2011 — 2017 |
Mcneil, Nicole |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Career: Predictors and Consequences of Early Understanding of Mathematical Equivalence @ University of Notre Dame
The purpose of this project is to longitudinally investigate (K-Grade 6) a child's understanding of mathematical equivalence. This project will answer two major research questions: (1) What are the origins of individual differences in a child's early understanding of mathematical equivalence? And (2) What are the long-term consequences of having a poor understanding of mathematical equivalence?
To answer the first research question, the PI will identify skills (early number sense, relational thinking, and cognitive flexibility) in kindergarten (Time 1 in the longitudinal design) that predict individual differences in understanding of mathematical equivalence in later grades, while controlling for gender, SES, and IQ. To answer the second research question, the PI will measure a child's understanding of mathematical equivalence at second grade (Time 2), and then she will use this measure to predict mathematics achievement at the third, fourth, fifth, and sixth grades. At the sixth grade, the PI will also measure algebra readiness. For answering research question 2, the PI will control for gender, IQ, and computational fluency.
The development of algebraic thinking is a timely topic with national and international interests. This project takes a unique approach to explore ways to develop student algebraic thinking, especially the use of a longitudinal design. In addition, this project is exemplary for interdisciplinary work on integrating cognitive psychology and mathematics education. The findings from this project can have both theoretical and practical implications.
|
0.915 |
2017 — 2020 |
Mcneil, Nicole |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Improving Children's Ability to Connect Counting to Cardinality Through Shared Book Reading @ University of Notre Dame
Individual differences in children's early math understanding are driven, in part, by differences in children's early learning environments. However, it is unclear exactly how early learning environments should be structured to support the development of children's math understanding. Lack of such knowledge is a critical problem because, without it, scientists cannot explain and predict children's understanding of foundational math concepts, and parents and educators are left to rely on their own, sometimes erroneous intuitions when choosing learning materials for their children. In the current project, researchers from the University of Notre Dame will study how the design of one type of early learning material - children's counting books - affects children's book reading behaviors and early math understanding. In this way, the project will further the mission of EHR Core Research (ECR) program to advance knowledge of children's math learning and the early learning environments that support it.
The central hypothesis is that counting books with tactile features (e.g., pop ups, textured graphics) will be less effective than those without tactile features for supporting children's understanding of counting and associated math concepts. Books with tactile features are expected to elicit at least two behaviors that may hinder math learning: (a) attention focused on the individual objects rather than on the set as a whole and (b) off-task utterances and actions. The research team will work with a diverse sample of preschoolers from Head Start, Title-I preschools, and private early childhood programs. The research methods include a pretest-intervention-posttest randomized experiment in which children will read assigned books with a trained tutor in school over the course of several weeks, as well as a less structured experiment in which children will read assigned books with their primary caregiver in a more naturalistic shared book reading context. By combining these approaches, the researchers will not only be able to determine how different types of books affect pre-to-post changes in math understanding, but also be able to conduct detailed observations and analyses of the language and behaviors that emerge during shared book reading. The project will advance the science of early math learning by testing theory-driven hypotheses. Findings will inform best-practice guidelines for the design of counting books and, thus, will help parents and early childhood educators make more informed decisions when selecting learning materials for their homes and classrooms.
|
0.915 |
2021 — 2023 |
Mcneil, Nicole Cheng, Ying (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Characterizing and Assessing Number Sense in Third Through Eighth Grade Students @ University of Notre Dame
One goal of mathematics curricular and instructional reforms in the United States is to help students build “mature number sense,” which involves making sense of numbers and operations, using reasoning to notice patterns, and flexibly selecting the most effective and efficient problem-solving strategies. In support of this goal, mathematics educators have developed a variety of instructional practices designed to move students beyond seeing mathematics as a set of disconnected procedures and facts to appreciating it as a coherent set of ideas and tools. These practices have been growing in popularity across mathematics classrooms, but it is unclear if students’ mature number sense is improving. One reason for slow progress is that the field currently lacks a rigorously validated measure of mature number sense that is both widely accepted and easy to use. Moreover, even though mathematics educators generally agree on the importance of mature number sense, there is little evidence demonstrating that it is a measurably distinct characteristic of mathematical cognition. Lack of such knowledge is a critical problem because, without it, researchers cannot explain, predict, and study mature number sense, and teachers are left to rely on their own intuitions about whether and how to focus on it in their classrooms. In this project, researchers will advance fundamental knowledge of mathematical cognition through the development of innovative metrics and methods to assess mature number sense with valid and reliable scores for use with students in grades 3-8.
The central hypothesis is that mature number sense is a measurable characteristic of mathematical cognition, separable from both domain-specific knowledge (e.g., arithmetic fluency, fraction knowledge) and domain-general constructs (e.g., creativity, cognitive flexibility), that predicts math-related beliefs and achievement. The research team will work with a diverse sample of students in grades 3-8 to refine, extend, and validate a brief assessment of mature number sense. They will start with a measure that they iteratively developed and validated in a large pilot study with middle and high school students, and they will optimize it as the “middle school form” (for grades 6-8). They will collect additional evidence of validity for this form by comparing it to other, more lengthy measures of mature number sense and by conducting a longitudinal study to examine if scores on the measure in fall predict grade-level mathematics learning and math-related beliefs in spring. Next, they will extend the measure downward to include upper elementary grades 3-5. Items will be iteratively developed and examined for construct relevance using expert ratings, classical and IRT item statistics, and retrospective think-aloud strategy reports of students during problem solving. The researchers will examine if the factor structure of the elementary form is the same as that found with the middle school form, testing measurement invariance across the two grade-level groupings. They also will develop a technical manual for researchers and teachers. By the end of the project, there will be a practical, validated assessment of mature number sense for students in grades 3-8 that is easy to administer in schools, after-school programs, research laboratories, and homes. The target audiences for this measure include basic researchers interested in studying mathematical cognition, intervention researchers interested in studying the effects of innovative instructional practices on students’ number sense, and teachers who wish to monitor their students’ progress toward the “processes and proficiencies” with longstanding importance in mathematics education.
This project is funded by the EHR Core Research (ECR) program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
|
0.915 |