Etcetera, etc….

I love it when students figure stuff out.

I love it even more when:

A.  Students figure out things that, as a teacher, I didn’t  notice myself.

B.  Students who are labeled as “not good at figuring stuff out” figure stuff out.

Here’s what we did today in Algebra 2:

number pyramids

This is a SMILE resource from the National STEM Centre.  The problem I thought I would encounter is the word “etc.”  Kids don’t do well with “etc.” Etcetera is vague, non-committal, and easily dismissed.  To a student, etcetera usually means “I’ll ignore this and see if no one notices.”

It is helpful for me to be more specific with my expectations of students, especially when their mathematical well being is at stake.  But today, I was feeling a little vague and non-committal myself, so I handed out the sheet, explained what was going on and let them go…etc.

There are no words I love to hear more in my classroom than “Mrs. Schmidt, look what I figured out.”  And today was chock FULL of those statements.  Here are a few:

  • The triangles are always as wide as they are tall.
  • The sum of the base of triangles 3-wide is 3/4 of the top number.
  • As the triangles get larger, the percentage of the peak number gets smaller.
  • The percentage decrease is related to the size of the triangle
  • If the triangle has an odd numbered base, then the center number in the base is always related to the peak number.

There were lots more.  I was very proud of this class’s resolve in addressing the Etcetera.

 

Moments from MCTM

My brother wisely told me when he saw who I followed on twitter to stop following dumb celebrities and start following some real people.  The problem was that back then, I didn’t know which real people to follow.  Luckily, I soon discovered that there were math teachers on twitter.  Lots of them.

I’ve been to MCTM a couple of times and NCTM once or twice. I felt energized, and motivated after those conferences definitely, but this year was different than any conference I’d previously attended. The difference was my willingness to make a face-to-face connection with people I knew from twitter.   I’ve loved twitter for a long time for a variety of reasons, but meeting some tweeps in person and getting to talk math and more math was a real thrill.  It mattered less which conference sessions I attended, although they were great,  and mattered more who I took the time to interact with in between.   Although Christopher Danielson says that he doesn’t remember me as a snarky student in one of his math ed courses, I was grateful to get to spend some quality time talking with the man behind the hierarchy of hexagons. I met many others, and truly got to appreciate the wide range of awesomeness that make up Minnesota’s mathematics teachers.  

Next time, though:  book a hotel room right away.  Lesson learned.

 

Chipotle for Everyone

I’m hard pressed anymore to find a classroom of high school kids who don’t absolutely adore Chipotle’s menu options.  They all have a favorite, and they own it as THEIR burrito.  (I like Chipotle in particular because as a vegan, I can get a delicious meal, as can any non-vegan meal companion.)

I came across this article from Vox claiming Chipotle’s menu calorie disclosures were inaccurate.  I’m going to give Chipotle the benefit of the doubt here because their website contains a very detailed nutrition calculator which allows you to determine the number of calories for your  customized burrito.

The article references a study from the Journal of Public Health Nutrition which reviews a study in which customers are asked to estimate the calorie content of their meal. Some groups were given no information at all.  Some groups were given a range of calories in which burritos in general fell.  Last, additional groups were given example burritos containing the low and high values in the calorie spread.

I had a randomly selected student create a burrito.  Each class was obviously something different which made it kind of fun.

First, I had them estimate the number of calories in the chosen student’s burrito.

Second, I gave them the calorie range of 410-1185 claimed in which Chipotle’s burritos are claimed to land.  I had them adjust their estimate and give reasoning for their adjustment based on the additional information.

I then showed them the calorie range with an example from the Journal article’s study:

IMG_5054

Third, I wanted them to use the examples above to adjust their estimate once more.

We then talked about how the range of our estimates changed and why.  We also had a discussion about ‘averaging bias’ and how healthy ingredients make us assume that certain food are lower in calories than they actually are.

We were able to discuss the surveying methods done for the study and the demographics of participants, which led to a nice discussion about sampling.  (Evidently high school 9th graders find it odd and quite a bit creepy that participants in the survey were given a “flavored ice pop” in exchange for 5 minutes of their time.)

As long as I had their attention with food, I asked them to estimate whether the student’s burrito had more or less calories than my vegan burrito.  I’ll let you decide:

Student’s Burrito:  chicken, white rice, pinto beans, tomato salsa, cheese, and lettuce

My Burrito:  brown rice, fajita vegetables, black beans, tomato salsa, corn salsa, guacamole, and lettuce.

