Last week a group of math-anxious parents hustled to solve that word problem as the start of the Lower School Parents’ Math Workshop, an annual event that introduces parents to the Kindergarten through 2nd grade mathematics curriculum.  The workshop was led by Mathematics Chair Fanny Sosenke and her fellow teachers including second grade teacher Jonathan Edmonds, first grade teacher Laura Leopardo, and kindergarten teacher Jane Morrissey.

 

Time was up.  “476 pennies” called out one parent.

 

“Does that answer work?” asked Fanny.

 

“You must use each type of coin at least once,” called out another (in addition to the fact that $4.76 is the amount Sadie spent, not her change).

 

“But it doesn’t say that,” said the first about the coin requirement.

 

“Yes, at the bottom,” said another.

 

Without realizing it the parents were coming pretty close to mimicking the way group problem-solving works with their young children during a real BFS math class.

 

“You will see some kids who need to see the coins and touch them. They haven’t made the transition yet to abstract thinking. Then you have students who will zoom right through this, so this particular problem covers all levels in the class,” Fanny explained of the fictional Sadie and her pocket change.

 

Beginning in kindergarten, students learn by exploring problems in depth.  “There’s a lot of talking and discussing, and learning that sometimes there are five or six solutions to a problem,” Fanny told the parents.  “They develop their own strategies rather than memorizing a procedure.” In such an activity-based curriculum students move to stations to work, or to pick up a math book or to examine a concrete aid such as the coins, when solving a problem.

 

The Lower School math curriculum is largely based on the recommendations of TERC (Technical Education Research Centers), a highly respected Boston-based nonprofit organization with the mission of improving and modernizing the ways math and science are taught. TERC endorses a "constructivist" approach to learning math in which students construct their understanding through their own investigations. They explore problems in depth, often in small groups, inventing their own strategies. They're then encouraged to articulate their thinking through numbers, words or pictures. This is in contrast to the older, straight "calculations" method in which students learn facts by rote memorization. TERC’s peer-reviewed research shows that their constructivist Investigations curriculum used in the BFS Lower School improves students' accuracy on word problem calculations among other positive results.

 

“They learn fractional work and decimal work but it’s not a ‘fractions unit’ or a ‘decimals unit’ until the later grades,” explained Jonathan to a parent.

 

Fanny stressed that the ultimate purpose of the curriculum is to encourage young learners to begin using math outside the classroom on their own.  “Is 4 x 12 closer to 40 or 50?”  she illustrated by asking the parents.  “Really that’s more important than knowing 4 x 12 is 48 if you’re in a store trying to decide how much you can buy with the amount of money you have.”

 

The group also played Close to 100, a third grade classroom card game. Parents were dealt cards and had to arrange them in such a way that they added up to as close to 100 as possible.  This might seem a simple endeavor until you give it a try, as many parents learned.  “Not only are the students playing a game, they are practicing real math,” said Fanny.

 

Jonathan gave an example at the board of what might happen if a student drew cards 5,3, 4 and 5 and made them into the numbers 53 and 45.  “53 + 45. What’s the answer?”

 

“98,” shouted one parent.

 

“Right.  Can you explain how you got that answer?”

 

“I added the 5 and the 4 to get 9, and the 3 and the 5 to get 8.”

 

“That’s perfect but with one correction. You added 50 and 40 to get 90, not 5 and 4 to get 9.  Place value is extremely important,” he said, pointing out that for example a 5 can also be a 50 or a 500 depending on where it sits. For a second grader this seemingly simple concept can be a tremendous leap in thinking abstractly about numbers.

 

He also stressed that there is no single correct way to solve a math problem, a fact which the faculty encourage students to explore as they learn their own thinking styles.  “As you do it, try and be aware of what kinds of math you’re using, what your thought process is like,” he told the parents.  The introduction of a wild card to the game didn’t necessarily make the game easier, but often demanded strategic thinking instead of simple addition and subtraction, as they discussed during their followup conversation.

 

As the workshop continued the parents seemed fully engaged as Lower School Curriculum Coordinator Diane Mackie watched the proceedings from the back of the room.  “We do this presentation every year in the fall,” she said.  “It surprises me the parents who come back a second or third time.  I say to them, ‘you’ve already done it, it’s the same thing!’ But they say, ‘I learned so much last year!’  And it’s true.”