Rubric as a learning tool in teaching application of derivatives in basic calculus

Leah Conejos Auxtero(1*), Roar Abalos Callaman(2)

(1) Department of Senior High School, University of Mindanao,
(2) College of Education, University of Southeastern Philippines
(*) Corresponding Author

Abstract

Rubric has been associated with the term assessment used for grading and/or scoring. However, it might observe less, but it is also designed as students ‘learning tool. This study was conducted to provide empirical facts on its effectiveness as a learning tool in teaching Applications of Derivatives in Basic Calculus. It used the quasi-experimental design called the pretest posttest design. The participants were the 96 students from two classes of Grade 11 STEM students at the University of Mindanao. The instruments used were the adapted and improved rubric designed from two different research, a 25-item teacher-made problem-solving test questionnaire that was used in both pretest and posttest to measure the performance of the experimental and control group. The test questionnaire and rubric were both validated by 3 experts in the field with a result of very good, and it has a good internal consistency. The data gathered were summarized, translated, and analyzed using the mean scores of pretest and posttest. Findings showed that both the experimental and control group showed improvement, however, the experimental group who used rubric as a learning tool showed more significant improvement than control group. Thus, using a rubric as a learning tool in teaching Applications of derivatives is effective in improving students’ academic achievement as it teaches students to develop their understanding of procedural knowledge.

Keywords

Rubrics, learning tool, effectiveness

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References

Andrade, H. & Reddy, M. (2010). A Review of Rubric Use in Higher Education. Assessment & Evaluation in Higher Education, 35(4), 435-448, https://doi.org/10.1080/02602930902862859

Bada, O. (2015). Constructivism Learning Theory: A Paradigm for Teaching and Learning. IOSR Journal of Research & Method in Education (IOSR-JRME), 5(6), 2320-7388. Retrieved from http://www.iosrjournals.org/iosr-jrme/papers/Vol-5%20Issue-6/Version-1/I05616670.pdf

Behera, D. (2017). Assessment of Students’ Learning through Constructive Approach. Retrieved from https://www.researchgate.net/publication/331134741_Assessment_of_Students%27_Learning_through_Constructive_Approach

Bradbury, J. (2010). Why is Teaching with Problem Solving Important to Student Learning? NCTM, 13(12), 1–6.

Brookhart, S. (2013). How to Create and Use Rubrics and Why Are They Important? ASCD: Professional Learning & Community for Educators. Retrieved from http://www.ascd.org/publications/books/112001/chapters/What-Are-Rubrics-and-Why-Are-They-Important%C2%A2.aspx

Callaman, R., & Itaas, E. (2020). Students’ mathematics achievement in Mindanao context: A meta-analysis. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 148-159. https://doi.org/10.23917/jramathedu.v5i2.10282

Chowdhury, F. (2019). Application of Rubrics in the Classroom: A Vital Tool for Improvement in Assessment, Feedback and Learning. International Education Studies, 12(1), 61-68. https://doi.org/10.5539/ies.v12n1p61

Clabaugh, G. K. (2010). The Educational Theory of Jerome Bruner: A Multi-Dimensional Analysis. Retrieved from http://www.newfoundations.net/GALLERY/BrunerTheory.pdf

Cox, G., Morrison, J. &Brathwaite, Beverley. (2015). The Rubric: An Assessment Tool to Guide Students and Markers. In 1st International Conference on Higher Education Advances, HEAd’15, Universitat Politècnica de València, València, pp. 26-32. http://dx.doi.org/10.4995/HEAd15.2015.414

Creswell, J. (2014). Research Design Qualitative, Quantitative and Mixed Methods Approaches. Thousand Oaks, CA: SAGE Publications, Inc.

Department of Education. (2019). PISA 2018 National Report of the Philippines. Retrieved from https://www.deped.gov.ph/wp-content/uploads/2019/12/PISA-2018-Philippine-National-Report.pdf.

Donlan, K. (2014). The Usefulness of Rubrics. ESSAI, 12, Article 15. Retrieved from https://dc.cod.edu/essai/vol12/iss1/15/

Francis, J.E. (2018). Linking Rubrics and Academic Performance: An Engagement Theory Perspective. Journal University Teaching & Learning Practice, 15(1). Retrieved from http://ro.uow.edu.au/jutlp/vol15/iss1/3

Gallego-Arrufat, M. J., & Dandis, M. (2014). Rubrics in a secondary mathematics class. International Electronic Journal of Mathematics Education, 9(1-2), 75-84. Retrieved from https://www.iejme.com/download/rubrics-in-a-secondary-mathematics-class.pdf

Garofalo, C., Holden, C. J., Zeigler-Hill, V., & Velotti, P. (2016). Understanding the connection between self-esteem and aggression: The mediating role of emotion dysregulation. Aggressive Behavior. 42(1), 3-15. https://doi.org/10.1002/ab.21601

Gleason, B. L., Gaebelein, C. J., Grice, G. R., Crannage, A. J., Weck, M. A., Hurd, P., Walter, B., & Duncan, W. (2013). Students’ Critical-Thinking and Problem-Solving Abilities across a 6-Year Doctor of Pharmacy Program. American Journal of Pharmaceutical Education, 77 (8), Article 166. https://doi.org/10.5688/ajpe778166

