|Title:||A Diagnostic Assessment of Meanings That Matter for Teaching High School Mathematics|
|Principal Investigator:||Draney, Karen||Awardee:||University of California, Berkeley|
|Program:||Effective Instruction [Program Details]|
|Award Period:||3 years (7/1/2016-6/30/2019)||Award Amount:||$1,265,993|
Co-Principal Investigators: Mark Wilson (University of California, Berkeley), Patrick Thompson (Arizona State University)
Purpose: Student achievement in mathematics in the United States continues to lag behind other developed countries. This relative underperformance in mathematics might be due to teachers' and students' view of mathematics as a collection of rules to be followed and their limited conceptions of mathematically important concepts. To understand this potential relationship between student mathematics knowledge and math meaning-making, this research team has developed the Mathematical Meanings for Teaching secondary mathematics (MMTsm) assessment to measure the mathematical meanings held by high school math teachers. Focusing on teachers' mathematical meanings rather than on their knowledge holds great potential for connecting research on what teachers know, what they do, and what students learn. In this project, the team will expand this diagnostic assessment of teacher mathematical meanings, investigate the properties of the assessment, and examine the relation between teacher meanings and student learning.
Project Activities: The project will unfold in three stages. First, researchers will develop additional items for an item pool that can be used to construct alternate forms of the instrument, and to investigate particular areas in greater depth. Second, researchers will develop an online version of the assessment. Finally, researchers will gather data from a sample of high school teachers, each of whom will take one or more sets of items. In addition, researchers will gather data from a smaller convenience sample of teachers, in whose classrooms researchers will administer items from the Partnership for Assessment of Readiness for College and Careers (PARCC) high school mathematics examination.
Products: Researchers will produce a fully developed and validated assessment for mathematical meanings of high school math for teachers, and findings regarding the relation between teacher meanings and student learning. The researchers will publish in peer-reviewed journals.
Setting: This project will draw their sample from across the county and from the Phoenix and the San Francisco Bay areas.
Sample: Study participants will include 500 high school teachers from around the country recruited via an established website that is visited by hundreds of thousands of math teachers each year (i.e., the Math Forum) and targeted mailing lists. In addition, study participants will include a convenience sample of 100 teachers in in the Phoenix and San Francisco Bay areas. All teachers in the sample will teach at least one calculus-track mathematics class.
Assessment: In the original MMTsm instrument, researchers designed rubrics to reflect levels of productive meaning, where "productive" is judged according to how useful this meaning would be for students' future mathematical learning were the teacher to convey it to them. The current version of the MMTsm includes items in areas that are closely connected to the Common Core State Standards for secondary mathematics: covariation, functions, proportionality, rate of change, structure, and frames of reference. Researchers intend to expand this assessment to include sufficient items to investigate each of these standards in depth, and develop an online assessment.
Research Design and Methods: The project will proceed in three stages. First, researchers will develop additional items for an item pool that can be used to construct alternate forms of the original instrument, and to investigate particular areas in greater depth. Second, researchers will develop an online version of the instrument, utilizing computerized item development to allow additional simplification of administration and scoring. Finally, researchers will gather data from a sample of high school teachers, each of whom will take one or more sets of items. The purpose of this portion of the study is to calibrate item difficulties and compare relative difficulties of different types of items. In addition, researchers will gather data from a smaller convenience sample of teachers. This sample of teachers will take both versions of the new MMTsm. The students in one class for each participating teacher will take selected items from the PARCC high school mathematics assessment at both the beginning and the end of the school year (i.e. as a pretest and posttest). Teachers in this second study will participate in cognitive interviews around some of the MMTsm items they take, and in addition will fill out a questionnaire about their classroom teaching practices.
Control Condition: There is no control condition in this study.
Key Measures: Researchers will use items from the PARCC high school mathematics examination to measure student math knowledge. Teacher measures will include type of degree received, length of time teaching, demographic variables and measures of teacher quality.
Data Analytic Strategy: Researchers will use the Random Coefficients Multinomial Logit model to analyze the data and to identify levels of item difficulty, coverage of person distribution, item and person fit, and Differential Item Functioning (DIF). In addition, they will use techniques such as correlation, latent regression analysis and hierarchical modeling to determine the relationships between teacher meanings and student change from beginning to end of year.
Journal article, monograph, or newsletter
Thompson, P.W., Hatfield, N.J., Yoon, H., Joshua, S., and Byerley, C. (2017). Covariational Reasoning Among US And South Korean Secondary Mathematics Teachers. The Journal of Mathematical Behavior, 48, 95–111.