The Human Grid, ‘All About Me,’ project-based learning, and the ‘amazing’ frontier of UB’s Summer Math Program

By Charles Anzalone

Published August 30, 2019

The girls are laughing, smiling, jockeying for position along a line of masking tape on the floor, gently bumping up against the three teachers in their classroom at Enterprise Charter School in downtown Buffalo.

It’s all part of the Human Number Line, a featured activity in the University at Buffalo’s Summer Math Program. The middle-school-aged girls – each wearing a signature blue Summer Math Program T-shirt and personalized lanyard -- place themselves along the line of tape in the proper order of decimals and fractions.

It’s clear they’re having a ball. What is also clear: This is not their parents’ summer math class.

It is, however, summer math according to Ji-Won Son. Son –- the Graduate School of Education associate professor and nationally respected expert in math education whose command of current math education research matches her ability to connect with her young students -- presented her second Summer Math Program Aug. 12-16. Once again, the mission for the weeklong, daylong summer classroom program was ambitious:

Make math for girls “exciting, beautiful and useful,” as Son has promised. Anyone fortunate enough to be around to watch the program in action on the program’s Wednesday Hump Day would agree: The Graduate School of Education’s Summer Math Program lives up to the hype.

“We really strive to make sure the girls are not sedative, that they're not just working on worksheets and doing algorithms or a process to get to an answer,” says Jeri Diletti, assistant program director of the Summer Math Program who teaches math at Akron High School, and is an adjunct math professor in the GSE.

“We really want the girls up and moving, and really even just getting their bodies involved in the activities. We want them having fun, laughing, working with other girls. A lot of times the girls don't know each other. They're not all necessarily coming from the same location, so we're also building relationships with them and between the girls as well.”

There is sound pedagogy behind it, and a strong intention to fulfill a cultural and gender deficiency. It’s specifically aimed at girls entering grades five to eight looking to improve their math skills. This is when girls have traditionally lost ground when keeping up with their male counterparts, according to Son.

“From all distances, education looks pretty gender equal,” says Son, associate professor of mathematics education in the Department of Learning and Instruction in UB’s Graduate School of Education who started the program in 2017.

“But if you look closely, you can see boys and girls are treated differently from a very young age in terms of expectations that are directed at them. Research shows that there is no gender gap at kindergarten when they just started their school experiences, but some gender gap and gender differences in mathematic attitude and skill appear during elementary.

“And it is at the middle school level that female students turn their attention away from mathematics. This gender gap and gender differences in mathematic attitude and skills continue to grow during high school.”

Studies show that the way female students and male students learn mathematics is different, according to Son. “Female students do better when they are collaborating and working together,” Son says. “In contrast, male students are more competitive, and they do better by doing independent work. So our program emphasizes more collaborations and project-based learning, and group activity.”

Clearly, the Summer Math Program had a mission to make math fun, active, engaging, as well as academically useful for the 47 girls enrolled this year. And clearly, based on the activities in these mid-week sessions, morning session, it was math delivered as promised.

A sample of the activities going on that day:

The Human Number Line assigns a fraction or decimal to each of the five girls in a class run by Diletti. The students and teachers then try to arrange themselves in the proper order, based on their ability to convert and compare the numbers.

That soon led to the scene described above, with the girls directing each other or their instructors with accompanying fractions in appropriate order, and then “schooching” each in the appropriate place on the Human Number Line.

Ani Senthil Kumar with the assigned fraction 2/7 correctly took her place in the spot below Jessica Park, who had 7/21.

 “How did you know you were bigger than Ani?” Diletti asked Park.

Because 7/21 is equal to one-third,” said Park, who will be entering fifth grade Transit Middle School in East Amherst.

“Awesome,” said Diletti. “I’m going to write that down.”

“What did you do, Ani?” Diletti asked Kumar, also about to enter fifth grade at Transit Middle School.

“Common denominator,” Kumar answered quickly. She needed to convert her 2/7 fraction to one with 21 as denominator.

“I multiplied both of the numbers by three, which equals 6/21,” she said.

“So 6/21 is less than 7/21,” Diletti told the class, and that correctly determined where Ani and Jessica would stand in the Human Number Line.

The Human Grid in a class room adjacent to Diletti’s also physically placed the girls in the middle of their math problem. Teachers including Son and Alexandria Porter set up a four-by-four grid on the floor, and the girls were asked to stand in part of the grid to solve problems.

This day’s Human Grid activity was about multiplying fractions. Students would figure out how many floor grids they needed to cover and then how many bodies they needed for the problem ½ times ¼.

