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Argumentative Discourse-centered Classroom to Hone Students’ Mathematical Comprehension and Confidence

Mae Antonette J. Ticar , Charita A. Luna, Rosie G. Tan
American Journal of Educational Research. 2020, 8(5), 304-308. DOI: 10.12691/education-8-5-13
Received April 12, 2020; Revised May 14, 2020; Accepted May 21, 2020

Abstract

The study determined the effect of argumentative discourse-centered classroom on the participants’ mathematical comprehension and self-confidence. It used a pretest-posttest quasi-experimental control group design. The experimental group was exposed to Argumentative Discourse-centered Classroom model while the control group was exposed to DepEd 4A’s model. Two research instruments were used: concept mapping to assess mathematics comprehension and confidence self-test. The data were analyzed using mean, standard deviation, and ANCOVA Equal n’s. The analysis revealed that the scores of those who were exposed to Argumentative Discourse-centered Classroom model are comparable to those exposed to DepEd 4A’s model in terms of mathematical comprehension and confidence. The researchers recommend that mathematics teachers may use Argumentative Discourse-centered Classroom model not only in Mathematics but also in other Mathematics related subjects to enable students experience how to express their own ideas with their classmates to exhibit their conceptual understanding and enhance oral communication skills.

1. Introduction

Mathematics influencers who are the educators play a critical role on how students experience, understand, and relate mathematics to life. Students are facing a future where mathematical comprehension and confidence are important to their success 1. Hence, a classroom must be an atmosphere that is prolific of students’ engagement with mathematical communication through argumentative discourse that may help resolve problems-solving difficulties. Felton, Garcia-Milla, Gilbert and Villaroel found that discourse goals can be achieved because arguing can affect student learning outcomes in both content knowledge understanding and reasoning in long term memory 2. Moreover, Boaler stated that reasoning and problem-solving are both critical acts in mathematics learning 3. He said that when students struggle in argumentation with mathematics, it is the best time for brain growth mindset. Argumentative discourse is the best atmosphere for brain growth mindset necessary for the accommodation of concept building vital for the development of conceptual understanding. The Department of Education (DepEd) of the Philippines has been doing changes in the curriculum including the teaching pedagogies. However, in spite of all the changes, students’ mathematics achievement in the international and national assessment in mathematics continues to log behind. The UbD, 5E’s and 4A’s to name a few, have not shown remarkable changes in mathematics’ performance of students because of lack of conceptual understanding and poor mathematics comprehension 4. This may be due to the none compliance of the NCTM five process standard in mathematics which includes problem-solving, reasoning and proof writing, representation, communication and connection 5. Emphasis is only given to problem-solving but the other four are given little attention in the classroom. Faucult’s in his idea of Discourse Analysis Theory stated that discourse is a way of constructing knowledge, together with others in a social phenomenon 6. Also, Bandura’s Social Learning Theory posits that people learn from one another, through observation, imitation, and modeling 7. With argumentative discourse-centered classroom, students are put in a society of learners where they are given opportunities to voice their own ideas, participate in doing the tasks and construct generalization in the outcome of the discussion together 8. In this scenario, student’s confidence in mathematics may be enhanced to create positive perception towards mathematics. Di Martino and Zan mentioned that if the self-confidence toward mathematics is low, it will defeat the purpose of learning mathematics 9. Belin stated that confidence affects students’ attitude toward mathematics because when students are motivated to learn, they will perform well in school 10. As Vygotsky’s Social Interaction Theory stated, when a student is in a Zone of Proximal Development (ZPD) for a particular task, providing an appropriate assistance will give the student enough support to achieve the task 11. He suggested that teachers need the use a cooperative leaning exercises where less competent students can develop their potentials with the help from their skillful peers through discourse. This research thought of an Argumentative Discourse-centered classroom which will emphasize reasoning, communication, connection and representation in addition to problem-solving to develop students’ mathematical comprehension and confidence; hence, this study.

