Problem Solving Ability of Integration Technique in Integral Calculus Learning Based on APOS Model of Mathematics Education Students

Abstract

This study aimed to determine the results of the posttest, and the students' problem-solving abilities in solving integration technical questions in learning Integral Calculus based on the APOS Model. The integration technique consists of: a) Substitution Method, b) Trigonometric Substitution, c) Substitution that rationalizes, d) Partial Integral, e) Integral rational function. The APOS model is student-centered learning and has a syntax that consists of phases: Orientation, Practicum, Small Group Discussion, Class Discussion, Exercise, and Evaluation. The research subjects were 28 students of the 3 rd semester of Mathematics Education FKIP Unib 2019/2020 who took Integral calculus class. The instruments used were posttest sheets and questionnaires. The method or flow used was: carrying out the posttest; checking answers based on the Polyas stages, which consisted of: 1) Understanding the Problem; 2) Plan; 3) Doing the Plan; and 4) Looking Back. Post-test questions for the integration technique consisted of 7 questions. Problem 1 was about Substitution Method, Problem 2 and problem 3 were about Trigonometric Functions, Problem 4 was about Substitution that rationalizes, Problem 5 was about Partial Integral, Problem 6 and 7 were about Rational Function Integration Technique. From the research results, it can be concluded that: the average value of the post-test results was 63.04. The average ability of students to solve problems regarding integration techniques: a) substitution methods, there were: 1) 96.43% was able to understand the problem: 2) 96.43% were able to make plans: 3) 96.43% were able to do the plan; 4) only 64.29% were able to do the looking back. b) Trig substitution, there were: 1) 51.79% were able to understand the problem: 2) 51.79% were able to make plans: 3) 51.79% were able to do the plan: 4) 51.79% were able to do the looking back. c) Substitution that rationalizes, there were: 1) 58.93% were able to understand the problem: 2) 37.5% were able to make plans: 3) 39.29% were able to do the plan; 4) only 14.29% were able to do the looking back., d) Partial Integral, there were: 1) 60.71% were able to understand the problem: 2) 53.57% were able to make plans: 3) 14.29% were able to do the plan; 4) only 14.29% were able to do the looking back., e) Integral rational functions, there were: 1) 85.715% were able to understand problems: 2) 75% were able to make plans: 3) 46.43% were able to do plan; 4) only 41,075% were able to do the looking back. Based on the answers to the open questionnaire, the difficulty faced by students in general was the confusion in determining the formulas to be used especially for the integration technique of trigonometric functions.

Mathematics Interest among O-Level Secondary School Students in Wakiso District, Uganda

“…For school students, mathematics is typically a difficult subject where they find trouble trying to build their conceptual mathematical understanding (Asmira et al, 2021). Their interest may be substantially affected by this.…”

Pengaruh Penggunaan Lembar Kegiatan Peserta Didik Berbasis Model APOS Berbantuan Geogebra Terhadap Keterampilan Berpikir Kritis Matematika

“…Berdasarkan hasil penelitian (Hanifah, 2021a) pembelajaran menggunakan model APOS dapat mengembangkan pemahaman dalam hal menemukan strategi*dan keterampilan untuk memecahkan*masalah, bahkan peserta didik yang*aktif dalam belajar baik dalam*kelompok kecil maupun diskusi*kelas peserta didik mendapatkan nilai diatas 70. Hal ini diperkuat oleh hasil penelitian (Fitriana, Yusuf, & Susanti, 2016) bahwa pembelajaran menggunakan Lembar Kegiatan Peserta Didik dapat meningkatkan keterampilan berpikir kritis matematika.…”