# Category Archives: Uncategorized

## Volume in Calculus: Conceptualizing before Formalizing

One of our PD sessions in the past was about how to support students with learning differences. One of the points that the presenter made was that most pedagogical tools that you would use the better serve these students are great tools to reach all learners. This struck me especially because I teach almost entirely students for whom English is their second language, and sometimes when I do something specifically to help students with the language of mathematics I come to larger and more general pedagogical understandings.

For example, this past week, I introduced solids of known cross-section in AP Calculus in a way that I thought would ease my students understanding of the tricky language involved in the problems, but what I ended up doing was really effectively let them develop their own conception of how these solids are formed and THEN interpret the AP problem language and integral notation in those terms. Conceptualize and then add mathematical formality to their own conceptual framework.

Here’s how it worked. I put 4 of these solids out around the room:

1. First, I gave them 1-2 minutes to SILENTLY write down in bullet points how they would describe to someone else how the solid was formed.
2. Then I gave them 2 minutes to share ideas in groups.
3. Then I cold called on 7 or 8 students via a deck small cards with their names on them (which is by far my new favorite teaching tool). After I called on some students, I called for volunteers with any other ideas.
4. LAST, I asked them to flip to the back of the paper and read the actual description.

During the “share” part, students said some of the craziest, random stuff, but most of the important parts of the description were said by various students. When it came time for them to read the description, at first they were like “whoa” because the language is still a bit daunting. But after a minute or so of close reading, they connected everything in that description with things that they themselves had said. So when it was time to do the actual integral, the intermediate notation I use made 100% sense:

So general pedagogical moral of the story? Letting students conceptualize something on their own before bringing in mathematical language and notation makes it more likely that the notation will aid in their understanding rather than provide another hurdle in learning.

A teaching fellow (a first year teacher) was observing my class (and has been observing periodically throughout the year). Afterwards, she remarked that she felt this was one of the most effective 10 minutes of the year, and I agree! And I think 10 minutes on this (instead of just 1 minute reading the question) will save lots of time in the future. Next week, I hope to try the same strategy with solids of revolution!!

## 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 9th 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!

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## 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.”

## Math Blogger Initiation Week 2

Without further ado, I present you the second post from 10 different new math bloggers as part of the Math Blogger Initiation.

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## Kristen Silverman | Numbers

Kirsten Silverman @klsilverman has a blog named Numbers. The second post for the Blogging Initiation is titled “Today“ and the author sums it up as follows: “Even when there are crummy days, now that I’ve started blogging, I can read about the better days. I can go back and read about the days I have been inspired.” A memorable quotation from the post is: “I’m trying to be more positive.”

–> My take: We all have those moments where we are like gaaah, why is everyone else making my life so hard!?!? Kristen brings up a really cool point about blogs being a place where you can go back and revisit positive moments on a particularly challenging day. Cool idea!

## That Math Lady | That Math Lady’s Blog

That Math Lady @thatmathlady has a blog named That Math Lady’s Blog. The second post for the Blogging Initiation is titled “A Teacher’s Legacy” and the author sums it up as follows: “My post is a futuristic account of what my students would say about me and my class at their 10 year reunion. I hope that my real legacy is similar to this one! “ A memorable quotation from the post is: “I would trade all the okra-powered hovering hybrid carriers in the world for that legacy to become true.”

–> My take: In 20 years, will kids remember how to divide polynomials? Probably not. What things will they remember then? I think passion for mathematics is as good an answer as any, so I approve of this futuristic vision.

## Maggie Acree | pitoinfinity

Maggie Acree @pitoinfinity8 has a blog named pitoinfinity. The second post for the Blogging Initiation is titled “Two Things Are Better Than One” and the author sums it up as follows: “I am looking to implement more investigative practice as I go throughout this school year. I did find two ‘things’ I have done in my classroom that is just that and is motivating me to do more. There are always concepts that just have to be done, but when the opportunity is there, it is important to do some sort of activity or investigation to get the students thinking.”  A memorable quotation from the post is: “Coming back to the prompt I decided on, it was important for me to find a few things I have put together myself to help my students with investigative practices or constructing their own reasoning.”

