Written by Robin Hojnoski, assistant professor of school psychology
It’s a relatively recent finding that has put the United States in a rather precarious academic situation. In 2007, former U.S. Secretary of Education Margaret Spelling testified before Congress that “…almost half of our 17-year-olds do not have the basic understanding of math needed to qualify for a production associate’s job at a modern auto plant.”
The troubles start long before high school, however. According to the National Mathematics Advisory Panel, between 5 and 10 percent of all children who enter school will be identified as having a math difficulty or disability—many of whom will face math frustration and failure throughout their school careers. The odds are even greater for minority children or disadvantaged students.
The benefits of early math education are not lost on policy experts. In 2009, the National Research Council issued a report that argues, “education and training for most [pre-K] teachers typically places heavy emphasis on children’s social-emotional development and literacy, with much less attention to mathematics. In fact, academic activities such as mathematics can be a context in which social-emotional development and the foundations of language and literacy flourish.”
It’s against this rather bleak backdrop that the educational community is seeking to revisit math education and intervention, beginning as early as preschool. But recognizing the importance of math skills in early education is only the first step. In order to know where a child stands, or what mathematical skills and knowledge a child already has (and most already have some informal understanding), teachers must be able to easily and accurately access his math skills. That’s where my research as a school psychologist with a particular interest in early education comes in.
Together with my research colleague, the University of Memphis’ Randy Floyd, I developed four specific tasks that reflect children’s early number knowledge: comparing quantities represented as two arrays of dots; oral counting; counting with one-to-one correspondence; and naming printed numerals. Collectively, the four tasks are called the Preschool Numeracy Indicators (PNI).
My work focuses on using a curriculum-based measurement (CBM) framework to assess early mathematics skills in preschoolers. CBMs look at a number of key abilities as indicators of overall performance. In our research, those key abilities are the four PNI.
To make things as simple as possible for educators, our PNI assessment tool promotes universal screening in math that can be used both for individual children and large groups in busy preschool settings. Our ultimate hope is that teachers and administrators will put more emphasis on math starting in the preschool years, thus building a stronger math foundation for all students.
So far, the results have been quite positive; our research with the PNI has had a meaningful impact on assessment and instructional practices in numerous classrooms. Not only do teachers better appreciate the importance of math, but they are more actively teaching math skills to their students. Using our tools, teachers identify children early on who may need more math instruction. Then based on these student assessments, teachers change their curricula to be more math oriented, for example, by using more mathematical language or boosting their inclusion of printed numerals.
“Dr. Hojnoski’s work helped our classroom teachers create individualized small groups that focus on math,” says Tricia Carrasco, Early Childhood Learning Coach in the SPARK Early Childhood Center in the Bethlehem Area School District (Pa.). “Each teacher received classroom results and individual results. Teachers were able to refer to this data as a tool when planning for math-focused small and large group activities.
“Dr. Hojnoski’s tool also helped the teachers see which children improved and which children still needed assistance.”
THE BASIS OF PNI
In the preschool years, children learn to understand numbers, represent numbers, recognize relationships among numbers, and comprehend number systems; the National Council of Teachers of Mathematics defines these tasks—the cornerstone of early mathematical thinking—as numbers and operations.
Children experience significant growth in numbers and operations in the preschool years. For example, between the ages of two and five, children move from nonverbally representing a collection of objects to counting aloud in sequence from a number other than one. Preschoolers also progress from counting small groups of items to counting larger groups of items, as well as symbolically representing the number of items in a set.
These critical numbers and operations parallel the four PNI tasks. The first study of PNI, conducted by Floyd and me in 2006, showed that these four PNI tasks could effectively assess early math skills.
Building on this research, my team and I decided to explore whether or not the PNI could be used to measure changes in children’s progress over time. Using a sample of over 100 children in Head Start programs in the southern United States, we conducted monthly assessments of the PNI.
The results were positive. We found that not only could teachers use the PNI to monitor their students’ progress over time, but they could also use the information they gathered to change math instruction in order to best meet each child’s needs.
AN EXPONENTIAL IMPACT
The positive results of our studies—as well as the similarity of PNI to the widely accepted measures of early language and literacy—have created great interest in PNI amongst educators across the country.
In response to this interest, my colleagues and I have partnered with several school districts in Illinois, Minnesota and Wisconsin to put the PNI into place. Each of our partnership sites collect PNI data regularly and structure early math instruction according to results. Here are some examples of the program’s effects thus far:
- As referenced by early childhood learning coach Carrasco, in partnership with the Bethlehem Area School District’s early childhood program, SPARK, a team of Lehigh graduate students in school psychology and special education collaborated to implement a system of data-based decision-making using the PNI coupled with early language and literacy measures. We assessed over 200 children and found PNI to be useful in making changes in instructional grouping as well as the frequency, intensity and content of instruction. Teachers at SPARK have responded quite positively to the use of PNI in their classrooms.
- In one Illinois classroom, a teacher modified her “circle time” to include counting, concrete representation (number of blocks), comparing quantities and identifying printed numerals. Children were actively engaged and enjoyed the mathematical interaction.
- On a recent visit to a site in Illinois, a teacher commented that she had not considered math an important area for her classroom until she began using PNI. Now increasing her knowledge in this area is one of her professional development goals.
CALCULATING THE POWER OF THE PNI
As a result of our research, we have seen measurable change in how teachers in our partnership sites approach early mathematics. By exploring the PNI as they function in actual settings with actual children, my fellow researchers and I are shaping directions for future research, both at Lehigh and beyond. We are currently thinking about the next steps in assessment and instruction in preschool math.
For example, one site has a significant number of children with identified special needs, and they are keenly interested in examining the growth of these children over time as compared with the children without special needs. My colleagues and I are currently evaluating the starting points, growth trajectories and overall growth of these two different groups of children.
Another site in Illinois with a large number of Spanish-speaking children translated the PNI into Spanish and got interesting results. The Spanish-speaking children performed similarly to the English-speaking children when they compared quantities (a nonverbal task). However, on tasks with a verbal component, such as counting or naming numbers, the performance of Spanish-speaking children dropped significantly, both in comparison with their performance on the nonverbal task and in comparison with their English-speaking peers. Despite this, both groups demonstrated growth on the tasks from winter to spring. I’m working with a team of graduate students at Lehigh to examine this phenomenon further and studying the issues surrounding second language learning and early math.
And response to feedback from partnership sites indicated the need to address other areas of math, so in cooperation with SPARK, I worked with Lehigh graduate students and fellow researchers to develop a set of tasks to assess early geometry and algebra skills. Specifically, the tasks look at children’s knowledge of shapes and patterns.
Shape is a central concept in general cognitive development in addition to its role in geometry and math. Pattern and structure underlie much of the domain of numbers and operations, spatial thinking (i.e., composition of shapes), and area and volume, and are related to later algebraic thinking. Plus, given the National Mathematics Advisory Panel finds that geometry and algebra are areas of particular weakness in U.S. students and differences in young children’s knowledge emerge at an early age, these tasks take us in an important new direction in measuring early math development with a goal of ensuring mathematical competency for all children.
I am also currently writing a federal grant to fund additional research and development on the PNI measures. In addition, my colleagues and I are investigating how to use the PNI in a Response to Intervention (RTI) format. RTI is a three-tiered approach of identifying specific learning disorders at an early age, a method pioneered by Lehigh University’s Ed Shapiro, director of our college’s Center for Promoting Research to Practice.
Overall, the PNI take us in an important new direction in measuring early mathematics development. As a result of our research, we hope more preschool children become competent in math, giving them a strong math foundation for the remainder of their academic careers and beyond.