## 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.

## Exit Post-Its for Calculator Mini-Lesson

I try very hard to make my supply list clear, concise, and simple. But I still wind up with kids bringing in calculators and protractors and compasses. I don’t mind students using calculators on many classroom projects, but I do like to have a mini-lesson for appropriate calculator usage before I wind up with students trying to spell out BOOBS on their screens.

I usually answer questions about what the different buttons mean. This year I explained that calculators are often used for finances, so we don’t usually use the percentage key, the square root key, or any of the memory keys. I also clarified that fractions are expressed as decimals on most four-function and scientific calculators.

This year, I had my students jot their learning on a post-it note before we left for lunch. Here are some of their insights, annotated with my responses.

Probably the biggest surprise for me was how many kids had their minds blown by the fact that calculators don’t represent fractions the way we’re used to seeing them in class.

Some students realized the limitations of calculators.

I’m pretty good at deciphering what students are trying to communicate, but if I really can’t understand, I let them know.

Some students focused on the practical expectations we discussed, such as appropriate calculator usage.

And then there were the notes that alerted me that I’d need to follow up with a few students.

The following two students are in their second year with me, so I felt comfortable pushing their thinking further, as well as admitting a lack of mathematical clarity of my use of the word “random.”

I originally taped the post-its to notebook paper so I wouldn’t have random sticky notes floating around my tote bag, but then I took the opportunity to give my kids feedback. What forms do you find useful for exit slips and reflections?

## A Day of Assessing

SoÂ Seattle teachers are still protesting the MAP. I don’t feel like I have enough information on the MAP to commentÂ knowledgeably yet, but I can take you through a day of mid-winter testing in my classroom. I don’t know any school that would let media in during that time, so here’s an opportunity to see what’s actually happening over the course of an ENTIRE DAY when teachers say they’re “testing.”

As a reminder, I teach in a 2nd and 3rd grade highly capable class. My students’ stamina for testing might be slightly higher than comprable gen ed classes.

8:20 AM: I arrive at school. Prepare classroom.

8:30 AM: Receive Gates-MacGinitie test bag from school assessment coordinator.

8:45 AM: Open doors, welcome students. Students begin bell work.

8:50 AM: Bell rings.

9:00 AM: Attendance to office. I check in with students, look at planners to see what they read last night.

9:05 AM: Ticket to Recess (math computational review). Students fill out planner.

9:15 AM: Class meeting. We go over the day’s schedule, nominate Wildcat Leaders, etc.

9:30 AM: Body break, usually yoga or a Gilbert & Sullivan tongue twister, led by student.

9:35 AM: Students move desks into testing positions, sharpen pencils.

9:40 AM: Math District Course Assessment (DCA) passed out. I read directions out loud to students.

9:50 AM: Brain Dance.

9:55 AM: Students begin Math DCA. I read all 2nd grade problems out loud. I finish correcting previous day’s DCA (the DCA has four parts)

10:20 AM: Brain and body break.

10:25 AM: Students return to Math DCA, resting or reading when they’re done. I collect tests from them individually to make sure they didn’t skip any questions.

10:50 AM: Students wash and pack up for lunch.

11:00 AM: Lunch.Â All food comes freshly wrapped in plastic. Which is another story for another day.

11:25 AM: Recess

11:50 AM: Pick students up from recess. They finish Ticket to Recess upon returning to class.

12:05 PM: Students come to carpet spot, we read a chapter or two from The Shadows.

12:20 PM: Pass out Gates MacGinitie assessment. Read all the OFFICIAL DIRECTIONS to 3rd graders. 2nd graders work on independent reading or writing. (The directions are pages long. Although not as long as the MSP directions.)

12:40 PM: P.E.

1:10 PM: Transition from P.E. back to academic work.

1:15 PM: 3rd grade students begin Gates MacGinitie. I give F&P Benchmark assessments to 2nd grade students.

1:50 PM: Brain and body break. I grade and students correct Ticket to Recess.

2:00 PM: Recess.

2:25 PM: Students return from recess, fill out their weekly report (daily reflection) and put homework, planner, etc. in their backpacks.

