The designers for Monte Vista Elementary School鈥檚 proposed outdoor classroom had some key questions to answer: What materials could they use while staying under the district鈥檚 $10,000 budget? How much square footage would work? How would they produce the scalable models the client wanted?
Those critical questions鈥攚hich could have been considered at a local architecture firm鈥攚ere part of just another math assignment in Robbi Berry鈥檚 5th grade class at the. The prototypes the students created in class ultimately helped inform the work of the professional architects hired for the job.
And the project helped Berry鈥檚 students master some important 5th grade math concepts鈥攕uch as adding and subtracting multidigit numbers with decimals. And the students did it without having to plod through boring math worksheets.
This problem-solving approach to teaching math to elementary school kids makes the subject much more intriguing and relevant, Berry and other educators say. It allows students to experience math the way it is used in real life, rather than as a pile of equations with no meaningful context.
It鈥檚 never too early to begin having kids learn math this way, experts say.
Today鈥檚 elementary school students need to learn how to analyze, reason, and make complex decisions to improve their chances of success later in life, said Jo Boaler, a professor of education at Stanford University.
In the world of work, 鈥渋t is not very useful to be somebody who has memorized methods to [answer] textbook questions, because the work that is in our world is very different from that,鈥� she said. 鈥淚n whatever job you go into, you need to problem solve, think critically, make connections between different areas. And we鈥檙e just not helping our students develop those kinds of capabilities鈥� in most schools.
The benefits of a real-world problem-solving approach can stick with students for years, Boaler said. For a published in 2017 in the Journal for Research in Mathematics Education , she followed a group of high school students who were learning math through real-world problem solving and another group鈥攚ith similar socioeconomic characteristics鈥攚ho were taught math in a more traditional way. (Boaler has not conducted similar research with elementary students.)
Eight years later, the students who had been exposed to the problem-solving methods were in higher-skill jobs and more likely to be looking at upward mobility in their careers than those who were taught more traditionally. The ones who had learned the traditional way said they saw math all around them in their professional lives but felt that their K-12 education had left them unprepared to use it for professional success.
What鈥檚 more, the problem-solving approach gives teachers the opportunity to introduce students to all kinds of possible careers.
Berry鈥檚 students, for instance, wear all sorts of professional hats to tackle math problems that she makes up based on real problems people face in the working world.
They鈥檝e been event planners tasked with coordinating transportation to a wedding with 76 guests and four cars that can hold differing numbers of passengers. They鈥檝e designed a house for a very picky client鈥攑layed by Berry, doing her best posh lady voice. The house had to be built to certain specifications: a particular range of square footage, number of rooms, and sizes for those rooms.
The strategy gives students insight into how professional mathematicians think, Berry said. 鈥淩eal mathematicians [see] a problem in the world, and they use math to solve it.鈥�
More than one right answer, more than one right method
While those tasks make sense for 5th graders, kindergartners鈥攁nd even preschoolers鈥攃an learn math through problem solving, Boaler said. She pointed to a lesson she created, called 鈥渇oot parade,鈥� in which children see pictures of the feet of different types of animals and are told to select as many creatures as they need to reach a particular number of feet. A cat and a bird, for instance, would be a total of six feet.
In the in Maryland, elementary school math classes typically kick off with a problem-solving exercise, such as a discussion of a level-appropriate 鈥渢arget鈥� number. For instance, students have a few minutes to brainstorm as many equations as possible to reach the number 147. Correct answers could be 100 plus 47, 823 minus 676, or other combinations of numbers. Students then share their answers in groups.
They must collaborate and recognize there are usually multiple ways to solve a problem, skills people in the working world exercise every day.
The goal is to expose 鈥渒ids to different ways of thinking, without telling kids, 鈥榟ere鈥檚 the different ways you have to think,鈥欌�夆�� said John SanGiovanni, the district鈥檚 elementary math coordinator.
These math problems often have multiple correct answers, and multiple pathways for getting to a solution. That鈥檚 exciting for kids, Boaler said. 鈥淥ne of the things that has [turned] off so many kids [to math] is that [they] think it鈥檚 a subject with one answer and one method,鈥� she said.
Whether the math problems are as intricate as Berry鈥檚 outdoor classroom challenge鈥攐r simpler, like Howard County鈥檚 鈥渢arget number鈥� exercise鈥攖he underlying goal is to 鈥渃reate interest and wonder,鈥� and help students unlock the concepts behind operations like addition, subtraction, multiplication, and division, SanGiovanni said.
