Mathematics in Civilization (1/n)

I picked up a great-looking book a few years back and I’m just now getting a chance to dig in. It’s a freshman math textbook for college folks: Mathematics in Civilization (H.L. Resnikoff & R.O. Wells, Jr.). It’s a 1973 book that shows how mathematics came to be and how it has shaped and continues to shape our civilization.

A few wise folks have recommended some number of times that I learn more about the history of math, and as folks usually are, it was wise advice.

This book is intended for students and others who desire to understand the role that mathematics plays in science and society. (p 3)

Way to start it off with a bang, fellas.

The purposes and consequences of mathematics are of serious concern for the growth and health of society and therefore are a proper and necessary part of the workaday intellectual baggage that must be carried about by every educated and effective participant in civilized life. (p 5)

I had no idea that folks teaching math up in the ivory towers saw numbers in that light. This was fascination, beautiful stuff, and I wish I had understood this aspect of it earlier.

And if you want connections to ELA (it obvi includes art and science, as both are requirements for math to work), here’s some explicit evidence:

It is conceivable that mathematical needs for notational symbolism were later developed into full-fledged pictographic writing systems. (p 11)

Wow.

You can place this initial blog post analysis of my book on the following rubric. I’ve used grade 12 standards for this rubric, which I would use if I were studying this book for an adult course.

