This dissertation examined high school students' skill with rational numbers and compared that skill level with the skill level of middle school students by testing 147 high school seniors with 16 rational number word problems released from the National Assessment of Educational Progress assessments. The questions included equal amounts of fraction and money problems. The seniors were grouped by gender and by whether they had completed only beginning algebra and geometry or had more mathematics than geometry.
The findings of this study replicated the high school seniors' low rational number skill level seen in other studies with various age groups. The seniors had higher levels of skill on problems that were more contextually based in common real world problems. Problems with percents were more difficult for the seniors unless the problem involved tipping. Fraction problems that involved operations on fractions were the most difficult.
The high school seniors performed better than the middle school students on all but one of the problems. Standardized middle school test scores predicted the seniors' rational number skills only for students with mathematics beyond geometry while students with only algebra and geometry demonstrated a higher level of rational number skills than was expected.
A gender gap was seen as female students generally performed better than male students on money problems and the male students performed better on the fraction problems, particularly those that assessed formal knowledge. A positive association was found between students' beliefs in their mathematics ability with the level of mathematics courses and with their rational number skill level.
While students must have some prior knowledge of the system of rational numbers in order to learn algebra concepts that are highly connected to that system, the level of rational number skill does not need to be at the mastery level for students to be successful and enroll in more mathematics courses.
|Advisor:||Erickson, David R.|
|Commitee:||Burke, Maurice, Cobbs, Georgia, Hirstein, James, Knott, Libby|
|School:||University of Montana|
|Department:||Curriculum & Instruction|
|School Location:||United States -- Montana|
|Source:||DAI-A 70/09, Dissertation Abstracts International|
|Subjects:||Mathematics education, Secondary education, Curriculum development|
|Keywords:||Algebra preparedness, Fractions, High school, NAEP, National Assessment of Educational Progress, Rational numbers|
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