Checkerboard Problem Re-Cap

The first day is over and the lesson was a success!  The "less is more" philosophy really paid off today. 

We did not take this problem to completion in one lesson.  I allowed plenty of time to wrestle with the idea, intersperse questions to assist in next steps, and left them dangling....I encouraged them to think more about the problem and to discuss it with their family but asked them not to Google this problem just to get an answer.

It was challenging for this teacher to not give away the answer and the procedure just to finish up the problem for the students! Letting them do the work means I need to ask thought-provoking questions and stay out of their way!

I asked students to complete an exit ticket and answer the following questions:

1. Something I liked about math class today...
2. Something I learned in math class today....
3. A question I have....

There was a pattern to their responses that was so gratifying and encouraging to me. Here are common responses to today's experience:

Students overwhelming said they liked the problem and found it fun, exciting, hard, and challenging. They liked working in groups and being able to talk the problem out with their friends and meet new students as well.

Here are some favorite quotes: " I liked that we really used our brain",  "we had to think", "it got me thinking real hard", "I had to really think, not guess", and "Our first problem was difficult and difficult problems help me learn."  WOW!  I did not prompt any of this thinking in them. They knew it all along no matter what their "level" of ability or achievement was.

In response to the second question, students commented frequently that they learned something about counting squares on the checkerboard, but they also remarked that they learned that you should "look closely for patterns," "you write down what you think", and "math can trick your brain."

Overwhelmingly, the students' question was all about finding the actual number of squares on the board (I've got them hooked for tomorrow!) and finding out if they were going to do more problems like this one.  My favorite comment: "How come math has so many cool things?"

I'd say I did my job today - get kids curious about math problem-solving, help them persevere, and make them beg for more! Need I say more - I'm eager for Day 2. The plan is to talk about the strategy of keeping an organized list, using a smaller case to help solve this bigger problem, looking at the emerging pattern of square numbers/square roots, and then predict how many squares on a 10 x 10 grid.

FIRST MATH LESSON OF THE YEAR

Do any of you teachers agonize over that first lesson of the school year as much as I do? I've decided that I want to spend the first hour with my new recruits diving into content more than yadda-yadda-yadda with my syllabus and class rules.  Let's get a taste of what this class is going to be like everyday! Then let's talk about how we're going to make that class operate like a well-oiled machine.

So, I've been agonizing about lesson plans. What to do? I want the lesson to be challenging, engaging, reflective, a learning experience, an assessment of general skills, and a little bit of fun as well. It's similar to the experience of Writer's Block - I just can't commit an idea to paper until I think it's "just right." This morning I'm taking the plunge.

 

After the usual attendance record-keeping, making sure the kids are in the correct class, and introduction of myself to those who didn't come to our summer school, we are diving into group problem-solving with Checkerboard Squares. The directions are simple: Find the number of squares on this checkerboard. Record your thinking. We're going to have our first math discussion and student display of their work. My objective is to see how my newbies work together and how they persevere in problem solving.

There are many descriptions of this activity online. Here's an interesting interactive model: http://www.donbeaty.com/CJHS/checkerboardmodel.htm. Or look at this: http://math.rice.edu/~lanius/domath/page2.html.  I might use these after students have quite a while to wrestle with this problem or as an explanation. Today I want to dive into allowing my kids the opportunity to struggle a little bit with some guidance a la Mathematical Practices.

It's going to be a great first day!


 

 

 

I Notice....I Wonder Part 2

I can definitely say that the professional development I have been doing recently has been sinking in! I was walking into the building the other day on my way to my classroom.  I've made this trek countless times over the last seven years, but this time was different! Do you see what I see? What do you notice?  What do you wonder?

Yes, that floor sure is shiny and clean!  I love the way it looks before about 800+ feet scuff it up and drag in half of the playground. But that's not what I noticed....

I had never noticed the potential of a math problem in the tile design of the hallway! My math nerd went into overdrive and began thinking of math problem-solving that could result from my observation!  There are three different colors of tiles in this hallway....I wonder if that is true all the way around the building.  I could quickly think of some area problems as well as a great connection to algebraic thinking! I wonder if the kids would enjoy roaming the hall and coming up with some problems of their own. Hmmmm.....

I would like to throw this picture out to the kids as a warm-up during that first week. And just ask them....what do you notice? what do you wonder?  I've been reading great math blogs by Dan Meyer and Fawn Nguyen about modifying the ordinary math problems kids see in math books and transforming them into rich mathematical experiences.  I wonder what they would do with this....

I Notice...I Wonder

Six days and counting until the new school year begins.  I have a mixture of knots in my stomach doing somersaults with the butterflies of anticipation.  In my early morning research today I came across a nugget I want to share with all my geeky math teacher friends and anyone else who wants to expand the conversations in their life.

