areas, volumes, and differential equations. The BC Calculus class also covers advanced integration techniques and Taylor series. The text for the course is Finney, Demana, Waits, and Kennedy, Calculus: Graphical, Numerical, Algebraic or Larson and Hostetler, Calculus.

Advanced Topics in Mathematics is comprised of three units: linear algebra combined with operations research; multivariable calculus; and game theory. The first unit explores the application of linear algebra (the study of vectors, matrix mathematics, and systems of linear equations) to operations research—a branch of mathematics concerned with finding optimal solutions to real world problems, gradually shifting focus to vector mathematics in two and three dimensions and the applications of vector functions (such as velocity and acceleration, arc length and curvature). The second unit, multivariable calculus, is a continuation of calculus. Vectors and the geometry of space, vector-valued functions, functions of several variables, and multiple integration from the Larson, Hostetler, and Edwards text, Calculus are covered. The course finishes with a unit on game theory, in which we analyze two-player games of perfect information using tree diagrams and induction proofs, games of imperfect information, games with dominating strategies, mixed strategies, Nash Equilibria, and zero-sum games.

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K12 now uses a two year prealgebra course beginning in 6th that is Dolciani. I am planning on using them, just compacting them somewhat for my DD (we are trying to fill in some holes).

 

Mathematics Structure and Method, Course 1 by Dolciani, Sorgenfrey, Graham McDougal Littell 2001 ISBN 13: 978-0-395-48098-4

 

I believe the same book but Course 2 is for Prealgebra 2.

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K12 now uses a two year prealgebra course beginning in 6th that is Dolciani. I am planning on using them, just compacting them somewhat for my DD (we are trying to fill in some holes).

 

Mathematics Structure and Method, Course 1 by Dolciani, Sorgenfrey, Graham McDougal Littell 2001 ISBN 13: 978-0-395-48098-4

 

I believe the same book but Course 2 is for Prealgebra 2.

 

Thanks for posting this. I've been looking for a 6th grade book for my ds who just finished up BJU 5 and LOF Decimals/Percents and Fractions. I'm not sure I'm ready to go right into pre-algebra yet because I don't want to miss any of the foundational information. This may be a definite possibility for us.

 

Thanks!

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I've found that Roxbury Latin, a prestigious private boys school in Boston, uses "Dolciani" texts until calculus, as described at http://www.roxburylatin.org/school_life/math.aspx and http://www.stanford.edu/~meehan/xyz/rls.html . An excerpt of the Roxbury Latin site is below.

Pre-Algebra is designed to give boys a strong background in basic mathematical concepts and skills. Students study arithmetic operations with fractions, decimals, and signed numbers before examining percents, ratio, proportion, and divisibility rules. The course also covers fundamental geometric concepts including perimeter, area, and volume. Basic probability and statistics are taught as well. Finally, in preparation for Algebra 1, students learn to solve elementary equations and word problems. The text for the course is Dolciani, Pre-Algebra, An Accelerated Course, supplemented by Bridgess, Exercises in Basic Mathematics.

Algebra 1 Algebra 1 presents a comprehensive overview of the fundamentals of algebra. The course emphasizes algebraic techniques, particularly factoring, solving equations, and analyzing linear functions. Strategies for solving problems form an important component of the course, and an assortment of word problems are taught throughout the year. Other topics covered include real numbers, operations with polynomials and algebraic fractions, variation, inequalities, systems of equations, radical expressions, and quadratic functions. The text for the course is Brown, Dolciani, Sorgenfrey, and Cole, Algebra Book 1.

Algebra 2 extends the foundation in algebra begun in Algebra 1. Students explore the classic elementary functions, namely polynomial, rational, exponential, and logarithmic functions. Other topics studied include conics, sequences and series, and triangle trigonometry. Students also become much more adept at using the numerical and graphing capabilities of their calculators. The text for the course is Brown, Dolciani, Sorgenfrey, and Kane, Algebra Book 2.