–> My take: Piecewise functions are what I use for review for my Calculus course because they seem to hit a ton of great things from lower math classes. I really like this idea of cutting out graphs, and I think I might try it in my own class! I wonder if there is a way to do this though without such step by step instructions. And I think it might be useful to have some part of the activity go the other way, i.e. to write down an equation from a piecewise function. Great idea!

## Duth Math | duthmath

DuthMath @DuthMath has a blog named duthmath. The second post for the Blogging Initiation is titled “I wish I had heard about the Ladder of Abstraction in Teacher Training” and the author sums it up as follows: “My post is about trying to start using the concept of Ladder of Abstraction with my developmental college math students.” A memorable quotation from the post is: “Only one week to go before I meet them for the first time!”

–> My take: Dan Meyer has been such an inspirational figure for a lot of us teaching math. It’s no surprise that he is continuing to do so!

## Nathan Kraft | Out Rockin’ Constantly

Nathan Kraft @nathankraft1 has a blog named Out Rockin’ Constantly. The second post for the Blogging Initiation is titled “Working for the Man: A Cautionary Tale” and the author sums it up as follows: “I did some work writing math-tasks for a company this summer. However, once restrictions were placed on how I could design the lessons, it no longer became something I enjoyed doing. Having creative freedom allows me to do my best work. Although getting paid sounded like a great motivator, it had the opposite effect.” A memorable quotation from the post is: “Once I was getting paid to write math lessons and had restrictions placed on how that should be done, what used to be fun became work.”

–> My take: I helped work on our school’s salary scale through a committee this past year and one of the coolest facts I learned is that most teachers don’t know their exact salary (do you? I don’t) unlike some other professions where money is much more of a motivator. Nathan captures this sentiment well in talking about getting paid to write math lessons. I don’t know if I could do that! I get super stressed out by planning, so the idea of doing just that part as a job kind of freaks me out.

## Lee Ann Smith | Expanding Horizons Through Education

Lea Ann Smith @SmithTeach has a blog named Expanding Horizons Through Education. The second post for the Blogging Initiation is titled “Useful teaching technique” and the author sums it up as follows: “I like to keep my algebra students engaged using a wide variety of activities. This post describes a way to use a little bit of stand up comedy to keep them attentive.” A memorable quotation from the post is: “If I have a concept that I really want my students (high school algebra 1) to remember, I will occasionally deliver the key point while standing on my desk.”

–> My take: This is a funny idea. I love making my classroom a little more whimsical, so I’ll have to try this out.

## Emily Allman | Algebra, Essentially

Emily Allman @allmanfiles has a blog named Algebra, Essentially. The second post for the Blogging Initiation is titled “Reflections and Transformations” and the author sums it up as follows: “I am not a new teacher and only a fairly new blogger, but this past year has been full of new experiences, new adventures, and new ambitions. Thanks to the mathtwitterblogosphere, it’s also full of new and wonderful ‘colleagues.’” A memorable quotation from the post is: “I spend lots of time thinking intensely about tiny details, which is a wonderful contrast to teaching – where you have teeny amounts of time to maneuver a plethora of calamities.”

–> My take: I love the reflective-ness of this post, and Emily’s ability to turn a situation that she could easily have just griped about into a great learning opportunity for her. I can’t wait to read some more of her thoughts.

## gooberspeaks | Reflections from an Asymptote

gooberspeaks has a blog named Reflections from an Asymptote. The second post for the Blogging Initiation is titled “Staying Sane” and the author sums it up as follows: “I am going to provide some vainglorious advice about my ways of staying sane through the school year.” A memorable quotation from the post is: “I think my motto this year may just have to be Keep Calm and Carry On (thank you British government).”

–> My take: What a great idea to write down the things that will keep you sane during the school year. I really need to do this too. My most simple one is “No work on Friday” (our weekend is Friday-Saturday) but some of the other things that she does are simple and great!

