The effect of assessment/instruction implementing a 'rule of four' on the mathematics achievement of elementary education majors
Nilsen, Cheryl Elaine
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The mathematics content knowledge of elementary education majors is well documented as being weak in most instances. Mathematics content courses, aimed at helping pre-service elementary teachers become more competent and confident in their knowledge of the mathematics they will teach, often provide inadequate time for practice and demonstration of mathematics knowledge and skills. As a response to this issue, this study examined how implementation of assessments based on a "Rule of Four" might increase the mathematics content knowledge of pre-service elementary teachers. The "Rule of Four" performance tasks used in the study required the students to demonstrate their understanding of mathematics concepts relating to addition, subtraction, multiplication and division of whole numbers, integers, and fractions. Three of the four performance tasks devised for each concept aligned with the following developmental levels advocated by Jerome Bruner: enactive (use of manipulatives), iconic (drawing a picture or diagram), and symbolic (writing the concept in words). The fourth performance task required demonstration of an application or real world representation of the mathematical concept.A quasi-experimental study was conducted using a control group taught and assessed using traditional methods and a treatment group taught traditionally and assessed using the "Rule of Four" performance assessments along with other traditional assessment tools. Pretests and posttests were given to both groups to determine whether there was a difference in the two groups' mathematics achievement and when gender, age, or class (e.g., freshman, sophomore) was factored in. Because the control and treatment groups were significantly different in their pretest scores (with the control group having higher scores), an analysis of covariance was used for data analysis. Results showed that there were no significant differences between the groups on their posttest scores, including when gender, age, or class was factored in. The study's results indicate that assessment by "Rule of Four" did not produce higher levels of mathematics achievement than instruction using traditional assessment methods. While there was no difference in performance on the posttest by the two groups, the treatment group made substantial gains from their pretest scores.