Stick-to-itiveness

It is interesting to see how students respond to a problem that they cannot figure out quickly. Some move to “I don’t understand” and get stuck there. Others have more stamina for taking on a challenge. They have a stick-to-itiveness that I want all of my students to develop. I want them to learn how to play around with a problem that is hard. The challenge is how to help them do this. I encourage a lot of experimenting and modeling with manipulatives as one way to get them thinking through problems. Viewing problems as puzzles is another way to get them to relax and explore possibilities. Hearing the approaches of other students can help them broaden the strategies they know how to use. I work hard to create an atmosphere where it is okay to take a risk.

When we were last visiting our granddaughters (and their parents, of course), I watched as the six year old once again untangled the Newton’s Cradle that her sister had once again gotten tangled. She clearly viewed it as a puzzle and patiently observed the way the cords connected as she worked out the tangles. A few times she was on the verge of tears, but she calmed herself and proceeded. Once it was restored, she proclaimed that after a challenge, her brain felt good. My hope is that all students can feel the pleasure of taking on a challenge and not just the frustration, perhaps seeing that the frustration can deepen the pleasure when they find a solution.

My husband’s poetic musings on this are on his poetry blog.

Exploring Shapes

This fall we have been looking at shapes in math group. First we looked at some different triangles and worked to come up with a way to describe a triangle that made it clear what a triangle is. I talked about this as a definition of a triangle. Working in pairs (generated by pulling colored cubes from a box), students shared ideas of what they noticed about the triangles. Then those pairs shared with the others what they came up with. Everyone had noticed the three sides right away. We talked about the difference between an open and closed shape. Several students mentioned the three corners. I introduced the term angle. Then we looked at the word “triangle” and broke it down to tri and angle. One student quickly made the connection to tricycle. That same day we looked at squares and talked a little about how we could describe them.

A few weeks later we revisited the square discussion. This time I drew a square on the board along with some other quadrilaterals. I asked them to work independently this time to describe what a square is in their journals. It was interesting to see how closely some observed the shapes and used terms that sounded more mathematical while others used more visual terms. For example in trying to distinguish a square from a parallelogram with equal sides, several students wrote that a square is not “squished.” Others said the square did not have diagonal lines as a way to describe the same attribute.

The next time we met we shared our ideas. We revisited the idea of angles. At that point one student made the connection to Logo programming which he had heard about from his older brother. We then explored the idea of different sized angles. Some students were recognizing the distinct angle in a square, so I introduced the term “right angle.”

Counting Around the Circle

A new warm-up routine that I am using with my math group comes from a book I read over the summer, Number Sense Routines by Jessica Shumway. The routine is “counting around the circle.” I choose a student to begin the counting and tell them how to count (by two’s, three’s, five’s, ten’s, etc.) At first we just practiced counting in different ways. Now as we get ready to begin counting, I ask them predict what number a certain student will say. Or we count around the circle once and I then ask what number we will get to when we go around a second time. It is a fun way to wake up their number sense.

Frog Riddles

Last week we did an activity from Marilyn Burn's and Bonnie Tank's A Collection of Math Lessons from Grades 1 through 3. Basing my lesson on the chapter on "Riddles with Color Tiles," I do frog riddles. First students use frog counters in four colors to come up with solutions to clues I give about what combination of frog counters are in a bag I have. They work in groups of two (generated by drawing a colored cube from a box). After we do a couple of riddles and talk about the process, each group is asked to come up with their own riddle of at least 4 clues. Each clue should move the solver closer to the solution, and the solver should be able to get the solution by the last clue. It takes some thought, logic, and planning to develop a riddle. After each group completed a riddle, we exchanged bags and clues and tested each others' riddles. Some were returned to the pairs that developed them for additional clues or clearer clues. Each partnership ended up with a successful riddle.

World of Math

On the first day my new math group met, I asked the students to think of all the things they could that were part of math. As they suggested things, I made a “map” of the World of Math. If we think of more things to add as the year goes on, we will put them on the map as well. I was happy to see that they were able to think of a lot of things to add in addition to arithmetic. Patterns, problem solving, and fun all had their place in the map we created.

Counting

On Thursday Tom took the old-timers and the new second year students to the multi, which gave me some time with our first year students. One of the students had repeatedly asked if we were going to do another scavenger hunt. (There was a Lower School scavenger hunt at our Open House for new students on Monday.) I came up with a number scavenger hunt that involved counting various things in the classroom. As the students went about counting and recording, it was a great chance for me to see how different ones took on the task. I observed how they went about counting the objects and how much confidence they showed in the counting. One student proudly shared that he counted by 3’s. I also watched as they recorded the results. A student asked if 8 was the number with “two balls.” Two girls consulted together about whether the 1 in 12 should go first or not. They had fun with the activity and seemed satisfied as they turned in their recording sheets.

Math Games Online

I have been working on assembling links to some good online math games to put on the computers that the students use at Centers time. We already have KidPix, Logo, and a couple of installed math games on the computers. The links will expand the choices.

As I evaluate which games to use, I found an online article that has been helpful. It was posted by NCTM (National Council of Teachers of Mathematics) and discusses math games and how to evaluate the many online games to finds ones that support students’ learning of math concepts in an interactive way. Here is a link to the article, which includes links to some games that they recommend:  http://www.nctm.org/resources/content.aspx?id=27612

I follow the Free Technology for Teachers blog which features a wealth of resources for teachers available online. Richard Byrne, who writes the blog, periodically includes math resources, including games, in his post.

Turtle Fun

Catching up on activities from November and December:
One focus was learning about a simple computer programming language called LOGO that was developed at MIT as an educational aid for children. In Logo the cursor is a “turtle” who moves across the screen creating graphics based on the commands given by the children. We learned some basic Logo commands, and students then worked on writing out programs (a series of commands) which they could type into the computer to see the results. This project has generated a good deal of excitement in our group. Initially the students worked in partnerships, helping each other as they learned. Then each student had an opportunity to work on a laptop solo. Logo helps students develop their spatial/geometric sense as well as providing good problem solving experience, as they try to figure out how to make the turtle create the drawings they want.

Dreidel Probability

In December we did a probability study with dreidels. We talked about the tops used for the traditional Hanukkah game of dreidel and what we would expect with a fair dreidel. Students said that each of the four sides should have an equal chance of coming up. A few talked about how they want gimel to come up the most. Then we speculated about why one side might come up more than the others. Students thought about how they were made, about whether the letters were painted on or were on the side in relief, and about how the dreidel behaves when it is spun. I shared that to get an accurate picture we needed to have a lot of spins. In our study we compared plastic and wooden dreidels to see if one kind was more consistently fair than the other. Students spun the dreidels in class and at home for homework. Then each student recorded the results in a spreadsheet. Here are our results: