|Title:||Understanding Students' Mathematical Competencies: An Exploration of the Impact of Contextualizing Mathematical Problems|
|Principal Investigator:||Sternberg, Robert||Awardee:||Tufts University|
|Program:||Cognition and Student Learning [Program Details]|
|Award Period:||3 years||Award Amount:||$749,974|
|Type:||Development and Innovation||Award Number:||R305H030282|
Previous University Affiliation: Yale University
Technology-driven societies require a high level of mathematics and science proficiency in the general population, and so deficiencies in mathematical competence can seriously limit students' educational opportunities and prospects for future employment in such societies. The purpose of this project is to examine whether making mathematical problems appear more practical (that is, related to the context of everyday life), will improve students' performance on those problems and their mathematical knowledge of how to solve them, compared to problems that appear more academic (that is, abstracted from any everyday context). The researchers will investigate which of the factors that contribute to making mathematical problems seem more practical also contribute to better student performance on those problems, as well as how to shape instruction to take advantage of those factors.
The researchers are carrying out two series of studies with fourth and sixth-grade public school students in an area serving a large proportion of low-income minority families. The first series of nine studies involve isolating various features of what makes a problem appear 'practical' to students tested on those problems, such as having physical objects to manipulate or being rewarded for the right answer, to determine whether those factors are related to better student performance. Using the results of these studies, the researchers will create a pool of test problems that reflect the presence or absence of those factors that contribute to giving problems a significantly practical context. In the second series of studies, classrooms of students will be randomly assigned to teachers using standard instructional materials or teachers using instructional materials designed to present mathematical problems in practical contexts, and the previously designed test problems will be used to determine the outcome. The topics covered by the instructional materials in these two studies will be equivalent fractions, which is relatively difficult to present in practical contexts, and measurement, which is relatively easy to contextualize.
Journal article, monograph, or newsletter
McNeil, N., Uttal, D.H., Jarvin, L., and Sternberg, R.J. (2009). Should You Show Me the Money? Concrete Objects Both Hurt and Help Performance on Mathematics Problems. Learning and Instruction, 19(2): 171–184.
McNeil, N.M., and Jarvin, L. (2007). When Theories Don't Add Up: Disentangling the Manipulatives Debate. Theory Into Practice, 46(4): 309–316.
Sternberg, R. (2008). Applying Psychological Theories to Educational Practice. American Educational Research Journal, 45(1): 150–165.