Evaluation of a Number Sense Intervention for High-Risk Kindergartners

Theoretical Framework

The mathematics achievement gap between low- and middle-income children in the U.S. is wide and persistent (National Center for Education Statistics, 2009).  Even more disturbing, achievement disparities between these groups have been documented before children enter school (Duncan et al., 2007; Lee & Burkham, 2002).  A disproportionate number of children from low-income families come to kindergarten without number competencies necessary for success in formal mathematics (Jordan & Levine, 2009; Jordan, Kaplan, Locuniak, & Ramani, 2007;  Jordan, Kaplan, Nabors Olah, & Locuniak, 2006).  

Although most kindergarten math curricula cover multiple topics, number sense is of primary importance during this period (National Research Council, 2009).   Virtually all of the kindergarten mathematics standards, such as the Common Core State Standards initiative and NCTM Focal Points, stress the importance of knowledge of whole numbers, number relations, and number operations.  Even measurement and geometry standards, which are not explicitly numerical in nature, require children to use number words and concepts.  Number sense is highly predictive of mathematics computation and problem solving through at least third grade, even when controlling for reading, age, and general cognitive factors (Jordan, Kaplan, Ramineni, & Locuniak, 2009)

            The goal of the present study was to refine and test a research-based number sense intervention for low-income kindergartners.  It is the second phase of a multi-year investigation. The importance of kindergarten achievement cannot be overstated.  Kindergarten test scores are associated with college attendance, earning potential, and financial management, even when background characteristics are held constant (Chetty, Friedman, Hilger, Saez, Schanzenbach, & Yagan, 2010).  Kindergarten mathematics, in particular, matters for long-term outcomes. Independent of background factors, kindergarten math concepts (e.g., knowledge of numbers and ordinality) are powerful predictors of adolescent learning outcomes across content areas (Dowsett, Claessens, Magnuson, Huston et al., 2007).

Method

Participants

Participants were recruited from kindergarten classes in five elementary schools serving high-risk children from low-income urban families.  In each of the schools and classes, children were randomly assigned to one of three groups: number sense intervention (n = 42), a contrasting language intervention (n = 42), and a “business as usual” control group (n = 44).  A language intervention was added to test whether small group instructional time alone increases children’s number sense.

Measures

The study used a pretest, immediate posttest, and delayed posttest (8 weeks later) test design.  Measures included a validated assessment of numeracy indicators, the Number Sense Brief (NSB) (Jordan et al, 2010). The NSB assesses competencies related to counting, number recognition, number comparisons, and number operations. A standardized measure of mathematics achievement, the Woodcock- Johnson III Tests of Achievement (WJ)/ Form C Brief Battery: Applied Problems and Calculation subtests (Woodcock, R. W., McGrew, K. S., & Mather, N., 2007) was also given to all participants.

Intervention Approach

For eight weeks, children in both intervention groups received instruction for 30 minutes, three times a week, for a total of 24 lessons.  The number sense intervention was designed to augment the regular kindergarten mathematics program with small group (four per group) intensive instruction which explicitly targeted whole number concepts related to counting, comparing, base ten concepts, and manipulating sets.  Four of the five schools used Math Connects (Macmillan/McGraw-Hill, 2009) and the fifth used Math Trailblazers (Teaching Integrated Math and Science Program, 2008) as their regular classroom curriculum.

Number sense intervention lessons drew from the most effective activities from a prior study. Lessons used a compare and contrast approach (e.g., before /after, addition/subtraction, n+1/n-1 were presented simultaneously).  Each lesson’s activities addressed the following: (1) Representations of number through base ten principles, (2) Number recognition, (3) Number sequencing, (4) Verbal subitizing, (5) Finger use, (6) Number List activities (more/less, before/after. +1/-1), (7) Part-whole relationships, and (8) Problem solving.  Each day’s lesson concluded with The Great Race game, which required children to move up and down a number list to 10 (Ramani &Siegler, 2008). Frequent progress monitoring, through regular, short assessments during the lesson, allowed for prescriptive instruction at regularly planned times during the lessons.  The language intervention focused on vocabulary learning through storybooks.

Results and discussion

Using raw scores, a series of one-way ANCOVAs were run to test whether mean gains between pretest and immediate posttest and delayed posttest differed by group for total and subarea scores from the NSB and Woodcock-Johnson (WJ) Achievement Test.  Three combinations of covariates or controls were used:  pretest scores from (a) the NSB, (b) the WJ, and (c) both the NSB and WJ.  In every instance of statistical comparison, the number sense intervention group showed greater gains than the language or control groups.  Of the 60 comparisons, 41 (68%) were statistically significant with medium to large effect sizes in favor of the number sense intervention group.  Children showed especially strong growth in areas targeted by the number sense intervention: number recognition through base ten concepts, magnitude comparison, and problem solving. There also was carryover to the more general WJ math achievement test results (e.g., the number sense intervention children went from a mean of the 8^th percentile on the calculation pretest to the 45^th percentile at delayed post test vs. the 18^th percentile to the 36^th percentile for controls). This was an improvement over the first cohort gains.  Possible explanations for gains will be discussed through error and strategy analyses as well as an analysis of the intervention curriculum. 

            In conclusion, in a randomized study the number sense intervention boosted children’s number sense and more general math competencies relative to the performance of controls.  We expect that the children will be more available for learning formal math in first grade and will test them again during this period.  The number sense intervention has good potential for use in RtI (Response to Intervention) settings in kindergarten.