Abstract

The advent of technology ushers major educational changes through the integration of digital learning tools in the classroom. This strategic and relevant practice can become an integral tool for achieving significant learning experience. Thus, this study aimed to determine the effectiveness of mathematics software Bagatrix Solved! in teaching and learning Algebra. This study employed a quasi-experimental design specifically a pretest-posttest control group design wherein the control group (n=30) were taught the conventional way while the experimental group (n=30) were taught using the Bagatrix Solved! software. The instruments used in this study were the pretest and posttest and an 8-item self-made questionnaire using 5-point Likert scale. Results showed that on the first stage of the research process, both groups has similar level of understanding on the topics based primarily on their foreknowledge about the topic Linear equations. However, towards the final stage, both groups showed improvement on their test performance after two weeks of teaching and learning Linear equations and both approaches resulted to effective learning of mathematical concepts. Furthermore, it also showed that the students were interested in the software since it was their first time experience and it was found helpful as evident in the motivation and involvement of the students in the teaching-learning activities. With this, the use of mathematics software Bagatrix Solved! in teaching Algebra as supplement to the conventional approach is highly recommended. Lastly, the combination of both approaches in teaching Algebra was also suggested to ensure higher impact to the performance of students in Algebra.

1. Introduction

Mathematics can be an intimidating subject for students, but with appropriate teaching strategies, educators can engage students in Mathematics topics and assist them in better understanding of complicated concepts. In this digital and Industry 4.0 era, it is considered as a critically important tool the use of technology in helping students develop all kinds of skills. The integration of technology in teaching Mathematics has been widely practiced to lessen the difficulty on learning mathematical concepts. The challenge is more complex on teaching and learning that arises the need for more advanced instructional materials, teaching strategies, teacher personality and relationship to real-life context ^{1, 2, 3}. When teachers are capable of the use of technology to engage students in mathematics and encourage them to cultivate math skills and understand the conceptual parts in depth, it will go a long way towards preparing them to succeed in the careers of the future.

This pedagogical approach has posted advantages to students such as increased learning opportunities ⁴; enriched student engagement ⁵; enhanced ability in solution visualization ⁶; learned mathematics innovatively ⁷; and involved in discovery of mathematics concepts ⁸. It is also believed that the use of mathematics software has a favorable impact on students learning ⁹ and highlights different opportunities in teaching mathematics ¹⁰. Kilicman, et al. ¹¹ stressed that using mathematical software coupled with samples and steps as evidences didactically enhances mathematical skills; students can easily visualize different functions from problem sets ¹²; and serves as powerful aides for manipulations and computations in Algebra and other mathematics. Vygotsky’s ¹³ notion of ZPD (Zone of Proximal Development) asserts that in developing the students mathematical reasoning the tasks should not be too easy or too difficult and the learners have to approach any task through meaningful activity ¹⁴. This ZPD enhances the students with skills that enable them to have information and visuals to fill the gaps on knowledge and explanations they miss on ordinary discussions ¹⁵.

Algebra is the most common and essential branch of mathematics included in the different programs of College and University students. It has been often referred to as one of the most important pillars in the domain of mathematics and is widely accepted that to ensure foundational concepts in higher mathematics such as Trigonometry, Geometry, Pre-calculus, Calculus and others. It is a crucial domain on students learning and development of mathematics skills ¹⁶. Thus, alternative models in teaching and learning algebra leads to the in-depth analysis on the precognitive paradigm for studying the subject ¹⁷.

The software was designed by Bagatrix Solution, Ltd., a US-based computer software company with pseudo mark under Mathway (www.bagatrix.com). The Tucows Incorporation made a version of the software on December 2002 and was launched publicly on November 2004 by David Jones, one of the experts in Bagatrix ¹⁸.

Bagatrix Solved! is a mathematics electronics tutoring software that is among the existing mathematics softwares used to aid teaching like Geogebra, Mathway, Maxima and others. It transforms mathematics education to innovative ways in teaching and learning. The software provides manipulative document and graphing interface with quick insert windows for mathematical symbols and operators used in solving mathematics problems that includes step-by-step solutions and explanation on coming up with answers. This provides numerous sample problems of varied level of difficulties, practice tests with options of multiple choices and graph construction that ranges to more than hundreds of mathematics topics. This includes plug and play (PnP) software on Algebra 1&2, College Algebra, Geometry, Pre-calculus, Calculus and Graphing.

Bagatrix Solved! offers freeware and commercial versions to be accessible for public use and can run on almost all Window operating systems. The freeware version includes almost all features of the software but short of software and program merging and importing (Bagatrix to MS Doc or to other mathematics software and vice versa), collective toolbars having shortcut icons on the different Solved! software as well as problem editors and whiteboards which are the included features on the commercial version.

