# Category Archives: Uncategorized

## 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!!!*

## Math Blogger Initiation Week 3

**Week 3 of the New Blogger Initiation! After three weeks, more than 90 people are still blogging. Awesome.**

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## Joe B | lim joe→∞

Joe B @forumjoe has a blog named lim joe→∞. The third post for the Blogging Initiation is titled “Everything is Mathematical” and the author sums it up as follows: *“I link to a new mathematical puzzle site called “Everything is Mathematical” and discuss the form of the content and how it will be useful. I then post my solution to the first problem, improving my Latex skills in the process”* A memorable quotation from the post is: **“I’m really impressed by the way Marcus du Sautoy presents the problem in an easy-to-understand way. There’s no pseudocontext here, there’s no anyqs.”**

*–> My take: Joe presents a really nice, accessible problem that could easily be used in the high school classroom – the question of how many palindromic numbers there are of a certain length. I love problems like this because I am totally biased to the application end of the spectrum in math in my teaching and I am looking for ways to introduce beautiful, rich, theoretical math into my curriculum. My favorite part of the post is that Joe makes a major error in his solution (one that I actually also made when I read the question) and graciously acknowledges this in in the comments. What a great model for students.*

## Joe Ochiltree | Brain Open Now

Joe Ochiltree has a blog named Brain Open Now. The third post for the Blogging Initiation is titled “Which Spawned the Title, “Brain Open Now” and the author sums it up as follows: *“Not sure if I’ve ever explained the name of this here blog. “Brain Open Now”, you can see it right up there. So, what does it mean? I’ll tell ya.”* A memorable quotation from the post is: **“This sounds suspiciously like blogging.”**

*–> My take: Great blog name, taken from a great Mathematician! I really like this little vignette. Side note: I have actually been subscribed to this blog for a while now, so I was a little surprised to see it pop up for this.*

## Ana Fox Chaney | Make Math

Ana Fox Chaney @AnaFoxC has a blog named Make Math. The third post for the Blogging Initiation is titled “Computer Multiplication” and the author sums it up as follows: *“I recently saw a video demonstration of “Egyptian Multiplication” in which the presenter described how both Egyptians and modern computers multiply using binary. It seemed so easy – I couldn’t resist the urge to take the technique apart and figure out why it works. Does it work with all bases? Is there a reason we don’t do all our multiplication that way?”* A memorable quotation from the post is: **“I like this because I talk a lot about multiplication strategies in my 5th grade classroom, modeling how multiplication works and what it means.”**

*–> My take: I really liked seeing Ana’s (Ana Fox?) thought process as she worked through Egyptian multiplication, comparing it to our modern algorithms in both utility and facility, and asking the all important question “WHY DOES IT WORK?” To be honest, I haven’t fully wrapped my brain around it yet, but it’s a great example of a perplexing problem that could be used with a wide age range of kids, one that grabbed me and one that might grab your students too, especially if you frame it in a mysterious, historical context. Also, Ana has ridiculously nice handwriting, something with which unfortunately not all teacher are blessed…*

## Mrs. W | Mrs. W’s Math-Connection

Mrs. W has a blog named Mrs. W’s Math-Connection. The third post for the Blogging Initiation is titled “Discovering and Teaching” and the author sums it up as follows: *“In this post, I write about how I let my students discover the rules for exponents and the question I used that got them thinking even more about dividing exponents!”* A memorable quotation from the post is:** “I’ve been using some more challenging questions and my questions are creating some incredible questions and discovery.”**

*–> My take: I like the idea of a parking lot for exit slips. Mrs. W has a nice way of organizing and keeping old exit slips, which might be helpful. I didn’t quite understand why it was necessary that a kid park their answer in their specific spot (as opposed to just handing it in) but I am all about all things that make the classroom run smoother, and this seems to be a routine that helps her students learn. She also has a nice aside where she talks about how she motivates the need for exponent rules.*

## Stephanie Macsata | High Heels in the High School

Stephanie Macsata @MsMac622 has a blog named High Heels in the High School. The third post for the Blogging Initiation is titled “When will we ever use this in real life?” and the author sums it up as follows: *“I wrote this blog post about how I address the constant “When will we use this in real life?” question. It is important to me that my students find the value in what I am teaching them, or at least to try my hardest to help them see the value in math. I also wrote about how I try to handle situations when a student has been told that it is ok that they aren’t good at math because their mom (or dad or brother or sister or someone important in their life) wasn’t either. “* A memorable quotation from the post is: **“It doesn’t matter what type of job you have or what is going on in your life…problems arise and you have to be adept at finding solutions to those problems.”**

*–> My take: Stephanie shares a lot of the same frustrations that we all seem to when faced with cultural acceptance of “being dumb at math” and reducing math to a utilitarian affair. The only thing that I think she leaves out is the idea that we should study math because math is BEAUTIFUL! There is a nice paragraph in this post where she talks about her view that anyone can learn math. Because of that, I can speak for everyone when I say that Stephanie, we’re glad to have you in the classroom!*

## Katie Cook | MathTeacherByDAY

Katie Cook @kjgolickcook has a blog named MathTeacherByDAY. The third post for the Blogging Initiation is titled “Why do we have to learn this?” and the author sums it up as follows: *“Why do we have to learn how to do geometry proofs? Why do we even bother teaching geometry proofs?”* A memorable quotation from the post is: **“No one is sitting in 9th grade English class asking their teacher, “why do we have to learn how to read and write?” (or maybe someone is…I actually wouldn’t be that surprised)”**

*–> My take: I think Katie’s answers to this question are adequate, but she seems to struggle with something that really bugs me too – how do we teach curricular objectives on standardized exam well if we don’t really believe in them? I think that Katie uses a few too many external reasons though for motivating the math in her course, and I think it would be better if we could comment for her on some reasons why geometric proofs are worth teaching in their own right. Come on people, answer her call for ideas!*

## Scott Keltner | Good for Nothing

Scott Keltner @ScottKeltner has a blog named Good for Nothing. The third post for the Blogging Initiation is titled “Remainders: Not Just The Rest of the Story” and the author sums it up as follows: *“Bar codes are a peculiar oddity to me, especially those newfangled QR codes (which I’m still trying to research how to decode and encode manually without the use of a camera). This post makes examples of UPCs and ISBNs and the structure that makes them what they are, including the algorithms behind each. This post shows a real-world application for remainders when using whole numbers to compose a code structure. I’m still trying (unsuccessfully, at present) to find a real world application for remainders with polynomial long division, though.”* A memorable quotation from the post is: **“I created (what I felt at the time was) a good introductory worksheet on modular arithmetic, using students’ complaints about “always having the same thing for lunch” and made up a rotating set of dishes served in a neighboring school’s cafeteria.”**

*–> My take: This is a detailed account of where we see remainders used in UPCs and ISBNs. I found it really interesting that there is a crazy complicated algorithm for this, and I still wonder why they do it like that after reading it. It’s cool to see the math behind something that we use every day. Scott asks “I’m still trying to find a real world application for remainders with polynomial long division.” My response is “Good luck.”*