Degree Date



Doctor of Philosophy (PhD)




Proficiency in mathematics has been identified as a critical skill in multiple aspects of daily life. Research has found that deficits in math achievement may begin with a lack of basic understanding of numbers, or “number sense,” in early childhood. The Response to Intervention (RTI) model of education incorporates the strategies of early identification and intervention to address skills deficits as they emerge. This study evaluated student growth in number sense skills over the course of kindergarten in an RTI-model classroom within an urban school setting, with primarily minority and low-income students.

Hierarchical Linear Modeling (HLM) was used to evaluate student progress on measures of Oral Counting, Number Identification, and Quantity Discrimination given in the Fall, Winter, and Spring. Students were also evaluated with a Missing Number task in the Winter and Spring only. Overall, most students showed progress on all measures. There were no significant effects of gender or ethnicity. On Oral Counting, Number Identification, and Quantity Discrimination, age was a significant predictor of intercept, with older students achieving significantly higher initial scores on all three measures.

For Quantity Discrimination and Missing Number, students who began with lower scores showed faster growth across time, narrowing the gap with their higher achieving peers. In contrast, there was some widening of the achievement gap for Number Identification.

Finally, this study evaluated the effectiveness of an intervention program targeted at students with weaker number sense skills. Students met in small groups twice a week for sixteen weeks. The intervention used a “toolbox” model to provide flexible, individualized instruction. Student progress in the Intervention group was compared with a similar group of students in a neighboring school who received only regular classroom instruction. GLM repeated measure analyses identified intervention effects for Number Identification, Quantity Discrimination, and Missing Number.

The results of this study describe number sense learning in this population of students and demonstrate the effectiveness of this type of intervention program. More research is needed to better understand how number sense learning trajectories might predict mathematics achievement in higher grades, and to better understand the mechanisms in remediating number sense skills.


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