It's about this time of year that I start getting nervous and wonder if I am doing the right thing by spending so much time developing number sense and place value with my students. Why, you ask? Well, my fellow second grade teachers, who I admire and respect very much, are far ahead of me in the math textbook. While we count objects and practice strategies for using mental math in my classroom, my colleagues are teaching their students how to add and subtract with regrouping! Yikes! I feel so behind!
And here's another little secret about me. I don't always use the math textbook and often don't follow the lessons or chapters in order. I skip around. And I don't do all the pages in the book! I know! I am such a rebel. But, as I said before, I always get a bit worried or nervous or guilty around January or February because I am not keeping up with my colleagues.
But here's what I tell myself during these times of doubt.
Place value can be such a difficult concept to understand and I believe one way to build that understanding is to provide lots of opportunities counting objects.
Observing students as they group and count objects helps me identify their understanding and misunderstandings about place value and number sense. I think many of our math textbooks and worksheets mislead us into thinking our students understand place value because they can identify the tens and hundreds place, tell you what a digit is worth or even build a number with place value blocks. But ask these same students to organize and count large numbers of objects and you quickly see that they can't count transfer their knowledge of place value blocks to objects that aren't already grouped for them.
When I give my students time to organize and count larger quantities I see first hand how they begin to internalize our place value system and see the patterns. I can tell them there are 10 ones in a ten or 10 tens in a hundred until the cows come home, but when they notice it themselves and share it with a peer or their teacher it sticks! Watching a student who preferred to count her objects by ones begin to group objects by tens, and then to move on to grouping those tens into hundreds shows me how that student is building a strong understanding of place value.
On the days we count collections it's a bit loud and messy. Groups of students are laying or sitting on the floor, cups and bowls for organizing are out and there's always lots of excitement. My job is to facilitate. I move around the room observing and asking questions like, "How are you counting." "What are you noticing when you count?" In the beginning I sometimes have to help students communicate with each other. Working cooperatively is very new to most of them. I also stop and share with the class when I notice a group using an efficient counting strategy or when a group has what I call their "Ah Ha!" moment. Since our collections are large with more than 200 objects to count it forces students to become more efficient with their counting methods. When one group becomes overwhelmed while counting by ones I can ask, "Is there another way to count so you don't get confused." Or I can share what another group is doing. "Look at what Katie's group is doing? They are organizing in groups of ten. Do you think that might be helpful?"
I love the math conversations I hear while we are counting collections. All students are engaged and motivated. Everyone, whether they struggle with math or excel are challenged and successful during this time.
I will continue to doubt myself and my methods periodically but that is probably good because it forces me to reflect on my practice and fine tune my lessons and activities.
You can visit my class blog to see counting collections in action.
Do you use Counting Collections in your classroom?
What are your thoughts regarding how students develop place value?
Showing posts with label math workshop. Show all posts
Showing posts with label math workshop. Show all posts
Sunday, January 6, 2013
Sunday, December 30, 2012
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?
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?
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