A Very Fractal Christmas, Part II

Here enjoying my last (very snowy) night in the northeast before heading back to warmer weather and lesson planning tomorrow, but I had to share how well our tree came out!!

All in all, it was about 3 feet tall and the kids were so excited they offered to come in before and after school to finish it. A great end to a long first semester!

May everyone have a happy new year and enjoy the fresh start January brings with the kiddos! 

A Very Fractal Christmas

Today is our last real day of classes before the break and, as would be expected, most classes have a test or quiz. Tomorrow we have the parties and the annual Christmas dance and then we'll have 10 glorious days off! One of my classes somehow got a day ahead  and took their test yesterday. I was at a loss of what to do with them until I found this great idea: build a 3-D fractal Christmas tree! I plan on introducing the idea with this video and seeing where it goes from there!

I'm looking forward to seeing how it goes, especially since this is one of my more challenging groups behaviorally. The fact that they get to do this when no other class does might just be privilege enough to motivate them!...or let's hope that, anyway!

Will update more this afternoon with pictures!

Aftermath of Sandy Hook

It's taken me 5 days to even begin to form words about what happened in Connecticut last week. As a teacher, as a person born in Connecticut, and as a human being, I have absolutely nothing but prayers and sorrow for all the families affected by the tragedy. I now live hundreds of miles away, but my school was personally touched by the tragedy and had to watch a familiar name on the nightly news reported as deceased. She was 6. Needless to say, my heart is broken.

I had been with my children the whole day on Friday and had seen nothing more than the email asking us to shelter the students from the news until they could be reunited with their parents. When the teachers were finally told the severity of what had happened, we cried together. We prayed together. We were in disbelief. 

The return to school Monday was more emotional than I ever could have expected....more tears, more prayers, but also a profound sense of gratitude. As I walked out of my weekly  staff meeting, eyes filled with tears, I was greeted with the faces of our own beautiful children. I got to see Pre-K students run and play; I got to laugh with my 8th graders about their weekend antics. It was a transcendent feeling...like I was floating above all of the work and exhaustion and stress and just being with my students. I knew why those brave teachers reacted they way they did....we love our children. 

Daniel Willingham wrote a blog post this week about guns in schools, namely whether school officials still have them. While making interesting and profound points (as Willingham is wont to do), Willingham said the following:

We love to teach because we love to communicate to students the beauty of the world, and to help them see beauty they did not know was there. We love to teach because teaching is about creation: the creation of new knowledge, the creation of better minds, and yes, the creation of a better commonwealth, nation, and world. We love to teach because we want to build--to build competence, self-confidence, and character in our students. 

 And he's right. By doing what those teachers did, they did exactly that. They showed all of us the beauty of our world- the beauty of a brave few who were willing to give their lives to protect the innocent. They created a future for their students. They are truly heroes and I feel proud to be a teacher knowing I share the profession with such a passionate and selfless group of people. 

RIP to all the victims of Sandy Hook. You and your family are in our prayers. 

Higher Level Confidence

Despite 4 weeks of practice and warnings over and over that I would never just give them a question like "find the slope between these 2 points," my Algebra class was still flabbergasted that I had the nerve to give them a world problem on a test. And let's just say....I gave them pretty much all word problems.  As you may have guessed, it was our first real, honest to God, Common Core aligned test. For everyone's testing pleasure- no questions below comprehension level here! And as of today, I have 26 new enemies.

The tests are graded and the students did wonderfully, but ohhhhhhhhh baby are they mad. I had 4 angry emails right after...all from the same parent....whose student got a 93% on the test. It's not that my kids don't know the material, but any challenging question shakes their confidence. They have had their hands held and been given knowledge level tests and quizzes for so long....I don't even think they know that they're capable of applying their knowledge!

Does anyone have some tips for helping to build students' confidence with higher level thinking? I always thought the challenge would be helping them be capable of it, but we've done so much practice that they've demonstrated to me that they can handle it. I know as we practice more, confidence will build. But, really, how do you break the "this should just be regurgitation" mindset? 

Giving back the tests tomorrow will be fun, though. That should help in the confidence department! 