The result of this study hopes that it will give benefits to the following persons: First, to the mathematics students that they may be given an opportunity to develop their verbal communication skills that contribute to the development of mathematical comprehension, creativity and self-confidence. Second, to the mathematics instructors that they may be encouraged to try student-to-student classroom discourse in their classes where students are given opportunity to talk about mathematics to develop fluency, flexibility, originality and confidence. Third, to the administrators that they may be given insights to allow their teachers to make use of argumentative discourse-centered classroom model to promote students possess quality mathematical communicative ability with fluency, flexibility, originality, creativity and confidence. Fourth, to the parents that they may have children who are ready to face the competitive world of work. Lastly, to the future researchers that they may use this study as springboard for another study with the aim of developing citizens with mathematical comprehension, creativity and confidence level.

2. Method

2.1. Research Design

The study used a quasi-experimental pretest-posttest non-equivalent control group design.

2.2. Participants

It was conducted at Lorenzo S. Sarmiento Sr. National High School, Davao de Oro, during the second quarter of the school year 2019-2020. There were two intact classes, one was randomly assigned as the experimental group who underwent argumentative discourse-centered classroom model and the other as the control group taught using 4A’s model.

2.3. Research Instrument

There were two questionnaires used. The first questionnaire assessed participants’ mathematical comprehension which required them to illustrate the relationship of concepts by connecting the terms through concept mapping of the topics discussed in Business Mathematics with reliability coefficient of 0.88. These topics are on simple interest, compound interest, simple annuity, general annuity, and deferred annuity. The second questionnaire is the self-test which assessed participants’ Confidence in Mathematics. This self-test questionnaire consists of 15 items with a reliability coefficient of 0.86.

2.4. Data Analysis

The scores in the pretest and posttest of the two groups of participants were analyzed using the mean, standard deviation to describe the data; and analysis of covariance (ANCOVA) was used to determine if there is a significant difference of the effects on the participants’ level of mathematical comprehension and confidence in terms of the two teaching models.

2.5. Data Collection

In the experimental group wherein the participants were taught using Argumentative Discourse-centered Classroom model, they were first given orientation how to go about the argumentation process which applied the Modified Oxford-Oregon debate model and procedure. Before the debate proper, all groups were given handouts to discuss the terms and processes in the specified topics in Business mathematics and the different solutions to the problem-solving tasks. After the time allotted for the group discussion, the debate followed. There were two groups to debate per set, each group containing 5 members. All groups were given opportunity to debate against all the other teams. Participants underwent debate based from the given proposition along with a Business Mathematics problem-solving task with its two different solutions. A group leader from each team picked between affirmative and negative side to agree or disagree on the proposition. Each speaker in the team was given time to speak. The debate started with the affirmative side then the negative side to interpolate. After the given allotted time for the affirmative side, the negative group defend their position. Then, the affirmative side interpolated them also. After each team’s turn to critic and rebut, a closing statement was presented by each assigned member of the team. After the debate, a winner was declared including the Best Debater and Best Speaker of each match, with the researcher as the moderator and adjudicator with a moderator of debating society and mathematics master teacher. Then, discussion was done by the teacher to correct misconceptions and made generalization. In the control group, the participants were exposed to DepEd 4A’s model. They underwent the following phases: activity, analysis, abstraction and application. However, this 4A’s model was conducted in a conventional teaching environment. They were grouped into five’s and was given handouts and activity sheets to discuss the terms and processes involving Business Mathematics concepts and problem-solving tasks with the same coverage as the experimental group. After the given time of discussion, three groups were randomly chosen to report their solution of the problem being asked on how they arrived at the answer, presenting one group at a time. In each group presentation, the teacher asked the members on the validity of their solution while their classmates also asked questions and critic. The member of each group explained and defended their answer by showing proofs. After each topic, the participants in experimental and control were given a quiz on the same topic followed by an assignment. The classes had three observers, the Senior High School Principal, the Mathematics Master Teacher, and the Debating Society Coordinator, to avoid bias. When all topics were covered, the two groups were given the posttest of the mathematical comprehension using concept mapping and the self-test for confidence. The data collected were used for the analysis to determine the effect.

