# Leon Chang

**Subject:** Math

## The Effects of a Daily Fraction Review and Extension Protocol on Middle School Algebra 1 Students

**Research Questions:**

How does a Daily Fraction Review and Extension Protocol affect middle school students’ ability to evaluate arithmetic and algebraic rational expressions in algebra 1?

Sub-questions:

* How does a Daily Fraction Review and Expansion Protocol help students relate the picture of an arithmetic fraction to a rational expression; thus, enabling students to evaluate simple rational expressions successfully before the topic is formally taught?

* How does a Daily Fraction Review and Expansion Protocol affect middle school students’ attitude and beliefs towards fractions, fraction reviews, and math in general?

* How does a Daily Fraction Review and Expansion Protocol affect middle school students’ ability expand arithmetic fractions and rational expressions, simplify each fraction separately, and then recombine it if possible?

**Research Activities:**

Theoretically, students have been exposed to the concept of fractions in the 2nd grade, but students failed to illustrate academic success of fraction operation when given a fraction diagnostic test. This study reviewed fraction operation using visual representations of fractions to evaluate and to extend their knowledge so that they may successfully evaluate rational expressions. I expected the protocol to be successful and provide students with a stronger understanding of fraction operation and the ability to extend their knowledge so that they may evaluate rational expressions before it is being formally taught in the course. The intervention class involved 33 7th and 8th graders and the comparison class involved 28 7th and 8th graders taking an Algebra 1 course in an urban middle school. The 20-day intervention involved giving students four problems each day that dealt with numbers and variables of different arithmetic operations; then, it reviewed the content using visual representation of the problem type. There were three sources of data: achievement data, attitude data, and personal observations. The data was collected through pre- and post-tests, attitude survey, and a daily personal journal, which was recorded with the students’ name hidden to remove any researcher bias. The achievement data used a two-tailed, paired t-test to compare the score of a pre-test and a post-test from the Fraction Protocol Class and the Comparison Class. After the intervention was conducted, there was reason to believe that the Fraction Protocol was beneficial to the intervention class in evaluating fractions due to a statistically significant improvement in evaluating fractions according to the data from the pre- and post-test. Students lacked the fundamental knowledge of fraction operation; however, with the intervention protocol using visual representation, students were able to successfully evaluate arithmetic and rational expressions.

**Grade:** Secondary

**Research Methods:**

Survey-Attitude; Math assessment

**Curriculum Areas:**

Math; Math-Algebra

**Instructional Approaches:**

Active learning; Assessment/Evaluation; Class discussion; Direct Instruction; Math-Journals; Math-Manipulatives; Warm-ups/Openers

The preparatory work for setting up the MA/Credential Teacher Research database was supported in part by the UC Language Minority Research Institute