 

 

 

Stripping Down the Stock Photo

Smack dab in the middle of all of the awesomeness coming out of Rafranz Davis’s blog was a gem that stuck in my brain:  Addressing the Edu Stock Photo.  In short, Rafranz challenged the twitter/blogging teaching community to take a reflective opportunity to address a difficult issue in your school or classroom.  Taking on this challenge made me feel a sense of freedom from what’s frustrating in my classroom by taking off the shiny bow and acknowledging what I could do more effectively in my classroom.   Today’s Algebra class ended up being a great opportunity to reflect on what hasn’t been working in my classroom.  It started very typically by doing some estimation.  I walked around the room and noticed who was jotting down an estimate milliseconds before I wandered past their desk.  I saw who was more interested in their snap chat than participating in sharing estimates and reasoning.  I let the frustration build and boil over a little with my raised voice.  The breaking point came when a student literally talked over me in a regular conversation-volume voice as if I weren’t leading a class in an objective.  I sat down at my desk and felt in that brief moment like I was never going to get these kids to care about math.  Didn’t they know how much time and effort I put into figuring out how to help them learn?  Why didn’t they appreciate how much I cared about their learning. I kept putting the estimations on the board, not really saying anything.  It would have been very easy to shut down at that point.  There were about 25 minutes left in the week, and learning meaningful mathematics seemed out of the question at this point. Then I had a profound realization that changed my whole view of my class in an instant.  I was angry and frustrated at the wrong thing.  The kids in this class are stuck in the same cycle of schooling that they have been in for years.  They know that they are tracked in the “low level” math class, and they have come to accept that math is not something they’ll be expected to be good at. And they also have come to expect the same cycle of student/teacher frustration:  kids will talk and goof off, the teacher will get angry, yell, punish, and send kids out.  Things will be calm for a few days and then they can begin the cycle again.  It’s not the student’s fault, they don’t know any better. And it’s always worked before for them because they got themselves this far. I know this cycle is playing out in my classroom because these are nice, likeable kids.  They’re creative and interesting.  They’re emotional and sometimes dramatic.  And I love them.  I have loved the opportunity to get to teach them.  But I could do a better job than I am.  I could complain about the size of the class.  And I do.  Or I can change what I actually have control of, which is helping these students learn mathematics.  I do have control over giving them opportunities to interact positively with a discipline that they have been fearful of going all the way back to timed-arithmetic.

Much of what impacts our memory of particular events as positive or negative is rooted in how the story ends.  I believe the same can be true for education.  My incurable optimism tells me that something else will work for these kids and I believe in them and in myself.  To end that class period on Friday, I called on a good friend, Nrich.

One hundred percent of them participated, 100% of them engaged and wanted to be the one closest to 1000.  It was a small victory, but was absolutely essential in ending the week pointed in the right direction again.  Mathematical curiosity ensued for a brief moment (Why did one person get 1008 and another 992?  Who is the winner?)  Now Monday won’t feel like more of the same for my students and me.  It’s a new chance to bring them together with mathematics and hopefully have some fun in the process.

Alright, Mr. Stadel. We’ve Got Some Bacon Questions

Greetings, Mr. Stadel.  We know that you are very busy.  We appreciate your brief attention.  Rather than bombard you with tweets, we decided to bloggly address our questions and comments about your Bacon Estimates.

First of all, bravo.  You dedicated an entire section of your estimation180 blog to a culinary wonder some refer to as “meat candy.”  Even our vegan teacher felt compelled to engage us with these estimates.  (She says it is for the sake of the learning.)

Second, the time lapse videos of the cooking are pretty sweet.  Too bad the school internet wouldn’t stop buffering.  But nice touch, Mr. Stadel.  Nice touch.

A question:  Did you know that the percent decrease in length of bacon is 38% after cooking, but the percent decrease in width is only 23%?  We figured that out adapting your “percent error” formula to the uncooked/cooked bacon.  Do you have any initial thoughts about that discrepancy?  Is it bacon’s “fibrous” fat/meat striped makeup that allows it to shrink more in length than width, inch for inch?

Also, did you know that the percent decrease in time from the cold skillet to the pre-heated skillet is 29%?  That one was a little harder for us to calculate, because we figured out that we needed to convert the cooking times to seconds rather than minutes and seconds.

To summarize, we wanted to thank you, Mr. Stadel.  Our teacher tells us that you dedicate your time and energy to the estimation180 site so that WE don’t have to learn math out of a textbook.  We wanted to tell you that we appreciate it.  And the bacon.  We appreciate the homage paid to bacon.

