# The Formative Evaluation in the Teaching of the Variance and the Standard Deviation

## Abstract

The institutions of higher education to promote students’ learning in each subject of the study program, formulated the learning outcomes, which students will be able to achieve at the end of the instruction. The research in the field of educational psychology suggests that students have two orientations; that somehow affect their learning; some students are driven by learning and some others students are driven by evaluation. The American Statistical Association (ASA) recommends the following: (1) emphasize the statistical literacy and developing statistical thinking; (2) using real data; (3) encourage conceptual understanding rather than knowledge of procedures; (4) support in the classroom active learning; (5) use technology to develop conceptual understanding and analyzing data; (6) use the evaluation to improve and assess students learning. In accordance with these three guidelines the purpose of this work was to improve the learning of variance and standard deviation using the formative evaluation. The formative evaluation it is defined as all those activities undertaken by teachers and students to assess themselves, which provide information to give feedback that modify the teaching and learning activities in which they are involved. During the assessment process the teachers applied the five strategies that are shown below and that are independent of the content and level of study: (1) clarify and share the intentions of learning and success criteria; (2) implement effectively the discussion, questions, and classroom learning tasks; (3) provide feedback that move students toward learning; (4) promote the empowerment of students about what they are learning; (5) encourage students that are considered to be an instructional resource for peer .The research hypothesis H_{1}: the difference between the average of the posttest and the average of the pretest is greater than zero. The null hypothesis H_{0}: the difference between the average of the posttest and the average of the pretest is equal to zero. The subjects were 40 students of business administration in a statistics course; their ages were between 19 and 20 years. The subject was statistics and the unit under study was measures of variability and the issue considered was the variance and the standard deviation. The procedure to teach the variance and the standard deviation is as follow: (1) Review the scientific literature related to misconceptions that students have on the variance and standard deviation; (2) Administer a test to determine the students’ prior knowledge; (3) Prepare an self-instructional module to teach the variance and the standard deviation; (4) Administer the pretest; (5) Submit students a problem to solve it in pairs and apply the five key strategies for formative assessment. (6) Administer the posttest. This study proved that the use of the formative evaluation promotes the statistical literacy and statistical reasoning.

## Location

Rooms 113 & 115

## Recommended Citation

Flores, Jorge R., "The Formative Evaluation in the Teaching of the Variance and the Standard Deviation" (2015). *SoTL Commons Conference*. 116.

https://digitalcommons.georgiasouthern.edu/sotlcommons/SoTL/2015/116

The Formative Evaluation in the Teaching of the Variance and the Standard Deviation

Rooms 113 & 115

The institutions of higher education to promote students’ learning in each subject of the study program, formulated the learning outcomes, which students will be able to achieve at the end of the instruction. The research in the field of educational psychology suggests that students have two orientations; that somehow affect their learning; some students are driven by learning and some others students are driven by evaluation. The American Statistical Association (ASA) recommends the following: (1) emphasize the statistical literacy and developing statistical thinking; (2) using real data; (3) encourage conceptual understanding rather than knowledge of procedures; (4) support in the classroom active learning; (5) use technology to develop conceptual understanding and analyzing data; (6) use the evaluation to improve and assess students learning. In accordance with these three guidelines the purpose of this work was to improve the learning of variance and standard deviation using the formative evaluation. The formative evaluation it is defined as all those activities undertaken by teachers and students to assess themselves, which provide information to give feedback that modify the teaching and learning activities in which they are involved. During the assessment process the teachers applied the five strategies that are shown below and that are independent of the content and level of study: (1) clarify and share the intentions of learning and success criteria; (2) implement effectively the discussion, questions, and classroom learning tasks; (3) provide feedback that move students toward learning; (4) promote the empowerment of students about what they are learning; (5) encourage students that are considered to be an instructional resource for peer .The research hypothesis H_{1}: the difference between the average of the posttest and the average of the pretest is greater than zero. The null hypothesis H_{0}: the difference between the average of the posttest and the average of the pretest is equal to zero. The subjects were 40 students of business administration in a statistics course; their ages were between 19 and 20 years. The subject was statistics and the unit under study was measures of variability and the issue considered was the variance and the standard deviation. The procedure to teach the variance and the standard deviation is as follow: (1) Review the scientific literature related to misconceptions that students have on the variance and standard deviation; (2) Administer a test to determine the students’ prior knowledge; (3) Prepare an self-instructional module to teach the variance and the standard deviation; (4) Administer the pretest; (5) Submit students a problem to solve it in pairs and apply the five key strategies for formative assessment. (6) Administer the posttest. This study proved that the use of the formative evaluation promotes the statistical literacy and statistical reasoning.