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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.
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.
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)
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!).
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!
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.
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
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.
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!!!
Week 3 of the New Blogger Initiation! After three weeks, more than 90 people are still blogging. Awesome.
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.”
Without further ado, I present you the second post from 10 different new math bloggers as part of the Math Blogger Initiation.
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!
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!
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?**