3. Results and Discussion

Table 1 shows the mean and standard deviation of the pretest and posttest scores in Comprehension level of Business Mathematics assessed using concept mapping as influenced by the teaching models. The table reveals that the pretest mean score of the participants in experimental group using Argumentative Discourse-centered Classroom is 4.51 lower than the pretest mean score of the participants in control group which is 5.62. This means that the participants in control group have higher comprehension level before the treatment. However, both groups had poor comprehension level in Business Mathematics because their mean is below 75% of DepEd standard. In the posttest, the mean score of the participants in experimental group is 12.35 which is also almost the same as the posttest mean score of 12.78 in the control group. This means that the two groups have increased their mathematical comprehension from pretest mean score. This means that there was an increase in the mathematical comprehension through concept mapping of the participants in the experimental group compared to the control group. Both groups have scores widely spread. To determine whether there is a significant effect of the treatment, the analysis of covariance (ANCOVA) is used.

Table 2 shows the result of the One-way ANCOVA of the participants’ Comprehension test scores using concept mapping in terms of teaching models. The analysis yielded a computed F-ratio of 0.30 with a probability value of 0.59 greater than at 0.05 level of significance. This led to the acceptance of the null hypothesis that there is no significant difference in the mathematics Comprehension score of the participants as an effect of the type of teaching models. This implies that the participants’ mathematical comprehension through concept mapping of experimental group is comparable with the participants’ score of the control group taught using 4A’s method who have higher pretest score before the treatment. This means that through argumentative discourse, participants are able to learn concepts in mathematics as well as express their ideas and correct their misconceptions in similar manner as the control group. This implies further that the experimental group were able to catch up the control group in understanding the concepts in Business Mathematics. This indicates that although the two groups were not comparable at the start, after the treatment, the group who underwent argumentative discourse-centered classroom model became comparable with the control group in the posttest. These results support the idea of Todd saying that participating in mathematical discourse is an essential component of students' mathematics learning 12. Classroom discourse-centered not only enhances the sharing of their understanding and new discernment but also facilitates deeper analysis of mathematics as well. It also confirmed to what O’Connor have stated that students learn more and better mathematics when students can discuss, interact, and make mathematical meaning together 13. Thus, comprehension skills in mathematics are developed and improvement of mathematical comprehension test scores using concept mapping is being attained.

Table 3 shows the mean and standard deviation of the pretest and posttest scores in Confidence level of Business Mathematics in terms of teaching models. The table shows that the pretest mean score of the participants in experimental group is the same as the pretest mean of the participants in control group which is 2.03 which has average confidence level. This means that the participants in experimental group have comparable confidence level before the treatment. After the treatment, the posttest mean score of the participants in experimental group is 2.60 which reached high confidence level higher than the posttest mean score of the participants in control group which is 2.49 still average confidence level. This means that the participants in experimental group gained a little higher confidence than the participants in control group. The standard deviation of the experimental group score became more spread in the posttest. The control group remains homogeneous. To determine whether there is a significant effect of the treatment, the analysis of covariance (ANCOVA) is used.

Table 4 shows the result of the one-way ANCOVA of the Confidence test in terms of teaching models. The analysis yielded a computed F-ratio of 0.86 with a probability value of 0.38 greater than 0.05 level of significance. This allows the acceptance of the null hypothesis that there is no significant difference in the Confidence level of the participants as caused by the type of teaching models. This implies that the participants in experimental group developed confidence in mathematics in similar manner as in control group. It is evident in the result of the posttest mean score of the experimental group which is only 0.11 above the control group. This means also that through the argumentative discourse-centered classroom model, participants’ confidence in mathematics have been developed in the process of exchanging ideas about the topic, the way they reason out with their solution. Furthermore, through argumentative discourse, participants were able to justify their answers and show perseverance when answering the problem. These findings support the ideas of Belin 10, Das & Kashyap 14, Di Martino & Zan 9, and Shaikh 15 who believed that self-confidence is a predictor of performance in mathematics because when students develop high mathematical self-confidence through argumentation, they are able to assimilate more concepts and processes and express their ideas in any way they wanted to. To Bandura, self-confidence is considered one of the most influential motivators and regulators of behavior in people's everyday lives 7. When students gained confidence in mathematics, they are able to use their mind to think critically to come up with the correct answer, not just guessing. They will be able to answer more mathematical problems because they find it fun and interesting. This result also supports the idea of Belin which stated that confidence affects students’ attitude toward mathematics because when students are motivated to learn, they will perform well in school 10.