## Rachel Tabak | Writing to Learn to Teach

Rachel Tabak @ray_emily has a blog named Writing to Learn to Teach. The first post for the Blogging Initiation is titled ““Special Number” Project” and the author sums it up as follows: “This post is all about a project that I’ve been using for a few years. I like it because it gives kids an opportunity to show their knowledge of number theory, and also to be creative and silly.” A memorable quotation from the post is: “This activity holds tons of potential to get your kids geeking out to the max – showing you how goofy and creative they can be over topics like prime factorization, GCF, LCM, and a bunch of other stuff.

–> My take: This is a nice idea! I love topics where students can be creative. My suggestions might be to take the [# pts] heading from each question. I think that takes away from the fun! Also, is there any way to make this more opened ended? Could the students figure out their OWN properties about the number they chose? This is a nice idea to do instead of toiling through a sub lesson!

## Matt Moran | Maximize Interest

Matt Moran @mathewpmoran has a blog named Maximize Interest. The first post for the Blogging Initiation is titled “What I Wish I Knew Before I Started Teaching/Being the Worst First Year Teacher Ever” and the author sums it up as follows: “This post is something I have really wanted to write but struggled to find the words to say. In it I talk about how horrible my start in teaching was and what I wish I knew when I started teaching. Namely, what I wish I knew was something really obvious; I wish I better knew myself.” A memorable quotation from the post is: “To begin, I want to share a little humblebrag: I believe I set the all-time record for Greatest Disparity Between Expectations of What I Would Do As a First-Year Teacher and Actual Results of Teaching in Year One. Respect to all the other competitors for this accolade, but sorry guys this contest was never even close.”

–> My take: This is great (though perhaps a bit scary?) inspiration for a first year teacher – you don’t have to get it right the very first time you do it, and it takes a while until you feel really at home in the classroom. For me, the transition was all about learning to view mistakes as learning opportunities. You wont ever be perfect, but you can always be improving. Also, Matt sets a record for the number of times citing Dan Meyer in his posts. Also, for the record, I totally disagree about the not-smiling-til-Christmas thing!

## Is your Google Reader feeling empty? [Math Blogger Initiation Week 1]

As full as my Google Reader is, I am so excited about the math blogger initiation going on right now, run by everyone’s favorite fairy blog father – the wonderful, ever-present, inexhaustible Sam Shah (my co-star in Magic Mike 2). Here are fifteen great posts in no particular order from new bloggers. Support their foray into math blogging by getting on their blogs and commenting! Those first bits of feedback really get people hooked on blogging!

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TJ Hitchman @ProfNoodlearms has a blog named **Circles and Tangents**. The first post for the Blogging Initiation is titled **What to do with linear algebra? Some Inquiry Based Learning!“** and the author sums it up as follows: **This is a “plan out loud” session for the basic structure of my linear algebra course. Writing is a good vehicle for finalizing decisions and making real commitment to change in the classroom.** A memorable quotation from the post is: **I have unreasonable expectations of the average undergraduate.**

Kyle Harlow @KBHarlow has a blog named **War and Piecewise Functions**. The first post for the Blogging Initiation is titled **New Blogger Initiative: Week One“** and the author sums it up as follows: **My AP Calculus students are weak in Precalculus skills, especially graphing functions and translations. They all have graphing calculators, which seems like a great aide in combating the problem. But so far, there is no evidence that the students are using them.** A memorable quotation from the post is: **I want to stand on my desk and loudly ask my Calculus students what they’ve been doing with those \$120 paperweights they carry around.**

Pippi has a blog named **Pippi’s Adventures in Teaching**. The first post for the Blogging Initiation is titled **Literacy“** and the author sums it up as follows: **My ninth graders have trouble reading and understanding complicated (and sometimes not-so-complicated) problems. This kills some of them on their state tests, even if they know the concepts the question is supposed to be about. I’m trying to find ways to help them practice reading and get better at it.** A memorable quotation from the post is: **I’d like for the answer to be something they can draw as often as possible, since that forces them to really think and synthesize information, rather than just picking words semi-randomly out of the paragraph and writing them for their answer.**

