A study showing that early math skills are one of the best predictors of later success in both math and literacy has become a cornerstone of the growing movement among early childhood educators to boost math instruction in preschool through 3rd grade.
The architect of the 2007 study, Greg Duncan, an economist and University of California Irvine education professor, is a national expert on the importance of strong early math skills. He shared key aspects of his research in interviews with EdSource earlier this year and following a forum on early math by the Silicon Valley Education Foundation in San Jose, where he was the keynote speaker. Excerpts from the interviews are below.
Why early math is so important:
“Math coming into school is important because kids who do well in math early on tend to do very well in school. And math is important later on because kids who do well in math in high school end up doing well in the labor market.
“(My research shows) the links between school success and achievement in, say, 5th grade or 8th grade, and the kind of skills that kids bring into school. It’s a pattern that seems to be showing up in a number of different data sets from several different countries and different historical periods: If you do kind of a horse race and ask, ‘What sort of skills and behaviors do kids bring to school that are most important for how successful they are in school?’
“Those skills and behaviors are elementary math skills – knowing numbers and ordinality, things like that. Literacy skills, knowing letters and word sounds and behaviors, things like being able to sit still and pay attention, being able to get along with other kids and teachers (aren’t as important).
“If you put all those things side by side and just say, ‘What’s most predictive of how successful kids are?’ it turns out that math skills are more important than literacy skills or behaviors.”
Why early math, in particular, has such a strong effect on school success:
“There are several possibilities. One is school-structure. You could imagine kids with a lot of math ability, a lot of high math achievement, are more likely to get into the kind of gifted and talented classes that provide accelerated learning. Perhaps more important, they might be less likely to get into special-education classes that might slow them down. There’s some preliminary work that suggests avoiding special education is one of the benefits of coming in with higher levels of math skills.
“Another possibility is more (about) self-perception. As (Carnegie Mellon University professor) Robert Siegler, who’s a wonderful math educator, points out, with math in the early grades, kids get a lot of concrete feedback. They get those worksheets back and they’re (graded) either 100 (percent) or 50 (percent) or zero. So one possibility is that kids who have initial difficulties come to think of themselves as not good at math and maybe even not good at school.
“This concrete math feedback might start kind of a cycle where kids are thinking, well, they’re really good at school and math or not very good at school and math. (Either way), that would be self-reinforcing and set off these other secondary effects. And there is some support for that.
“And then a third possibility is that math skills develop what are called executive-function skills, the ability to kind of keep a lot of balls in the air at the same time. There’s not as much support for that, but you can think of math as promoting these other kinds of thinking skills that might serve kids well in a variety of areas.
“It’s very much an active research area. We haven’t nailed that down as much as we have the overall relationship (between early math and later school success) which seems very consistent across a number of different studies.”
What specific math skills children need for entering kindergarten:
“Stay tuned. We’re actually looking at that. There’s a whole interesting set of questions (about that). The Common Core (standards) has a very well-defined progression of math skills that kids are supposed to master at different grades and it’s a real open question to what extent they’ve got it right. Do kids really need to know about patterns early on or shapes? It’s fun to learn shapes, but are shapes really an important building block for later math skills? I don’t think we know that.
“The short answer is we really don’t know much about the particular skills. But if you’re communicating this to parents, I think one of the messages is that there are ample opportunities, as you interact with your children, to promote these kinds of elementary skills.
“There is good evidence that board games, Chutes and Ladders, for example, give kids a good sense of what the number line looks like and card games give them a lot of elementary counting skills (and the ability to make a) comparison of what’s bigger.
“A lot of the kids know their numbers coming in, but they don’t really have a sense of what the relationship is with the numbers. They don’t have a sense that five is halfway between zero and 10. If you put out a scale with zero and then 10, (leaving the middle blank) and say, ‘Where’s eight?’ a 4-year-old is going to say ‘halfway in between.’ They really don’t have a sense of the proportionality of the distances between the numbers, and board games (give students) a visual sense, a tactile sense.
“Robert Siegler runs an experiment and he has this little, simple version of Chutes and Ladders, a straight line with different color squares that are numbered zero to 10. Someone sits down with a child and they play a little game. They spin a spinner and the child is supposed to say the number that their token is on. If (they’re on) three and they get a two (on the spinner), then they’re supposed to say ‘three, four, five’ (as they move their token).
“Siegler shows that if you compare kids playing that several times to kids playing exactly the same game with no numbers in the squares, so they’re spinning a color and they go to the next color, they’re quite different in terms of their ability to place numbers on a number line and their general math achievement several months later. It’s really a remarkable demonstration of how fundamental a number line is to later math skills.”
Why Common Core, which Duncan calls a better way of teaching math, could produce a higher level of math skills:
“It’s a huge challenge for teachers … because what’s required is a much higher level of math competence (than many teachers have). And elementary school teachers (generally don’t) select into elementary school teaching because they like math a lot; it’s often the reverse.
“There needs to be a tremendous amount of support for teachers through coaching and mentoring of various kinds – and perhaps training in math concepts that teachers need to know that will enable them to be effective in teaching the Common Core.
“It’s really the set of goals in each grade that (is similar to what) high-achieving countries have in their curriculum (that matter). If kids can maintain a level of competence with respect to the grade-by-grade Common Core goals, that would be a tremendous achievement and would represent a level of math proficiency that’s well above all but the highest performing kids in American schools. Even some of the better districts are finding that relatively small fractions of their kids are fully proficient at Common Core levels.
“In the past, our system of (allowing states and districts to set educational standards) has served us very well. There’s been a lot of innovation in the last 100 years that’s come about because we’ve been so decentralized. But I think with the kind of technological changes that have taken place in the last 40 years (and) globalization, the ante has been upped very markedly. I think efforts like the Common Core are really an attempt to have a voluntary national curriculum, essentially. That’s socialism in some people’s minds. But it’s being rolled out, developed by business and state school superintendents. It’s meant to be a bottom up way of teaching both math and literacy and science standards as well.
“I’m very optimistic. I’m big fan, but it’s a huge challenge.”