# Category Archives: Uncategorized

## Can Writing Styles Be Boiled Down to Statistics?

Twas the week before Christmas Break, when all through the school, students were complaining, and trying to do new content would make me a fool… so we did something kind of interesting in my statistics class that was a cool application and reviews a lot of great stuff with inference testing. Inspired by this book called Nabakhov’s Favorite Word is Mauve by Ben Blatt, a super cool statistics-based analysis of literature, and this post on the Stats Medic, “Does Beyonce Write Her Own Lyrics?”. The basic questions are **“How can we use basic statistics to examine and tell apart writing styles? What do statistics about your own writing say about your style?”**

### STEP 1: WHICH OF THESE AUTHORS ARE THE SAME?

To start, I gave them a page (available here, spoilers down below) from three different books (page 154 from each book, thanks Siri for the random number!). I told them two of these were written by the same author and one was written by a different author. How could we tell who wrote what? I told them the story of Hamilton, Madison and the disputed Federalist Papers to whet their appetite as a “real-world” example of this, but to be honest, they didn’t care about this, but were VERY intrigued just by the puzzle of figuring out which authors were the same.

And the statistics began, but not from a canned dataset that they ran pre-prescribed tests on – in fact, I was scrambling that week and hadn’t tried anything myself. I had no idea this was going to work! * What things could we measure about the text to tell the difference between them?* Some suggestions were too difficult to measure (i.e. tone), some had nothing to do with the writer (i.e. how many lines there were on the page), but others seemed easy to measure and perhaps distinctive of a writer (frequency of commas, length of words etc.). The students were skeptical that those things could distinguish authors, but we went after it anyway! We spent about a half-hour counting various things about the text, collected them on a document and then highlighted which two of the three were roughly more alike on each measure:

Of the 16 things we measured, 8 were the same between writers G and U (and 2 others were pretty much the same between all 3). Here come some interesting statistical questions… Why might one random page be off *(one sample could be skewed for no reason other than randomness)*? What’s the advantage and disadvantage of measuring a bunch of things *(more things = more opportunity for random associations, but more opportunity to see a pattern)*. Which of these differences are “significant”?

We then spent about a class on that last question. Given that we know a chi-squared test and a t-test, how could you use those on these things we measured? We did this in R, and I can give some details about that for anyone interested, but the interesting part here is getting kids to imagine how you format data so that you could use a statistical test. What do you stick in about the sentence length in a t-test? How could -ly adverbs be a chi-squared test? Are either even appropriate here? (Meh, mostly… )

**THE REVEAL:**

Page G is from The Causal Vacancy by J.K. Rowling.

Page U is from The Cuckoo’s Calling by Robert Galbraith.

Page S is from Big Little Lies by Liane Moriarty.

Wait… what? Those are three different authors. NOT SO FAST! Robert Galbraith is actually a pseudonym for… J.K. Rowling! (I wish I had played that up a bit more) So our statistics worked in a way – there were more similarities between G and U than the other combinations. So even when J.K. Rowling was writing under a pseudonym, her writing style was similar **Cool!!!!!!**

### STEP 2: WHAT DOES YOUR WRITING STYLE LOOK LIKE?

Now, I wanted them to do something similar with their own writing. They had just written a joint paper with a partner, and I wanted them to see * if their joint paper more closely resembled their own writing or their partners* HAHAHAHAHAHA. They were hilariously sheepish about this idea, which told me immediately who had done what 🙂 (but it was all in good fun).

Enter a new tool, Count Wordsworth, an online tool that automatically measures a WHOLE BUNCH of statistics about any text that you paste in there (at which point they got mad at me because they had done so much by hand for the pages of the books, but they’re always mad at me for stuff like that). For example, here is just part of the output when I put in my teaching philosophy from my teaching portfolio:

I had them all put in a recent English paper and then find the * THREE biggest differences* between their paper and their partners. Again, a bunch of fun data questions – do the quotes in the paper mess things up? How about the number of words? What about the topic (English vs. a lab report)?

Then, once they had discovered the three biggest differences, I had them put in their joint paper and try to figure out whose writing style is more closely resembled. This class was a blast, and once they finished this, they were so curious so just kept exploring… Some kids put in their freshman year papers, some put in the headmaster’s emails etc. Lots of fun curiosity!

