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Characterizing and assessing number sense in third through eighth grade students

表征和评估三至八年级学生的数感

基本信息

批准号：
2100214
负责人：
Nicole McNeil
金额：
$ 55.34万
依托单位：
University of Notre Dame
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-04-15 至 2024-03-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2100214&HistoricalAwards=false
关键词：
Characterizing assessing number sense third

项目摘要

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.

美国数学课程和教学改革的目标之一是帮助学生建立“成熟的数感”，这包括理解数字和运算，利用推理来注意模式，灵活选择最有效和最有效的解决问题的策略。为了实现这一目标，数学教育者开发了各种教学实践，旨在使学生不再将数学视为一组不相关的程序和事实，而是将其视为一组连贯的思想和工具。这些做法在数学课堂上越来越受欢迎，但目前还不清楚学生们成熟的数感是否在提高。进展缓慢的一个原因是，该领域目前缺乏一种经过严格验证的成熟数字感测量方法，这种方法既被广泛接受，又易于使用。此外，尽管数学教育家普遍同意成熟的数感的重要性，但很少有证据表明它是数学认知的一个可测量的独特特征。缺乏这些知识是一个关键问题，因为没有这些知识，研究人员就无法解释、预测和研究成熟的数感，教师只能依靠自己的直觉来决定是否以及如何在课堂上关注数感。在这个项目中，研究人员将通过开发创新的指标和方法来评估3-8年级学生的成熟数字感，并使用有效和可靠的分数，从而提高数学认知的基础知识。核心假设是，成熟的数感是数学认知的可测量特征，可从特定领域知识（如算术流畅性、分数知识）和领域一般结构（如创造力、认知灵活性）中分离出来，预测与数学相关的信念和成就。研究小组将与3-8年级的不同学生样本一起工作，以完善，扩展和验证对成熟数字感的简要评估。他们将从一个测量开始，他们在一个针对初中生和高中生的大型试点研究中反复开发和验证，他们将把它优化为“中学形式”（6-8年级）。他们将通过将该表格与其他更长的成熟数感测试进行比较，并进行纵向研究，以检验秋季测试的分数是否能预测春季的年级数学学习和数学相关信念，从而收集更多的证据来证明该表格的有效性。接下来，他们将把测量范围向下扩展到小学3-5年级。将使用专家评分、经典和IRT项目统计数据以及学生在解决问题过程中的回顾性思考策略报告，迭代地开发和检查项目的构建相关性。研究人员将检查小学形式的因素结构是否与中学形式的因素结构相同，测试两个年级水平分组的测量不变性。他们还将为研究人员和教师编写一份技术手册。到项目结束时，将会有一个实用的、有效的对3-8年级学生成熟数字感的评估，这很容易在学校、课后项目、研究实验室和家庭中实施。该测量的目标受众包括对数学认知感兴趣的基础研究者、对创新教学实践对学生数感影响感兴趣的干预研究者，以及希望监控学生向数学教育中长期重要的“过程和熟练程度”进步的教师。该项目由EHR核心研究（ECR）计划资助，该计划支持推进STEM学习和学习环境基础研究、扩大STEM参与和STEM劳动力发展的工作。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。