Jennifer Wilson @jwilson828 has a blog named **Easing the Hurry Syndrome**. The first post for the Blogging Initiation is titled **The Title“** and the author sums it up as follows: **We often hear that technology speeds things up. In my classroom, however, I find that using technology actually slows down the pace. When students explore difficult concepts using dynamic technology, they ask questions that they haven’t thought of when thinking about the concept in a static environment. When I use a student response system to check for student understanding, I find out during class what misconceptions need to be addressed, instead of waiting to find out on a summative assessment. Using technology “eases the hurry syndrome” in my classroom.** A memorable quotation from the post is: **Using technology eases the hurry syndrome, forcing me to pay attention to the questions students have and allowing me to assess their progress in a timely manner.**

Meagan Bubulka has a blog named **variablesofmath**. The first post for the Blogging Initiation is titled **Hello World!“** and the author sums it up as follows: **About 2 goals I have for this year: more/better parent contact and making my flipped classroom more effective and useful!** A memorable quotation from the post is: **I want to make this process better for the students, streamline the videos and make them more my personality while making them even more valuable. **

Erin @ErinYBaker has a blog named **Math Lessons on the Loose!**. The first post for the Blogging Initiation is titled **Yay for Blogger Initiation: A Goal for the First Week of School“** and the author sums it up as follows: **I focused on the goal to start a robotics club team at my school by participating in a STEM program called FIRST Challenge. I also have an interesting link to free online Stanford classes.** A memorable quotation from the post is: **Through this robotics club, I am hoping to create an outlet for students who may not have had that moment/opportunity in school yet to let out some of the creative and explorative minds. **

Pamela Rawson has a blog named **rawsonmath**. The first post for the Blogging Initiation is titled **The Evolution of a Teacher“** and the author sums it up as follows: **It’s about how graphing calculators have changed over the years that I’ve been teaching, from non-existent to TI-Nspire. It’s also about how those changes affect how and what I teach. Well, more how than what.** A memorable quotation from the post is: **After all, it’s just a tool. If I can’t use it to teach something, then what’s the point?**

Pam Rissmann has a blog named **PPerfect Squares**. The first post for the Blogging Initiation is titled **PPerfect Squares — It’s a rap!“** and the author sums it up as follows: **Why did I name my blog PPerfect Squares? I wrote this math rap my first year teaching, and my classes love singing it in class, and I’ve been known to rap the song at school talent shows. Kind of corny, but fun. My blog post includes the lyrics and an avatar singing it.** A memorable quotation from the post is: **PPerfect Squares, perfect squares goes on and on, but this is the end of this song!**

haversine has a blog named **Bowditch’s Apprentice**. The first post for the Blogging Initiation is titled **Like a Butterfly’s Wings in China“** and the author sums it up as follows: **What an inspiration Nat Bowditch has been to me since 5th grade me read about him in Carry On, Mr. Bowditch. ** A memorable quotation from the post is: **Nat famously steered his ship home to Salem during a blinding snowstorm one Christmas, confident in his calculations.**

Tad Snaith @TadSnaith has a blog named **What Does Math Mean**. The first post for the Blogging Initiation is titled **Why are students “good” at math?“** and the author sums it up as follows: **An attribute that I believe helps students or anyone understand a math concept is the ability to play a movie in their head of the idea.** A memorable quotation from the post is: **From my experience talking to students about their inadequacies which impede these skills we take for granted I strongly believe that if students or anyone for that matter are able to play a movie in their head of the math concept at hand then that person will have success at deciphering tougher math problems.**

Erin Wade @ewade4 has a blog named **wadingthrumath**. The first post for the Blogging Initiation is titled **This year…“** and the author sums it up as follows: **While it’s my 8th year teaching, it is my second at my current school and I’m still adjusting. These are some of the areas I’d like to improve this year! ** A memorable quotation from the post is: **PS…any suggestions on how to best utilize 43 minute class periods?? **

Ann Gorsuch @AnnGorsuch has a blog named **anngorsuch**. The first post for the Blogging Initiation is titled **My Goals for Student Teaching“** and the author sums it up as follows: **Here are my six hopefully attainable goals for student teaching. ** A memorable quotation from the post is: **Goal 2: Teach students to justify (explain why) and challenge (ask why) their thinking**

