Kids Master Mathematics When They're Challenged But Supported
Math test scores soar if students are given the chance to struggle.
by Bernice Yeung
Credit: Getty Images
New Jersey teachers have found a surprising way to keep students engaged and successful: They let underachieving youngsters get frustrated by math.
While working with minority and low-income students at low-performing schools in Newark for the past seven years, researchers at Rutgers University have found that allowing students to struggle with challenging math problems can lead to dramatically improved achievement and test scores.
"We've found there is a healthy amount of frustration that's productive; there is a satisfaction after having struggled with it," says Roberta Schorr, associate professor in Rutgers University at Newark's Urban Education Department. Her group has also found that, though conventional wisdom says certain abilities are innate, a lot of kids' talents and capabilities go unnoticed unless they are effectively challenged; the key is to do it in a nurturing environment.
"Most of the literature describes student engagement and motivation as having to do with their attitudes about math -- whether they like it or not," Schorr says. "That's different from the engagement we've found. When students are working on conceptually complex problems in a supportive environment, they do better. They report feeling frustrated, but also satisfaction, pride and a willingness to work harder next time."
Former Newark middle school math teacher Debra Joseph-Charles says the Rutgers training taught her to see her role as that of a guide. In her classes, she assigned rich word problems, then gave students a few minutes to work individually in a way that emphasized their strengths.
"If you are good at computations and you want to do it that way, you can," says Joseph-Charles, now a math coach in the school district. "If you are a visual learner and you want to draw, you can. Or if you want to use manipulatives, you can. You hear this rhetoric about there being this and that type of learner, but no one really gives students the opportunity to learn in different ways in the math classroom."
Using the Rutgers method of group learning, Joseph-Charles's students organized themselves into groups so that each student could explain how she arrived at an answer. The other students in the group gave constructive criticism about the pros and cons of each approach. Each group then decided which method was best and presented it to the class.
"Children who were failing are now quite successful," Joseph-Charles says of her former math students. "They're solving problems in ways we didn't see as a possibility but which were valid."
Naga Madhuri Philkhana, another former teacher turned math coach in Newark, says the Rutgers approach gave her students a sense of accomplishment. "You bring out their confidence by letting them have their own way of looking at problems and sharing it in the classroom," she says.
After teachers like Joseph-Charles and Philkhana began applying the Rutgers techniques in the classroom, students showed more interest in math, and the math test scores at what were among the lowest-performing schools in the state began to soar. (In comparison, the language arts scores often remained the same or decreased.) Schorr was delighted but admits she was also surprised at the rising scores and how they have continued to improve year after year.
Since 2003, the average standardized math test scores among fourth graders in Newark schools have risen from 45 percent to 79 percent. As a result of its success, math teachers across New Jersey are now receiving professional development in the Rutgers method through a federally funded series of webinars called MathNext.
Schorr and her colleagues at Rutgers, with the help of MetroMath researchers in New York City, have begun identifying how and when students appear to be most engaged in math so they can train teachers to create and sustain that engagement. A number of their academic-journal articles on the subject have been published, and more are forthcoming.
"Motivation is a key aspect of achievement that we often ignore in math; it's the missing link," Schorr says. "We need to provide kids with conceptually challenging math problems in an emotionally safe environment, and the teacher plays a critical role in that. Kids can view frustration as an opportunity for success instead of an indication of failure, but that won't happen without teachers letting the students experience productive struggles."
Bernice Yeung is a contributing editor for Edutopia.
This article was also published in the Oct 2009: The Waldorf Way issue of Edutopia magazine as "Let 'Em Sweat ".
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Reader Comments
"...the opportunity to learn in different ways..."
This is a great article, and certainly aligns with my own experience. As a high school student, math was not particularly challenging or interesting to me--I was able to get by with fairly little effort. It wasn't until I started an engineering curriculum in college that I found the motivation to really work to learn the mathematics that were behind my chosen field of study.
Perhaps this research provides an additional data point to the discussion around what role real-world applications should play in mathematics teaching.