Geometry provides an introduction to geometric techniques and ideas. Though different sections approach the subject in different ways, all sections develop results involving lines, planes, inequalities, triangles, circles, polygons, perpendicularity, congruence, similarity, area, and volume. Algebraic techniques are revisited through topics such as inequalities, proportions, and coordinate geometry. Mathematical writing and axiomatic reasoning form a natural component of the curriculum. Further topics may include vectors, constructions, and similarity transformations. The text for all sections is Brown, Jurgenson, and Jurgenson, Geometry. Teachers also rely on problem sets developed both internally and externally.

Trigonometry has its roots in the relationships between the sides and angles of a triangle. Students derive equations involving the sine, cosine, and tangent functions, and then investigate a wide array of real world applications. Further study focuses on identities, analytic properties of the trigonometric functions, and features of their graphs such as periodicity, symmetry, amplitude, and phase shift. The text consists of relevant chapters from Brown, Advanced Mathematics.

Analysis continues the development of topics studied in Algebra 2. Exponential, logarithmic, polynomial, and rational functions are revisited in greater depth. Students have by now become proficient with their calculators, which aid them in their study of these functions and their graphs. Other topics include sequences and series, probability, conic sections, and polar coordinates. The text is relevant chapters from Brown, Advanced Mathematics. Upon completion of this course, students will be prepared to take the Mathematics Level 2 SAT Subject Test.

Statistics is the science of collecting, analyzing, and drawing conclusions from data. Both the Advanced Placement and regular Statistics courses cover four major topics: exploratory data analysis—students use graphs and numbers to describe and analyze data; experimental and sampling design—students discover the proper ways to collect data via sampling and controlled experiments; probability—students learn fundamental principles of random variables and sampling distributions; and statistical inference—students draw conclusions from data using confidence intervals and tests of significance. The text is Bock, Velleman, and Deveaux, Stats: Modeling the World.

Calculus is one of the masterpieces of mathematics. In this course students extend the concepts of slope and area to all the non-linear functions they have studied. This Advanced Placement course is offered at two levels: AB and BC Calculus. Both sections study the derivative and integral in depth, covering topics such as tangent lines, curve sketching, related rates, implicit differentiation, slope fields, optimization problems, areas, volumes, and differential equations. The BC Calculus class also covers advanced integration techniques and Taylor series. The text for the course is Finney, Demana, Waits, and Kennedy, Calculus: Graphical, Numerical, Algebraic or Larson and Hostetler, Calculus.

Advanced Topics in Mathematics is comprised of three units: linear algebra combined with operations research; multivariable calculus; and game theory. The first unit explores the application of linear algebra (the study of vectors, matrix mathematics, and systems of linear equations) to operations research—a branch of mathematics concerned with finding optimal solutions to real world problems, gradually shifting focus to vector mathematics in two and three dimensions and the applications of vector functions (such as velocity and acceleration, arc length and curvature). The second unit, multivariable calculus, is a continuation of calculus. Vectors and the geometry of space, vector-valued functions, functions of several variables, and multiple integration from the Larson, Hostetler, and Edwards text, Calculus are covered. The course finishes with a unit on game theory, in which we analyze two-player games of perfect information using tree diagrams and induction proofs, games of imperfect information, games with dominating strategies, mixed strategies, Nash Equilibria, and zero-sum games.

 

I'm confused about where you said they are using Dolciani until Calculus... or are there other books not listed? Under trig and analysis they say the text is Advanced Math by Brown and for stats someone else...:confused:

 

Is there another part where they talk about the Dolciani books?

 

Thanks,

Joan

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Fan? I am the self proclaimed WTM Dolciani proselytizer.

 

Jane (who apparently needs a title :D)

 

 

She converted me, and my eldest did it. Great book. My middle one, however, has chosen something else.:glare:;)

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I have uploaded some pictures of book covers along with the publication dates that may be helpful to some of you. I have uploaded them to the pictures section on my profile.

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I found Dolciani by the grace of God. :001_smile:

 

Background -- I had been investigating prealgebra texts and had looked at gazillions of them (couresy of a math teacher friend) and found nothing I liked.