Nick Gerhard @nickgerhard has a blog named **Gerhard’s World**. The first post for the Blogging Initiation is titled **New (School) Year’s Resolutions“** and the author sums it up as follows: **I have a lot of goals for this year that will hopefully improve my teaching and my students’ learning. If I can not procrastinate, change up my teaching styles, continue working with my PLN, and stay positive this will prove to be a great school year. ** A memorable quotation from the post is: **Most resolutions are stop smoking, lose weight, yada yada yada.**

Lori Ferrington @loferrington has a blog named **Shift(ed)ucator**. The first post for the Blogging Initiation is titled **Standardized Grading Setting the Standard?“** and the author sums it up as follows: **I’m reflecting on last year to see explore some changes to be made for the upcoming school year. Specifically, I look at the possibility of implementing standards based grading to more accurately reflect student achievement.** A memorable quotation from the post is: **I like the ideas and am just beginning to form the thought of how this will look in my classroom environment, but I’m excited about making changes for this next year and refuse to let a standardized grading policy be the measure of my students’ achievements.**

Dave Enrico @denrico1 has a blog named **Me Dot**. The first post for the Blogging Initiation is titled **New Blogger Initiation: A Star Is Born“** and the author sums it up as follows: **I used to want to become a “master teacher.” Now I prefer the ring of “improving teacher.” I think this could be a sign of growth.** A memorable quotation from the post is: **So I should be, what, a third-degree master now, right?**

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–> OTHER COLLECTIONS OF NEW BLOGGER POSTS FROM WEEK 1: JulieFawnAnneMeganBowmanSamLisaJohn@druinokTinaKateSue

## Guest Post: Letter to a First Year Teacher from Emily

*I had a few friends submit letters that do not have blogs, and I couldn’t figure out a great way to include them other than just making a post on my blog with their awesome advice.*

This is from Emily H, who teaches history at the same school as I do in Jordan and is a dear friend of mine.

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Dear first year teacher,

I’ve heard somewhere that the first three years of teaching will determine whether or not someone stays in the profession – if you make it past three years and still have a passion for it, then chances are you will remain a teacher for the majority of your career. I suppose it is because I just finished my third year of teaching that this fact came to mind when I thought about what to write in this letter – why is it after three years I have decided to continue teaching? Why has it not lost any charm, and in fact why do I feel even more secure about my decision to be a teacher than I did my first year? Because I can tell you that I had some experience teaching at university before I chose to teach at a high school, and when I put my pen to my contract and decided to teach at a high school, I had literally no idea how I was going to feel about it, or whether I would stay longer than a year. So now, as twenty-seven months or so of teaching are behind me, I want to reflect on why thankfully this has been a successful journey and offer advice to you, because in all honesty I am not sure this profession would have been as rewarding without the help and advice from the other great teachers, both young and old, that I have had the privilege of working with. The organization of my ideas below is rather random, but I hope they provide you with both theoretical and practical advice.

There is only one word you need to know about teenagers: “I”
Before I left my former job to start teaching high school, I had a lovely farewell lunch with my employers, one of whom had a wife who worked as an educational consultant. Her advice above in bold was one of the first I ever got about high school age students, and it has proven to be extremely helpful to remember the image of her telling me this over our food. The essence of her advice is that teenagers are going through a phase of their life in which everything is about them – they will make mountains out of molehills because they can only see a problem from their own point of view, and they will explain everything from only their point of view. This little piece of advice has helped me find eternal patience when dealing with students who are otherwise frustrating – it helps me to remember that they are (depending on the extent to which their parents have encouraged this kind of self-involvement) incapable of thinking beyond themselves sometimes.

Don’t get me wrong – this isn’t the case with every teenager, but it does help to remember that it is our job as adults to not only provide them with the ‘traditional’ education of knowledge and skills, but also with a moral compass that guides them to thinking that the world is in fact not always just about them. So when you find yourself completely unable to fathom why a student is behaving the way they are, it is helpful to remember this little piece of advice and have a little patience, because in fact it is often those kids who are most self-involved that need the most mentoring.

