PRE-SERVICE TEACHERS’ COMPREHENSION OF FRACTION OPERATIONS THROUGH THE USE OF AN INTERACTIVE VIRTUAL CLASSROOM

Author

• Juan Baltazar Cruz Ramirez, Southern Illinois University CarbondaleFollow

Date of Award

5-1-2026

Degree Name

Doctor of Philosophy

Department

Curriculum and Instruction

First Advisor

Lin, Cheng Yao

Abstract

The purpose of this study is to analyze mathematics performance using an Open-Ended Approach Instruction linked with a Virtual Educational Environment to determine if this approach improves Pre-Service Teachers’ achievement in their Procedural Knowledge, Conceptual Knowledge, and formal mathematical knowledge across eight fractional dimensions, as follows: fraction concepts (CON), equivalent fractions (EQU), fraction ordering (ORD), fraction addition (ADD), fraction subtraction (SUB), fraction multiplication (MUL), fraction division (DIV), and fraction transferring (TRA).

Even when it is desirable that students and teachers must learn to think mathematically, and they must think mathematically to learn, most of mathematics teachers do not encourage their students to perform as mathematicians and there are not enough evidence that Preservice Teachers in their usual practice, show an evolution from their Informal Mathematical Knowledge to a Formal Mathematical Knowledge and a Profound Understanding of Fundamental Mathematics, because traditional teaching of fractions is mainly focused on Procedural Knowledge with little intention to teach Conceptual Knowledge, with a lack of Formal Mathematical Knowledge and Profound Understanding of Fundamental Mathematics.

The population in this study was pre-service teachers enrolled in a seven-semester Mathematics teacher education program of a major in bachelor’s in mathematics education at the Autonomous University of the State of Guerrero (UAGro), México. The population in this program was 124 students in October 2024. The method for selecting a representative sample from this population was the Simple Random Sampling Method and the sample obtained was homogeneous because subjects were gathered from the same population and the same academic level, and this method was used to assign membership to the experimental groups: HYBRID and ONLINE, and CONTROL group (32 subjects for each group).

This study is a quasi-experimental mixed methods design. Two instruments were used in this study for collecting data. The first one was the Fraction Knowledge Test for the Eight Fractional Dimensions, and the second instrument was the Survey for Satisfaction using a Virtual Education Environment. The Fraction Knowledge Test for the Eight Fractional Dimensions was applied to 96 subjects, with no excluded cases in the Pretest and Post-test, and the items have relatively high correlation and high internal consistency. Acceptability of the quantitative data was measured by an analysis for conditions of Normality, Validity, Reliability, and Correlation. These conditions were confirmed before any statistical analysis, determining that these values were within the range expected for data from a normal distribution.

Results of percentages of correct answers for the eight fractional dimensions in this study, we found that for scores in Post-test for Procedural Knowledge (PK), Group HYBRID scored 62.86% and Group ONLINE scored 40.95%, and for Conceptual Knowledge (CK), Group HYBRID scored 48.1% and Group ONLINE scored 31.7%. In the case of Traditional Fraction Operations, Group HYBRID scored 81.44% and Group ONLINE scored 70.32%. The results of the multiplication of fractions for Group HYBRID had a score of 71.75%, and the Group ONLINE scored 66.5%. In the case of division of fractions, Group HYBRID scored 69.5% and Group ONLINE scored 47%.

Analyzing the results of the Survey for Satisfaction using a Virtual Education Environment, we found that the level of subjects’ satisfaction showed strengths such as engagement to learn, benefits and success using VEE, and learning motivation. In the same way, there is a positive impact on the development of sessions as well as the generation of autonomy for their learning. Levels of usability of the VEE show the effectiveness perceived by subjects related to promoting interest in using the VEE and achieving desired competencies and satisfactory progress. Results showed preferences for face-to-face classes and using pen and pencil. These results could be compared with a high preference for using technology in face-to-face courses, referring to the resources (teaching techniques and assets) that the teacher uses to ensure that the educational act takes place and produces expected results.