2:40 PM: Students finish Gates MacGinitie. I give F&P Benchmark assessments to 2nd grade students.

3:00 PM: I collect Gates MacGinitie assessments and put them back into the official testing bag. Students pack up and stack up their chairs.

3:10 PM: I give students hugs and handshakes, and we remind each other to “Be well, do good work, and keep in touch.”

3:15 PM: We leave class 5 minutes before the bell rings because I help with safety patrol.

3:20 PM: Dismissal bell rings.

3:35 PM: Put Gates MacGinitie assessment bag into testing coordinator’s mailbox.

3:50 PM: Contracted teacher hours end.

This year I completed my district testing in record time â€” four days of testing that lookedÂ similarÂ to the day detailed above.

Thoughts? Questions?

## Pathways to the Common Core: Writing PD Documents

Tonight is the second book study Twitter meeting for Pathways to the Common Core: Accelerating Achievement.

As a member of the FWPS CC Transition Team, I have a few documents that I think might be useful to districts trying to disseminate information about the standards.

For the three types of writing (K-5), here’s a concept sort I made using definitions, book covers, and writing exemplars from CCSS Appendix C.

Download it as a Word document here:Â ConceptSort Modes of Writing.

Additionally, we’re going to give teachers time to explore writing resources by doing a jigsaw WebQuest.

Download it as a Word document here:Â WebQuest Modes of Writing.

I’m posting these because I assume some of my book study peepz might want to see them. If you use them, please acknowledge somewhere that they were designed by MOI!!! Shannon Houghton!!! for Federal Way Public Schools.

Another cool thing our district did was put together an “Intro to CCSS” video. Check it out here:

Send a note my way in the comments if you found any of this useful! Godspeed!

## Creating Fancy Scanable Assessments!!!

Word on the street is that they’re going to permit us, the lowly elementary teachers, to make our own scannable assessments this fall!!! (Middle school and high school teachers have already been able to do this for a year.) In preparation for this, I’m starting to scan some social studies items so my students can be assessed on Document-Based Questions. But I really didn’t know what to do, step by step, and since I use a non-district-supported Mac, I couldn’t go to my IT department. I mean,Â I’m COMPLETELY AWARE you can just open the PDF then take a screen capture of the image you want, but I wanted to preserve the quality of the scan as much as possible.

So if you’re in the same boat as me, here’s a step by step guide to scanning your current hard-copy assessments in and getting them ready to be turned into a Pinnacle assessment.

1. Scan in each page of your current assessment. If you can scan them in as JPGs, then you’ll just be able to crop the image out of each page, then re-save. Mine were scanned in as PDFs, so there are a few extra steps.

2. Open the PDF in preview.

3. Use the selection tool to capture the image you want to save. Go to Edit, Copy.

4. In the File window, open “New from Clipboard.” This option won’t be available unless you copy your image!

5. Go to File, Save As.

6. Make sure you change the format of your document from PDF to JPG.

All done! Not too bad, if you didn’t have to spend 384925671254 minutes trying to figure out how to get a high-quality image. That’s what I’m here for friends, asking the stupid computer questions so you don’t have to.

## Book of the Week: Big, Bad, and a Little Bit Scary

Every Monday, I highlight a book from our school bookroom along with lesson plan suggestions. I hope you find this useful, and please leave a comment with any suggestions or additions!

We have two copies of this book, in case you want to develop a team lesson around it. It’s guided reading level P, so it’d be perfect to use as a formative assessment for end-of-3rd-grade standards (Federal Way 3rd graders should be at an instructional level of O-P by June).

Each poem is by a different author, and at least three of the poems meet the cognitive rigor detailed in Common Core Appendix A. I’ve copied “The Alligator,” “The Eel,” and “The Barracuda” into a document for your shared reading pleasure.

On an unrelated note, you should definitely take a look at Zahares’ website, which includes a pretty impressive body of work. If I had unlimited funds, I’d get this print for our classroom. They feel like super-color-charged versions of art deco era WPA posters.

