An Assessment of Grade 10 Students’ Conceptual Understanding of Geometry

An Assessment of Grade 10 Students’ Conceptual Understanding of Geometry

Rejohn M. Peligro

Prosperidad National High School, Prosperidad, Agusan del Sur, Philippines

DOI: https://dx.doi.org/10.47772/IJRISS.2024.8100253

Received: 16 October 2024; Accepted: 21 October 2024; Published: 21 November 2024

ABSTRACT

Conceptual understanding refers to student’s ability to reason, explain and apply mathematical concepts using its definitions, relations and representations especially in Geometry. Students need to develop fluency in Mathematics for global competencies and geometry is a best vehicle. This study was undertaken to assess students’ achievement and conceptual understanding of geometry. The study was designed to determine whether Grade 10 students possess good conceptual understanding of Geometry before instruction to remedy and correct concepts which are misunderstood. It utilized descriptive design of research and was conducted at Prosperidad National High School, Prosperidad, Agusan del Sur, Philippines. The participants were the two intact classes of Grade 10 students assigned as experimental and control group. A teacher made two tiered achievement and conceptual understanding test in Mathematics were administered to both groups. Results revealed that there is no significant difference in the achievement of experimental and control group in achievement test with a means of 7.97 and 6.19 and standard deviation of 2.44 and 2.26 and conceptual understanding with a means of 0.35 and 0.21 and a standard deviation of 1.15 and 0.68 respectively. Both groups had a poor conceptual understanding of theories, could not apply, interpret and explain mathematical concepts and process.

Keywords: assessment, conceptual understanding, geometry, grade 10

INTRODUCTION

Mathematics teaching requires efficiency and mastery of concepts to make students mathematically proficient citizen of the 21^st century. Mathematics instruction need to be restructured so that students can use concepts with fluency and flexibility (Samarji, 2012). Thus, understanding the basic concepts plays a pivotal role in in their learning. The results of Trends in International Mathematics and Science Study (TIMSS) 2019 showed that teachers’ way of instruction influence students cognitive learning (TIMSS, 2019). Today, many countries around the globe align their mathematics curriculum to teachers needs and competencies as well as assessments to have a tangible end results of a better equip and holistic students not only in Mathematics but with other subjects (Suweken et al, 2017).

In vast continent of Asia, many countries throughout the region give emphasis on the significance of conceptual understanding and teaching practices as it is the fundamental in learning Mathematics and connects it with other discipline through critically thinking (Linn, 1994 and Heibert et al, 1986). For instance, the instructional attributes of teachers in the five high performing Asian educational systems during TIMSS 2011 namely Japan, Singapore, Chinese Taipe, Hong Kong and South Korea influence their students grasp of mathematical concepts that lead to better understanding (Cheng, 2014).

In the Philippines, one of the objectives of the its education system is to produce human capital which are life-long learners. This can be achieved if schools around the country focuses on uplifting the quality of education by providing equitable educational opportunities especially in Mathematics subjects. The Philippines’ Department of Education (DepEd) and Commission on Higher Education (CHED) emphasized that mathematics must be taught in ways that promote continuity in applying concepts with understanding and skills in real life that will enable students to use these in the future situations (Marquez, 2017). Many teachers did innovations and applied varied teaching techniques to improve students’ abstraction of mathematical concepts. EDHH However, most of them were unsuccessful, since students learned less concepts and had difficulty in applying the mathematical concept in their life (Clark-Wilson et al, 2015).

Classroom problems are teachers’ responsibility to orchestrate the class activity to help the students learn the lesson if the environment is unfavorable. These problems are reflected in students’ low scores in written examinations especially in Mathematics subject. The results of assessments are also revealed in the National Achievement Test (NAT) where students got unsatisfactory level of conceptual understanding in Mathematics. Institutional profiling of schools released by National Education Testing and Research Center (NETRC) of the Department of Education (DEpEd) further revealed that most of students have difficulty in answering the mathematics items in NAT. Most of the competencies required students to apply basic knowledge in Mathematics but they failed (NETRC, 2008).

The existing problem of students’ low performance in assessments may be due to poor conceptual understanding of mathematical theories and terms. It is the vital role of teacher to design instruction where students’ are engaged to participate in learning the concepts and process to foster conceptual understanding. Conceptual understanding is characterized by deep assimilation of mathematical concepts. At this level of understanding, students can interpret, explain and apply mathematical concepts and processes in real life situations (Greene & Shorter, 2012). Assessment of students’ conceptual understanding is necessary for the teachers’ to determine why and how students’ failed to learn mathematics. This may help teachers to design instruction that will match to their students learning difficulties. Assessments is important since the government wants to monitor the quality of human resources who can contribute the economy of the nation.

AMATYC (1995) said that assessing students’ conceptual understanding is important because it enable teachers to have a holistic plan of their instruction to give meaning and application of mathematical concepts and teacher’s pedagogical technique is a need. Mathematical Association of America (MAA, 2004) further said that assessment of mathematical concepts prior to instruction serves as springboard and is a very powerful tool to remediate students’ misconceptions.  Carlson et al (2010) agreed that assessment of students’ concepts learned before instruction is essential to identify what they already know and how appropriate process they possess so that teachers can change and employ appropriate learning experience. Molina (2014) emphasized that there are vast opportunities to improve students’ acquisition of mathematical concepts by knowing students’ conceptual understanding to develop appropriate mathematical skills.