Proofs by David Bowie

When I was in college, I felt like proofs had personality. I have no doubt this came from years of pouring over them- from intrigued amusement to hopeless despair (I'm talking to you, hyperbolic planes). They joined the list of mathematical characters friends and I would create to numb some of the mathematical stress: the Jacobian who liked going on African safaries, the data my professor loved to put in the freezer, the triangles evil cousin Cryangle. And proofs? These were just some:

• The cute little ones which were made you giggle....toddlers, anyone?
• The elegant ones which so effortlessly seemed to make such a profound impact. These were definitely always wearing elbow length ladies gloves and pearls.
• The beastly ones that took up a lot of space without really saying anything. Any Planet Fitness members out there? These made my inner lunk alarm go off. I usually walked away going..."Well that's just dumb!"
• The ones with a trick up their sleeves. These always struck me as the salesmen of the group.
• The wise old grandfathers....proofs by induction. Figuring out what we definitely know is true. Building on that experience. These always seemed so reasonable to me. 
• The ones that are just really, really, really annoying. 

Then there was my favorite type...the smart, sassy, sarcastic ones....indirect proofs. The let you think something was true until BAM...they proved you wrong. They had attitude. They were the Real Housewives of my mathematical world. 

My students have not spent the endless hours pouring over proofs that I have and they also haven't needed such a mental break from the stress of a 500 level math class that they would begin to understand these characters. However, I wanted to do my favorite proofs some justice and let the kids do some exploring.

I set up 2 stations:

1) A set of sudoku puzzles 

2) This video from the 1980's movie The Labyrinth

1, 2, 3....

DEBATE! CONJECTURE! CONTRADICTION! 

All of this, of course, after the debate and conjecture about Jim Henson and David Bowie. Middle schoolers of 2012 cannot fathom the 1980's.

 

Great first day of the lesson. Wrapping it up tomorrow with discussing how we gave hypothetical conjectures, then tested them to try to see if there was a problem with them. 

Word of the Week: Centroids

Each week I have my students for a Math Lab. This was supposed to be an extra enrichment or intervention period, but it's turned into organized chaos. I have 20-30 students in 3 different courses all vying for help and attention. It's that class that I dread leaving for a sub....chaos. 

My Geometry students are at the top of the food chain and it breaks my heart to give these critical thinkers "drill" practice when they could be exploring. Today was one of those days when you're not sure if an activity it will bomb or fly. And this one? It flew!

We have been studying centers of triangles (orthocenters, incenters, centroids, and circumcenter). This has had 2 highlights for the kids: a foldable that they used to keep them all straight and giggles when one student kept slipping and saying "circumcision" during an oral presentation. They are always cooperative and brilliant, but I wanted to give them some reference into why this stuff might matter. Good thing I spent 3 semesters of college teaching physics! Centroids.....centers of gravity....suspending random objects around the classroom? Sounds like it's worth a try. 

I used this video on center of gravity to introduce the topic. One their interest was piqued, this video related the information to our chapter. I had each student design a triangle out of cardboard and find its centroid, then suspend it. Then they had to find some weird shape other than a triangle and try to find its center of gravity. Can you find a centroid for that? How is it alike and different? All questions to be examined! 

Anytime you get to hear "whoa!" and "that's so cool" is a good day in my book. I had to shoo students out of the room when the bell rang and we spent the first minute of class later that day balancing our triangles on smaller and smaller points around the room. One student got it balance on the head of a pin....he took it home because he just HAD to show his parents. Here's a great activity that I wish I had thought of before today....could have been integrated nicely. 

The only problem? The 20 Algebra students I had in the class found it nearly impossible to focus on their linear equations project with all excitement! They wanted to build their own centroids and were even starting to use the vocabulary. I love when, at the end of class, I catch students who aren't even in the course watching videos I've posted for other classes (also a problem with Vi Hart's videos!). As I was walking out to my car I found 3 triangles, centroids labelled, that had been made by students outside my class. Love when math leaves the 4 walls of my room! 

