Urban Public Education

Just returned from a great panel discussion at NYU entitled Looking Ahead: What is working in New York City for Educating Our Children?  As one might imagine from such a title, there were amazing and thoughtful conversations happening, some of which bring out strong opinions from the audience. 

To keep this short, here are the six biggest thoughts that resonated with me:

1. While we are doing a good job of recruiting passionate people to teach in NYC public schools, we really need to make sure we provide them with a high level of quality preparation for the field. 

2.  While some schools are failing or teachers are struggling, there are multiple and varied successful schools and master teachers out there that struggling schools and teachers can learn from.  The problem is in the lack of networking created or encouraged by the DOE. 

I pause here for a shout out to Math for America.  As it continues to grow and adjust to the needs of the teachers in the NYC public school system, the organization is working hard to fully prepare passionate teachers and network those who are struggling with those who can provide help.  Go MfA!

3. In addition to quality instruction, what students want is a teacher who cares about them on an individual level, believes in them and develops strong relationships.  What students remember is when the teacher played the role of counselor/advisor/parent/mentor more so than the quality of math activities.

4. While we use our passion to try to help close the achievement gap and give students who have very little a whole lot of hope, we need to be honest with our students about the reality.  We need to let them know that there is a disparity between public schools and expensive private schools, and if our students want to succeed, then they have to “run twice as fast.”

5. The structure of our school and the school day has not been updated too much since we upgraded from the one-room school house.  What new structures can we imagine?  What would best serve the students in an urban school?  Has anyone ever asked students what they wish their education looked like?  Can we extend the school day without extending the work put on teachers?

6. This question may be more relevant to NYC than many other places: can neighborhood schools work?  They often work in the suburbs and help strengthen a community.  Why have we moved away from this in NYC and can we find a way to productively return to this concept?

I have to end with two last thoughts.  The first is a quote shared by one of the panelists on tracking:

“Tracks are only a problem if the tracks lead nowhere.”

Second, as a follow up question, what are your thoughts, dear reader, of what the current city administration (i.e. Bloomberg) has done to better the public school system in NYC?  As well as thoughts on any of the six points I listed.

What is Algebra?

If anyone is still out there reading this blog after I took a long hiatus, please indulge me with a response.  How do you define algebra?

I just came from a great PD led by the lovely Kara Imm.  She brought research concerning the lack of “algebraic thinking” in K-6 math, where arithmetic is taught almost exclusively and algebra is the step that follows for “those who are ready.”  (I think some high school teachers have this mindset about Calculus.  Students need to learn Geo/AlgII/PreCalc really well “to be ready” to start Calculus.)

So if (as research shows) it would be better to teach arithmetic and algebraic thinking from the start, can we first define algebra?

A New Year of Debating…

After a lovely dinner with the splendid Sam Shah, I realized how much I love discussion of math and pedagogy and want to get caught back up on this blog!  I can’t believe I haven’t written since September.  I will get better.  I promise…

Anyway, classes have been going well, but one thing I wanted to mention (encouraged forever ago by Sam) is how I handle a lot of theorems and conjectures in my class.  I try to make my class as “discovery based” as possible.  It is also of interest to me to model how real math discoveries work.  So, in my class, students are encouraged to be “the first” to discover a new pattern/idea/conjecture, and as a reward, they get to name the conjecture.

Here’s a great example: I start of PreCalc every year with logic.  We explore and/or/if…then statements with concrete examples, abstract symbols (p’s and q’s) and kinesthetically (with this cool note card idea I will blog about someday).  When it comes time to discuss the negation laws, students are given a task to find the negation on their own.  The students struggle with it the first time, but eventually someone comes up with and names the rule for negating an “and” statement.  In the past, it’s been called Kira’s Law or Janelle’s Law, etc…much more fun than DeMorgan’s Law or what my textbook blandly calls Negation Law #1.  Blah…After the first one is named the students go crazy (like, CRAZY) to get to name their own law, and they look forward to new laws being discovered (and sometimes come up with their own side laws!) throughout the year.

What was especially fun this year was students started sharing the naming with their partners.  So instead of Trevor or Moses claiming they were the true founder of the law, they named it the Mosever Law.  Catchy, fun and led to a brief discussion on why some more advanced theorems in math have double names!

 

Student Engagement & Ownership, Day 1

One other start of year success I want to mention:

I was thinking about ways to make my classroom very student centered, as my school has really taken on the Danielson framework for teaching, focusing on select specifics such as Domain 2b: Establishing a Culture for Learning and Domain 2d: Managing Student Behavior.  In this subtopic, a teacher can be rated as distinguished with evidence like:

• Students demonstrate through their active participation, curiosity, and taking initiative that they value the importance of the content.
• Instructional outcomes, activities and assignments, and classroom interactions convey high expectations for all students. Students appear to have internalized these expectations.
• Standards of conduct are clear to all students and appear to have been developed with student participation.

