Chung (2004)

Chung, I. (2004). A comparative assessment of constructivist and traditionalist approaches to establishing mathematical connections in learning multiplication. Education, 125(2), 271-278

Introduction
In the context of third graders learning multiplication, Chung’s quantitative study assesses the effectiveness of traditional and constructivist teaching methods. This study was chosen because it represented a simple qualitative analysis of the two theoretical models in practice, with a focus on the positive and negative aspects of applying constructivism to a classroom. This article selection may be deemed an odd choice based on the article’s findings that there were no statistically significant differences between the traditional versus the constructivist teaching methods; however the choice was strategic. Coming from the paradigm that there is value in triangulation as well as error, we as researchers can learn more about constructivism by examining its strengths and weaknesses as a means of delivering instruction.

The Study
Chung’s rational for the study is the incongruence between the call to reform mathematics education into meaningful, constructivist-based learning experiences, and the traditional teaching approach teachers take. Chung felt that a comparative, quantitative study was needed to provide hard data in support of Constructivism in order for teachers to incorporate the methodologies into their instruction. Thus, the researcher predicted that the outcome of the study would show that constructivist teaching methods were effective. The study was based on previous research that found that teachers do not necessarily teach using constructivist or traditional teaching methods, but instead teach students using the methods that they were taught with themselves. Other research used as a basis for this study sited the need for a “broad approach” to mathematics teaching is needed in order to promote meaningful learning.

Purpose
The purpose of the study was to assess third grade students conceptual development, acquisition and retention of multiplication skills in two instructional contexts; traditional and constructive. Chung defined constructivism as a way of teaching students to choose learning tasks that link to prior knowledge and allow students to “build mathematical connections through active learning using concrete materials.” Chung does not define “traditional” teaching methods, although it is presumed to be text-book based learning and rote assessment.

Methods
The student participants were 71 third-grade students ranging in age from eight to ten years old. The students were from four different classrooms in two public schools in one school district. Participant schools were mostly comprised of students from middle to low socio-economic status.

The four classrooms were divided into two groups; each group was made up of two intact classrooms. One group was taught using the constructivist approach, and the other was taught using traditional methods. Both the constructivist and traditional groups received 10 lessons, which were 30-40 minutes in length. The traditional group received lessons that were based off of the districts adopted 3rd grade mathematics curriculum. One of the traditional classrooms was taught by the classroom teacher and the other was taught by the researcher. The constructivist group’s lessons were developed by the researcher and the classroom teacher, and were designed based on constructivist theory. Both the researcher and the constructivist classroom teacher had backgrounds in constructivist teaching methods. One of the constructivist classes was taught by the regular classroom teacher and the other was taught by the researcher.

Data was collected through a 2 x 2 factorial, pretest-posttest quasi-experimental design. There were three tests that were used in the analysis of the data: the Forth Edition Stanford Diagnostic Mathematics Test, the Revised KeyMath Diagnostic Inventory, and a Researcher made test composed of 10 open ended questions. All three of the tests were administered to each student participant both before and after the lesson. Data was analyzed using Analysis of Variance with a probability level of less that 0.05. The survey developed by the researcher was scored using a scoring rubric developed by the researcher.

Results
Chung’s most noteworthy finding was that no one methodology was significantly better than the other. There were no differences (p>0.05) between the mean scores of the three assessments for traditional vs. constructivist instructional groups. However, there were gains in the pretest posttest scores for both the constructivist group before the lessons vs. after the lessons demonstrating that students from both approaches improved their multiplication skills.

Discussion
Although there were no significant differences in performance between the traditional and constructivist instructional groups on the three assessment tools, Chung still believed that the research findings contribute to our understanding of how children learn as well as how to teach mathematics. Most notably, Chung stated that the findings support the use of constructivist methods.

A previous study sited by Chung reported that constructivist teaching methods were avoided by instructors because of the significant amount of class time required for a lesson paired with minimal student gain. Additionally, one of the teachers that participated in the study felt that when constructivist instructional methods were used it was difficult to control the classroom compared to a traditional approach. Because of the change in routine and the novel use of manipulatives, the teacher reported that students had higher energy levels and classroom management was challenging. Despite these criticisms, Chung maintained that the fact that the constructivist methods had a similar effect to that of traditional methods demonstrates that it is an effective instructional methodology. After only ten constructivist lessons the constructivist group had statistically improved mean scores on all three assessments. This success is also demonstrated through student’s improved pretest and posttest scores in spite of the fact that the students were not accustomed to that approach to teaching. Thus, if “using concrete materials for only 10 lessons demonstrated increased scores, what could gains be for these same students in this learning environment with their regular teacher using manipulatives for the entire school year?”

Chung details that the present study had limitations as well as implications for future research. Training in constructivist teaching could have increased the teacher’s confidence in utilizing the methodology. Chung also recommends videotaping lessons so that confounding and irrelevant variables that are difficult to observe in the busy classroom setting can be controlled. The validity of the study could be improved with an increase from 10 to 25 lessons as well as an increased sample size. It was also recommended that the teachers utilizing the constructivist methodologies have training prior to teaching the lesson in how to use the instructional materials.

Critique
Strengths of this research include the simple and succinct design as well as compelling findings. However, the major issue with the research was the omission of details, leaving the reader guessing on several of the procedures. This was particularly evident in the methods section, which lacked in necessary detail. First, it is unclear how the participant district, classroom and students were selected to participate in the study. Additionally, the researcher neglected to give needed specifics about how the traditional and constructivist classes were taught. For example, it is unclear if the teacher and the researcher consistently taught their own respective classes or if they alternated. Some aspects of the methodology could have impacted the study outcomes. One example of this is if the students were accustomed to a particular instructional style, a change of instructor -such as the researcher conducting a lesson as opposed to their regular classroom teacher- could have impacted student performance. Teacher and researcher training also could have impacted the student’s performance. If the teacher was used to implementing more traditional teaching methods during instruction, changing to constructivist methods could be awkward and difficult. It is also unclear if the researcher had any previous teaching experience. In regards to the assessments used one criticism is that although two of the tests were preexisting, there is little description of how the researcher-made test was developed or if it was field tested. Finally, in the findings section, Chung does not include in the narrative any statistics addressing the improvement within the traditional and constructivist methodologies between pretest and posttest even though this gain was later included as part of the discussion section. Inclusion of this information would have given the reader a more thorough composite of the results.

Conclusions
The theoretical implication of this study is that both traditional and constructivist teaching methods are effective in teaching third graders multiplication. Chung clearly started out the study to prove that constructivist teaching methods are effective, which was done; they were statistically similar in effect to that of traditional teaching methods. However, constructivist teaching practices were not found to be more effective than traditional. Indirect implications for teaching practice based on these findings could be that since the outcome of both constructivist and traditional teaching methods are similar, why would instructors bother to change their teaching style, a way students are accustomed to learning, in order to incorporate constructivist methodology? An answer to is this is in the practical implications for the research. In a classroom context, which typically serves a broad range of students with varied learning styles, practical implications include utilizing both methodologies to enrich student’s comprehension of the subject matter and reach a broader base of learners.