Wednesday, March 17, 2010
Start by reading the problem to the children. Let them work individually or in small groups to solve it. If the answer requires writing, encourage them to use “kindergarten” (phonetic) spelling. It may not be pretty (or even decipherable) at this point in the year, so expect to go around and do a lot of dictation. It is more important, right now, for kids to be able to talk (than write) about their solutions.
When most of the children have completed their solutions, bring them to Mathematician's Chair to share/discuss their answers. (See tips here.)
You will be amazed with the variety of answers kids will come up with for this question. Of course, there is The fish--because it lives in the water. But then again, it might be The cat--because it can't swim. Or The fish--because it doesn't have legs. Or The cat--because the dog will chase the cat and the cat will eat the fish, but the dog and the fish will get along just fine!
Seems simple--3 tails, 3 cats, right? But wait--maybe it's 10 cats, but only 3 are sticking out their tails. Or maybe its Zero cats--there are puppies in the box. Here's a great question for Mathematician's Chair: Can there be just 2 cats in the box?
Is it a dog? Cat? Elephant?
Tuesday, March 16, 2010
This problem serves several purposes. First, it's very easy, so it will let the children experience success and gain confidence early on. (We want them to love--not dread--problem solving!) Second, it gives them a chance to practice the expectations they just learned (especially the One page at a time and Do your best work!)
During Mathematicians' Chair, focus on notebooks that have neat, organized work (i.e.the eyes are clearly present). Look for children who wrote the number 2, but look for other ways that children may have represented the number 2 (for example--did anyone make two dots?) If nobody did, ask the kids for ideas about how they could represent the number 2. Call for volunteers to show different ways to represent the number 2 in the Big Class Notebook.
Day 2 is another fairly easy problem. The focus should be on How can you show your answer? Some children might draw a literal picture. Others might draw symbols. Many may write the actual number. During Mathematicians' Chair, ask the children how they found their answer. Get them to use the word count... "I counted!" Ask for several volunteers to demonstrate how they counted. Also, point out the variety of ways that children showed their answers. Point out children that used more than one way to show their answer.
This is a good problem, because there is such a variety of answers. During Mathematicians' Chair, call on several volunteers to write their names in the Big Class Notebook and demonstrate how they counted. Begin to point out good counting strategies! Showcase journals that are neat and organized. Look for alternate ways to represent numbers.
This problem introduces pattern blocks. It also allows children to practice counting and representing number in a neat/organized way. I introduce the pattern blocks in warm-up, and go over all expectations for using them (i.e. do not throw them or stick them in your nose...) Then I let them have at it and "play" all they want.
When we are ready to problem-solve, I give each student a baggie that has 20 pattern blocks that they can choose from so that they do not get carried away and create a monster that has 72 green triangles! They still have freedom to create what they want, but are limited in number.
During Mathematicians' Chair, have children demonstrate how they counted their blocks. Did they leave them in their design, or did they mess up their design and line them up, or push them away as they counted? Did they touch each block as they counted? Have the children discuss what they think the best counting strategies are and record them in the Big Class Notebook.
This problem introduces unifix (or linker) cubes. I introduce them during warm-up--going over all the expectations (see pattern blocks above) and then letting them play.
When it is time to problem-solve, I demonstrate how to use one hand to grab as many cubes as I can. (This is a great problem to use throughout the year. Differentiate by using smaller manipulatives to produce bigger numbers and bigger manipulatives to produce smaller numbers!) Again--look for good counting strategies. If a child is unorganized and mis-counting, ask, "Can you think of an easier way to count the cubes? How can we make sure that we count all of the cubes? How can we make sure that we don't count a cube twice?"
During mathematicians' chair, call on several children to demonstrate how they counted their cubes. Add to the list of Good Counting Strategies. Hang it somewhere very visible so the children can reference it later.
(For all of the Investigations fans out there, this is a variation of the classic Grab and Count!)
Thursday, March 11, 2010
Before you begin Mathematician’s Chair, talk with the children about what it means to be a good listener. I always tell them I want them to listen with their eyes (look at the speaker), their ears (listen to the speaker), their brains (think about what the speaker is saying) and their hearts (care about what the speaker is saying).
Then teach the kids how to respond appropriately to someone else’s solution. I often ask, “Do you agree?” and then, without talking, all the kids give me the sign for either yes or no (we use the American Sign Language signs, but you could also use thumbs-up/thumbs down). I will then call on specific children, “Joey—tell me why you agree.” “Alex—tell me why you disagree.” In either case, the students MUST be respectful.
We talk a lot about hurtful words vs. helpful words (not just in mathematician’s chair—but in every part of our day!)
We also talk a lot about mistakes—and how wonderful they are!
So it is OK to make them. (I also point out all the mistakes I make. But before long, I don’t have to—the kids are more than happy to point them out for me!) Bottom line—I want the kids to feel comfortable sharing, whether their answer is “correct” or not.
Once the kids are sharing, your job is to guide them. In the beginning, you’ll have to do A LOT of guiding. Tell me what you did. Why did you do that? What did you do next? What did you do next? Expect a lot of one-word answers.
Ask them questions that might get them to think of something they hadn’t before…What would happen if…?What else could you have…? If there is a particular strategy you would like them to use that they just don’t seem to be discovering on their own, guide them in that direction by asking questions. But make them think they thought of it all by themselves!
Always end Mathematician's Chair with a big round of APPLAUSE for the kids who shared!
Remember… as with everything problem-solving, Mathematician’s Chair gets easier as the kids gain confidence and experience!
Wednesday, March 10, 2010
I use a notebook so I can keep all of the kids' problem-solving together in one place. It's amazing to see their growth over the course of a year! I do not send my notebooks home (I can't risk them getting lost!) So how, you ask, do parents know what we're doing in math? I constantly communicate with my parents through e-mails, my classroom blog and even Twitter to let them know what we're doing and how they can reinforce what we're learning at home. I use the journals during conferences to show parents all of their children's strengths and weaknesses.
So, where to start...
1. Choose your notebook. It's really up to your own personal preferences (and what's on your school supply list!) I prefer marble composition books, because those things can take a beating and never fall apart! Pages are sewn in, so they don't fall out. The cover is nice and sturdy. There are plenty of pages. (I do wish they came in a regular 8 1/2 x 11" size).
You could also use blank copy paper in a 3-brad folder.
3. Put helpful information inside the front cover. I put a page that has numbers 1 through 20 (because most kindergartners can count at the beginning of the year, many need a visual reminder of how to write the actual numbers).
4. Glue in the Problem-Solving Notebook Expectations. I actually do this as a whole lesson with the kids. We go over each expectation. We learn how to find the next blank page (so the kids won't flip to the middle of their notebook to do a problem). We learn how to use the glue properly (both glue stick and bottle) to glue problems and activities in our notebooks. I continue to revisit these expectations throughout the year.
5. Now you're all ready. Please remember that the first few days (weeks) of problem solving might be a little ugly. Despite your best efforts, kids will still glue their pages together. They will still flip to the middle of the notebook to do a problem. Their drawing/fine-motor/writing skills are still developing, so the journals will be messy (messy...messy!) And I promise you at least a couple of kids will flip their journals completely upside down and start in the back--happens every year! But everyday, it gets a little better. You'll be amazed at how different their notebooks look in a month or two. Don't give up!