 

Story -- I was waiting for my kids to finish up their 4-H meeting in a church basement. I noticed that there was a LARGE unorganized pile of books strewn across the floor, and, being a homeschooler, I started poking through the books. Most were boring textbooks, but one was Dolciani's prealgebra. I fell in love at first sight! It was just what I was looking for!

 

The church was closed, but on Monday morning I called up the surprised secretary and asked about the books and if I could have/take/buy the Dolciani one. She said yes -- and I even found the TM in the pile!!!!!

 

The rest is history. Having found a great text, we stuck with it. The funny thing is that there is an outstanding school district in MA (with a fantastic website) that I use as a general resource when contemplating texts, and it used the Dolciani sequence until quite recently and it still uses the Brown Geometry.

 

I got a phone call just a few weeks ago from dd in grad school saying that she appreciated our algebra 2 text so much!!!! I am so incredibly thankful for the Dolciani texts and for the funny way in which I found them! Finding out that others (like Jane in NC) love them too was an exciting discovery -- I'm not alone!

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I am an 8th grade Algebra teacher and have been using the Algebra Structure and Method Book 1 for years. I will be teaching 6th grade next year. The advanced 7th grade is using Mathematics Structure and Method Course 2. I have been wanting to use a Dolciani book for the 6th grade. What are the relationships between Mathematics Structure and Method Course 1, Mathematics Structure and Method Course 2, Pre-Algebra and Pre-Algebra Accelerated Course? Are there any others that would be appropriate for Middle School? My school splits the class into advanced and regular. Mathematics Structure and Method Course 2 and Algebra Structure and Method Book 1 are used by the advanced 7th and 8th grades. I am using the Algebra Structure and Method Book 1 for the regular level this year but it is just a bit too difficult. Any advice/recommendations appreciated.

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I've found that Roxbury Latin, a prestigious private boys school in Boston, uses "Dolciani" texts until calculus, as described at http://www.roxburylatin.org/school_life/math.aspx and http://www.stanford.edu/~meehan/xyz/rls.html . An excerpt of the Roxbury Latin site is below.

Pre-Algebra is designed to give boys a strong background in basic mathematical concepts and skills. Students study arithmetic operations with fractions, decimals, and signed numbers before examining percents, ratio, proportion, and divisibility rules. The course also covers fundamental geometric concepts including perimeter, area, and volume. Basic probability and statistics are taught as well. Finally, in preparation for Algebra 1, students learn to solve elementary equations and word problems. The text for the course is Dolciani, Pre-Algebra, An Accelerated Course, supplemented by Bridgess, Exercises in Basic Mathematics.

Algebra 1 Algebra 1 presents a comprehensive overview of the fundamentals of algebra. The course emphasizes algebraic techniques, particularly factoring, solving equations, and analyzing linear functions. Strategies for solving problems form an important component of the course, and an assortment of word problems are taught throughout the year. Other topics covered include real numbers, operations with polynomials and algebraic fractions, variation, inequalities, systems of equations, radical expressions, and quadratic functions. The text for the course is Brown, Dolciani, Sorgenfrey, and Cole, Algebra Book 1.

Algebra 2 extends the foundation in algebra begun in Algebra 1. Students explore the classic elementary functions, namely polynomial, rational, exponential, and logarithmic functions. Other topics studied include conics, sequences and series, and triangle trigonometry. Students also become much more adept at using the numerical and graphing capabilities of their calculators. The text for the course is Brown, Dolciani, Sorgenfrey, and Kane, Algebra Book 2.

Geometry provides an introduction to geometric techniques and ideas. Though different sections approach the subject in different ways, all sections develop results involving lines, planes, inequalities, triangles, circles, polygons, perpendicularity, congruence, similarity, area, and volume. Algebraic techniques are revisited through topics such as inequalities, proportions, and coordinate geometry. Mathematical writing and axiomatic reasoning form a natural component of the curriculum. Further topics may include vectors, constructions, and similarity transformations. The text for all sections is Brown, Jurgenson, and Jurgenson, Geometry. Teachers also rely on problem sets developed both internally and externally.