4. Conclusions and Recommendations

Based on the above findings, the following conclusions are hereby forwarded. The Argumentative Discourse-centered Classroom Model is as effective as DepEd 4A’s Model in honing participants’ mathematical comprehension and confidence. In addition, participants’ perception on Argumentative Discourse-centered Classroom Model is positive and it challenges them to verbalize their thoughts and enables them to orally communicate their answer clearly and concisely. The researchers recommend that Argumentative Discourse-centered Classroom Model be implemented at Lorenzo S. Sarmiento Sr. National High School to hone students’ comprehension and confidence in Mathematics. They also urge mathematics teachers to try this new teaching model in their classes not only in Mathematics but also in other Mathematics related subjects. They also encourage researchers to conduct similar studies for a wider scope and longer period using different populations from different institutions to establish the generalizability of the results.

Acknowledgements

The researcher would like to express her gratitude to the following persons who, in one way or another, have helped in making this research possible: To Dr. Charita A. Luna, her external dissertation adviser, for her tireless support, professional guidance, supervision, encouraging comments and patience in reviewing the work; to Dr. Rosie G. Tan, her internal dissertation adviser, for sharing her valuable insights and comments; to Mr. Felixberto L. Leray, School Principal of Lorenzo S. Sarmiento Sr. National High School, for allowing the researcher to conduct the study; and to Dr. Reynante O. Solitario, Schools Division Superintendent of Compostela Valley, for approving this research study. Likewise, to the Department of Science and Technology for awarding a scholarship to the researcher under project STRAND.

References

[1]  National Council of Teachers of Mathematics. Are you ready to create positive change in high school math? Mathematics Teacher. Vol. 112, No, 7. (2019).
In article      
 
[2]  Felton, M., Garcia-Mila, M. and Villarroel, C. Arguing Collaboratively: Argumentative Discourse Types and Their Potential for Knowledge Building. British Journal of Educational Psychology, v85n3 p372-386. (2015).
In article      View Article  PubMed
 
[3]  Boaler, J. Prove It to Me. National Council of Teachers of Mathematics (NCTM). Mathematics Teaching in the Middle School. Vol.24, No.7. (2019).
In article      View Article
 
[4]  Trends in International Mathematics and Science Study (TIMSS) (2017). National Achievement Test (NAT) Result (2017).
In article      
 
[5]  National Council of Teachers of Mathematics. Principles and standards for school. Reston, VA:National Council of Teachers of Mathematics. (2000).
In article      
 
[6]  Adams, R. Michel Foucault: Discourse. Critical Legal Thinking. (2017). Retrieved on July 29, 2019 from http://criticallegalthinking.com/2017/11/17/michel-foucault-discourse/.
In article      
 
[7]  Mcleod, S. Bandura - Social Learning Theory. (2016). Retrieved on July 29, 2019 from https://www.simplypsychology.org/bandura.html.
In article      
 
[8]  Becker, B. Informal Arguments. NCTM. Mathematics Teacher. Vol. 112, No. 6. (2019).
In article      View Article
 
[9]  Di Martino, P. and Zan, R. Students’ Attitude in Mathematics Education. Urban Mathematics Education. pp.572-577.
In article      
 
[10]  Belin. Effect of Students Confidence Level toward Mathematics Performance among Southern Thailand Primary School Children. (2016).
In article      
 
[11]  McLeod, S. The Zone of Proximal Development and Scaffolding. Vygotsky’s Social Interaction Theory. (2019).
In article      
 
[12]  Todd, J. Standards of Mathematical Practice. (2012).
In article      
 
[13]  O’Connor, C. The Silent and the Vocal: Participation and Learning in Whole-class Discussion. (2016).
In article      View Article
 
[14]  Das, G.C., Das, R. and Kashyap, M.P. An Investigation on the Relationship Between Performance in Mathematics and Students’ Attitude Towards the Subject in Secondary Schools of Guwahati. Indian Journal of Applied Research. (2016).
In article      
 
[15]  Shaikh, S.N. Mathematics Anxiety Factors and their Influence on Performance in Mathematics in Selected International Schools in Bangkok. Journal of Education and Vocational Research. (2013).
In article      View Article
 

Published with license by Science and Education Publishing, Copyright © 2020 Mae Antonette J. Ticar, Charita A. Luna and Rosie G. Tan

