Carl's Teaching Blog

A place to talk about teaching and learning

Category: Classes (Page 9 of 10)

Where I Teach

I am just wrapping my ninth year of teaching.  I am surprised that I have found a career that has provided such a consistent amount of challenge and reward, right from the start.

As a teacher, much of my day-to-day decisions are unique to the context of my teaching and the lessons I have learned from those experiences.

About My School

Currently I teach at an alternative school called City-As-School in New York City.  It is a very unique school and one that probably needs a little bit of an introduction as there are a number of things that make the school special. The one thing that I enjoy the most about the school is the appreciation for creative instruction and effort towards getting students to be successful.

The students in our school are all transfer students meaning that they leave in their junior or senior year from previous schools around the city.  We end up with a student population that demographically represents the entire city with a diverse range of races, classes, and genders.  For a student to arrive in my algebra class it is safe to say that they must have failed algebra at a previous school, but it is never clear exactly why.  Teaching in a transfer school, therefore, has an interesting layer of gaps in student learning that differ from class to class.  I go down to the middle school and  blame their previous year’s teacher.  I can’t create a curriculum map and expect the entire city to follow, either.  This means I need to accept that my students are going to come in on a variety of levels and I have to figure out how to make my teaching adapt to the student’s needs.

Our school operates on quarters, with classes being changed entirely every 8 weeks.  The classes are asynchronous meaning students who are in my eight week class in cycle 1 might not be in my class cycle 2, and might just show up again in cycle 4.  This means each of the 8 week segments are one big unit which is both able to be taught standalone, yet still fits inside of a larger curriculum that doesn’t overlap.

Internships

The primary goal of our school is to provide students with a real world experience.  Our school has a set of internships which have been studied and replicated across the country and in Europe.  Students spend over half of their week at internship, and take classes the other days, either (usually either on MWF or TH).  As a Math teacher, it is difficult to incorporate outside of school experiences into my “Equations and Patterns” class like the people in the “Documenatary Filmmaking” class, but that is something I hope to improve on.

Opting Out Of Testing

My school is also part of the New York State Performance Standards Consortium, which are a group of schools who, thanks to a New York State court ruling, substitute the standardized tests with their own performance based assessment tasks.  These tasks have to be presented, graded on a rubric ( based on the NCTM process standards) and scored by outside teachers.  Presentations are open to outside evaluators who come to ensure that they are rigorous.  One of the challenging parts of the job is coming up with portfolio tasks that are actually worthy of the rubric.  It is a good challenge, though, because it forces you to really create something worthwhile.

Student Relationships

Last but definitely not least, our school really requires a lot of inter-personal relationships.  Students at my school are often there because something at their previous school made them unsuccessful.  Sometimes no matter how hard you try with the curriculum, students won’t do any work in your class until you convince them that it’s ok to trust you, and that they can be proud of themselves if they finish.  You  may discover that, in fact, the opposite is true, that Students who really believe in you, and in themselves, will be successful no matter how hard the curriculum is.  Certainly the most challenging and rewarding thing I do all day is talking with kids and figuring out how to engage, or re-engage, them so that they can be successful.

 

P.S.  If you want to come live the dream, let me know.  We’re hiring!

 

20/33 MTBoS30

Helping My Student Assistants Change Their Thinking About Math

A number of kids this cycle came to my desk begging to have a teaching assistantship to fill their schedules.  Since I have boundary issues, I now have to plan for these kids on top and their learning as they watch the rest of the class learn.  These teaching assistants are not student teachers from a local college. They are high school students, who are not necessarily stronger than any of their peers.  One student said they have a really bad history with math and another had not passed a class in over two years.  With these student assistants I could have pursued very talented math students, but they usually don’t have any trouble filling their schedules, nor would they have as much to gain from the experience.

Why have assistants at all?  Isn’t just more to manage?

Having assistants is certainly a job, and it is not worth doing if you do not have goals for them.  My goals for them is to have them view math from my perspective.  They will help students in class, grade the assignments that I grade, and talk with me about misconceptions students might have before giving feedback.  At the end of this I hope the students take a different view of mathematics.  Perhaps they could go on to take a serious interest in math in college, but I would be happy if they just approach the subject differently.  At the least, I hope the students would view math as something they can work to improve, and mathematical “bad”-ness isn’t a terminal illnees, but can be treated through correcting their misconceptions and developing a productive disposition.

For the rest of this cycle I am excited about getting them to finish the rest of the work for the class.  I want them to have a working version of the project that the rest of the class.  In addition, they could learn a lot from having to think of ways to scaffold the project, or re-word the current project.  Lastly, I will ask them to write about their approach to math, and if it is different than it was when we started. Their reflection will be informed by Approximately Normal’s posts on student teachers, but I’m open to suggestions…

We’ll see if any of the kids want to follow their teacher’s footsteps and teach a lesson their peers, but if they do I hope they will be able to get through it.

 

#19/33* MTBoS  *I took two days off over the weekend, and I missed another one a week ago, so I am going to keep this thing going longer to make up for it (Or maybe I’ll just be one of those once-a-day bloggers).