### STEP 3: HOW DOES A PROFESSIONAL STATISTICIAN DO THE SAME SORT OF ANALYSIS?

Lastly, we read a short 10-page segment of the book I mentioned in the beginning,Ben Blatt’s Nabokhov’s Favorite Word is Mauve, specifically a chapter called “Searching for Fingerprints.” It was fun to see what a professional statistician does and we talked about how he could possibly measure some of the things that he did with the computing power we have nowadays.

*Good stuff! Happy Holidays everyone!*

## Rock, Paper, Triggers

I played a quick, but fun and mathematically rich game in precalculus the other day that I thought I’d share. Let’s call it **Rock, Paper, Triggers **for now, (it’s kinda like Rock, Paper, Scissors but with Trig functions) but if you have a better name, let me know.

Each person secretly picks a trig function (SINE, COSINE or TANGENT) for themselves, and an angle to send to the other person. Then, once ready, both reveal and each person thinks about…

**TheirFunctionOf(**theAngleSentToThem**)**

Whoever’s value is higher wins. No need for exact values, just figure out which one is bigger (and DNE automatically loses). So for example:

PERSON 1:

sin()

269°

PERSON 2:

cos()

190°

Person 1 has sin(190°) and person 2 has cos(269°). Well, both are negative, but 269° is so close to 270° that cos(269°) is a little less negative. So person 2 wins!

This was really good for number sense (no calculators), for thinking about what values of the different functions are possible, and where those values are on the unit circle.

## Dear Community; Sincerely, Math Teacher

*Our school has a bi-weekly community newsletter that goes out to the school, alumni, parents and whoever else wants it. Often, a teacher writes a little introductory letter about their philosophy of teaching or their journey to the profession. I wrote for this week’s newsletter, and got a great reaction from a lot of lay people (i.e. non mathletes) so I thought I would just share it here too. The ideas in it should be familiar to the MTBoS, so get your head nod ready…*

Dear St. Andrew’s Family,

When I meet new people out in the wild, I can usually predict their reaction when they hear that I’m a high school math teacher. Often, they immediately express to me how much they hate math. I have to admit I think it’s rather odd to tell someone you just met how you loathe the very thing to which he has dedicated his life’s work. (“You work for the Red Cross? Yeah, I absolutely detest charities.”) Another, even more common reaction is to tell me just how awful they are at math, taking pride in how colorfully they can describe the extent to which they struggled with the subject in school. Again, I find this a bit odd. Would we boast of our inability to read or write to an English teacher? Why is it not only okay but apparently a point of pride to be “bad” at math?

I love math. To me, it is a beautiful, complex web of ideas that can delight us with a puzzle, or shed light on the world around us. How could the math I love be a groan/panic/boredom inducing menace for so many people? The only resolution to this paradox that I can see is that the math I love and the math they hate are really two totally different entities. Without a focus on beautiful ideas, math’s procedures and operations lose their larger meaning and purpose, and math becomes a boring, repetitive, unconnected series of challenges that demand rote memorization without real understanding. This lack of connection to the deep conceptual backdrop of mathematics is not only the reason math haters don’t enjoy the subject—it’s also the reason they struggle mightily to learn it well.

As a math teacher, the painful part of this disconnect is that I believe it’s all our fault. The way math is taught often creates an oppressive and obfuscating imposter subject.

I aspire every day to fight against this imposter math, and to connect my students to the idea-rich math that I know and love. I try to make every problem we tackle in class or in homework one that a student cares about solving, whether by framing the class with a running conceptual thread that makes learning feel like unearthing the next piece of a mathematical mystery, or by investigating an application of real import, or by just engaging with a curious puzzle. I try to never tell a student something that they can figure out for themselves, because math is about discovery and exploration. Newspapers don’t print already-filled-in crossword puzzles; it’s not the answers but getting to the answers that’s the point. And I try to help students become vulnerable enough to take risks productively and make mistakes confidently, so that the more difficult, but more satisfying, work of idea-making (as opposed to procedure-regurgitating) is accessible to them.

As I write out these aspirational teaching goals, I am struck by how often I fail to meet them, and, how when I don’t, I am contributing to the creeping oppressiveness of “imposter math” by default. But it’s this awareness of my sworn enemy that keeps me engaged and excited about my profession every day.