Standards Expert Proficient Apprentice
Art.Anchor.11.CConnectingRelate artistic ideas and works with historical context to deepen understanding.
Related artistic ideas and works with historical context to deepen understanding. Evaluated the historical impact of artistic ideas and works.
Related artistic ideas and works with historical context to deepen understanding.
Identified the historical context of artistic ideas and works.
Struggled to identify the historical context of artistic ideas and works.
HS-PS1-1Physical SciencesUse the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.
Used the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms, including quantitative understanding of ionization energy.
Used the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level of atoms.
Used the periodic table as a model to explain the patterns of electrons in the outermost energy level of atoms.
With support, used the periodic table as a model to identify the patterns of electrons in the outermost energy level of atoms.
HS-PS4-2.APhysical SciencesEvaluate questions about the advantages of using a digital transmission of information.
Evaluated and refined questions about the advantages of using a digital transmission of information.
Evaluated questions about the advantages of using a digital transmission of information.
Asked questions about the advantages of using a digital transmission of information.
Identified questions relevant to the advantages of using a digital transmission of information.
HSA.APR.D.6.AAlgebra: Arithmetic with Polynomials & Rational ExpressionsRewrite simple rational expressions in different forms.
Clearly demonstrated and explained how to rewrite simple rational expressions in different forms.
Rewrote simple rational expressions in different forms.
Understood simple rational expressions in different forms.
Struggled to understand simple rational expressions in different forms.
HSS.ID.A.1Statistics & Probability: Interpreting Categorical & Quantitative DataRepresent data with plots on the real number line (dot plots, histograms, and box plots).
Represented data with plots on the real number line (dot plots, histograms, and box plots). Applied this concept to solve real-world problems.
Represented data with plots on the real number line (dot plots, histograms, and box plots).
Understood data with plots on the real number line (dot plots, histograms, and box plots).
Struggled to understand data with plots on the real number line (dot plots, histograms, and box plots).
HSS.ID.A.3Statistics & Probability: Interpreting Categorical & Quantitative DataInterpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Clearly demonstrated and explained how to interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Interpreted differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Understood how to interpret differences in shape, center, or spread in the context of the data sets.
Struggled to understand how to interpret differences in shape, center, or spread in the context of the data sets.
MP.2.EMathematical PracticesPause as needed when manipulating symbols.
Did not rush through manipulations. Paused and double-checked as needed when manipulating symbols.
Did not rush through manipulations. Paused as needed when manipulating symbols.
Did not rush when manipulating symbols.
Rushed when manipulating symbols.
MP.2.FMathematical PracticesProbe into the referents for the symbols involved.
Looked deeply into and explained the meanings for what the symbols represent. Evaluated how well the symbols represent what they mean.
Looked deeply into and explained the meanings for what the symbols represent.
Described what the symbols represent.
Identified what the symbols represent.
MP.2.GMathematical PracticesCreate a coherent representation of the problem at hand.
Created a coherent representation of a complex or real world problem.
Created a coherent representation of the problem at hand.
With some support, created a coherent representation of the problem at hand.
Created a coherent description of the problem at hand.
MP.2.HMathematical PracticesConsider the units involved in a problem.
Clearly explained the units involved in a complex or real world problem.
Explained the units involved in a problem.
Identified the units involved in a problem.
With support, identified the units involved in a problem.
MP.2.IMathematical PracticesAttend to the meaning of quantities in a problem, not just how to compute them.
Explained to the meaning of quantities in a problem, not just how to compute them. Evaluated how well the quantities represent their meaning.
Explained to the meaning of quantities in a problem, not just how to compute them.
Identified to the meaning of quantities in a problem, not just how to compute them.
Understood the meaning of quantities in a problem, not just how to compute them.
MP.2.JMathematical PracticesKnow and flexibly use different properties of operations and objects.
Evaluated when to use different properties of operations and objects.
Flexibly used different properties of operations and objects.
Identified different properties of operations and objects.
Understood different properties of operations and objects.
MP.4.BMathematical PracticesWrite an addition equation to describe a situation (Elementary).
Wrote and solved an addition or subtraction equation to describe a complex situation.
Wrote an addition equation to describe a situation.
With support, wrote an addition equation to describe a situation.
Identified the situation that a given addition equation represents.
MP.4.EMathematical PracticesKnow and make assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
Made assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. Checked assumptions and approximations against other situations.
Made assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
Made assumptions and approximations to simplify a complicated situation.
Made assumptions and approximations to simplify a situation.
MP.4.FMathematical PracticesAnalyze relationships mathematically to draw conclusions.
Analyzed complex relationships mathematically to draw conclusions.
Analyzed relationships mathematically to draw conclusions.
Identified mathematical relationships and created assumptions.
Identified mathematical relationships.
MP.7.AMathematical PracticesLook closely to discern a pattern or structure.
Looked closely at complex problems to discern highly useful patterns or structures.
Looked closely at problems to discern a pattern or structure.
Recognized a pattern or structure in a problem.
With support, recognized a pattern or structure in a problem.
MP.7.BMathematical PracticesStep back for an overview of a problem and shift perspective.
Generated an overview of a complex or real world problem. Considered the problem from multiple relevant points of view.
Paused to look at the overall problem and to get an overview. Looked at the problem from different points of view.
Paused to look at the overall problem and to get an overview.
With support, understood the overall problem.
RST.11-12.4.AReading in Science and Technical SubjectsDetermine the meaning of symbols as they are used in a specific scientific or technical context
Clearly explained the meaning of symbols as they are used in a specific scientific or technical context
Explained the meaning of symbols as they are used in a specific scientific or technical context
Identified the meaning of symbols as they are used in a specific scientific or technical context
Struggled to identify the meaning of symbols.
RST.11-12.4.CReading in Science and Technical SubjectsDetermine the meaning of domain-specific words and phrases as they are used in a specific scientific or technical context
Clearly explained the meaning of domain-specific words and phrases as they are used in a specific scientific or technical context
Explained the meaning of domain-specific words and phrases as they are used in a specific scientific or technical context
Identified the meaning of domain-specific words and phrases as they are used in a specific scientific or technical context
Struggled to identify the meaning of domain-specific words and phrases.
W.HST.11-12.4Writing in Science and Technical SubjectsProduce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
Produced clear, coherent, and engaging writing in which the development, organization, and style are best suited to task, purpose, and audience.
Produced clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
Produced writing that was sometimes clear and coherent and the development, organization, or style was somewhat appropriate to task, purpose, or audience.
Struggled to produce writing that was clear or coherent or where the development, organization, or style was appropriate to task, purpose, or audience.

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