Any other ideas for integrating more physics into high school math? Obviously with calculus, but with lower level? Share share share!

Giving Thanks

Teachers have a relatively thankless job. We spend 40 hours a week with students who are learning what it means to respect and appreciate. Translation: we sometimes go unrespected and unappreciated. We all have those students in our classroom who try our patience each day, the parents who attack before they ask any questions, and the administrative hoops that must be jumped through. 

After a particularly trying day, I read this article from Edutopia and thought it was a perfect sentiment for Thanksgiving week. The trying people in our lives so often become "bigger" than the people who are doing the right thing. It's sad, really....when so many people are doing the right thing. Let me tell you a little bit about my students:

- I have one student who, on her way out of my classroom, thanks me everyday. 
- I have a student who takes it upon himself to encourage his classmates to be respectful and kind, inside and outside the classroom.
- I have my wonderful basketball team who displayed such amazing leadership during their scrimmage with the Special Olympics. 
- I have a student who, when a friend faced with the typical "middle school" girl drama, told me she'd always wanted to be someone people could go to and she was just happy she could be there for someone else.
- I have a student who spent my first 3 months at the school pushing back on my authority because I was young. Now, a year later, he treats me with respect and amazes me daily with maturity and insight. 
- I have one student who offers me a hug whenever he senses I'm having a bad day. 
- I have a posse of 7th grade boys who give me all the fantasy football advice I could ever want.
- I have many students who come on time, come prepared, and come ready to learn.
  

And you know what? I rarely, if ever, thank them for that. On a small scale, I try to thank them when they carry something for me or when they check to make sure I've set my line up before the NFL's Thursday night game. But I don't thank them enough for being role models, for being leaders, and for making good choices. It might be a little early for New Year's resolutions, but I know this. One of my goals this year is to thank at least one more of my students everyday. 

Have a happy, safe, and restful Thanksgiving! And a word of advice....Put. The. Grading. Down. 

Success: Redefined

There are lots of different ways I define success for my students. Yes, I am happy when my they "succeed" on a quiz and get a good grade. This success comes easily to some and only by labor and pain for others. No matter how small the victory, I try to celebrate it with that student. Then there are the times when the student who struggles through math every day makes the game-winning goal at the soccer game. Those moments are just as proud for me and often more enlightening. Getting to see someone at their best makes you re-examine your biases about them- something every teacher needs to do sometimes. Flash to tonight...

I played basketball in middle school. No one said I played it well, but play it (and love it) I did. I am an avid college basketball fan.....including an NCAA tournament trip and quite nearly 1.000 college basketball games throughout my life. So after a wonderful weekend, I spent my Sunday evening at school watching some serious hoops action. The JV and Varsity teams were having their first scrimmages and were also assisting with drills and practice for a local Special Olympic team. 

Tonight defined for me a third type of success....the type where I see my students succeed as people. These 12, 13, and 14 year old students tirelessly walked through drills and talked with people who are very different from them. My students were not afraid or "too cool"; they were inviting, gracious, and supportive. After drills and games, the Special Olympic team scrimmaged for the crowd. My students cheered on every success and supported every failure. They offered hugs and congratulations to all the players. 

One of those moments that reminds me that I teach kids, not math. Really amazing kids. Just something to be thankful for during this Thanksgiving week. 

Dimensional Analysis

While working extensively on rates of change, my class ran into the speed bump known as dimensional analysis. For some of my students, it came easily....they have a natural intuition about these types of relationships that makes it much easier for them. For others, it was agony. I was the dentist and they were having their mathematical teeth pulled. No one cares that there are 5,280 feet per mile when google can just tell you the answer, Ms F! Even Bill Nye's new "Solving for X" video was annoying to them....and if BILL NYE can't make it work, who can??

The turning point for all the kiddos came when I posed the following questions to them:

How many difenwarps is 2.931 yipyaps if there are 436.9 difenwarps per yipyap?

After a heated argument about the pronunciation of "difenwarp" (which, mind you, included them informing me that my pronunciation was wrong despite the fact that I invented the word), even the fast kids started to realize that their intuition wasn't always going to serve them in unfamiliar territory. 