Even if I can’t lead every student I teach to fall in love with math the way I have, I hope that at the very least I am connecting them with math’s big ideas in some real way. I like to think I am helping to rear a generation of students who won’t, twenty years down the road, regale every stray math teacher they meet with stories of how much they hated nasty old mathematics.

All the best,

Bowman Dickson

Mathematics Faculty; Cross-Country & Swimming Coach

bdickson@standrews-de.org

## Data Driven: Authentic Assessment and a Data Based Business Case Study

What is **authentic assessment** in the math classroom? It’s probably not a math test. Tough to admit, as I give lots of math tests, but a test is so limited, so contrived, so singular. The most authentic assessment I have been part of in the math classroom was our culminating project for Data Driven this summer – **a business case study presented to people in the business world.**

A friend of mine from college who now works for a predictive business analytics company ran a case study on my students. The case was for **a bagel store that wanted to expand** – they had data on the profit of their current stores over time, and data on features of the current stores. In teams of four, students had to advise the bagel company on where the company should build 10 new locations, and what the layout should be. My friend served as the lead of the company’s expansion team – the students had a halfway call with him and could email him at any point during the week with questions or requests for data. At the end of the week, students presented (via Skype) their recommendations and defended them with questions.

**HOW WAS THIS AUTHENTIC?**

- We learned a billion things and amassed a ton of data analysis tools this summer – instead of being directed what to use where,
**students had to sift through their knowledge**to figure out what was appropriate. Though they received an initial prepackaged dataset, the problem was wide open and had very little hand holding. If they wanted to use census data about median incomes in zip codes, they had to go find that data, clean it up and attach it to the given dataset before they could use it. - All the math that they were doing was supporting a
**genuine and interesting, multifaceted problem**, instead of being motivated by just being a question on the test. If they needed to do a multiple linear regression, it was because they wanted to figure out something about the data, not because a question asked them to do a multiple linear regression. -
In addition, it was a problem that forced them to

**translate their mathematical knowledge into human decisions**. They had to tell the story that the data was presenting, had to make choices that didn’t have a “correct” answer, and had to defend everything they were doing in a way that a naive non-math outsider could understand. - Presenting to an
**outside audience**forced them to be as prepared as possible, and also taught them a lot of lessons about communication! I wish I had taken a picture of one group when they were on a conference call with my friend. They were pacing around the room, hands on heads, brows furrowed, goofy smiles from feeling awkward – so much more learning was happening than if they were presenting to me! I also just had to sit and watch them struggle through things, like explaining what a t-test was, during their final presentation, which gave me deep insight into the results my teaching. - There were
**many points of entry and many different depths**that students could take it. There were immediate things that anyone could do, and things that only a professional data scientist could have done, which made the problem perfect to test everyone, but give the students needing a bigger challenge a place to go.

**HOW WAS IT STILL INAUTHENTIC?**

- The
**data was fake**, the business fake, the audience fake. The advantage to this was that I could ensure that the math involved was the right level, and that the problem was doable, but perhaps this took something away from the motivation for the students. - There was no
**followup from the final result**. Wouldn’t this have been even more awesome if they were presenting to a real company, or community organization, that was trying to make a real decision? And then they could see what the company actually decided and see what the results were. - There were
**students in each group that didn’t contribute**. I don’t think anyone didn’t*want*to contribute, but it’s really hard to work in teams. I think that this exercise tested their collaboration skills, but perhaps didn’t assess every single student’s math skills.

## THE UPSHOT:

Though this course was unique in its format (long 4 hour classes, only 12 students, no curricular pressure) and did not come with grades, there is so much from this to take to my school-year classroom. How can I include more authentic assessments in my day to day classroom life? Assessments with **multifaceted, human problems** that motivate great math along the way; ones with **many points of entry** and many places to go; and ones where they have to **defend their decisions** to audiences other than me.

It’s important to remember that “authentic” is not a binary designation, so my goal is to add pieces of the above to my normal classroom assessments one step at a time.