That last one really struck me as new, as I’ve always been a dictator about classroom rules.  So, I was contemplating how to go about activating students to develop their own rules while keeping things in order.  I also wanted to up the level of student discussion and participation.  As a result, my first thought was to have students to come up with the classroom rules on the first day. They could write them down, or we could have a class discussion, and together we would come up with appropriate rules, rewards and punishments (and we’d all be one big happy family…).

However, I had a chance to talk it over with the AMAZING Sam (of Continuous Everywhere…), and he had the same fears I did about such an open policy on rules.  His suggestion (which I implemented [and it worked wonders!]) was two-fold.  First, I had a discussion with students after reading through my syllabus (where I came up with my rules already) about what makes a productive student.  The class came up with great ideas and examples of what a productive student looks/acts like.  I also had them give a why to each statement, as in “a productive student is not on his cell phone because that would keep him from focusing on his work” or “a productive students works through the problems slowly and thoroughly so that she has a strong understanding of the problems.”

Then, as class came to an end, I gave students an exit slip, where they answered four brief questions, reflecting on the classroom rules in the context of our discussion.  I asked questions about the classroom rules, such as if there was anything they would like to change/add to the syllabus.  Students gave great feedback.  Most were happy with the way thing are, a few gave great suggestions.

I spent 4 or 5 minutes at the beginning of the next class discussing some of the results.  I explained one or two rules that students had mentioned that I (unfortunately) would not change, but I was able to discuss exactly why that rule is important (like my cell phone policy).  Then, I discussed the two rules changes/additions I was going to make.

Overall, I think the students are all happy with the classroom rules, many of which are fueled by debate structures I’m using.  What’s new is that the standards of conduct “appear to have been developed with student participation.”

The Mathdebating Begins

The school year has started, and I’m already falling behind with this blog.  Eek!  Today I read (or maybe did some skimming of…) the 43 latest blog entries in my Google Reader (that I had also fallen behind on), and I finally fell inspired to get to work.

I’ve already started implementing various debate structures and activities in my classroom, and it’s already making a difference in the student discussion.  Here are some of the things that I started with:

1. Stand Up to Talk.  The first day, when I was going over the syllabus and having students introduce themselves, I talked about the upcoming year and how they would be debating in math.  Eyes started lighting up.  With this buy-in, I told the class that one important part of debate is standing to give your argument.  So as we went around the room, students quickly stood and briefly introduced themselves.  Easy structure, nothing new, but sticking to it comes in handy…

2. Argument Structure.  I am beginning both my PreCalc and Geometry classes with a brief unit on logic and proof, and debating is fitting in oh-so-nicely.  One of my first lessons was about arguments, which I blogged about in the last post.  Students quickly caught on (and got excited about) the “Argument = Claim + Warrant” structure.  I informed the class that whenever they were discussing their work/solution, they should format their discussion as “I claim…, and my warrant is…”  Again, nothing complicated, but it’s reinforcing the need to always have an explanation to follow any statement you make in class…

3. Soapbox Debates.   For our first debate activity, I used the Soapbox Debate format, where students take turns standing and voicing their arguments.  After a brief laugh with my class about the fact that I was the only person in the room who had ever heard the phrase “get off your soapbox…”, we proceed.  I started with the statement All students should wear uniforms, (we are a uniform public school) and eventually got to some stuff a little more “mathy” like Some functions must cross the x-axis or Between any two numbers there is always another number.  Though the latter two have more of a definite answer, this answer was not apparent to the kids, and led to a good, clarifying discussion. Also, the wording led to a great discussion of the importance of words like sometimes, always, must, etc.  (Thanks Bill for putting this in my mind with your last comment!)

4. One Mic.  The students and I discussed how we can only listen to one argument at a time and how important listening is in order to respond in cross-examination.  We also talked about how winning a debate is somewhat influenced by your appearance and behavior.  So, right away, students had a strong need to behave in my class and listen to each other.  When we started the soapbox debate, students were awesome about only talking one at a time and listening to each other.

5. Students take charge.  Because of the debate format (even the simplicity of soapbox), students become engaged and passionate about the discussion.  I started off the soapbox debate by cold calling on one or two people.  (I have a stack of index cards with student names that I use for cold calling.)  I told the students that I would pause after each person spoke.  This allowed a chance for a student to stand up and start talking (“I claim…) before I did another cold call.  It only took two cold calls before students took over the discussion for each of the statements I gave them.  Each statement had about 7 or 8 people standing up to say something about it, and most debating came to a natural end when there was a pause in the debating.

I was so excited at the success of this lesson!  It was totes in line with PCMI’s non-negotiables with classroom discussions and activating student ownership AND with the Danielson framework that my school is working in depth with this year.  It’s a win-win!

