Developing Multiplication Concepts - the value of games and hands on activities

Well, it's been awhile since my last post.  I have changed schools and grades, so this has occupied a lot of my time.  I went from 2nd to 3rd and am very happy.  It was time for a change.  I am still in the same school district, but have moved to a grade 3-5 school.

Today it's all about the multiplication.  And I promise to get to that...

First, I want to say that while I absolutely can't stand the politics behind the Common Core I would like to say that some of the standards aren't that bad.  If you really read them you will probably agree that we fabulous educators were already teaching the standards as well as infusing critical thinking into our lessons all along.  But today I want to complain about textbooks, particularly my math textbook, which our district adopted because it was aligned to the Common Core.  I don't like it.  In fact, I don't like most textbooks.  I think I could write a much better version.  Gosh, I'm so humble, aren't I?  Why don't I like it? It is neither teacher or student friendly.  Most lessons are cumbersome and have 2-3 objectives for students to learn in one lesson.  Manipulatives are not built into the lessons and instead my students carry around a 2 inch thick workbook.  The lessons are teacher-centered and require the teacher to stand and talk for hours. (ok, that is an exaggeration, but it feels like hours, especially when the kids are zoning out)  Worst of all, is the fact that my third graders hate math.  At least they did when I tried to stick to the textbook lessons.  No elementary student should hate math!  But, the textbook can be used with my Smartboard, you say.  Isn't that wonderful?  Who cares when I, the teacher, am still the center of the lesson.  Sure, a few students can come up to the board and "interact" while the other 23 students draw smiley faces on the edge of their 2 inch workbook.

Enough of the complaining.  Now I'm going to get to the good stuff.

I am fortunate enough to work in a district that does not require I use certain materials or programs.  My superintendent and principal want me to use best practice in my teaching.  Isn't that fabulous?  So, put those bulky workbooks in your desk boys and girls - we're gonna learn some math.

Back to the multiplication.  I have always been a fan of Marilyn Burns, the guru of math education.  I was introduced to her lessons early when I was in college and continued to use many lessons and ideas from her books, published by Math Solutions.  But it had been a while since I had done multiplication.  Last week I pulled out my Circles and Stars lesson and it was a huge hit.  I forgot how powerful this simple little game was, and how much insight it gave me into my students' thinking about multiplication.

Our discussions after a round of playing the game were energetic.  Hands were up and everyone was engaged and wanted to share what they were beginning to notice.  How do you write 1 group of 4 as a multiplication sentence?  Oh look!  Every time you do 1 times another number it equals that number!  And they are equally delighted when they figure out zero groups of something is always zero.  Did you know that 2 groups of 3 is the same answer as 3 groups of 2?  And an investigation begins to find out if that is true for other numbers.  And it's fun to see them comparing and contrasting multiplication to addition.  Sometimes it seems I can see their little minds figuring it out and working through their confusion right there in front of me.  These hands on activities are priceless.  We must not let a textbook publisher determine how we teach a concept.  We must remember their first priority is selling a product, not educating children.  I do not think its wrong to make a profit, I simply think we, as educators. need to be smarter about the products we purchase and use in our classroom.

I've also involved my class in a study of multiples over several days.  We began with brainstorming things that came in groups - these lists will be used in future problem solving as well.  My students enjoyed creating T-charts to list the multiples of groups.  How many legs on 1 spider, 2 spiders, etc?  I thought using the hundred charts to color skip counting patterns would be baby-ish.  I was wrong.  This visual not only helped them see the pattern, but watching them incorrectly color the hundred charts showed me that many of my students didn't truly understand that skip counting was adding the same number over and over!  If they didn't know that how could I expect them to connect skip counting to multiplication?  Repeating these activities over several days helped my students to begin constructing their own understanding of  multiplication.  A worksheet could never do that!

So my teacher friends out there in blogging land - my message is to trust yourself.  The textbook makes us feel rushed. Look at how much we have to cover!  How will I get all these pages complete?  You know there is no reason you have to do every page in the book.  And a good hands-on activity often is a better bang for your buck - and covers several days of boring textbook instruction.  If you don't like the lesson in the book, don't use it!  Do you keep wondering why your students aren't "getting it"? Then try something different.  Play a game.  Do some hands-on activities.  Do it more than once. There is so much value and learning in playing over several days.  Slow down and enjoy the math!