“If we’re taking 1/2 of ¼, how much of this grid do we need to cover?” asked Porter, an algebra and STEM teacher in the Niagara Falls City School District. “So, how many student will we need first?

 “We’re covering how much of this space?” asked Porter. “A fourth, which would be eight students.”

So students got up and covered a fourth of the 16-square floor grid.

After the students did the ¼ of the grid, they were asked to cover ½ of that ¼.  They would then see that ½ of ¼ is 2/16 or 1/8 .

“This is the way we showed the multiplication,” Porter said.  “One-half times ¼ equals 1/8.”

It was all about multiplying fractions to find parts of numbers that are parts in themselves. And all about the girls using their bodies to show they understand the meanings of fraction multiplication, not just a procedure.

“When it comes to fractions and fraction multiplications,” Son said, “students tend to use procedures by multiplying numerators and denominators. For example, when they are looking at the problem of ¾ times ¼, they are just multiplying three times one. And then four times four. And figuring out the answer as 3/16.

“In order to develop a good understanding of multiplying fractions, they should understand the ideas behind the procedure. And one important idea is finding portions of the portions. With these type of problems they should be able to represent which fraction or portion they need to represent first and then figure out how to represent portions of the portions.

“The Human Grid and counter activities help them understand conceptually how those ideas can be represented.”

Down the hallway from the Human Grid classroom is Window Shopping, this time for seventh graders.  It’s an activity instructed by Christina McCarthy, a graduate student in the GSE’s adolescent mathematics program. Students were given paper money and then allowed to visit displays with various items – Disney World for a week, a jet ski, a puppy and a kitten – all with prices and a discount percentage. They needed to figure out the discounted price before they could spend their money.

“We had to figure out the discounts and make sure we had enough money to pay for the items,” said Paige Kerr, who will be going into seventh grade at Heim Middle School in the Williamsville School District. “I bought a jet ski, a safari trip and a pool.”

The activity was vintage UB Summer Math: hands-on, fun and clearly tied to the real world.

“Math is everywhere,” Son said.  “They do not realize where they use mathematics.”

The girls also do scavenger hunts. They design and color graphs based on figure what fraction of their day is spent on eating, or doing crafts, or dancing, or whatever their interests are, “something important in their lives they can represent as fractions,” said Diletti. It’s called “All About Me.”

Since fractions and decimals are the announced focus of the week – equal to the fun -- the girls learn how to express these fractions in unique ways, in Egyptian numbers, for example, or what they now know is the “measurement” model. Or an area model. Where will it stop?

Once again, Son’s mantra comes through: Math is everywhere.

Son made it clear the Summer Math Program benefits the teachers as well as students. There is extensive teacher planning and preparation, including test runs on their Summer Math Program lessons with each other before the camp begins.

“We are helping teachers to be more reflective about their teaching and better practice learning opportunities for their own students,” she said.

Son wants them to see how math is important in real life, and for them to have a conceptual understanding of why things happen the way they do.

“Our team of teachers has worked very hard to provide high quality, creative and engaging activities,” said Son. “Students work through real-world problems, games and activities to explore mathematics.

“These methods bring life to the mathematics and help reveal the beauty and excitement of mathematics to kids. How do I know? I’ve witnessed it all week; the excitement in our students’ voices, the motivation to try solve math problems using various methods, and the hard work spent working on their final projects.”

As for the girls, they can’t say enough good things about their camp, both on and off camera

In the end, for the girls, it’s mostly about the fun.

“Teachers are kind and they make a lot of jokes, and they all make us laugh,” said Senthil Kumar. “I thought this would be like school. But it’s like home and like Mom and Dad teaching.”

What would she tell a friend?

“I would tell them it’s interesting, and amazing,” Senthil Kumar said.

Park unabashedly brightened up when asked why she liked math.

“Because it requires you to think outside the box,” she said. “Kind of think of different ways about how to solve problems and how it helps us.”

How has the camp been so far?

“It’s been really amazing,” Park said.

Would you recommend it to a friend?

“Of course I would,” Park said. “It’s really amazing.”

“The teachers are really nice, and they teach … I wouldn’t say better, but I can understand more of what they are saying,” said Lauren Truman, who will enter sixth grade this fall at Amherst Middle School, “It’s helping me understand you can use math in the real world.

“If I wanted to be a baker, I could use 2/3 cup of flour, or 4/5 cup of butter, and then I could make the right cake, so it can come out right.”

Kerr says she enjoys math because “it infuses itself into our daily activities.”

Take her final project, she said. She’s a dancer, and she found a way to merge the two interests.

That project is about how math “infuses itself into dance and how paying for dance has multiplication and division,” Kerr said proudly, “and how listening to the beats of the music has fractions and decimals.”