Lego Robotics

I had an incredible day with students. As part of the Flynn Elementary School Inquiry Fair, I teamed up with Amy Truchon and Nina Madore to offer a workshop on Lego Robotics. We’d borrowed 8 brand new kits from Professor Tim Whiteford of Saint Michael’s College, opened the boxes and played around with them just recently.

We used both Lego WEDO and Lego Mindstorms kits. I had only taken them out of the box and dabbled a teeny bit, so I was experimenting along with the students. Kids built alligators that chomp your finger if you move it close enough, kicking soccer players and goalies, tweeting birds, and more. My afternoon Mindstorms duo programmed a car to drive until it got close to a wall or other obstacle, stop, back up, change direction, make a fiendish laughing sound, then start driving again.

Students didn’t want to leave at the end of the workshop to go to lunch or home. They were having too much fun. I highly recommend these for school or home. In the end, what they are learning is software and hardware engineering, a very relevant set of skills in these times.

Radiolab Numbers

Radiolab is so cool. It’s a public radio show you can listen to on your public radio station or online. My dad recently told me about a Radiolab show called Numbers. It originally aired in November 2009. Each show is an hour long and has several segments on a single topic. If you listen to the Numbers show, you’ll first hear a Johnny Cash song, then learn about the innate number sense of infants, and move on to other fascinating topics like Benford’s Law, a surprising observation about the first digits of numbers, and a forensic accountant who uses it to investigate fraud, and on and on. The show is a very human take on numbers. I’m sure you’ll enjoy it.

Ada Lovelace

It is always good to hear about female mathematicians. Today, Google featured a graphic with the tag “Ada Lovelace’s 197th birthday”. Investigation revealed that Ada Lovelace was the daughter of the poet, Lord Byron, and lived in the 1800s.

A paragraph in the Washington Post caught my attention.

At the age of 17, Lovelace was among the first to grasp the importance of Babbage’s machines, Google noted. In her correspondence, as reported by New Scientist magazine, Lovelace said that “the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” She also noted that the Analytical Engine “does not occupy common ground with mere calculating machines” and had the potential to run complicated programs of its own.

Apparently, Lovelace wrote the first algorithm designed to be run by the Analytical Engine. Some say she should be considered the first computer programmer.

Here is another Lovelace quote to ponder (from Wikipedia:Ada Lovelace)

[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.[58]

The Wheel Shop

There’s a great website called Inside Mathematics. I learned about it at the Common Core Math sessions this year with Bob and Judi Laird, Sandi Stanhope, and Fran Huntoon, of the Vermont Mathematics Initiative.

Inside Mathematics is a treasure trove for teachers. It has problems of the month linked to Common Core standards. The best part about the problems is the fact that they begin with an easy level and progress to more difficult levels related to the same math and situation. It’s kind of like how the Bedtime Math website works.

Here’s one we tried today with Sandi Stanhope: The Wheel Shop. It starts innocently enough with Level A. There are 18 wheels in the shop that sells tricycles. How many tricycles are there in The Wheel Shop?

Then we went on. The Wheel Shop sells other kinds of vehicles. There are bicycles and go-carts in a different room of the shop. Each bicycle has only one seat and each go-cart has only one seat. There are a total of 21 seats and 54 wheels in that room. How many are bicycles and how many are go-carts?

Nick Mack had a lovely way to solve this one today at the workshop which involved doubling 21, then adding 2 wheels to bicycles until he had the right number of wheels. The bikes with the added wheels became the number of go-carts.

Nick said his second graders did a similar problem involving ducks and sheep. They drew a bunch of ducks then added 2 more legs to several of them in order to “turn them into sheep”. He said the sheep that began as ducks were fairly ugly, but the math worked out.

Today Sandi said, "Math should be hard. Let kids figure it out." 

Here is the Level C problem:
Three months later some vehicles have sold and new models have been brought into the Wheel Shop. Now, there are a different number of bicycles, tandem bicycles, and tricycles in the shop. There are a total of 135 seats, 118 front handlebars (that steer the bike), and 269 wheels. How many bicycles, tandem bicycles and tricycles are there in the Wheel Shop?

Today Nick started making a spreadsheet for this one and I did something similar tonight. My spreadsheet had columns for handlebars, seats, and wheels and did some multiplication and addition with formulas to get the totals. I guess-and-checked my way as the spreadsheet did the calculation. Setting this up took about 10 minutes, but my husband, Jim, had already gotten the answer and was eating muffins with the kids in the kitchen by the time I figured it out.

Jim had written his solution on an index card. He explained it as follows:

There are 118 total bikes (because there were 118 total front handlebars).
Multiply that by 2 and get 236 (so there must be 236 wheels).
But there are 269 wheels, so I subtracted. 269-236=33. There are 33 tricycles.
There were 135 seats but only 118 steering handlebars, so I subtracted. 135-118=17.
There must be 17 tandems and 33 tricycles. This left 68 regular bicycles because I subtracted 17 and 33 from 118 to get 68.



Enjoy the problems of the day! We did.

Math Warmups

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.

Is Welding a STEM job?

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

The Struggle

John J. Flynn Elementary Principal Graham Clarke alerted me to a very nice piece on NPR today. It’s called Struggle for Smarts? How Eastern and Western Cultures Tackle Learning.

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.

Fact Fluency

What is it about fact fluency that is so challenging for some students? It’s not uncommon for students to lack automaticity with their addition, subtraction, multiplication, and division facts into middle school and beyond. Struggles with fact fluency sometimes accompany low achievement in math, but that is not always the case. Sometimes struggling math students know their facts. Sometimes high-achieving students do not know their facts.

I am reading John Tapper’s excellent new book entitled Solving for Why: Understanding, Assessing, and Teaching Students Who Struggle with Math.  Tapper devotes a section of the book to students who face challenges in short term, long term and working memory. He weighs in on the fact fluency question there.

What students need to understand are underlying mathematics concepts. Multiplicative and proportional reasoning are, for example, critical to moving on from elementary mathematics. Fact retrieval certainly facilitates learning in these areas, but the inability to retrieve facts will not prevent students from reasoning at higher levels. Knowing math facts is important, but fact retrieval is to mathematics what spelling is to literacy: we want students to be proficient at the skill, but the skill is a small part of the overall picture. If a student is able to spell but cannot write a coherent essay, the spelling does them little good. The same is true with math facts. (p. 138)

This is interesting for students, parents, and teachers to ponder. Try spending ten minutes a day or less studying math facts. Learn them in a way that reinforces conceptual understanding and is fun. Enjoy higher level, rich mathematics. Like the Fibonacci spiraling Hurricane Sandy picture above.