The Basics of Mathdebating

After a great three weeks in Utah, I flew over to Boston for a one week conference run by the Boston Debate League on using debates and debate techniques in all subjects.  Formerly called Debate Across Curriculum, the program is now called Evidence-Based Argumentation (EBA).  The week I went to was particularly focused on math and science teachers.  More information can be found on their website here.  I have a TON to say about this conference: thoughts to express, ideas to share, projects to try out, etc etc.  So the next few posts will slowly unravel all that is bouncing around in my head about this.  Many people may wonder how debate works in math or why try to blend the two.  I have tons to say on that and maybe my next post will explore the why.  For now, I just want to get some of the basics of debate (at least as the Boston program taught it) to give a starting point.

The program has a 5-step process to developing EBA, and the first step is making a basic argument. The formula for an argument is:

Argument = Claim + Warrant

where

     Claim = a controversial statement

     Warrant = reason why your controversial statement is true

I know many people instantly think arguments fit well in an English or History classroom but believe that “controversial statements” are rare in math.  This is not the case, but I will expound upon this in a future post.  Right now, I want to focus on the basics.  Suppose I said: “Exponents make a number bigger.”  All the math teachers may instantly snap to a counterexample.  However, from the point of view of a student (especially one who has not seen rational exponents), this may appear controversial.  What I would want from students at the beginning of the year, when they are first learning to mathdebate, is a response such as

“I claim the statement is true, and my warrant is that an exponent makes a number multiply by itself and thus get bigger.”

Other students can agree or disagree and add their own comments.  When developing basic arguments, a warrant can be a bit general or could be an example.  The focus here is on the structure.  A lesson or two later things will get more serious…

I begin my classes (Geometry and PreCalc) with a bit of basic logic (conjunctions, disjunctions, conditionals and negations), and I think it’d be great to define argument on the first day, as we define statement and open sentence.   This will blend debate into the basic structure of the class and help as develop explanations and proofs.  I think students will get so accustomed to the gimmick of “claim + warrant” that explanations will become second nature to them in a more natural way.

One last note: controversial statements can come in a wide variety.  From less mathy opinion questions (math or non-math related) to more mathy equations and applications.  Using words like best or worst easily make many statements controversial.  Some quick examples off the top of my head are:

• Math is the most important subject in preparing for a future career.
• A calculator is the best tool for solving a math problem.
• Every number has a square root.
• The best way to solve this quadratic is by completing the square.
• Verizon has the best cell phone plan for someone who uses a lot of daytime minutes.

I particularly like the last one as it requires students to research on their own.  Much of the research these days encourages teachers to give less direct scaffolding and promote student “struggle.”  Controversial statements and open ended application problems provide these opportunities for students struggle.

I will get into more interesting (and complex) uses of arguments and debate in math in the upcoming posts.  I hope this post summarizes the basics.  I could easily get students engaged in this first lesson by making several of these controversial statements (ones that don’t require research) and having students respond in one of two ways.  First, I could set up the room for a “Four Corners” activity, where each corner of the room has a label (agree, strongly agree, disagree, strongly disagree) and have the students react to each statement by moving to the appropriate corner of the room.  Students would then be called on to explain their stance with a basic argument.  Second, I could use a “Soapbox” activity, where I call on students one at a time to stand and give a basic argument.  Again, this is all very simple, but my focus is on developing the structure (and build excitement around debate).  We will get to the really fun stuff quickly.

If anyone has good ideas for some simple but controversial math statements, please comment below!

Lastly, as I said in the last post, I want to end each post with a topic for debate.  However, I ask that you please reply in the basic argument format, explicitly using the words “I claim…and my warrant is…”

CLAIM: High school math’s most important aim is to prepare students for Calculus.

Ode to PCMI

After three weeks at the Park City Math Institute (for the second summer in a row!), I have to begin this blog with love for the folks at PCMI.  If I hadn’t attended, I would not have met the lovely people that guided me to this blog.  It’s due to them that I am now blogging, tweeting, polling, facebooking, texting, youtubing, metubing…Shameless brown nosing aside, let’s move on.

I’m now at a Debate  Across the Curriculum (DAC) conference in Boston, and it is the perfect complement to PCMI.  After three weeks of theory and discussion, I’m now attending a week of concrete lesson planning (but more on this conference later).  Looking back at my three weeks in Utah, I’m realizing that for me the most important part of most conferences and professional development opportunities is the free time.  By this, I mean the chances we get to talk with colleagues about our ideas and practices.  My first summer at PCMI there were so many “parking lot conversations” that just happened as we were walking, rambling about our lives and somehow getting into a deep discussion about teaching.

That said, in the spirit of debate, I’d like to hear your thoughts, for or against the following claim.  Since debate is in the title of the blog (and a large part of my job), I thought it’d be great to end each blog with a topic to debate.  I’m starting easy this time.  Please leave comments below with your thoughts.

CLAIM: Professional development opportunities and conferences should be reduced to allow for more conversations between teachers.