Classroom management
Do not underestimate how important it is to set the right tone the first week of class. The most important thing you can do from the start is to get the students to trust you. You need them to trust you both in terms of knowing that your class will be productive and that you will, in general, be predictable both in expectations and content. So put time into thinking about how you will structure the class – will you give them a guideline at the start of every week that explains what they will learn and the homework in advance? Will you always write the topics to be covered on the board before class? What routine can you create so that students know it is time for class to start?

Think of yourself as a coach more than a teacher. You want your class to work as a team as much as possible, so don’t ever have what’s meant to be a class discussion, for example, without the whole class listening. In fact, that will role model that you want them to practice the skill of listening.  The more you can create a climate in which everyone feels like they are responsible for the material, the better your class will run.

Don’t be afraid of silence! If you ask a question and there is an awkward silence, have patience. The students may simply be thinking. This means you want to avoid calling on the people who immediately have their hand up (if I don’t have to think because I know someone else will always be chosen to answer, I won’t) and when lecturing don’t hesitate to pause and give students a chance to write – it may feel awkward for you up front, but for the students it shows that you value their ability to be engaged.

Be aware of what every single student is doing during class. This is easier said than done if you are in a room with over twenty students, but the more you are able to do this, the more your students will come to trust that you are there to ensure they are learning. If students know they can get away with playing on their computer for half of class, they will. If they know they can disappear to the bathroom for over ten minutes, they will. Students know in what class a teacher is more likely to be aware that they are engaged, so do not get so caught up in getting through class that you lose what is even more important: as much of their attention as possible.

If students are chatty in your class, it is completely unproductive to yell over them. One of the best methods of classroom management that I learned before I started, and which has proved completely invaluable to me, is using silence as a way to control the room. It may seem counterintuitive, but the best way to get students to calm down and focus is to actually remain silent in front or use less hand gestures to individual students so that they are quiet. This strategy is also great because it role models calmness and patience rather than frustration, and it also allows the leaders in the class to silence their own peers.

Get advice from other teachers
I was lucky to work with colleagues who enjoy talking about teaching and who offer practical feedback. If you have others as a resource, take advantage of them! Visit their classes, talk about your problems and or successes over dinner – this has probably been the greatest key to my success because the ability to bounce ideas off of people helps us get excited about getting back into the classroom. If you feel embarrassed to either ask for or share information, this honestly may not be the right profession for you. And don’t just talk to people in your field – some of the best lessons I have ever developed came from talking to teachers in completely different subjects.

Think about who you are
I was once told that in high school the teacher’s personality is of fundamental importance to how much a student will engage in a class. Now I know that may sound awful, and it’s an ugly fact, but to a certain extent it is true. As I said in the first bolded bullet point, teenagers are very self-involved, and so they will allow themselves to gravitate toward those whom they feel they can be most comfortable with, and they will be less forgiving if they do not like you, even if we all know that is very selfish. So it is really important that you are comfortable with yourself before you step into a room of teenagers – you will be dissected more than you have probably ever been, more than even on any first date, but if you are ready for it and can remain true to yourself, I can guarantee the students will like you. It is when you are uncomfortable, or try too hard, or try too little, that they get turned off.

Variety doesn’t mean effective teaching
Don’t feel like your lessons need to have a huge amount of variety and don’t be afraid to be simple. While it is smart to have lots of tools when making lesson plans, don’t be too experimental and irregular your first year because it could make you lose what really matters. Always focus on how your plans allow students to most effectively: 1. understand your expectations 2. reflect on and 3. be able to articulate and/or apply what they have learned. Students may say they want a lot of song and dances in order to do this, but really what they need is a good framework into which they can put content and skills. Mike Schmoker is an author with good advice on this.

Be ready to change the way you teach a subject every year. This doesn’t mean that you completely revamp a class every year, but my best teachers have always been those who constantly reflected on their classes and tweaked it both during and after the year was over in order to consider what would actually work best given new circumstances or information. My worst teachers were always those who stuck to a formula and never changed it – firstly that is bad role modeling if we expect our students to become reflective adults, and second that will make this profession a lot more tedious.

