I Notice, I Wonder (Part 1)

Over the past month or so my Honors Geometry students have begun to have issues with my class. Not issues with me personally, but issues nonetheless. The bane of their recent mathematical experiences?  The thing that gives some of them nightmares of broken pencils and worn out erasers?  Yes, the very thing that I personally loved about Geometry in high school has become the new four-letter word in Geometry.  OK...so it has five letters.  

Why don't students like proofs??  I think after 21 years of teaching I may have found the answer!  Well, at least part of the answer from attending a talk at ATMOPAV (Association of Teachers of Mathematics of Philadelphia and Vicinity) last Saturday.  The reason students don't like proofs...(insert drumroll here)...is because they don't understand them!  Thanks to Annie Fetter (@MFAnnie) from The Math Forum for helping me re-think this based on ideas from her talk "Ever Wonder What They'd Notice (If Only Someone Would Ask)?"

Gee - students don't like proofs, because they don't understand them.  Not really an earth-shattering piece of information there, Leigh.  I agree, but do we ask students to understand what is in front of them before they see the given information or what it is that they are to prove?  Do we require them to take some time to notice and wonder what is happening in a given diagram?  I know I had never done that before with my students. 

So on Sunday night, I found a problem from our textbook that I would turn into a 2 day "Notice & Wonder" problem.  The image shown here is what my students got from me.  Notice that it doesn't have any information about angles or segments.  There is no "Given" information.

First, my students worked individually for a few minutes, completing what they noticed and wondered about the diagram.  Then, they were put into randomly assigned groups (Did I mention that I love playing cards for random assignment?) to discuss what they noticed and wondered.  Last, we came together as a class to compile a master list.

Before I share their lists with you, what do you notice and wonder?  Be sure to check back to see their lists and how we moved some items from the wonder column to the notice column.

What I Like About Twitter and PLC's for Math

One of my favorite (buzzword altert!!!) PLC's is all the Twitter Math & Teaching peeps that I follow. It was only last spring that I realized how invaluable Twitter can be for math teachers. (A shout out and thanks to @mgolding for getting me hooked on Twitter and interested in/involved with The Global Math Department.)

Here is what I really love about Twitter: Within 2 minutes of looking at math tweets, I have found either something I can use in my classroom or something that someone in my department can use in their classroom.  Really - that is no lie!

Example #1: Finding alternative assessments that give each student something different to do is not always easy.  When looking through Twitter in April of last year, I found an idea that I shared with the PreCalc teacher at my school.  It was called the Birthday Polynomial.  She used the idea and made it own.  Plus we had tons of student created posters to decorate the math hallway.  I think I got it from here: Birthday Polynomial

Example #2: (From about 5 minutes ago) I am going to be renewing my National Board Certification this year and I need to find more ways to get students to reflect on what they are learning and how they think class is going.  While searching one of the suggested math blogs http://made4math.blogspot.com/, I found something that I can use!

You might be saying, "Sure - it's easy for you to find useful items, but I don't want to wade through tweets that don't apply to me."  You don't need to! I organize my Twitter feed in TweetDeck.  Here is a screenshot of my twitter feed as organized in Tweet Deck. This pic shows only 4 of my the twenty columns I have set up in Tweet Deck.  

If you want to learn how to TweetDeck, here is a link to a youtube video and here is a link to a wikihow on How to Use TweetDeck.

Mrs. Nataro's Postulates of Learning

This year I have set a goal to post to my blog twice a month.  Thanks to the blog prompts at Exploring the MathTwitterBlogosphere I may meet this goal for the next 2 months.  For this blog, I have decided to address the following:

What is one thing that happens in your classroom that makes it distinctly yours? 

Here is what makes my classroom unique to me:

About 10 years ago, I was writing my opening letter to parents and students and came up with the idea of Mrs. Nataro's Postulates of Learning.  I wanted students and parents to know what I personally believed about learning mathematics in my classroom.  These postulates are also prominently displayed in my classroom.  Here are my five postulates:

1)  All students are capable of learning math.

2)  The use of prior skills and knowledge is required to build new skills and knowledge.

3)   Learning is a collaborative effort.  Helping others learn will help you to learn.

4)  Asking thoughtful questions is a primary way to open your mind to learning.

5)   Choosing not to do an assignment will rob you of the opportunity to learn.

These postulates really do guide my teaching and what happens in my classroom.  First, I really do believe that all students are capable of learning math.  Once the student believes this of himself or herself progress can be made more easily.  The second postulate may seem obvious, but many times students start to have difficulty in math because of a misconception or shaky foundational knowledge.

The third and fourth postulates can be seen in action on a daily basis in my classroom.  Students quickly come to learn that I want them to work together on assignments.  Sometimes they are randomly assigned peers for a specific project and other times I have them compare work with their neighbors.  After I help a student with a problem, I have them explain the solution to one of their peers.  At first students think this is a little strange.  However, they soon see that they really do understand better after explaining an idea to someone else.  In addition to working together, students are not afraid to ask questions.  I encourage questions with phrases like "I am really glad you asked that question." or "That is something I hadn't thought about.  What an interesting question."  I often find myself sharing the questions that my first period class had with my second and sixth period classes.  The questions are that good and I want all my students to benefit from them.

For the fifth postulate, students quickly see that my assignments aren't "busy work" and that they really are an opportunity to learn more.  If a student doesn't have an assignment completely done on the day it is due, he or she still does the assignment to show to me, even when a point or two is deducted for the assignment being late.

As we review my postulates in class on the first day of school, I point out that these postulates are about learning in general.  And I encourage my students to apply them to any subject they are studying.