There is aÂ CAFE menuÂ included with this mentor text, and Iâ€™ve highlighted these as suggested lessons:

• Check for understanding.Â Remind students that although many of the poems are short, it’s still important to pause and make sure they fully understand what was read. One reason this is particularly important is the use of figurative language. If a student reads too quickly and is somewhat familiar with the animal featured, they may assume some qualities, such as “They’ll strip off your flesh like you’d skin a banana” (from Dick King-Smith’s “Strippers”) can be taken literally.
• Determine and analyze authorâ€™s purpose and support with text.Â November’s literacy focus of the month at Wildwood is author’s purpose, so I’ve been a bit fixated on this skill lately. Each of the poems (particularly the three I shared in the link above) are written in a distinctly different style, each of which seems influenced by the animal that’s the subject of the poems. Talk about the word choice, rhyming patterns, and phrase length in each of the three poems. How did the author’s choices change the mood of each poem?

Please add any lessons or supplemental materials to the book bag so future teachers can utilize your good thinking!

Comments and constructive feedback are always welcomed. Please let me know if these lessons were useful in your class!

###

## Author’s Purpose Performance Task

Wildwood’s literary focus of November and December is author’s purpose, so I used some of the ideas I got from our district’s Standards-Based Assessment team.

For the fiction task, students are picture book publishers trying to convince elementary school teachers to purchase books for their lessons. For the nonfiction task, students are interns at National Geographic trying to score a top photographer to shoot images for a new nonfiction text. Students have a variety of ways to show their understanding of both the surface-level author’s purpose as well as their deeper themes or messages.

I designed this assessment for my 2nd/3rd GATE class, but I think it could be modified for 4th and 5th grade just by changing the text grade levels. I’m basing the end-of-the-year Fountas & Pinnell grade levels off district standards, with an eye toward our future adoption of Common Core Standards. If your students aren’t ready to be assessed at the end-of-the-year reading level, no worries — just give them more appropriate texts.

Here are the books I’m using for the fiction task. I picked books we had multiple copies of in our school library, so I could get a few extra copies checked out from the public library and then have enough for my whole class.

2nd (Guided Reading Level L-M)

• Alexander, who’s not (do you hear me? I mean it!) going to move, Judith Viorst (M)
• Barn Dance!, Bill Martin (L)
• A Chair for my Mother, Vera B. Williams (M)
• Cinderella’s Rat, Susan Meddaugh (L)
• Galimoto, Karen Lynn Williams (M)

3rd (Guided Reading Level O-P)

• Animal Snackers, Betsy Lewin (O)
• A Bad Case of Stripes, David Shannon (P)
• Legend of the Bluebonnet, Tomie DePaola (O)
• Mrs. Katz and Tush, Patricia Polacco (P)
• Sam Johnson and the Blue Ribbon Quilt, Lisa Campbell Ernst (P)

4th grade would use level S-T, and 5th grade would use U-V.

There are rubrics included with both the fiction and the nonfiction tasks. Download and enjoy; I always appreciate comments and feedback!

Author’s Purpose Fiction Performance Task â€”Â Book Publisher

Author’s Purpose Nonfiction Performance Task â€” National Geographic

## 3rd Grade Geometry Unit Practice

After the positive reception from my students about our Uno’s Garden review activity for estimation and multiplication, I decided to create a similar activity to practice the skills from our geometry unit.

You can see our district power standards here. I’ve modeled the activity directly from the state standards, though, because there are a few holes. Also, looking to the future, here are the geometry Common Core standards. I linked each of the problems to Barbara Kerley’s great biography, What to do About Alice?

We’d been reading So You Want to be President, and I remembered this image from Kerley’s book:

The couch! We could find the perimeter of the couch! So I developed a set of six questions related to the book, posted them around the room, and had students move from question to question at their own pace. Because we’re a 2nd/3rd grade class, there are questions at a variety of difficulty and depth of knowledge to permit everyone some successes.

You can see the questions and my answer booklet below (I always print it on special paper because students have told me it makes the activity feel more like a quest or a scavenger hunt rather than just skills practice).

WATdoALICE

Please let me know if you found this lesson useful! I’ve found it to be a much better alternative to a straight-up assessment.

## 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…