The Secret of Mathematics: Daydreaming

Here’s an awesome article I just read from staff-writer Kenn Rodriguez from the Valencia County News-Bulletin.

It’s really encouraging to hear about active visualization and mind-developing techniques in today’s classrooms!


Daydreaming? Creativity? It’s part of their math lesson

After being introduced by teacher Elizabeth Gomez, Holly Davis talks a bit to Gomez’ fifth-grade class at Raymond Gallegos Intermediate School.

“One of my favorite things to do in school was to daydream,” she admits to them. “Today we’re going to use our imaginations. Who’d like to be in my story?”

Asking students to use their imaginations and telling a story aren’t an unusual occurrence in most American classrooms.

Saying those things while teaching mathematics is.

Davis, who is the math coordinator for the Los Lunas Schools, has come this morning to model teaching techniques for Gomez – teaching techniques that are at the forefront of the district’s “numbers literacy” initiative.

“It’s a national trend,” said Davis after the class. “Ninety-three percent of the state is using some variation of the math approach. There are a couple of districts that aren’t quite there yet, but they’re going to have to be.

“Because the goal is to teach kids to think and process, the goal is not valuing the answer only.”

In the classroom, Davis tells a story about a girl named Alexis who has five coins. She says two of the coins are the same. The students are asked how many other coins Alexis has and what kind of coins they are. They enthusiastically answer.

Another exercise Davis goes through involves the number 678.

That’s the number of the day.

Using magnets representing numbers grouped in hundreds, tens and ones, she shows the students several ways of grouping them to understand and visualize the number.

It’s all part of the new approach, one that Gomez, who is in her fifth year with the Los Lunas Schools, said works on many levels.

“I’ve done some of this with the kids, done some using overheads,” she said. “A lot of the stuff up there is actually mine. So I’ve done this with the kids where they work out problems together. We’ve done the same thing with fraction bars and papers like this or the place value units. So they’ve done it before.”

Eventually the students pair up to work on problems. In the past, such a thing would be unthinkable for math teachers — but not with the new approach.

“They work together a lot because sometimes they can compare answers then, if they’re different, they can talk about them and figure it out,” Gomez explains.

Even with her experience teaching using these same math literacy methods, Gomez said she likes being able to see Davis model the lesson.

“She’s our coach so she’s elaborating on some of the stuff I’ve done here,” Gomez said. “So I’m actually learning from her and so are the kids. But it’s neat that they’re taking what I’ve taught them and applying it and kind of expanding it.”

Many times, Gomez said, she will have students teach part of a lesson, showing the other students how they came up with the answer.

“I’m always using things like this or actually having the kids be the teacher and present their problems,” she said. “It’s kind of fun for them, but I think it makes them more excited about it and be creative and know that there’s more than one way to get somewhere. I always tell them that.”

The new approach also incorporates a lot of writing and reading. The days of “reading, writing and ‘rithmatic” being separated are gone, Davis said.

“Now you see writing in math because there just aren’t enough hours in the day, and we have standards that we have to meet so you have to be artful in your planning to integrate them together. If you’re going to do art, you have to integrate it into some standard.”

After the class, Davis said her co-workers at the district offices were teasing her for being so happy that morning.

The office staff knew she was happy, she said, “because I got to go out and teach.” Davis said she’s also been happy with the new math initiatives.

“I feel so fortunate in this district because I really do feel like we have leaders at all levels that are instructional leaders,” she said. “They’re not just managers. They know how to do instruction. And they can go into a classroom and teach it, all the way up to the superintendent and even my boss.

“When you have a group like that, they’re valuing individuals. This district is lucky to be able to use a comprehensive literacy approach, which is the same thing. It’s not ‘Open up your textbook and we’re reading this story.’ It’s ‘I picked a book for you’ and in the teacher’s mind it’s up to their instructional level and meets their interest.”

David said she’s found a lot of support in the district for the new teaching methods, which also encompass all other subjects, not just math, she said.

“The feedback I get as math coordinator is that they like it, but I definitely know it is a process for the teachers to change too,” she said. “Change is a big deal, and teaching is hard.”

Gomez, who said she “loves math personally,” welcomes the new approach as a teacher.

“I always tell the kids there’s always earning and teaching. As a teacher, I learn every day, and that excites me. I’ve been real excited with the programs we’ve started, and the kids are more excited. I look at it as things that reel them into the joys of math rather than constant bookwork. Not higher level thinking.

“I think I love math, and I’m more excited that the kids are liking it and applying it so it’s like ‘Yes, they actually get it,’” Gomez said. “That’s been exciting for me.”