What seems most salient is the statement "you hear this rhetoric about there being this and that type of learner, but no one really gives students the opportunity to learn in different ways in the math classroom."
The unfortunate reality is that the reason this doesn't happen as often as it should is simply logistics. Keeping a class of 20+ students roughly at the same place in the curriculum at the same time, while adapting their teaching style to meet the needs of 20+ individual students, is nearly impossible.
As an example, imagine a teacher that wanted to spend just 15 additional minutes per week with each of his/her 20 students. Doing that would add an additional 5 hours to that teacher's work week. If he/she had four classes (which many teachers do), the teacher would be spending an additional 20 hours per week, every week.
The vast majority of students would likely benefit from customized, one-to-one attention to understand mathematics. Unfortunately, the lecture model in use in most classrooms doesn't support individualized attention. It would be great to see research like this spawn new classroom management strategies that target students as individuals.
So true
Many years ago I began using George Polya's problem solving steps with students, providing them with challenging problems, a supportive environment and time to discuss, share, solve and defend their interpretation and solution. It is a time consuming and difficult process in the beginning, however, the pride and accomplishment the students obtained were well worth the effort. There will always be a level of frustration, something we often try to "protect" students from, if they are truly challenged and learning. We need to allow this, but I believe a key point in this article is the fact students are provided a safe, nurturing environment. Mutual respect between students as well as teacher/student is a must. I believe this is also true with all students, inclduing gifted. So excited to see there is data to support what I've been doing for years!
cooperation
There are several variables in this experiment. I believe that the researchers mistakenly attribute the result of the experiment exclusively to «difficult math». Much more powerful motivational and structuring factors present were the following:
extra attention given to these students;
nurturing environment;
structured learning,
and above all: cooperative learning techniques.
You could teach them Mandarin or chemistry using these measures and obtain the same results. Math was only the context.
Engagement
I so agree with this article. In the research my co-writer, John McDermott, and I did for our book Clock Watchers, we kept seeing over and over how challenge was vital for students to be both motivated and engaged as long as students were in a nurturing environment. Work that's too easy bores them while work that's too tough -- or work that isn't supported -- frustrates them. Csikszentmihalyi has a great chart in his book Flow on page 74 that shows the importance of challenge.
Along with challenge, students need to be in a caring classroom environment, to work collaboratively, to have ongoing feedback, and to have their work celebrated. It's a complex process and requires close attention to the culture of the classroom.
Puzzlement and increased learning is nothing new . . . Piaget coined the term "disequilibrium" to mean a state of imbalance when new learning does not fit into a learner's existing schema. Students may grapple with a problem until reaching a solution, thus influencing their future learning. It is wonderful to have new research supporting his theories . . .
This is a great article. Basically it boils down to this:
In order to learn how to think, you have *practice thinking*. And when you get the brain's gears turning, it can feel pretty great!
Math Lesson
Thanks for the refresher, doc!
management
As a second grade teacher, trying to integrate this method of teaching math causes me to struggle! However, I believe the struggle is worth the effort and discomfort. I want my students to believe it is worth it also. I want them to know that grappling with a problem, of any sort, is okay...and exciting!
I look forward to reading research on the management strategies that target students as individuals. I worry about this too. However I feel that I have a more authentic understanding of what my students know now more than ever because I know WHY and HOW they know what they do. I feel more confident with addressing their mathmatical issues becuase of the conversations I am having with the students as they "struggle". I didn't have this confidence when using more traditional methods.
Adapting this way of teaching is so important despite how it makes us feel!
teachers learn too
As we as teachers struggle and feel that dissonance or disequilibrium, we will also have the greatest opportunity for learning to occur! Recognizing that path from struggle to success in ourselves will help us to help our students on this path as well.
Reinforcement!
This article reinforces many of the concepts my students are learning right now in their math methods course. My first reaction was to think of Piaget and his idea of disequilibrium. (Others had the same thought.) I look forward to reading what my 2:00 TR math community members have to say about this article.