Be ready to think on your feet
This is advice that applies particularly during your first year, but then also for the rest of your professional life. I think the best teachers are those who find the somewhat paradoxical balance that leads to structured classes which encourage the development of organic discussion and learning. You can’t hesitate to let go of what you may have planned nor of letting the class develop into a student-centric place, but you also can’t hesitate to rein in students and know when it’s time to take the lead as well. Finding this balance may not come immediately, but with practice it will become easier.

Don’t hesitate to listen to students
Teaching requires thick skin – there are days when students will validate your very existence with their profusion of gratitude, and then there are days when you feel like you are achieving absolutely nothing and that your students are unbelievably frustrating people. Yet overall it is important that you listen to them. Don’t hesitate to give anonymous surveys in the middle and end of the year – you will often be pleasantly be surprised by how helpful student feedback can be, particularly if you have created enough trust as a team that they are unafraid to offer both unconditional praise and productive criticism. Yet I will also recommend you design the surveys yourself and tailor it to your class. Do your research and consider what kinds of questions make for productive feedback.

Don’t expect immediate results
If you are someone who wants immediate results, whether it be in expecting students’ writing and thinking to improve or to know that you have made an impact on a student in some way, this may not be the right profession for you. This is not to say you won’t actually witness such transformations – I certainly have and they have made this job incredibly rewarding – but you also need to remember that you may be doing a lot of good that won’t be recognized for years to come, so always keep that perspective in mind.

Finally, to end, I will offer one last piece of advice: keep a journal of how your teaching went. There are a couple of ways you can do this, I am sure, and I will suggest two. First, you can try to update it daily, even if it’s just a few sentences, so that you can reflect on what worked and what didn’t. Or, secondly, one friend of mine keeps a journal only with those teaching moments that were positive. She decided to do this because anytime she got frustrated she could pull out the journal and remember why she is doing this, and her journal has gotten pretty long. May that will be the case with you as well, and good luck!

Emily

## Folding Stories and Math

One of my goals this year is to add different “evergreen” activities to my teaching toolbox that can be for used for basically any topic, especially ones that are less open to application and need drill type skill practice. Especially for these topics, I always feel like I need things to break up the routine and find ways to get students more involved. Here is one that we did today which the class really enjoyed:

## FOLDING STORIES:

A real Folding Story is one where you start out by writing two lines of a story. Then, you fold the paper so the next person can only see the second line and pass it on. Based just on this last line, they write the next line of the story. You keep going for a while and then in the end open up to read the whole thing. They are usually very funny because the story quickly veers in different directions.

The idea in the math classroom is similar, but using a step by step math problem instead of a story. I put them in groups of three and gave them derivative problems involving negative and fractional exponents. The first person rewrote the expression to put it in a power-rule friendly form, the second person differentiated it, and then the third person rewrote the expression back into one with exponents in the denominator or radicals instead of fractional exponents. They folded the paper down each step of the way so that they could only see the step above theirs. Then in the end, they opened up and checked the final answer with the answer I gave them at the top. As a group of three, they attempted to find and fix their errors.

I had three rounds ready that got progressively harder, so when a group finished I would just hand them the next round. The groups worked at their own pace, but most did 2 rounds in about 15 minutes and then got partway through round 3 when class ended.

## REFLECTIONS:

1. Students are often really bad at diagnosing their own errors, but I think this is because we have never trained them. They had a tough time at first finding their errors in this exercise, but I think the step by step nature of it helped them figure out which part of it that was wrong and follow it up to the step where it got messed up. I want to do this more often to help them diagnose their own mistakes.
2. My role was reduced to “person who hands out the next round of three when the group finishes,” which I loved. I answered a few questions individually, but for the most part, people helped each other and talked math.
3. Lots of students cheated by opening up the paper to make sure the step above theirs was correct. Don’t know how to avoid this, but maybe it’s not the worst thing in the world.
4. I think that next time I might hand out colored pens too so that when they get to the mistake stage, they correct it with a different color and can more easily see where they went wrong. The correcting stage this time just involved lots of scribbling all over the strips (as you can see above).
5. The only thing I didn’t like is that the students left with nothing in their notebook to review afterwards. Some students took the completed strips, and I will post the whole exercise on our course website, but that is always less than ideal for me.
6. FINAL REFLECTION: Keep this one in my toolbox.