Since assessment gives guide to appropriate instructions, the objective of this study was to assess students’ conceptual understanding in Geometry. This was done to help the teachers design pedagogical strategy suitable to students’ ability. The result would be the basis for class intervention and further teaching innovation.

METHODS

This study employed descriptive type of research using mean and standard deviation to describe the data. The respondents of the study were the two intact classes of Grade 10 students with 46 students each who were randomly chosen. They were chosen from among the six sections Grade 10 students of Prosperidad National High School, Prosperidad, Agusan del Sur, Philippines. The first instrument used in the study was the teacher made two tiered achievement test which is a 22-item multiple choice test. The first tier determined students’ prior knowledge in Geometry while the second tier is a follow up question on how they arrived at their answers. The second instrument was the conceptual understanding test which is 5 open ended questions that assessed students’ ability to interpret, explain and apply mathematical concepts and processes. The test covered the lessons in circle and coordinate geometry that included the topics in chords, arcs and central angle, inscribed angle, sector and segments of a circle, tangents and secants to circle, tangent and secant segments of a circle, rectangular coordinates, distance formula, midpoint formula and equation of a circle. Students’ answers to the second-tier test were assessed using rubric and the 5 open ended questions answers were evaluated based on Wiggins and Mc Tighes (1998) facets of understanding using a scoring rubric. In determining students’ proficiency level, the K – 12 level of proficiency was used.

RESULTS AND DISCUSSIONS

The results of the analysis are shown in the following tables.

Table I. Mean, Standard Deviation and Descriptive Level of Students’ Mathematical Achievement Score

*Perfect score is 110

Table I shows the mean scores of the experimental and control groups which are 7.97 and 6.19 respectively. The table revealed that their scores did not reach 10% of the total score which is 110. This indicates that both groups proficiency level is at the beginning stage. The small mean scores of students in achievement test of both groups is an evidence of low assimilation of concepts in Geometry.  Even though some students got correct in their choice in the first tiered test, yet they failed to explain how they arrive at the answer. This explains why most of their scores are low. Most of the students also answered only the first tier in the mathematics achievement test which shows that they have difficulty to convey how they arrived at their answers. The results indicated that these students have acquired little knowledge and understanding in Geometry in their previous years. Their difficulties may be attributed to none exposure to the topics. These results confirmed the findings of Boud (2007) that assessment of students conceptual understanding prior to instruction is important since it will enable teachers to design instruction to remediate misconceptions and learning difficulties.

The standard deviations of both groups which are 2.44 and 2.26 are comparable. The smaller difference of 0.18 of the participants’ standard deviations means that their scores are not widely disperse and very close to each other. Table 1 also showed a computed F ratio of 1.16 less than F critical value of 1.64 at 0.05 probability level which means that the scores of students are comparable. This indicates that the students have the same level of knowledge acquired in their preceding years.

Table II. Mean, Standard Deviation and Descriptive Level of Students’ Conceptual Understanding

*Perfect score is 60

Table II showed result of the analysis of the participants’ conceptual understanding score. The table revealed the mean scores of the two groups of 0.35 and 0.21 which are very low. This indicates that both groups level of conceptual understanding is at the beginning. This means that students’ conceptual understanding is very poor and unsatisfactory level. The results is an indication that students of both groups lack the ability to interpret mathematical problems, cannot used appropriate formulas and algorithm and unable to give justifications of their mathematical solutions which are vital in conceptual understanding. The very low mean scores of the students’ respondents in conceptual understanding suggests that Geometry subject is difficult and needed more effort for the teacher to help the students attain mastery of the concepts. Both groups have unsatisfactory level of conceptual understanding which suggests that students have little idea of geometric concepts. Students’ cognitive level and difficulties are the same as shown in their very low mean scores. These results is challenge to the teacher to ensure that students can develop critical thinking and problem solving skills as element of a 21^st century learners since these skills are basic in conceptual understanding (Tekin-Sitrava et al, 2014). This means that there is a need of every teacher to assess students’ conceptual understanding before the mathematics instruction is implemented to determine misconceptions and misunderstanding of mathematical concepts and remediate these difficulties in the process of learning.

The standard deviations of both groups which are 1.15 and 0.68 are not close to each other. The variance of 0.47 indicates that their scores are slightly scattered and they do not have comparable scores in conceptual understanding. The incomparable standard deviations of both groups is an indication that students have different level of acquisition of the topics in Geometry. The table also revealed a computed F-ratio of 2.86 greater than the critical at 0.05 probability value which further suggests that the scores of the experimental and control group students were not comparable. This result indicated that students from experimental group have a better conceptual understanding in Geometry in their previous years compared to the control group. These are demonstrated in the second tiered test where most of the students from control group failed to justify their answers. This means that students have less assimilation of the concepts in Geometry discussed from their preceding year levels.

Moreover, students low scores conceptual understanding tests is due to their learning difficulties and misconceptions of the geometric concepts which clearly showed in their written answers of both in the second tier and open ended questions.

CONCLUSION AND RECOMMENDATIONS

Based on the findings of the study, the researcher concludes that students’ respondents do not possess basic knowledge in geometry and they have difficulties and misconceptions of geometric terms. Hence the researcher recommends to teachers to conduct assessment of students’ conceptual understanding before instruction begin to design instructional strategies that can effectively remediate students’ misconceptions.

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