The Evolution of My Math Workshop

I love the workshop style of teaching.  I love that it provides choice for students and instantly helps me differentiate my lessons to meet the needs of individual students.  I have used reading and writing workshop for many years now, and have been trying to use the same ideas during math instruction.  Here's how my math instruction has evolved over time:

When I first began teaching, I taught whole group lessons each day.  After the lesson students would work independently on the textbook assignment.  I would run around trying to make sure students were "doing it right", answering questions, checking work, and the most annoying part - reteaching the lesson over and over.  As I scanned the classroom, all I saw were hands up in the air.

Fortunately, my teacher preparation courses included an introduction to Marilyn Burns.  Her book,  About Teaching Mathematics, was  required reading.  I used her ideas for cooperative problem solving and began using them in my 4th grade class.  Soon, I began to dread the "textbook lesson" days and began looking for more ways to include hands-on lessons and problem solving.  There was so many parts of the math textbook that I didn't like - so I gave myself permission to use it as a resource.  As long as I was using my state's teaching and learning standards to guide my instruction I would be okay.  I started including lots of games in my math instruction.  Some of them were to practice skills and some of them included critical thinking.  While some days were "game days" I found myself using these Math Menus for those early finishers or for when I wanted to work with a group of struggling math students, the rest of the class played math games.  I could meet with those struggling students over and over and they still would be struggling!  I knew my struggling students would benefit from these math games and activities so I began searching for ways to create a math workshop.

When I began teaching second grade I tried creating Math Centers and even designed a rotation schedule.  This did not last long!  I found myself continually designing new centers and activities that often were just busy work.  Students were often off task and needed constant redirection.  (Probably because the activities were just busy work or designed poorly.)

My New and Improved Math Workshop

My new Math Workshop that I am trying out this year is inspired by the 2 Sisters, Gail Boushey and Joan Moser, creators of The Daily 5 and Math Daily 5 and also the book, Math Exchanges by Kassia Omohundro Wedekind.  I can't say enough about this book.  It was exactly what I was looking for and I gobbled up the book in one day!  (And of course have reread sections over and over.)  Kassia's idea of a small group math lesson, or Math Exchange, is very different than what I have done in the past.  Most of Kassia's small group lessons are problem based and the groups are not necessarily formed by ability.  She chooses who will be the group carefully.  Perhaps one student is using a strategy that she would like other students to see and learn.  The word "exchange" is used to describe them because she wants students to share their thinking with each other.  I have always done this in whole group, and hoped that other students would catch on to new ideas.  Wow!  Doing this in a small group sounded amazing.  With 5-6 students I could really facilitate some great math thinking.  But what would the rest of the class be doing? Yikes!  The same problem as before.  So after a weekend of thinking and reading about how other teachers create a Math Workshop this is what I have come up with.

Math by Yourself - Usually this is where students will complete a math assignment from their textbook.  I also have those Enrichment Worksheets available if necessary.

Math with a Partner - Students select a partner and play a math game.  I have a list of games they can choose from that pertain to the concept or skills we are working on.

Computer Math - They use the Netbooks that I am currently borrowing from a local teacher center.  We have a class website that lists math games they can play.

Math with the Teacher - Students work in a group with me!

I manage Math Workshop very much like the Daily 5.  Each round is about 20 minutes.  We may have 2 or 3 rounds depending on the schedule.  I usually start out with a short lesson or whole group activity.  Then I ask students to sign up for each round.  I announce the names of the students who will be doing Math With the Teacher, and which round, so they can plan accordingly.  We don't do Math Workshop every day because sometimes I need the whole math time for other lessons or activities.

How's it going so far?
Students love having choice and are more responsible and motivated to succeed.  They also love doing Math with the Teacher.  I introduced Math Workshop to my class at the end of November, so we have had about a month of experience.  My small group work, or math exchanges, are going well.  There are many bumps in the road, but that is to be expected.  For instance, trying to get the focus on their conversation and ideas instead of just my talking.  Reminding myself to talk less!  It's the quality of my talk, not the quantity.  When a student has great thinking that I want others to hear, I make a big deal about it.  "Wow!  Karen has something really interesting here.  Let's all listen."  I am also really getting to know my students math abilities in a more deeper level, which allows me to guide my instruction and learning better.  Most of all, my struggling mathematicians are moving along and not stuck anymore.

How do you use Math Workshop or Daily 5 Math?
Have you read Math Exchanges?