When students veer off in the wrong direction, it鈥檚 a chance to learn, Berry said.
鈥淢istakes grow our brain, we celebrate them,鈥� she said. Going over a misstep is 鈥渨hen we have the best conversations.鈥�
If a kid gets tripped up, Berry will ask the student privately if they are OK sharing their process with the class as a 鈥渇avorite mistake.鈥� If they aren鈥檛, Berry will still share their work, but pretend the blunder was her own.
Should teachers throw out their worksheets?
Teachers using the real-world problem-solving approach can present the problem without initially giving instruction in the operations they might use to solve it, such as multiplication, Boaler said. That鈥檚 the reverse of how it鈥檚 done in a typical classroom where teachers say, 鈥溾�夆�榟ere are your methods, now do some questions that practice them.鈥欌�夆��
Flipping that traditional process on its head means giving students a rich problem first. Then, once they鈥檝e given it some thought, a teacher can introduce methods that might help students find a solution.
鈥淎t that point, kids are interested. They鈥檙e like, 鈥極h, yeah, I need that method.鈥� Whereas, when you show them the methods first kids are like, 鈥榃hy? Why am I doing this?鈥欌�� Boaler said.
SanGiovanni agrees with that perspective, to a point. But in his mind, the occasional worksheet still has its place. 鈥淭en [math] problems on a paper from time to time, it鈥檚 probably good for maintenance of a skill,鈥� he said.
Plus, he emphasized that most kids won鈥檛 be able to learn all they need to know just by solving a big problem, he said. 鈥淭here has to be some explicit instruction about some of the math,鈥� he said. 鈥淵ou can鈥檛 just discover it all.鈥�
The problem-solving approach can be problematic for some
Teaching math this way can be a lot to ask of teachers, students, and even parents.
Many teachers learned the subject through more traditional methods back in their student days, such as practicing math problems on worksheets before applying that knowledge to real world situations. They鈥檙e skeptical that young kids can learn this way, SanGiovanni said.
鈥淪ome of our teachers [believe] that you can鈥檛 solve this huge problem or this really cool problem, because you don鈥檛 know how to add three plus four yet, or better yet, you don鈥檛 know how to do it quickly,鈥� he said. They say they 鈥渄on鈥檛 feel like I can take the time鈥� for the real world problem-solving approaches.
It鈥檚 also tough for some teachers to give up control, said Latrenda Knighten, a mathematics instructional coach in Baton Rouge, La.
鈥淚t is scary because you don鈥檛 know what answers you鈥檙e going to get,鈥� she said. Children may get frustrated with the open-ended process, or a class discussion may veer off topic if every kid is encouraged to talk about the problem in their own way.
Another big hurdle: 鈥淭here isn鈥檛 always access to good materials that frame lessons in [real world] problems,鈥� SanGiovanni said.
While Boaler and others have created , he said, 鈥測ou teach kids for an hour and a half of math every day,鈥� he said. 鈥淭hat means you need 180 lessons, or 180 [real world] problems. And I know that some of those problems could be two or three days. But just the sheer volume isn鈥檛 there.鈥�
Teacher preparation programs often don鈥檛 help prospective educators teach math through rich problem solving, particularly at the elementary level, he added.
District and school administrators may also push back against the approach. They worry students taught this way aren鈥檛 going to perform well on standardized tests, though those assessments increasingly measure students鈥� problem-solving abilities, Knighten said. 鈥淚f we allow children to really internalize the concept, so that it sticks, you鈥檙e going to see [good test scores] because they鈥檙e going to make sense of it.鈥�
Teachers get grief from parents, too, SanGiovanni said. 鈥淎 lot of parents say they want their kids to be able to think and reason. They just don鈥檛 want it to look different from the way they learned,鈥� he said.
Berry is quick to point out the real-world problem solving approach was not the way the subject was taught when she was a student. That, she said, is largely why she grew up hating math and now makes it her mission for students to love it by the time they leave her classroom.
鈥淪itting in a seat, just doing problems out of a textbook, or me walking the kids through step by step on how to do a procedural. That, to me, is not authentic learning,鈥� she said. 鈥淚 don鈥檛 want them just to be test takers. I want them to be productive citizens when they leave me.鈥�
