Daniel Phu of Superior was trying to corral his children.
Kevin, 8, and Jenny, 5, were bouncing up and down in the living room earlier this month. They were excited to have visitors, invited by their father to show off their algebra and calculus skills.
That’s right, advanced math.
When the two children did settle down to a white board of a math problem written by their father, they did it without a hint of difficulty, like it was second nature. Jenny worked the formula for converting Celsius temperature to Fahrenheit. Kevin was given some integral calculus problems.
“Boom, like that,” their talkative and excited father said.
When done, the children darted away and continued their Tigger-like bouncing.
“They love to play around,” Daniel said.
And that’s a part of the way the engineer for the Wisconsin Department of Transportation has taught a math system he’d like to write about in a book someday.
Daniel fully admits his children aren’t fully cognizant of all the workings of the problem-solving. That will come. For now, he teaches math like language, with his children understanding the flow of the numbers.
“Mathematics is four things,” Daniel said. “Addition, subtraction, division and multiplication.”
His children solve by “seeing, not thinking,” he said.
They love to play Duck, Duck, Gray Duck, he said, and he reminds them that going around in a circle patting heads is a way of counting.
He began using his weekends to teach both Kevin and Jenny some algebra at age 4. He starts small, using games to get them to grasp how the numbers interplay, and just keeps pushing them along incrementally. They don’t know the exact terms connected to what they’re doing, something Daniel says hampers the natural flow of math.
“A lot of teachers don’t believe in it,” Daniel said.
But he has a track record. He’s taught a cousin and a niece his math system, and they went on to math-related degrees in college.
Friends have asked him about it, wondering if their own children could learn like his own. Of course, Daniel said, but you have to keep at it.
Kevin does well at the conventional math he learns at school, scoring in the 90th percentile on standardized tests, Daniel said.
“We try not to teach too much,” he said of the home lessons. He and his wife, Pov, let the children guide where they want to go with the math.
“I show her and ask her not to learn,” Daniel said of his work with Jenny, whom he expects to be grasping advanced algebra in a few months. He doesn’t want his children to be “scared” away from math with all the terminology.
“When they know it, they just blow it out,” he said.
The monthly magazine “The Atlantic” offered a story earlier this year titled “5-Year-Olds Can Learn Calculus.” Daniel said he’s been influenced by stories about how children can grasp what is traditionally considered out-of-reach advanced math.
A passage from the article, after describing the typical “hierarchical sequence of math instruction” as students get older, states:
“But this progression actually ‘has nothing to do with how people think, how children grow and learn, or how mathematics is built,’ says pioneering math educator and curriculum designer Maria Droujkova. She echoes a number of voices from around the world that want to revolutionize the way math is taught, bringing it more in line with these principles.
“The current sequence is merely an entrenched historical accident that strips much of the fun out of what she describes as the ‘playful universe’ of mathematics, with its more than 60 top-level disciplines, and its manifestations in everything from weaving to building, nature, music and art. Worse, the standard curriculum starts with arithmetic, which Droujkova says is much harder for young children than playful activities based on supposedly more advanced fields of mathematics.”
The article drew 34,000 shares on Facebook and hundreds of comments, a mixture of agreement and warning.
One comment represented a majority assessment:
“The article just reinforces that there is no single right way to teach, that rote math is way overvalued, and that to get the best out of teaching kids you have to be flexible to a degree.”
Daniel talked about his own proclivity in math as a student.
“I learned the hard way,” he said. “But I was questioning: Why does algebra take so long?”
“You can cheat,” he said. “You can cheat smart.”
He keeps one theory in mind at all times.
“You have to want to know,” he said.
There is a 2-year-old waiting in the wings as Kevin and Jenny whirl around their math-centric basement. Daniel thinks he’ll start teaching the youngest at age 3.
He repeated his mantra for learning math.
“Only little steps at a time,” he said.