I decided to introduce KWL charts to them as a means of gathering information. I always liked the idea of them, but for other subjects....kids want to know about their bodies or wars. Kids are less likely to want to know about combining like terms. Here's a sample of the one I used with them:

We included what we KNOW...the amount we start out with, what we WANT to know....the units we are aiming at, and anything and everything we've learned at that might help. After a few practice problems, I let them loose. Here were the results!

Ohhhh happy day! Seems like most of the resources I could find were high school chemistry labs. I'm thinking next year maybe we bake...they have to convert, they get a delicious baked good as a reward!  Any other good ideas for dimensional analysis?

The Wonderful World of....Foldables?

I am like my middle schoolers in some sense....there are "cool kids" in the "class" with whom I really, really want to hang out. Go to the mall, braid each other's hair, share secrets....you know? I just haven't quite figured out how to infiltrate their world yet. Obviously, I am talking about foldables. I see teachers who do these elaborate interactive notebooks and I think....those are SO COOL!!! But do I have time for them? Will they be helpful or are they just a bigger waste of time? How do I get a class of 28 to listen to elaborate directions for a foldable without wanting to pull my hair out? 

So today, I decided to go over to the cool kids lunch table and sit right down. We tried a (very simple) foldable for slope intercept form in Algebra. My students spent extensive time last year studying the topic, so I'm not dwelling on it for long. A foldable seemed like a good way to re-establish our relationship with good old m & b, then do some practice. Thanks to Sarah at Math=Love for the idea!

The kids LOVED it. To some extent, it was the "anything different than what we normally do is AWESOME" syndrome. But I genuinely think the found it informative and useful. 

My geometry class recently finished their own "foldables" project....making pop-up cards using triangle vocabulary. We established what an altitude is and what properties it has without even cracking a textbook. It was a nice transition to a really dense chapter (Euler line project, anyone?). 

Came out pretty cute, right?

The turkey card was from a pattern the students followed.  The Easter card was one the student designed on their own, then wrote out directions using chapter vocab.

I've seen tons of foldable ideas, but anyone have any that really hit the ball out of the park for Pre-Algebra, Algebra, and Geometry? 

Anyone have any tips on how to make and use them most effectively in class?

In the meantime, I'm going to keep creeping on their lunch table. Cool kids, here I come!

I hate...

I have a weakness. I know it. Everyday I fight it, but I just can't sometimes. Here it is...I got into teaching to teach concepts. I love the exploration lessons that engage students in problem solving and showcase their critical thinking skills. I did not go into teaching with a heated passion for standardized test review, nor did I go into teaching with a strong desire to be asked the same question 15,000 times in a 42 minute period. My students know that a multiple choice test from me means that either myself or a family member is deathly ill....or the Giants are in the Super Bowl and I just can't pull it together to write a thorough test. All of this sounds like a good thing right? At certain times....it is. But what my students do not know is that I dread almost every test and quiz review day.   So my goal has been to find activities that are engaging, provide good practice , and can somehow lessen the mass hysteria known as a room of 28 seventh graders. 

I am strictly anti review packet. The classroom I took over during my first year of teaching left me with students who relied so heavily on these they never learned how to study. I've tried what feels like a million strategies since- with mixed success. One of my favorites is having the students write their own version of the test, complete with answer key. Not only do they get some practice with the concepts, but I get to see what they view as important. I try to sneak the best question or two from the kids' tests on to the actual test....an added bonus for doing good work on the review. 

Cue this wonderful Row Game from Molly Kate at Mathemagical Molly. I adapted it for my Pre-Algebra students. Anytime I heard, "Ms. F, I don't get it!" from Student A,  I would ask Student B if they could tell me A's question. They couldn't? Guess they better work together on it first! This eliminated 98% of the questions and allowed me to move seamlessly from group to group, helping and encouraging. Goodbye gaggle of question-askers, hellooooooo critical thinking and correction of mistakes! 

Anyone have more fun ways to practice that don't make me want to say, "But Mommmm, I don't want to go to school today!"?Any other brilliant ideas for self-checking activities? Happy sharing!