## Data Driven: A Syllabus

As I start reflecting on the course I taught this summer, I thought I’d start by sharing my Syllabus for anyone curious. The course was a functional data course – the focus was more on being able to DO things rather than on abstract statistical work. We used data visualization software geared at businesses (Tableau), coded in R, conducted election polling, performed original research projects, wrestled over issues of data privacy, cracked codes, and put together advice for a business on how they should expand (amongst many, many other things). It was exhausting and awesome. More reflections to come!

(if that is too small below, here is a google drive link)

## Data Driven Day 1: Data Speed Dating & Dear Data

*This summer, I’m teaching a 5 week intensive course called Data Driven (course description) at this amazing summer program at St. Paul’s School in NH called the Advanced Studies Program. It’s an enrichment program for rising high school seniors. We are doing class 3-4 hours a day, 6 days a week for 5 weeks, with tons of time for independent work at night. The class is about creating functional data mavens – think statistics, plus data science, plus research, plus data ethics/privacy, plus cryptography, with a whole lot of reading, coding, writing, computing and interacting with the community along the way.*

**DATA SPEED DATING**

After a quick math-themed icebreaker, we started our data class this summer with a few data themed get-to-know-you activities, the first being data speed dating. Each student picked a categorical variable and a quantitative variable that they wanted to collect from every student in the class. They then sat across from each other and “speed dated” to collect the info from each person in the class.

It was nice to knock out the kind of dumb and easy idea of variable types in an icebreaking activity, and it was great that every single student had a conversation with every other student in the class (only 12 students).

Then, I paired them up and each pair had to **pick one of the sets of data to present visually to the class**. I wanted to get them started on culling the most interesting data from a data set, picking appropriate visualizations, and translating data for others. One group did this kind of funny infographic describing how many pairs of pants were owned by people who preferred certain movie types. Problems with the visualizations, of course, but interesting nonetheless (and hey, it was the first half hour of class). In retrospect, I wish I had explicitly said * “Combine TWO of your pieces of data in a visualization”* because I think that would have been a much more interesting intellectual challenge (and would have led to a bunch of silly things!).

**DEAR DATA**

Then, I introduced our homework for the night, which fell on similar lines. It was based on the project Dear Data by two data scientists Giorgia Lupi and Stephanie Posavec. They picked a broad topic (like “laughter”, “books”, “thank yous”) at the beginning of a week, and each chose what data they were going to collect about that topic. At the end of the week, each turned their data into a beautiful visualization on a postcard, with the key on the back, and sent the postcards to each other (one was in London, one in NYC).

For my students, we picked the topic * “New Encounters,”* as they are all starting this program with a bunch of people they don’t know. They each brainstormed the data they were going to collect, and I gave them mini-reporter notebooks to carry around. From what I saw when they were working on them earlier tonight, some of the visualizations that the students did were just as beautiful as these professional data scientists (and some managed to collect 70-80 points of multidimensional data in a day and a half). Will post once I see them tomorrow!

## AP Calculus AB Skill Drills

I have had MANY requests for the actual files for my AP Calculus Skill Drills – a 5-10 minute start to class every day for a couple of weeks leading up to the AP Calculus AB exam. Below is the file. Know that it is fairly specific to my class – they are categorized based on my standards and we voted which standards to keep reviewing that day – but still should be a decent review for anyone if you want to modify. There are 10 days of review goodness, which according to the file, I started on April 9th a few years ago. Forgive any errors of course.

- Skill Drill PDF
- Skill Drill Word Doc (will show up as a file on Google Drive missing tons of stuff, but hit download)

Best of luck prepping kiddos for the exam soon.

<3,

Bowman

## Blogging About School Leadership for Klingspace

I have been quieter here than I normally would be during summer planning because I have been blogging at Klingspace, a blog run by the graduate school program from which I graduated in May. Below are the posts I have published there with a brief summary, if you are interested in reading about topics that may not be as math education focused as I usually am.

I am excited to rejoin a math classroom in the fall and hope to re-engage in the math education discussion on this blog that I am used to!

