Monday, November 19, 2012
Lately, we are experimenting with math warmups in elementary school classes. Today, I tried one on a fourth grade class. I think someone else tried the same warmup in a fifth grade class, so I will have to ask them how it went.
Math warmups take just 5 to 10 minutes at the start of math class. For maximum effect, they are done every day or almost every day. With math warmups, it is possible to teach specific skills related to number sense. Lots of math gurus talk about these, including Sandi Stanhope and Bob Laird from the Vermont Mathematics Initiative, Marilyn Burns, Cathy Fosnot, etc. etc.
Here’s the one from today:
4 x 8 =
8 x 4 =
8 x 3 =
4 x 6 =
2 x 6 =
1 x 6 =
½ x 6 =
¼ x 6 =
I asked the students to solve these mentally and write the answers. I didn’t want anyone to struggle, so, if they didn’t know it, I just told them or had another student tell them the answer. I encouraged students to use what they knew from the previous equations to help them find answers without the usual calculation.
When asked what they noticed, students were able to share that they saw the commutative property in action (without using that vocabulary word) and could see halving and doubling relationships.
For example, 8 x 3 and 4 x 6 both equal 24, and that 4 is half of 8 but 6 is double 3. When you double something then halve it, you are back to where you started.
Getting down to the series of _ x 6 was interesting. Students noticed the pattern of the 6 staying the same while the other factor kept getting reduced by half. By the time they got down to the fractions, they were able to use their knowledge of the properties of multiplication to help them through a potentially difficult task. These students haven’t yet studied much about multiplication of fractions, but were able to do it easily.
I am thinking in the future it might be fun to try a number times ¼ and let students work back up to one through doubling if necessary to assist them in solving the equation without an algorithm.
|New York Public Library Digital Gallery|
Victor Prussack, Burlington’s Coordinator of Magnet Schools, found this Thomas Friedman article in the New York Times over the weekend and was kind enough to send it to me.
The piece begins with a profile of a sheet metal business owner from Minnesota named Traci Tapani. She can’t find enough skilled welders.
“Many years ago, people learned to weld in a high school shop class or in a family business or farm, and they came up through the ranks and capped out at a certain skill level. They did not know the science behind welding,” so could not meet the new standards of the U.S. military and aerospace industry.
“They could make beautiful welds,” she said, “but they did not understand metallurgy, modern cleaning and brushing techniques” and how different metals and gases, pressures and temperatures had to be combined.
Welding “is a $20-an-hour job with health care, paid vacations and full benefits,” said Tapani, but “you have to have science and math. I can’t think of any job in my sheet metal fabrication company where math is not important. If you work in a manufacturing facility, you use math every day; you need to compute angles and understand what happens to a piece of metal when it’s bent to a certain angle.”
Who knew? Welding is now a STEM job — that is, a job that requires knowledge of science, technology, engineering and math.
I was reading this article to my kids tonight and it occurred to me that even today’s doctors and lawyers - always regarded as professions for the highly educated - have undergone a STEM transplant. Doctors of today have unprecedented levels of information access and global collaboration, and are using online medical records, sophisticated medical imaging technology, gene therapies, remote robotic surgery, and more. Lawyers might have to deal with things that didn’t exist not long ago like various forms of DNA and IT evidence.
If you wanted to be an administrative assistant or a librarian, you used to be able to use a Rolodex and the card catalog. Now these jobs are all about technology.
|New York Public Library Digital Gallery|
Monday, November 12, 2012
A researcher was studying students in a Japanese school, and ended up observing a fourth grade math class.
"The teacher was trying to teach the class how to draw three-dimensional cubes on paper," Stigler explains, "and one kid was just totally having trouble with it. His cube looked all cockeyed, so the teacher said to him, 'Why don't you go put yours on the board?' So right there I thought, 'That's interesting! He took the one who can't do it and told him to go and put it on the board.' "
Have a listen. It’s only 8 minutes.