With this, the study aimed to determine the effectiveness of the mathematics software Bagatrix Solved! on the students’ understanding in learning Algebra of the freshmen students of BSEd Mathematics major taking up College and Advanced Algebra (Math 211) course. This also tried to determine the perception of the students on the integration of technology in studying mathematics. Lastly, this study attempts to develop an instructional material involving the use of Bagatrix Solved! in various Mathematics subjects.

2. Objectives of the Study

This study sought to determine the effectiveness of use of the mathematics software Bagatrix Solved! In teaching and learning Algebra. Specifically, it aimed to: (1) compare the pretests of the control and experimental groups; (2) assess the difference of the pretests of the control and experimental groups with their posttests; (3) compare the posttests of the control and experimental groups; and (4) determine the perception of the experimental group on Bagatrix Solved! software.

3. Materials and Methods

This study employed a quasi-experimental design specifically a pretest-posttest control group design. The participants of the study were divided into control and experimental groups by which each groups were sub-divided to their level of academic performance during the Midterm grading period. The control group composed of 30 participants were taught the conventional way while the experimental group composed of thirty (30) participants were taught using the Bagatrix Solved! software.

The research has four (4) stages that can be seen in Figure 1; for the first stage, both groups were given pretest consisted of twenty (20) multiple choice questions in four (4) topics on Linear equations, specifically on solving and graphing linear equations; slope-intercept form; point-slope formula; and two-point formula. The second stage was the intervention stage wherein the control group were taught the topics on Linear Equation in conventional approach (lecture-discussion method) without the aid of any technological tool while the experimental group were taught the same subject matter using the mathematics software Bagatrix Solved! (Algebra 2) and was conducted for six (6) contact hours or two (2) academic weeks. The third stage was administering the posttest to both groups. The results of the pretest and posttest were tabulated to measure the effectiveness of the mathematics software Bagatrix Solved! to the test performances of the students. In the final stage, a self-made questionnaire was administered to the experimental group to elicit the perception of the students on the use of Bagatrix Solved! software.

The respondents are freshmen students of Bachelor of Secondary Education (BSEd) program major in Mathematics taking up College and Advanced Algebra (Math 211) course. The population of the control group consists of fifty-two (52) students while the experimental group consists of forty-eight (48) students. The researcher was handling both groups on the aforementioned course for the second semester of academic year 2018-2019. The breakdown of sample was shown in Table 1 were chosen through stratified random sampling and were divided into three (3) classifications based on their weighted grade: Above average for 2.00 and 2.25, Average for 2.50 and Below average for 2.75 as shown in Table 2.

The instruments used in this study were the pretest and posttest and an 8-item self-made questionnaire using 5-point Likert scale, both instruments were validated by Mathematics faculty and mathematics experts that were found reliable with Cronbach alpha’s reliability of 0.8 (p<0.05) and 0.87 (p<0.05), respectively.

Descriptive measures such as mean and standard deviation were used to describe the pretest and posttest performances of the participants as well as students perception on the mathematics software Bagatrix Solved!. T-test analysis was used to compare the performances of the control and experimental groups.

Prior to the conduct of the study, the respondents were informed of the stages of the research procedure and each group was aware of the approaches used on them to avoid comparison and confusion. The respondents signified their consent of voluntary participation in the conduct of the study and that the data gathered were treated with confidentiality and anonymity by not disclosing their names and identity.

4. Results and Discussion

The data on Figure 2 shows the pretest performance of the control group has median that were homogeneous to that of the experimental group. On the other hand, Figure 3 shows the heterogeneous result of the students’ posttest performance reflecting the interquartile deviation that were concentrated on the third quartile (Q₃) and fourth quartile (Q₄) for the control group than that of the experimental group with interquartile deviation concentrated mostly on fourth quartile (Q₄).

This implies that on the first stage of the research process, both groups have similar level of understanding on the topics based primarily on their foreknowledge about Linear equations. This is analogous with the findings of Grubisic, Stankov, Rosic and Zitko ¹⁹ that typically, control and experimental groups may statistically alike though not numerically during the initial phase of the study. Towards the final stage, both groups showed improvement on their test performance but the experimental group mostly got perfect scores on the posttest with few outliers than that of the control group.

Table 3 shows that there was no significant difference between the control group (M=10.6, SD=3.38) and experimental group (M=11.2, SD=2.88) pretests performances; t(57)=0.73, p=0.469.