**5/22 – Structure Is Not the Opposite of Autonomy**– We shy away from procedures, structures and limitations in the name of creativity, but that structure can actually*promote*creativity.**5/28 – Keeping the Change: How > What**– Success naturally breeds resistance to change, which means we must be sensitive to the fact that our change-filled futures are challenges to our success-filled pasts. Give people time to process change.**6/4 – Teacher Observation: Informing Practice, Not Judgment**– The way most schools structure observations and evaluations make us see them as moments of judgment instead of opportunities to improve our practice.**6/11 – Have a GSA? Great! But It’s Probably Not Enough**– There are queer students at our schools who aren’t served by simply having a GSA. More generally, we should not assume that because we have programming for X type of students that it serves every student who identifies as X.**6/28 – Using “Creative Tension” To Communicate Change**– If leaders effectively show faculty the gap between their vision and the current program, faculty will be more likely to feel the need to move toward the vision**7/11 – Cultivating a Growth Soulset**– Just as we can always learn more with a growth mindset, we need to tend to our emotional intelligence with the attitude that we can always become more emotionally adept.**7/21 – The Case Against a Linearly Sequenced Curriculum**– Research about distributed practice suggests that studying something with space between is always more effective than studying it for the same amount of time uninterrupted. How can we incorporate this finding into our curriculum design?**7/29 – TBA****8/15 – TBA**

## Tuesday, November 13, 2012

I am a math teacher at a boarding high school right outside of Amman Jordan. This is a day in my life.

*(read here to see what this is all about)*

## Tuesday, November 13, 2012

**7:00 – Wakeup.** The nice thing about living literally 2 minutes (walking) away from classes is that my wake up time is a little later than everyone else’s. But as I walk out of my apartment, a student grabs me to unlock the storage room – the downside of living in such close proximity?

**7:30 – Breakfast.** Sometimes, I eat 19 meals a week in our dining hall, which saves a ton of time and money (Why only 19 you ask? Well, when you wake up at noon on the weekend, there’s really only time for 2 meals). Tuesday is bagel day which is my absolute favorite (ah the small pleasures in life)! This morning, a student asks me to tie their bow tie for them, which is actually a fairly common occurrence. I have to say, bringing the bow tie to our school has been one of my proudest accomplishments.

**8:05 – Class starts.** Except that I have two prep periods in the morning on Tuesdays, which makes life kind of nice. This year, because I am head of one of the dormitories, I only teach 3 classes, which makes for tons of prep time during the day (but lots of stuff to do in the evening). This morning, I made tests for my non-AP Calculus class and began to cobble together review materials for my AP class for our upcoming final.

**10:45 – 12:20 – Back to back to back classes.** I have three 45-minute classes in row, switching between non-AP Calculus and AP Calculus. Normally I find only having 5 minutes between classes stressful and exhausting, but today was pretty relaxing as my AP class was working hard on a packet of Related Rates problems, and my non-AP class was reviewing for a test the next day.

**12:25 – Advisee Lunch.** Two days a week, we eat lunch with our advisees (and every other day is formal, rotating assigned seating lunch – I have duty for one of those days). My advisees are four freshman and two sophomores from the US, Saudi Arabia, Jordan and Nigeria. They are an awesome group of kids, and a real breath of fresh air from the jaded older students (who are the only ones I normally interact with). I really love spending time with them, mostly because I feel like some of the things they say should be published in a book.

**1:05– Class meeting.** I’m associated with the twelfth graders so I trudge into the Lecture Hall with the senior class. I feel like my week is really filled with meetings. We have school meeting 3 times a week for 5 minutes and once a week for 45 minutes, class meeting once a week for 45 minutes and advisor meeting once a week for 45 minutes. Today, the class gave announcements and then watched a TED talk.

**1:55 – One more prep period.** That’s right, 3 prep periods in one day… I used this one to make reassessments for my Standards Based Grading system. Right now, I’m averaging almost exactly half of my students reassessing every day (I only teach 45 total, but still… making 2 standard checks each for 22 kids every day is ridiculous and takes forever). Luckily this is an end-of-the-term-my-parents-will-see-my-grade-soon phenomenon.

**2:45– Arabic Class.** Three times a week I take Arabic class, which they offer to the ex-pat faculty (a little less than half of our faculty is ex-pat, and about 15% of our student body is non-Arab). I love these classes. It is fun to be a student again, and we learn a lot. I’m in the most advanced level, so we usually just sit around and talk in Arabic for 45 minutes about really random things. Last year, I took class with the students too – I took 9^{th} grade Arabic – which was quite a trip. It’s funny to me that teachers are really the worst students. We don’t do homework, we’re always late for class, we forget about tests etc etc. Bust at least we’re enthusiastic?