Possible Misconceptions: Loan Interest Payments

So I was going to start teaching simple and compound interest in my banking and investment class so I started off with this question for the do now:

If you borrow $100 from someone and they charge you 4% interest, how much will you have to pay them after the five month loan is finished.

Before giving students time to work I asked eight people to weigh in with estimates, or guesses at what they could expect.  Each person in class had time to think and make a choice and gave an answer after considerable thought.  They also were told to estimate, they didn’t use calculators or much pencil/paper calculation.  They came up with quite a variety of answers, but (SPOILER ALERT) none of the answers were $104.  Here are some of the answers that were interesting.

  • $102.50 – Here students seemed to think the 4% means divide by 4, and perhaps they knew the ‘slide the decimal over’ rule. So it seems did 100/4=25.00, and then moved the decimal over.
  • $120 – Here a student was very certain that this was the correct answer. This student assumed that the interest was applied for five months straight, so they used the $4 of inters and multiplied it by 5 to get $20.
  • $145, $140, $160 – It seems that these answers were blind stabs in the dark.  Students probably picked a number that was sufficiently bigger than $100.

All these students were having trouble with guessing what would be an appropriate amount to have to pay back for this loan.  We talked about how easy it would be for them to get duped into paying large amounts of money for the different loans like the student loans and credit card offers they will see in college.  This set a clear context for the day’s lesson, which was talking about credit card APRs.

Numeracy is really important, as I saw in a recent blog post at Algebra’s Friend, there are a number of ways to help students build this skill.  I Plan to have students start focusing on doing that kind of thinking during the Do Now activity at the beginning of each class.  Students will start by working on tasks like the one below and ask them to think through it.

Which is a better deal?

Store A Store B Store A Store B
1 Television15% off of $300 Television250 5 Microwave20% off of 120 Microwave30% of 150
2 Stove
5% off of 500
Stove10% off of 530 6 Table60% off of 400 Table15% off of 200
3 Ipod30% off of 200 Ipod10% off of 180 7 Monitor25% off of 100 Monitor15% off of 320
4 Shake Weight50% off of 30 Shake Weight15% of 20 8 Health Master25% off of 120 Health Master10% off of 90

 

Each day we do it we will work on little tricks with percents.  I have taught a number of tricks before to help students do this (i.e. 50% is just half, 25% is half of half, 10% is just moving the decimal place over, etc.).  While it may be successful, I would like to have students understand the deeper concepts of number sense. (Perhaps I should take “Nix The Tricks” off of my Amazon wish list?)

 

What do you think?  What is the best way to teach percentages and number sense to high school students?

17/30 #MBToS30

Beware Of The Awesome Lesson

It started when I decided to take a topic and teach it out of context. Expected value is usually taught as part of the carnival project, but it’s also the thing that kids understand the least.  This year I thought that teaching it outside of that project might make it easier.

Teaching it separate from the larger context, is dangerous because it’s always clear if the kids will transfer the ideas to between the two contexts.  However, because the context uses expected value in a really structured way, t’s real easy for kids to only see it as a set of procedures.  This time I figured I could avoid this if I came up with a new, amazing context!

Deal or No Deal immediately pops in to my head. Through understanding how to win the game, kids could understand expected value!  So I plan it. I make a power point, I find a deal or no deal  game online, (then I find another game online that isn’t blocked by the school filter) and I get ready to teach.

I get up in front of class and suddenly the game starts expanding. The two minute explanation of the rules becomes five minutes of a really enthusiastic student describing her favorite episode. The five minute example game which should show how to make decisions using expected value turns into 10 minutes of me explaining to everyone that “I’d  just keep playing, ’cause, ‘why not?'” isn’t the best strategy.

All of a sudden, 45 minutes fly by and I realize the awesome lesson that I envisioned turned into almost a whole period of my voice.  Perhaps I should have been more cognizant of what students would need to be doing for this topic to be explored, instead of trying to squeeze in all the “flash”.  Instead I tried to squeeze a whole separate exploration with a big meaty context inside of one the kids were already invested in. We’ll see on Monday if we can get back on track.

13/30 #MTBoS

Helping Kids To Write Proofs Of Mathematical Phenomena

My observation was scheduled for today, but it didn’t happen because I had to attend a meeting so I won’t post about that today.  Since I am probably more concerned about keeping this #MTBoS30 streak alive than I should be, I am going to post a link to something else instead.  Below is one of my “Mathematical Thinking” worksheets from last cycle and I want to see if anyone could help me encourage students to write proofs on some of these tasks.

Generalizing Problems

In this worksheet I wanted students to work on proving ideas, by that I mean taking something that works in some situation, and showing that it works in many, or infinite situations.  I wanted it to appeal to a broad range of student content levels so all of the proofs are based on number concepts, not really algebra or geometry.

Students struggled in writing proofs, although most were able to make appropriate guess as to what the proof would show.  Students would largely show an example of any of these statements with different numbers, but wouldn’t know the first steps to actually come up with a proof.

For the first page, lots of students would say “7+8+9=24, 3*8=24, It works” and have nothing else to say.

I need help figuring out how to get students to write a statement describing how the phenomena present in their examples can be applied to the rest of the number system.

 

10/30 #MTBoS30

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