This result reveals that the level of understanding of both groups were similar and that they may have based their answers on their limited prior knowledge and learning as they have encountered before. Some of them might have been confused with the procedural aspect of solving the problems and may have used different kinds of heuristics to be able to arrive at an answer. This is in line with the findings of Marewski, Schooler and Gigarenzer ²⁰ that students are not omniscient, thus, when faced with calculation difficulties, limited information and knowledge tends to use shortcut comparisons of data by anchoring to an example that they may have previously knew (Ryan, 2017).

The results shown in Table 4 indicated a significant difference between pretest and posttest performance of the control group (M=14.65, SD=2.37) with t(29)=11.94, p=0.000; and experimental group (M=14.97, SD=2.67); with t(29)=14.67, p=0.000.

This revealed that after two weeks of teaching and learning Linear equations both groups have shown improvement in their test performances. The control group that was taught through the conventional (lecture-discussion) approach learned the topics that resulted to better performance in the test. This implies that lecture-discussion method is still one among the numerous pedagogies used in classroom learning that is effective in teaching Mathematics. This is consistent with the findings of Olutola, Iliyas and Abdulsalam ²¹ that this method has a significant impact on students’ performance as previously revealed by Lewis & Abdulhamid ²². The experimental group that was taught using the mathematics software Bagatrix Solved! similarly showed improvement in their test performance. This means that the software is a significant tool in understanding topics in Algebra specially lessons on problem solving and graphical representations. This confirms the findings of Ganyaupfu ²³ that the use of different methods in teaching is effective to the students as they gain more understanding of the concept and also revealed by Arbain and Shukor ²⁴ that mathematics software have positive impact to the performance of the students in Mathematics. The students’ improvement using both approaches can be attributed to the twin concept of zone of proximal development (ZPD) and scaffolding model. The Bagatrix Solved! acted as a scaffold that directed the students to achieve the attainment of their ZPD.

The results revealed in Table 5 that there is no significant difference between posttest performance of the control groups (M=18.70, SD=1.37) and experimental group (M=18.73, SD=2.36); t(46)=0.07, p=0.947.

This implies that the teaching methods applied to both groups are effective as it was revealed that both groups gained from both approaches that is consistent with the findings of Shadaan and Leong ¹⁵ that technology integration is now felt as a necessity alongside with the usual approaches in teaching. The conventional method and mathematics software Bagatrix Solved! posted an impact to the students taking up Algebra course specifically in the Linear equation topics.

The results on Table 6 revealed that the students in the experimental group generally have positive perception on the use of the Bagatrix Solved! as most of the means were described as agree and there were two items described as strongly agree. In utilizing the mathematics software featured in this study, the students learned the detailed understanding of linear equation (M=4.56) and have the enthusiasm to discover more on Algebra through it (M=4.52). This indicates that the students were interested in the software since it was their first to use such and they find it helpful as they became more motivated to be involved in the teaching-learning activities. Parallel with various studies ^{25, 26, 27, 28} the aid of technology in teaching Mathematics has been widely encouraged to enhance the capability of students and transform their mathematical knowledge.

5. Conclusion and Recommendation

Prior to the conduct of the study, both groups have limited knowledge about topics on Algebra specifically in Linear equations. However, upon the culmination of the study, there was a notable improvement on the performance of the group taught using a conventional approach and the group taught using the mathematics software Bagatrix Solved!. It shows that both approaches resulted to effective learning of mathematical concepts. The experimental group showed positive perception on the use of the mathematics software Bagatrix Solved!. The mean results of the students’ perception prove the effectiveness of the software on the students’ understanding in learning Algebra. There were several studies on the impact of technology use in teaching and learning Mathematics conducted ^{4, 6, 29, 30, 31} but we can still never let go of the fact that conventional approach in teaching also proves to be effective to the students as revealed in the study.

Based on the findings of the study, the use of the mathematics software Bagatrix Solved! is highly recommended in teaching Algebra as supplement to the conventional approach. This study had revealed that the two approaches were both effective, thus, the combination of both approaches can have a higher impact to the performance of students in Algebra. Emphasized in the report of the U.S. Department of Education ³² that though it has been proven that technology being used as a teaching approach uplift the competitiveness of the students it should not be used solely but rather as an integral part of a well-designed learning environment. It is encouraged that teachers explore the use of combined conventional and technological approaches in teaching Algebra. It is further recommended that the software be introduced to College Mathematics teacher through training to give opportunity for them to utilize it to enhance the teaching and learning process and expose the students to the effectiveness of technology in understanding Algebra that corroborates with what Zakaria and Khalid ³³ stressed in their study.

References