**3:35 – Reassessments.** 23 students reassessed today, crammed into our math classroom, which fits about 18 comfortably. I find these times so stressful – I sit up front and correct their reassessments when they are done, but a line starts to build up and then I feel like students who are still taking reassessments take advantage of my attention being diverted to cheat. It’s frustrating and stressful, but I’m not really willing to give up the learning opportunities for many just because some people are complete jerks.

**4:45 – Faculty vs. Student Swim Meet.** Normally we have co-curriculars in the afternoon from 4:45-6. I advise the newspaper, and we meet once a week (which is an incredibly light load for co-curriculars at my school). But the co-curricular season ended last week, so this week we had a faculty vs. student swim meet! One of the boys in my dorm talked so much smack to me the night before, it was unbelievable… and then I completely crushed him in the water, muhahaha. Overall, it was very fun event, and one that must be repeated because we ended up losing to the students 75-72.

**6:30 – Dinner.** Again, my meal occurred at the dining hall. The food wasn’t very good, but I put up with it to avoid shopping, cooking and cleaning. Sometimes, I just don’t want to see students at night and get frustrated being there in the thick of it, but other times it’s kind of fun to be eating dinner at the table next door to some of your Calculus buds (I’m sure that’s how they think of me). This is when my day usually ends unless I have duty…

**8:00 – Meeting with a student.** One day a week and one weekend a month, I do evening duty in the dorm from 7:45 pm until 11:15 pm. Those days are long, and not much gets done during the duty time so you have to really plan well to get your work done. But even though tonight is not my duty, two students needed to schedule a makeup quiz so we did it at night. I was feeling sick because I have a sinus infection, so while the student sat at my kitchen table doing the quiz, I was lying on my couch with my hood over my head listening to RadioLab. My student must have thought I was nuts, but I guess that’s what they get for invading my house during chill time. Another student came at 9:00, so I didn’t really get time to myself until around 9:30.

**9:30 – Colbert.** Daily Show and Colbert come on at 9 and 9:30, which is awesome. I try to watch one every night. It’s sad, but it’s one of the best ways of keeping up with American pop culture.

**10:00 – Finish prepping.** I didn’t finish my test earlier, so I spent about 45 minutes putting the finishing touches and sending it off to our copy dude who prints our copies for us (amazing luxury).

**11:00 – Read.** I always read before I go to bed, every night, no matter how late. Right now I’m reading *One Hundred Years of Solitude*, which I’m liking enough, but is going really slow.

**11:30 – G’night.** I’m pumped because this is on the slightly early side for me.

*One of the best things about being a teacher is that whenever you had a bad day you get a chance to do it all again better, but one of the frustrating things is that whenever you have a good day, it’s almost like there’s no time to stop and celebrate your victory. Moving forward, onward and upward… a new day begins.*

## Math Blogger Initiation Week 4

**And the fourth and final installment of the New Blogger Initiation. Some great new blogs popped up, ones that I definitely will be adding to my Google Reader. Please, click below and comment away!**

**_________________________________________**

## Making Paper Airplanes | Making Paper Airplanes

Making Paper Airplanes @makingairplanes has a blog named Making Paper Airplanes. The fourth post for the Blogging Initiation is titled “Change is in the air” and the author sums it up as follows: “*Faced with a schedule change resulting in taking on a new, mixed-grade class a week into the school, I have to re-think my plan for this year’s math support class! It sure pays to be flexible…”* A memorable quotation from the post is: **“This isn’t quite what I signed up for, but it will be an adventure!”**

*–> My take: So many things about teaching feel so out of our control (the schedule, the students we get, the room we’re put in etc) that changes like this can be so frustrating! This blogger has quite a challenge ahead of shim (I don’t know if it’s a woman or man) and seems a bit pessimistic – the online math teacher community to the rescue! People have already given some great advice already. My advice: have the older students teach topics to the younger students. *

