Chances are, few preschool students can recognize a tetrahedron, let alone build one. When it comes to math, class time is more likely to involve counting objects in unison with the teacher.
Yet, teaching four-year-olds to build a tetrahedron — a three-dimensional object constructed from four two-dimensional, equilateral triangles — not only helps them better understand shapes, but also sharpens skills such as mental imagery, analysis, and reasoning that are key to effective mathematical thinking.
That is one idea behind Pre-K Mathematics, an innovative math curriculum aligned with the Common Core State Standards for Mathematics and designed by Alice Klein and Prentice Starkey, Senior Research Associates at WestEd. The curriculum features small-group instruction on topics such as number, operations, space and geometry, and informal measurement; classroom activities that can be adapted to a range of student abilities; home activities that parents can complete with their children; and a professional learning component.
“It’s a matter of changing teacher practice to support math instruction in ways that impact the growth of young children’s math knowledge,” says Klein.
Closing the math achievement gap
According to Klein and Starkey, quality preschool math instruction is key to boosting school readiness and long-term math learning, especially for children from low-income families who generally enter kindergarten exhibiting lower math achievement than their more advantaged peers. “Because math knowledge is cumulative, once children fall behind in math, it is very difficult to catch up,” explains Klein. What’s more, she cites research indicating that students’ math knowledge in kindergarten is a strong predictor of their overall school achievement in later grades.1 “Research shows that most children with low math achievement in kindergarten continue to struggle through elementary school,” says Starkey, “and those with persistently low math achievement through elementary school are less likely to complete high school and attend college.”
Part of the problem, they contend, is that preschool teachers typically spend only about 8 to 10 minutes per day on informal math instruction. “That mostly includes counting and some calendar activities, and perhaps an activity involving shapes,” says Starkey. “Instruction tends to be repetitive and delivered either to only a few children during play time or to all at once in a whole-group setting.”
Differentiating math instruction in small-group settings
Pre-K Mathematics, on the other hand, emphasizes small-group instruction. In such a setting, Klein says, teachers can engage more effectively with individual children and adapt their teaching to make an activity easier or more challenging, as necessary. When building tetrahedrons, for example, a teacher can reinforce some children’s knowledge of two-dimensional shapes while helping others construct the three-dimensional shape. Teachers keep records of which children have participated in each small-group activity and ensure that all children get to participate in the activity during a given week.
These small-group activities are designed to produce specific outcomes, such as an understanding of measurement. Of course, even without Pre-K Mathematics, some preschool teachers undertake measurement activities, but usually in large groups and often it is the teacher who uses a measurement strategy rather than children doing the measurement, says Starkey. “It’s not enough for young children to simply observe a teacher measuring. They need to actually do measuring activities themselves.”
“It’s not enough for young children to simply observe a teacher measuring. They need to actually do measuring activities themselves.”
Engaging parents to help their children
Another key component of Pre-K Mathematics is its home-activity component, designed to engage parents in their children’s learning in meaningful ways. “A problem that many parents face is that they don’t always know what math looks like in young children or how to help their children learn it,” Klein says. “Some parents end up buying a workbook or a number coloring book, which is not optimal for young children. The home activities from our curriculum are more engaging, developmentally appropriate, and tied to what their children are learning in the classroom.”
Parents are shown, for example, how to play a game with their children in which they work together to help a puppet (made by the child at school) learn to count. “We teach parents to have the puppet make certain kinds of mistakes, see if their children recognize those mistakes, and, if possible, say what the mistake was,” says Starkey. The idea is for parents to focus on a small set of principles behind counting and then help their children use these principles. Children come to understand that counting lets them know how many, and parents focus on their children’s mathematical thinking in a more analytical way rather than giving unhelpful feedback such as saying, “That’s wrong. Try again.” Teachers send parents information (in English or in Spanish) with the math materials that encourages parents to spend 10 to 15 minutes per day on the activities for several days each week.
Klein notes that despite the social and economic stress that many low-income parents are under, they usually try the math activities that the teacher sends home. Feedback has been overwhelmingly positive, she says. “Parents tell us that they like the home math materials and that their children enjoy and benefit from them. Most describe the experience of using the materials as more like playing a game than doing math homework.”
Given that preschool teachers typically receive very little, if any, preservice training in teaching math, Klein and Starkey say the professional learning component of Pre-K Mathematics is critical to its success. Teachers attend a multiday workshop where they learn about — and get to practice — classroom activities, which are presented in the context of early math development. Once teachers begin implementing the curriculum, coaches visit their classrooms to provide formative feedback and support.
Teachers also learn to monitor student progress, a practice that not only promotes differentiated instruction, but also empowers teachers. According to Starkey, “It’s very reinforcing for teachers to see evidence that their students are making gains.”
Klein and Starkey have found that providing preschool teachers with a dedicated math curriculum significantly changes the way they approach the subject in their classrooms. Time spent on math generally doubles, from 10 or fewer minutes to 20 or more minutes per day, with more instruction taking place in small groups. The range of math content introduced expands, and instruction is more likely to be individualized.
Study results have consistently found that math achievement improved for students whose teachers implemented the curriculum. Reviews by the What Works Clearinghouse, an initiative of the U.S. Department of Education’s Institute of Education Sciences that evaluates research evidence for educational programs and products, reported strong evidence of Pre-K Mathematics’ positive effect on children’s math knowledge.
Klein and Starkey are now leading a randomized controlled trial, which began in the 2013/14 school year, that includes examining the impact of Pre-K Mathematics with teachers and students in both rural and urban schools from multiple regions throughout California. The main questions of interest are whether this enrichment results in more growth in children’s mathematical knowledge and whether children are able to achieve at the high level required by the Common Core State Standards for Mathematics. This study is funded by a federal Investing in Innovation (i3) Validation grant from the U.S. Department of Education and funds from private foundations.
Thus far, the study has found positive benefits of the Pre-K Mathematics intervention for prekindergarten teachers and children at a statewide scale. The intervention resulted in teachers’ spending more time using effective math practices and more time on math overall. Moreover, children who received the intervention experienced significantly more growth in mathematical knowledge during the prekindergarten year than their peers in the control group did.
Klein and Starkey attribute much of the curriculum’s success to the professional learning for teachers and the involvement of families. Administrators and teachers interested in boosting early math instruction, particularly for children most at risk of struggling academically, would do well to provide professional learning opportunities around effective math instruction and to bring parents into the equation. As Starkey notes, “It is very risky to sit back and do nothing academically in the early childhood years and simply assume that the children who start off behind will catch up with their peers. Instead, we know that teachers who implement effective math activities can make a big difference early on.”
1 Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., . . . Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. doi:10.1037/0012-1622.214.171.1248.
The Investing in Innovation (i3) Validation grant to investigate the efficacy of Pre-K Mathematics was supported by the U.S. Department of Education as well as private funders. The content of this R&D Alert article does not necessarily reflect the views or policies of the funding agencies.