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Angelique Connor has been teaching for eight years; four of them with the same students she’s had since they were in kindergarten. Now they’re in third grade, and this is her last year as their teacher.
James Unger teaches fourth grade math at an elementary school where children circulate for their classes. In his fourth year of teaching, he wears a tie so his students don’t confuse him for their older brother. He was exposed to technology while in college, and is taking a leadership role in his school helping other teachers get up to speed with things like digital cameras, computers and projects like the National Math Trail.
Angelique Conner helping her students create problems for the National Math Trail. “With some students, problem solving is a weakness,” says Conner. “But in our class, problem solving is one of the things that my students are good
at. By doing the math trail they’ve learned that there are different ways to get the right answer.”
Conner set up the project by first dividing her students into groups, and then taking a walk around the school grounds. “I told my students to look for anything that grabs their attention,” she recalls. “We spent a whole morning walking around the building, outside and inside, looking for things that might relate to math and taking pictures with my digital camera. Then we came in and I printed out sheets with the pictures on top, so they could start thinking about some ideas for math problems.”
 James
Unger also started with a walk, but his students first drew pictures of the math they found. Then each team compiled their pictures, math problems and narratives into a booklet they designed.
Only after they can effectively communicate their problems to their classmates are they given access to the digital camera and are allowed to enter their text into the computer.
“I gave my students some ideas to get their thinking started,” says Unger, “like ‘look at the front door and see how many rectangles you see. Then look again, how many do you see this time?’ It’s amazing the way their faces light up when they take that second look and see so much more.”
Math and Communication
Communication skills are an important aspect of the math trail. Students must document background information about their math problems, and they must also be able to effectively present their problems to their classmates. Master teacher Kay
Toliver, who taught math and communication skills for more than 30
years, places heavy emphasis on a student’s ability to communicate mathematics concepts.
“Mathematics is a subject in which we have to create thinkers not memorizers," Toliver says. "It is a subject that involves history and literature as well as numbers; it is more of a communication art than anything. If students are to become the thinkers of tomorrow, we can't just concentrate on getting them to pass tests. We have to show them the real reasons for learning various mathematical concepts. These reasons have to do with math being alive, related to every aspect of life.
I want students to discover this for themselves.”
Conner has her students study the pictures from their walk and think about the type of math problems they could possibly come up with. She lets them read each other’s problems. “Often they will get a fresh idea when they share problems,” she says, “and then go back and make their own problems sound a little better. That way they help each other with the writing. When we get the final draft, it’s ready to go on the computer.”
She notes that she is able to assess students’ critical thinking
skills while they are creating problems. “The students do math problems every day, but they’ve never had to come up with their own math problems. That really gets them thinking and talking together about math, and working together.”
Math problem from Angelique Connor’s third graders
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This is Mr. Diggs. He is our principal. When you come into Robert Shaw, make a left and his office is the first one on the left.
Problem: If Mr. Diggs gets to work at 6:00 am and he leaves at 5:30 pm, how long does he work?
Answer: 11 hours and 30 minutes
Solution: Start at 6:00 am and count up the hours. 7:00, 8:00, 9:00, 10:00, 11:00, 12:00, 1:00, 2:00, 3:00, 4:00, 5:00. That is 11 hours. Then you have to add 30 more minutes to get to 5:30.
Problem: If Mr. Diggs gets 12 calls a day, how many calls does he get in a month?
Answer: 360 calls
Solution: You have to multiply 12 calls each day times how many days in the month which about 30. 12X30-360
Growing with the Project
Connor began the project early in the year, and she had only introduced some
basic math concepts. Because the math trail is an ongoing project, her students are adding skills to their problems as they learn them. At first their problems were mainly about adding and subtracting, then they began bringing in multiplication, division and estimating.
“I can tell it is a growth process,” she said. “The math trail is something I can go back to and see where they are using their new skills.”
The National Math Trail incorporates many of the problem-solving
objectives in the Georgia Quality Core Curriculum, according to Unger.
"One of the objectives is 'employs problem solving skills
daily,'" he said. "For our math trail questions, we use
estimation and rounding, and we just started talking about division.
Every time we do a new concept, I ask the students to think about using
it in their math trails. I'll give them extra credit if they add
something like, say, decimals, which we haven't done a lot of work with
yet."
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