## Bruno Reddy | Mr Reddy’s Maths Blog

“Bruno Reddy @mrreddymaths has a blog named Mr Reddy’s Maths Blog. The fourth post for the Blogging Initiation is titled “Language Revelation” and the author sums it up as follows: *“I attend a real eye-opening training session on speech and language difficulties. There are 3 very short video clips of the training to help demonstrate what was going on.*

* I came to realise, through a very innocent activity that the trainer had us do, that I was getting it wrong for my pupils. Wrong in the way I interpreted their behaviour and wrong in the way I posed questions.”* A memorable quotation from the post is: **“Suddenly my mind was racing through the faces of my pupils who do exactly the same – they find it hard to look you in the eye, their movements are pronounced and they look pained when stuck for words.”**

*–> My take: It is great to see someone get excited about Professional Development – a great experience seems to be more rare than it should. I really like some of the conclusions Bruno makes from this activity, as language is a something I am intensely interested in as someone who teacher 95% students for whom English is not their first language. It just makes me appreciate how important communication is in math. Random question that the British vocab in the blog title reminded me of: some of my students here say “factorize” instead of “factor.” What’s that all about? Is that a British thang?*

## Nathan Kraft | Out Rockin’ Constantly

Nathan Kraft @nathankraft1 has a blog named Out Rockin’ Constantly. The fourth post for the Blogging Initiation is titled “Exploiting My Son for Math” and the author sums it up as follows: *“I use my son in pictures and videos to teach 7th/8th grade math.”* A memorable quotation from the post is:** “Over the last year I’ve been using him for all sorts of math lessons – many times under the guise that I’m spending quality time with him.”**

*–> My take: You have to watch some of the videos in this post. This kid is so cute! And the problems that Nathan poses are really interesting problems, totally fitting in the whole 3-acts type of lesson design. I am so intrigued by the first one I want to go try it out!*

## Tim Reinheimer | Asymptotically Cool

Tim Reinheimer @timreinheimer has a blog named Asymptotically Cool. The fourth post for the Blogging Initiation is titled “abstract misconception” and the author sums it up as follows: *“I believe a lot of students have difficulties with algebraic rules because they don’t have any connection on which to base the abstract. In short, I believe the real world could help this problem.”* A memorable quotation from the post is: **“I believe a lot of students have difficulties with algebraic rules because they don’t have any connection on which to base the abstract.”**

*–> My take: I like this small idea to help students with the idea of the distributive property, though the science teacher in me is aaaagck-ing at the mismatch of units. Some of the basic rules for math seem arbitrary (like order of operations) but arise out of little situations like this. I guess the trick is to find these situations to latch onto.*

## Paul Gitchos | Second Thoughts

Paul Gitchos has a blog named Second Thoughts. The fourth post for the Blogging Initiation is titled “Thank you, Mrs. F” and the author sums it up as follows: *“I’m feeling thankful that the majority of my students have had good training in working cooperatively in groups. In the post I acknowledge a colleague’s hard work.”* A memorable quotation from the post is: “**The most successful parts of my first couple days were due to the math teacher down the hall.”**

*–> My take: I usually express the opposite sentiment (I curse the teacher who didn’t really teach them what graphing meant) so I really love this positive post thanking a previous teacher for a job well done. It also made me realized how intensely satisfying a smoothly running classroom is. It feels like a waste of time to train students in things like that, but once they are trained, it is really worth it because it really facilitates learning.*

## Michelle Riley | A Year of Growth

Michelle Riley @mathwithriley has a blog named A Year of Growth. The fourth post for the Blogging Initiation is titled “Foldables and My Turn to Give Back” and the author sums it up as follows: *“I stole a few foldables, charts, etc. from other bloggers, and this shows the way I tweaked them to work for me. I also created a (very) simple foldable for kinds of angles and shared that as my first thing I have shared with others. This is an older post… first week of school caught up with me and I ran out of time and brainpower to post something new.”* A memorable quotation from the post is: **“First of all, I need to say a huge thank you to the blogging community for being so willing to share!”**

*–> My take: Michelle totally gets the blogosphere – steal and share, steal and share, steal and share! I have to be honest that I’m not totally sold on the idea of foldables yet, but I do teach seniors, and I would probably be far more into them if I had younger students. From what I can gather with no experience with them, these seem like great foldables to steal if you use them in your classroom!!!*