Hierarchical Linear Model for Formative Assessment of the Mathematics Learning of Middle School Students

• In Event: Formative Assessment for Mathematics and Science Standard Test

Abstract

Objective
The major goal of this FA intervention was to generalize the powerful FA-based strategy that could be integrated into an ongoing mathematics curriculum. The outcomes of FA can serve as an important source of feedback for teachers and students. Despite the importance of FA practices that influence student achievement, teachers often have difficulties generating feedback that helps their students with next steps for learning (Heritage et al., 2009). Furthermore, misconceptions concerning its use and practice in the classroom are rampant in educational contexts in classrooms. The purpose of the study is to examine the benchmark test and interims in which a FA provides to both the teacher and learner, which in turn can positively adjust instruction.
Theoretical framework
The effect size of FA in improving teacher’s knowledge and student learning has been reported as medium (Black & William, 1998a) or small (Kingston & Nash, 2011). The current study, which was part of a large FA project, used hierarchical Linear Models (HLM) with students’ posttest scores as dependent variables to examine the impact of our FA intervention. This approach incorporates the variance occurring at the classroom and student levels. Both random and fixed-effects model were used to evaluate the effect of the intervention on the students learning in the 8EE5, 8EE6, and 8EE7 units.
Methods
The HLM was applied to examine the effect of two posttests on the students’ Mathematics standard test on the teacher’s level. The results indicated that large effect size for the FA on the 8EE5 and 6 score (Cohen’ f = .447), but not for 8EE7 unit. For the 8EE5 and 6 scores, about 38.9% of the variation occurs at the teacher level. The best fitting model indicated that 42.4% of the level-1 variance in outcome is accounted for by the pretest score and ELL status predictors.
Results
The grade 8 students in the classrooms where the teachers used FA made significant achievement from the pretest and the posttest. For 8EE5 and 6, the pretest score and ELL status were also found to have small-sized effects, and they were also associated with the students’ performance locally. However, for 8EE7, the condition a teacher was placed into did not influence the posttest 7 scores. However, we found a medium effect of teacher post-survey (Cohen’ f = .297) and a large effect of pre-test score on posttest 7 scores (Cohen’ f. = .515), suggesting that these predictors were associated with small effects locally.
Scholarly Significance 
The HLM model provides data-based evidence that supports how the FA components can be used in Grade 8 Middle school classroom instruction. We believe that the finding accurately reflects the current knowledge of FA in the field, and our hope is that it will inform teachers, educational practitioner, and assessment developers to increase the use of FA practices in classrooms.

Authors

• Yu Zhang, University of California - Davis

• Susan E. Rowe, University of California - Davis

• Krisitine Christianson