I notice that I am always excited about the new school year...even after 34 years.  I wonder if my students are as excited about the start of the school year as I am.

What are you noticing and wondering?

http://youtu.be/C_DgSWEAUbQ

Mistakes

This morning I've been listening to more of the material from the How to Learn Math course. The focus today has been on the importance of making mistakes in the process of learning. Too often, students are afraid of making mistakes and not looking or feeling smart.  We teachers have not done enough to create an environment where students feel safe to muck about in learning. We have given them the deadly impression that you've got to get that answer right the first time and you'd better be quick about it as well! This takes more than "think time" before answering. In math, it means spending lots of time digging into challenging problems that require students to persist in the face of wrong turns and dead ends.  That's where the real brain growth and learning takes place! The culture of testing and results has put us on a speeding train to nowhere with our students. It's time to slow down, dig deeper, enjoy the process, and really learn. Thanks, Joan, for offering this course. Here is my poster I've made to remind me and my students that there is great value in those mistakes!

Reforming Mathematics Instruction

Joan Boaler  Stanford University web site

Currently I am one of the 20,000 (yes, you read that correctly!) people signed up to take an online course from Stanford professor, Joan Boaler, called How to Learn Math.  This online course is a FREE version of a course that she teaches at Stanford which helps students change their mindset about math.  What a great opportunity!

We read a portion of an article by Paul Lockhart in which he describes what is wrong with mathematics education. He compares the teaching of music to the way we currently teach math to students. In his analogy, we would teach students all about the notation of music, how to write the different scales, transpose keys, and take tests yet never listen to music or write music. His description of such a ridiculous method makes his point clear.
                                                                                                                 
The current movement to Common Core standards is not just a re-arranging of objectives throughout grade levels although some of that is occurring.  It is more than just another opportunity for textbook publishers to slap a new sticker on the front of their current over-priced, lackluster books that say "Common Core aligned."  It is more than just "hands-on" activities with manipulatives. This change in mathematics education is a fundamental way of teaching and learning.

What we are demanding of ourselves is to teach in ways that are challenging for both the student and the teacher. These methods demand that we have high expectations for children through problem-solving and digging into their thinking. It is not rote memorization (but there is some of that, too!) - these methods ask us to approach mathematics with curiosity, wonder, beauty, and innovation. We will ask students to wrestle with a situation where mathematics can be employed. We are asking students to nurture the joy of solving a puzzle, discovering a pattern, devising a rule, and creating new ways of looking at the world. We are asking students to persist even when they struggle.

After teaching thirty-four years, I have seen the waves of teaching reform ebb and flow. One thing is certain, none of those waves has made enough impact for our children.  Today I am attending a day-long class with my fellow math colleagues to dive more deeply into the Common Core. The Common Core is the tidal wave of changes! I've got my surfboard, and I'm ready to ride!

P.S. I'm back from my "training" today. So disappointed and discouraged. We were treated to two fine examples of engaging activities. The rest of the day was a bore, not challenging, unenlightening, and a waste of my time. Sorry to say that but 'tis true. I would have enjoyed more time listening to Joan!

Concept Map Assignment for EDUC115N

Summer Vacation?

(This is for all of you folks who believe that we teachers "work only nine months, have three months of vacation, and go home at 3:00 every day.") Summer vacation. I have two glorious weeks of unstructured time left before the school year begins July 29. I have relaxed and had time for my private, creative pursuits.  I finished teaching summer school at the end of June and spent a few days in the cool mountains of northern Arizona.

My mind, however, has not stopped working. I've been reading several new books - three of which are about teaching and teaching math, in particular. Oh, yeah, I finished reading a novel also. Today I am looking forward to the start of an online course I'm taking from a Stanford University professor. I couldn't pass up the opportunity to take a free course on teaching math. Next week I have an all-day workshop with middle school math teachers in my district.

A teacher is never really totally on vacation. With computers, the Internet, and, now, Pinterest, there are so many ways to link up, blog, and find the best of the best ideas for teachers. We are pretty much on it 24/7. Would I trade it for a 9 to 5 desk job without 140 papers to grade into the evening? No way! Although I stretch myself thin during the school year with very little free time for myself, I wouldn't trade a single moment of the last 34 years.

Retirement? I've been thinking a lot about it. Sometimes the demands of documentation and accountability to legislators just about does me in. Sit at home and find a closet to re-organize?  Nope. Not for me. As long as I look forward to those young faces, want to find new ways to reach their mathematical minds, and love shopping for school supplies, you'll find me in my classroom.

As for vacation, I'm learning to include a little vacation every day in my life. Not waiting for the big moments. Two weeks and counting...in my world, a new adventure is beginning very soon!