## 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.

## SBE Assessment Training

Today, I kept it real at a rad meeting of the minds. Folks from across the district came together to take the next step in creating common assessments that will be used district-wide. I worked on 3-5 reading assessments with some incredibly inspiring folks district-wide. I finally had the chance to meet Erin Hassen, who I had heard about for YEARS from Garrett and Siobhan Chan, the educational power couple. I want to hang out with her every day. I have so much to learn from her.

Common core is pretty darned awesome. It is going to kick us in the FACE if we are not prepared.

Today, I also learned about Dan Meyer from Kimmie Choi, who is brilliant. His work made me think about how much I would love it if I could finagle a doctoral fellowship some time in my future. If you can help me plot this scheme, let me know. I’m not terribly picky about schools……..

Â Â

… or anywhere that would have me.

Anyway. I had a chance to see the math team coach from SacajaweaÂ Middle School, who helped me answer the NCTM’s Twitter math problem of the day. (Half is one-third of it. What is it?) The coach didn’t seem to remember me from the TJ math competitions we’ve been at together, but it’s OK, because there were a lot of people at the meeting who I knew but who didn’t know me. Besides, I’d rather people not remember me than immediately know me as OH THAT person.

I thought a lot today about what impact an effective principal is able to have outside of the school building. I was freaking out this morning, all, “WHAT IF MICHAEL LEAVES US SOON AND PEOPLE GET CRAZY NEGATIVE?!?!?!” and about halfway to Federal Way (and halfway through my iced pumpkin spice latte), I realized that even in that worst-case scenario, it wouldn’t be the end of the world. Even if negativity descended on the school, I am now MUCH better equipped to have power over my own experiences within that negativity.

Speaking of having POWER over crappy situations, Miss Washington came to our school yesterday. I was EXTREMELY SKEPTICAL up until about a half hour into her assembly. Then she blew my mind and I wanted to hug her and hire her. I’ll tell you more about that tomorrow.

Now. Off to catch my bus. Even though I grumble about it right after I wake up, I really love taking the bus. I just wish my funds permitted me to purchase an iced pumpkin spice latte both on the way to AND from Federal Way…

## Lessons learned from our family liaison.

This year, Wildwood was fortunate enough to be able to hire a FamilyÂ Liaison. I worked with Greta Holtz when she was a paraeducator at Silver Lake Elementary,* and we are incredibly fortunate to have her at our school. She is available to help us connect with parents and translate conversations and information into Spanish or English.

Sra. Holtz is amazing. HerÂ reportÂ with families and the quick connections she’s making dazzle me. But I’m also having a chance to learn directly from her. A week or so ago, I asked if she would speak to me only in Spanish, so I could improve my vocabulary and grammar. She said yes, and not only have I been learning the Spanish language, but I’ve also been reminded what good teachers do.

Good teachers make quick, informal assessments, then adjust their instruction accordingly.

After a day of indulging my desire to speak entirely in Spanish, Sra. Holtz handed me a well-used book and made a rare slip back into English. â€œThis should help you understand the verbs and conjugations better,â€ she said. So she realized that my vocabulary was OK, but my grammar wasÂ atrocious. â€œThis is the best book there is.â€ I carefully turned the book over. â€œIâ€™ll take VERY good care of it,â€ I said, understanding the importance of this book â€“ her only copy.

Good teachers take measured risks when they think they might have a chance to take the next leap.

Sra. Holtz didnâ€™t HAVE to give me the book. She also didnâ€™t ORDER me to read it. But just knowing that I had it and that she thought itâ€™d be appropriate for me gave me confidence that she thought I had a pretty good vocabulary, I just needed to work on my grammar. Imagine how a student might be empowered from your risk.

Good teachers persist, even when they worry students may have lost interest.

I hurriedly said, “Hello!” to Sra. Holtz the morning after open house. “Hola, Senora,” she responded. “Como estas?” Well, I would have looked stupid if I answered her in English, so I reverted back to sophomore year Spanish and said, “Asi asi.” She persisted (we’re both walking in opposite directions down the hall at this point), “Estas desconsada?” “Haha, si, si, Senora!” I won’t be forgetting how to say “tired” any time soon.

Repeating what students say but saying it with correct grammar is powerful, not insulting.

In the past, I hesitated to use the ELL strategy of repeating what students say but correcting their grammar because I worried they’d be irritated that I just repeated everything they said. With Sra. Holtz, I realized I liked when she repeated what I said because it let me know the “right” way to pronounce the words, but it ALSO gave me a little bit of time to think of what I wanted to say next.

I know I’ll continue to learn plenty more from Sra. Holtz, and I’d love to learn more from you too! Leave me a comment or write me an e-mail in Spanish, and I’ll do my best to respond!

* You think teachers are underpaid? Paraeducators, who often work with our most at-risk and challenging students, earn poverty-level wages.