The Darndest Things

I was reminded today, as I often am, of just how young my students are. Let me set the scene....flash back to those 5 minutes between 4th period and lunch today. I am sitting at my desk wrapping up an awwwwesome jigsaw activity (if I do say so myself) and trying to shoo my students down to lunch so I can run to the bathroom and scarf down a sandwich. I have Ella Fitzgerald playing in the background as I work. In walks a 7th grader....

Student: "Ms. F, why are you listening to 80's music?"
Me: "Really? Do you REALLY think this is 80's music?"
Student: "Well, yeah. It's old!"

Now let me remind you: I am only about 12 years older than my students. Many of them have older siblings my age, if not older. I listen to bad pop music, see all the stupid movies, and have to restrain myself from asking my students where they got all their outfits. I chaperoned a dance and could not be told apart from the kids in the dark because of my height. But there is one thing I know....Ella Fitzgerald is NOT 80's music.  

What is Math?

One of the most worthwhile tasks I was asked to do in my graduate course work was write a detailed investigation of the history of mathematics, along with a personal statement detailing my own philosophy of math. My "What is Math" paper is still my baby- that paper you've moved from laptop to flash drive to laptop (to iPad). Maybe it's the sentimental memories of my roommate's dog peeing on my library books in the wee hours as I wrote. Or the fact that my entire thesis was based around the fact that I've seen the movie Inception too many times (more on that later). Somewhere along the line, though, this became what defines me as a teacher. 

So what is math? My investigations led me to some great books  and some interesting theories. To anyone interested, Joseph Mazur's Euclid in the Rainforest seemed the most reader-friendly for those who didn't decide a theoretical math degree was the best path into teaching (I mentioned I LOVE math, right?). Hours of Diet Coke, dance parties in the School of Education computer lab, and mindless babbling to my poor boyfriend later....I was struggling with putting my own theories of mathematics into words. They say the best cure for writer's block is to get your mind off it....so I put Inception into the DVD player and cuddled up with the aforementioned roommate's dog (this might explain the incident that ruined my reputation at the library). And there it was....

"Well, imagine you're designing a building. You consciously create each aspect. But sometimes it feels like it's almost "creating itself", if you know what I mean...Genuine inspiration, right? Now, in a dream, our mind continuously does this. We create and perceive our world simultaneously, and our mind does this so well that we don't even know it's happening. That allows us to get right in the middle of that process."
-Inception

 I grabbed a pen and started writing....
"I believe that at its core the subject of mathematics represents the study of relationships. It is simultaneous perception and creation, which function in an endless cycle. The more we perceive relationships, the more mathematics we are able to create.The more mathematics we create, the more we are able to perceive new relationships."

This has become the way I view my own learning and the way I teach my classes. By studying relationships and patterns, we are able to make conjectures. From these, we are able to perceive new relationships and new patterns. And it's one of the reasons I love my job....getting to see the genuine problem solving and sense of curiosity present in my students each day. 

So think about it.....what is math to YOU? It might just change how you teach! 

"You'll love it...It's like a soap opera everyday"

These were the wise words of a  teacher I observed during my undergraduate work- a time when I couldn't imagine spending 40 hours each week with 12 year olds. But, 5 years later, here I am.....spending 40 hours a week with (and at least 40 more preparing for) my 6th-8th graders in all their awkward glory.

I always imagined myself to be a high school teacher because..well...I LOVE math. And I had my big shot when I got to teach AP Calculus, Algebra 2/Trig Enriched, and a remedial Geometry course. What I learned was that all the things I loved about math were lost on my students. Their excitement for learning had already been lost in the interest of top grades to get into top colleges or the apathy that comes with struggle. They wanted "tricks" and "steps," not to experiment with problem solving or be ready to learn from failure. I found my passion with middle schoolers- the age when everything can be new and exciting, even math!

So here it is...My attempt to marry my loves of teaching, math, and writing. I'll be sharing some of the wonderful strategies, lessons, and ideas I've found and can't wait to start exchanging ones with all of you!

**Photo credit from Pinterest