Sincerely,

Mrs. Schmidt’s Math Class

St. Francis, MN

When the Answer is E: He Falls Off the Roof and Breaks His Neck

Our annual state testing season is almost here. The juniors will partake in the Minnesota Comprehensive Assessments in Mathematics a week from Tuesday. Our department decided issuing a practice test to all of our juniors would help re-familiarize them with long lost skills. After distributing copies during our monthly staff meeting, I’m always curious if any teachers in other disciplines look at the practice materials. Much to my delight, the choir director approached me at lunch on Friday, test in hand.

Mr. Warren: Is this test just like the MCAs?
Me: Most likely similar. Why?
Mr. Warren: Ok, well look at this one.

 

Mr. Warren: I think the answer is E, Xai s going to fall and break his neck.

The conversation went on for another few minutes, with me agreeing  that what’s been called “math education” includes ignoring the context of situations and focusing on a procedure.  In fact, I was curious how many juniors who completed this practice test even noticed that the situation was outrageous.

Since we were running on a 2-hr delay schedule Friday, I thought it would be the perfect opportunity to present the problem to my algebra class. They are mostly juniors who have been continually frustrated with a mathematics curriculum that doesn’t make any sense in the real world.

Me: Read through this problem. Does it make sense?

Student: ok, it looks like 32.

I didn’t expect any of them to apply any trigonometry, so I thought we needed to approach the problem differently.  In fact, I wasn’t even concerned about the angle measure.  I wanted them to look at the scenario itself.

Me: Imagine this scenario. We’ve done a lot of estimating in here. We need to envision a 20-foot ladder, three feet away from a house. Does this seem reasonable?

Unfortunately, it did seem reasonable to most of them. I needed another approach.

Me: ok, how could we simulate this in classroom-scaled size?

Student: Get a ruler.

Me: Perfect. How close does it need to be to the wall?

Students: (a chorus of answers)

After exploring multiple methods of calculating exactly how far, we arrived at 1.8 inches.  With as much drama as possible, I set the ruler against the wall, exactly 1.8 inches away.

Me:  Does this look like a ladder that any of you would want to stand on? (of course, a few did).  Keep in mind, this is a TWENTY foot ladder, not a 12 inch ruler.

Student:  Yea, I don’t think anyone is climbing up that ladder and coming down in one piece.

Another Student:  What if they had a spotter?

A spotter!  Now we’re talking.  To be honest, I have no idea if a spotter could hold a 20-foot ladder so that it could be placed three feet from the wall.  But now I’m interested to find out!

I know Mathalicious investigated a similar scenario using a claim from Governor Janet Napolitano.

In my mind, these are the questions that should be circulating Facebook and aggravating parents.  This is the kind of math that should rile up Glenn Beck and company.  Our state of Minnesota opted not to adopt the Common Core State Standards in Mathematics, but requiring this kind of math instead is what is actually dumbing down the curriculum.  It assumes that the real world doesn’t apply, only rote procedure does.  “Just figure out the answer, don’t question the situation,” is what kids read and do over and over when problems like this are solved without real context.  A richer classroom experience for both teachers and students comes when we ask students to assess the reasonableness of situations, create new scenarios that are more appropriate, and solve the new problems they develop.  The CCSS Standards for Mathematical Practice tell students that it’s vital that they “construct viable arguments and critique the reasoning of others.”  I don’t think “critique the reasoning of others” should be reserved for only reasoning created in the classroom.  I’d like my students to critique the reasoning of the creator of these types of problems and others like it that have been deemed a necessary component of high school math success.

Thank you, Mr. Warren for igniting the exciting conversation in my classroom.

 

Creative Craziness

I teach a lot of 9th graders this trimester. We offer a class called probability and statistics 9 and it is open to 9th grade students who also will have had the quadratic portion of algebra 1 this year. I really enjoy this class for multiple reasons. First, it lends itself very well to applying math to real-world scenarios.  Secondly, the hands-on opportunities are endless.
One of the issues I have been committed to improving with my own professional demeanor is the way I deal with 9th grade boys. Nothing brings out my sarcastic, short-tempered, disagreeable side like the antics of freshman boys. There’s something about the decision to play soccer with a recycling bin that just invokes the my inpatient side. Regardless, I need to develop more patience with this demographic. Boys are unique, both in the way that they act and the way that they perceive acceptable behavior. I’m not talking about “I’m bored” acting out. I’m talking about the “I really need to see if this eraser will fit in this kids ear” kind of acting out. I think that my short fuse has more to do with my failure on my part to  fully understand them rather than gross misbehavior on their part. What I’m really trying to grasp here is not “why can’t these kids sit still?” But more “when they can’t sit still, what makes them want to kick a recycle bin around the room or toss magnets at the learning target?” I think if I had a better understanding of what drives those behaviors, I could deal with them more productively. Suggestions?