## 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.
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.

## Tacoma Art Museum

Planning field trips over the summer is THE BEST. It’s easy to take care of a few e-mails and phone calls in July, and then POOF LIKE MAGIC suddenly it’s October and you’ve got everything squared away for a rawkin trip.

Today both of Wildwood’s HCP classes headed down to the The Shape of Things tour at the Tacoma Art Museum. It’s awesome going on field trips with Ms. Stock because we get to nerd out with all of our baby nerds. I also love seeing my former students now that they’re all grown up. And our trip was double-great because we had a TON of family members join us.

You know what else was fantastic? Everything and everyone at the Tacoma Art Museum. Their pre-and post-trip curriculum is SOLID. My favorite museum-going tip was to use “game show hands” to gesture toward artwork, rather than pointing. Yesssss.

We had a chance to explore geometric and organic shapes with watercolors, and then we headed into the gallery.

Our first stop was Richard Rhodes’ “stone wave.” It was suuuuuuper mathy. It made me think of Vi Hart’s work with hyperbolic dried fruit. Man, do I love Vi Hart.

My other favorite part of the trip was stepping into a portrait exhibit and BAM seeing a Chuck Close painting (Lucas, 1991). I’m a HUGE fan of last year’s Face Book, and it was amazing to see one of his pieces in person. My third graders kept saying, “He’s the guy whose book we saw in Seattle Public Library last year!”

The education coordinators were able to give us half off for our tickets. We would not have been able to go had they not made this funding possible, so we are VERY grateful for their support.

My only regret is that we weren’t able to time our visit with a children’s book illustrator exhibit. I’ve had the chance to see an Eric CarleÂ show and a David Macaulay exhibit, and they blew my mind. BLEW MY MIND. Maybe next time, though.

Because we will absolutely be coming back.

## Depth of Understanding in Math

The first few days of school in September are precious. You’re setting the tone of your community, establishing expectations and routines, and keeping your fingers crossed that you’ll be able to squeak some content in along the way.

I’ve noticed that a lot of beginning-of-the-year activities center around literacy. In a sense, that’s fantastic, because high-quality children’s literature has an incredible power to bring people together. But I can’t shake the niggling feeling that yet again, math receives the short end of the stick.

After years of gentle coaxing from colleague Siobhan Chan (you’ll hear plenty about her in the year to come, I assure you), last fall I committed to starting my year using The Art of Problem Solving from Teacher to Teacher. The Teacher to Teacher curriculum has its flaws, and it hasn’t been aligned to our district and state standards in a bajillion years, but I have yet to find a better way to kick off math than with The Art of Problem Solving (I refer to it as AoPS in my lesson plans, but I don’t know if that’s an official acronym).

Last year, I launched AoPS at the same time as Math Minutes (again, a practice not without its flaws, but my students ADORE it, so I’m willing to concede the three minutes of class time it takes, start to finish, including transitions). I struggled with a way to share with my students that although Math Minutes DID place a focus on speed, they couldn’t let it hamper the work they were doing to deeply understand problems. So I came up with this visual:

While explaining it, I used hand motions to indicate that understanding was the biggest, most vital piece of our work in math, then we assure accuracy, then we strive for fluency. It guided our practice throughout the year, and they emerged the most successful class of mathematicians I’ve had in six years.

So this year, based on the success I saw in taking the Gallon Man activity to the next level, I decided to give more ownership to my kids with these three levels of understanding in math. I redid my introduction lesson, providing this as a metaphor:

Understanding: This is the whole ocean. Nothing further can happen until we get here. If we’re not there yet, that’s fine, because at least we know what we’re striving for â€” our understanding is the most critical piece.
Accuracy: Kelp and other seaweed will die if it’s out of the water. Our accuracy is meaningless unless it is grounded in our understanding.
Fluency: If we work on our accuracy in a dedicated way, fish and other critters will come to live among the seaweed. It often happens naturally, but we can use strategies that improve conditions for fluency to flourish.

Then, students created their own representation of the three levels of understanding in their math notebooks. They provided remarkable metaphors, and also gave me insight into their thinking. I’m not really permitted to post student work on a non-district site, but you can view the work of everyone whose parents signed a release at our Artsonia site. So I’ve cropped a lot of these and removed student names, etc.

Many kids drew something very close to my example, which was totally fine.

And some started with my basic example, but took it a step in a different direction. Behold, two representations that take place on the savannah and on a farm, respectively.

And then, some of my students blew my mind. I didn’t have them write their explanations, as this was our first activity of the year and I wasn’t ready for that piece. I did record some of their comments, though.