Trigonometry has its roots in the relationships between the sides and angles of a triangle. Students derive equations involving the sine, cosine, and tangent functions, and then investigate a wide array of real world applications. Further study focuses on identities, analytic properties of the trigonometric functions, and features of their graphs such as periodicity, symmetry, amplitude, and phase shift. The text consists of relevant chapters from Brown, Advanced Mathematics.

Analysis continues the development of topics studied in Algebra 2. Exponential, logarithmic, polynomial, and rational functions are revisited in greater depth. Students have by now become proficient with their calculators, which aid them in their study of these functions and their graphs. Other topics include sequences and series, probability, conic sections, and polar coordinates. The text is relevant chapters from Brown, Advanced Mathematics. Upon completion of this course, students will be prepared to take the Mathematics Level 2 SAT Subject Test.

Statistics is the science of collecting, analyzing, and drawing conclusions from data. Both the Advanced Placement and regular Statistics courses cover four major topics: exploratory data analysis—students use graphs and numbers to describe and analyze data; experimental and sampling design—students discover the proper ways to collect data via sampling and controlled experiments; probability—students learn fundamental principles of random variables and sampling distributions; and statistical inference—students draw conclusions from data using confidence intervals and tests of significance. The text is Bock, Velleman, and Deveaux, Stats: Modeling the World.

Calculus is one of the masterpieces of mathematics. In this course students extend the concepts of slope and area to all the non-linear functions they have studied. This Advanced Placement course is offered at two levels: AB and BC Calculus. Both sections study the derivative and integral in depth, covering topics such as tangent lines, curve sketching, related rates, implicit differentiation, slope fields, optimization problems, areas, volumes, and differential equations. The BC Calculus class also covers advanced integration techniques and Taylor series. The text for the course is Finney, Demana, Waits, and Kennedy, Calculus: Graphical, Numerical, Algebraic or Larson and Hostetler, Calculus.

Advanced Topics in Mathematics is comprised of three units: linear algebra combined with operations research; multivariable calculus; and game theory. The first unit explores the application of linear algebra (the study of vectors, matrix mathematics, and systems of linear equations) to operations research—a branch of mathematics concerned with finding optimal solutions to real world problems, gradually shifting focus to vector mathematics in two and three dimensions and the applications of vector functions (such as velocity and acceleration, arc length and curvature). The second unit, multivariable calculus, is a continuation of calculus. Vectors and the geometry of space, vector-valued functions, functions of several variables, and multiple integration from the Larson, Hostetler, and Edwards text, Calculus are covered. The course finishes with a unit on game theory, in which we analyze two-player games of perfect information using tree diagrams and induction proofs, games of imperfect information, games with dominating strategies, mixed strategies, Nash Equilibria, and zero-sum games.

 

 

I also noticed that the recommended geometry text is the one by Brown, Jurgensen, Brown, not the one with M. Dolciani. We found that text to be both thorough and challenging ... and the solutions manual to be frustrating. I haven't looked at many geometry texts, but out of the ones I've seen, I think it's the best for formal geometry. :)

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The list originally posted by Bostonian gives the sequence for PreAlg and later. I am still needing to know the sequence for:

 

Mathematics Structure and Method Course 1

Mathematics Structure and Method Course 2

Pre-Algebra New Edition

Pre-Algebra An Accelerated Course

 

We are currently using Mathematics Structure and Method Course 2 for 7th grade and Algebra 1 Structure and Method Book 1 for 8th grade. Would MSMC Course 1 be appropriate for the 6th grade or is one of the Pre-Algebra books better? What is the difference between the two Pre-Algebra books?

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I don't know about the MSMC 1 and 2, but I would assume the Pre-Algebras are interchangeable. What year is the "New Edition"? If later, it may have filtered out the references to computer programming in BASIC.

 

I am actually using both the Pre-Algebra Accelerated Course and Dolciani's Modern School Mathematics Pre-Algebra (1973) together for my son's Pre-Algebra. The Accelerated version has more word problems and more practice drills (and is visually more appealing), but the 1973 version is based around set theory and includes other number theory (like base number systems through base 12 and converting repeating decimals to fractions). I couldn't choose, so I use both.

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