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Cite this article:

Normal Style
Mae Antonette J. Ticar, Charita A. Luna, Rosie G. Tan. Argumentative Discourse-centered Classroom to Hone Students’ Mathematical Comprehension and Confidence. American Journal of Educational Research. Vol. 8, No. 5, 2020, pp 304-308. http://pubs.sciepub.com/education/8/5/13
MLA Style
Ticar, Mae Antonette J., Charita A. Luna, and Rosie G. Tan. "Argumentative Discourse-centered Classroom to Hone Students’ Mathematical Comprehension and Confidence." American Journal of Educational Research 8.5 (2020): 304-308.
APA Style
Ticar, M. A. J. , Luna, C. A. , & Tan, R. G. (2020). Argumentative Discourse-centered Classroom to Hone Students’ Mathematical Comprehension and Confidence. American Journal of Educational Research, 8(5), 304-308.
Chicago Style
Ticar, Mae Antonette J., Charita A. Luna, and Rosie G. Tan. "Argumentative Discourse-centered Classroom to Hone Students’ Mathematical Comprehension and Confidence." American Journal of Educational Research 8, no. 5 (2020): 304-308.
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  • Table 1. Mean and Standard Deviation of Participants’ Comprehension Test Scores (Using Concept Mapping)
  • Table 2. Summary Table of One-Way Analysis of Covariance (Equal n’s) on Participants’ Comprehension Scores (Using Concept Mapping) in Business Mathematics
  • Table 4. Summary Table of One-Way Analysis of Covariance (Equal n’s) on Participants’ Confidence Scores in Business Mathematics
[1]  National Council of Teachers of Mathematics. Are you ready to create positive change in high school math? Mathematics Teacher. Vol. 112, No, 7. (2019).
In article      
 
[2]  Felton, M., Garcia-Mila, M. and Villarroel, C. Arguing Collaboratively: Argumentative Discourse Types and Their Potential for Knowledge Building. British Journal of Educational Psychology, v85n3 p372-386. (2015).
In article      View Article  PubMed
 
[3]  Boaler, J. Prove It to Me. National Council of Teachers of Mathematics (NCTM). Mathematics Teaching in the Middle School. Vol.24, No.7. (2019).
In article      View Article
 
[4]  Trends in International Mathematics and Science Study (TIMSS) (2017). National Achievement Test (NAT) Result (2017).
In article      
 
[5]  National Council of Teachers of Mathematics. Principles and standards for school. Reston, VA:National Council of Teachers of Mathematics. (2000).
In article      
 
[6]  Adams, R. Michel Foucault: Discourse. Critical Legal Thinking. (2017). Retrieved on July 29, 2019 from http://criticallegalthinking.com/2017/11/17/michel-foucault-discourse/.
In article      
 
[7]  Mcleod, S. Bandura - Social Learning Theory. (2016). Retrieved on July 29, 2019 from https://www.simplypsychology.org/bandura.html.
In article      
 
[8]  Becker, B. Informal Arguments. NCTM. Mathematics Teacher. Vol. 112, No. 6. (2019).
In article      View Article
 
[9]  Di Martino, P. and Zan, R. Students’ Attitude in Mathematics Education. Urban Mathematics Education. pp.572-577.
In article      
 
[10]  Belin. Effect of Students Confidence Level toward Mathematics Performance among Southern Thailand Primary School Children. (2016).
In article      
 
[11]  McLeod, S. The Zone of Proximal Development and Scaffolding. Vygotsky’s Social Interaction Theory. (2019).
In article      
 
[12]  Todd, J. Standards of Mathematical Practice. (2012).
In article      
 
[13]  O’Connor, C. The Silent and the Vocal: Participation and Learning in Whole-class Discussion. (2016).
In article      View Article
 
[14]  Das, G.C., Das, R. and Kashyap, M.P. An Investigation on the Relationship Between Performance in Mathematics and Students’ Attitude Towards the Subject in Secondary Schools of Guwahati. Indian Journal of Applied Research. (2016).
In article      
 
[15]  Shaikh, S.N. Mathematics Anxiety Factors and their Influence on Performance in Mathematics in Selected International Schools in Bangkok. Journal of Education and Vocational Research. (2013).
In article      View Article