Although I’m all for partner collaboration and I don’t mind if students’ work is similar, I was concerned that my CLD student (CLD, or Culturally & Linguistically Diverse, is the new, politically correct way to refer to ELL or ESL students) couldn’t explain his picture, while the person sitting next to him had an extremely similar representation and could explain his. This was a signal that I need to follow up with my CLD gentleman.

I’m excited to see what comes up next week in math! I always love comments and suggestions!

## Landscapes from Junk

Look!

It’s Monet! But these pictures are made from bits of rubbish! They reminded me of the work we saw in Here Comes the Garbage Barge.

I learned about the artist, Tom Deininger, from CRAFT, who learned about him from Nag on the Lake, who learned about him from Twisted Sifter.

Pondering this medium for our upcoming Pop Art unit…

## Olympic Sculpture Park, revisited!

When we went to the Seattle Art Museum in spring of 2010, we had a chance to see some of the pieces at the nearby Olympic Sculpture Park. One of the works that caused a lot of conversation was “Untitled” by Roy McMakin:

The black chair looks like one of the plastic ones you can get at WalMart, but it’s metal, just like the white “paper” box.

When my significant other Toby was in San Francisco for WordCamp last weekend, he sent me these neat pictures. Look familiar?

This last one is designed to look like what giant computer servers sometimes look(ed) like.

Thanks, Toby!

## DIA Highlights!

I’m constantly amazed at the quality and sheer volume of work in the Detroit Institute of Art. The highlight of my day was definitely the iPad interactive guide to the Diego Rivera Detroit Industry mural. I’d learned some about the meaning and symbolism in the mural in the past, but the effort and detail that went into this new guide gave me chills. That alone was more than worth the price of admission.

Here are some of my other favorites. I’ve included myself or other visitors to show you the scale of the art, not just because we’re so beautiful.

I’ve had Audubon on the brain because of his connections to Gary Schmidt’s brilliant Okay for Now. **SPOILER** I asked a docent if this print was a plate that was removed from a folio or a book, and he said that’d be something I needed to ask the curator. I don’t know how to contact a curator, but you can bet I’ll find out!

We studied Andy Warhol briefly in class both last year and the year before. This self-portrait is on loan. As you can see, it’s worth pondering deeply.

RIght across from Mr. Warhol was this lovely ClaesÂ OldenburgÂ sculpture. I love that it’s made of wood.

We talked last year both in art and just during literacy about how artists make objects larger to show that they’re supposed to be closer to the viewer. I think this piece makes that point really well, and I love how huge it is.

Another Claes Oldenburg creation, this one featuring a drawing of a car that then has a plastic model laid on top of it.

In one of the hallways of glass cases, they had a bunch of marionettes displayed. These were used in a production of 20,000 Leagues Under the Sea. They have to switch out the marionettes every six months because they’re fragile and sensitive to light.

Fox! They had a special exhibit of animal prints and drawings, including some of the original illustrations to Edgar Allen Poe’s “The Raven.”

Embroidery on comic book covers!

Close-up of the embroidery.

I couldn’t find any Chihuly glass on display, but I did see this amazing contemporary glass sculpture.

That’s about all I have energy to share with you right now! I hope you enjoyed this little peek into some of the amazing items at the DIA. I miss you, ladies and gentlemen, and I’m so excited to start learning with you again in less than a month!

###

## DIA Museum Trip!

If I had a travel budget to take my class around the world, you can bet a big part of our visits would be spent in museums. Art is such a tremendous way to learn about history and the world around you, and I wish we could spend time close to the masters more often.

I’ll do my best to document my trip today to the Detroit Institute of ArtÂ and post it here. The DIA is one of my favorite museums in the world (The Henry Ford is undoubtedly the best, of course, and I also like the National Museum of Scotland and the National Gallery of Art in DC), and going there was about the only thing I told my parents I REALLY wanted to do when I came back to Michigan this summer.

Here are a few pieces by artists we’ve studied that I’m REALLY excited to see.

And no visit to the DIA would be complete without an extended visit to the jaw-droppingly magnificent Diego Rivera mural (It’s the one you’ve seen in the Chrysler Imported from Detroit commercial).

Rad pictures hopefully to come tomorrow!

## New OK Go video!

Pretty much every single OK Go video has made it into our classroom in some way or another, whether we’re talking about Speed Stacks…

Rube Goldberg machines…

And now I can see this video being used for (among other things) discussions of lateral and radial symmetry! Amazing!