Gulikers, J., & Oonk, C. (2019). Towards a Rubric for Stimulating and Evaluating Sustainable Learning. Sustainability, 11(4), 969. https://doi.org/10.3390/su11040969

Gurat, M. G. (2018). Mathematical problem-solving strategies among student teachers. Journal on Efficiency and Responsibility in Education and Science, 11(3), 53–64. https://doi.org/10.7160/eriesj.2018.110302

Darling-Hammond, L., Flook, L., Cook-Harvey, C., Barron, B., & Osher, D. (2020). Implications for educational practice of the science of learning and development. Applied Developmental Science, 24(2), 97-140, https://doi.org/10.1080/10888691.2018.1537791

Jeong, H. (2015). Rubrics in the classroom: do teachers really follow them?. Language Testing in Asia, 5(1), 6. https://doi.org/10.1186/s40468-015-0013-5

Jönsson, A. (2014). Rubrics as a way of providing transparency in assessment. Assessment & Evaluation in Higher Education. 39(7), 840-852. https://doi.org/10.1080/02602938.2013.875117

Kinne, L., Hasenbank, J, & Coffey, D. (2014). Are We There Yet? Using Rubrics to Support Progress Toward Proficiency and Model Formative Assessment., Grand Valley State University. EJ1052581, XI, 109–128. https://files.eric.ed.gov/fulltext/EJ1052581.pdf

Kumar, R. (2014). Research Methodology: A Step-by-step Guide for Beginners Fourth Edition. London, UK: SAGE Publications LTD.

Malang, O. (2016). Effectiveness of Rubric as a Learning Tool in Teaching Mathematics of Investment.College of Education. (Unpublished master’s thesis).University of Southeastern Philippines. Philippines.

Manikandan, S. (2011). Measures of Central Tendency: Median and mode. Journal of pharmacology and pharmacotherapeutics, 2(3), 214.

McKenzie, J. E. (2019). Randomisation is more than a coin toss: The role of allocation concealment. BJOG: An International Journal of Obstetrics & Gynaecology, 126(10), 1288-1288. https://doi.org/10.1111/1471-0528.15559

Muhammad, A., Lebar, O., Mokshein, S.E., Mohamed, R., Ridzwan, S., & Khairil, L. (2018). Assessing Student Teachers’ Soft Skills Using Rubrics in E-portfolio. International Journal of Academic Research in Business and Social Sciences, 8(10), 1245-1255. http://dx.doi.org/10.6007/IJARBSS/v8-i10/5295

OECD. (2017). How does PISA for Development measure mathematical literacy? PISA for Development Brief, I (February 2014), 0-1. Retrieved from https://www.oecd.org/pisa/aboutpisa/9-How-PISA-D-measures-math-literacy.pdf

Oliveros, J. C. (2014). Adversity Quotient and Problem-solving Skills in Advanced Algebra. JPAIR Multidisciplinary Research Journal, 17(1). Retrieved from http://ejournals.ph/form/cite.php?id=12385

Palmay, A. (2015). Improving the Problem Solving Performance of Struggling Learners in Mathematics. Retrieved from https://www.semanticscholar.org/paper/IMPROVING-THE-PROBLEM-SOLVING-PERFORMANCE-OF-IN-P%C3%A1lmay/17def322cbbaaddcf689f8a9ebf9f287307c7c5a.

Panadero, E., & Jonsson, A. (2016). Chapter 7 The Use and Design of Rubrics to Support

January 1–14. https://doi.org/10.1007/978-981-10-3045-1

Philominraj, A., Bertilla, M., Ramirez-Muñoz, B. & Fuentealba, A. (2018). The Interconnectedness between Experience and Intelligence to English Language Teaching. English Language Teaching, 11(5), 68-73. https://doi.org/10.5539/elt.v11n5p68

Pongsakdi, N., Laine, T., Veermans, K., Hannula-Sormunen, M., & Lehtinen, E.(2016). Improving Word Problem Performance in Elementary School Students by Enriching Word Problems Used in Mathematics Teaching. Nordic Studies in Mathematics Education, 21(2), 23-44.

Raposo, M., Cebrian-de-la-Cerna, M., Martinez-Figueira, E. (2014). Electronics Rubrics to Assess Competences in ICT Subjects. European Educational Research Journal, 13(5), 584-594. https://doi.org/10.2304/eerj.2014.13.5.584

Raymond, R., Alkrisat, M., & Hebda, T. (2018). Improving Students through Rubric Redesign. Corpus ID: 117226503. Retrieved from https://www.semanticscholar.org/paper/Improving-Student-Outcomes-through-Rubric-Redesign-Raymond-Alkrisat/470253cc597d00e791cf17e32eafc61c378892f5

Reitmeier, C. A., Svendsen, L. K., &Vrchota, D. A. (2004). Improving Oral Communication skills of students in Food science courses. Journal of Food Science Education, 3, 15-20. https://doi.org/10.1111/j.1541-4329.2004.tb00036.x

Reynolds-Keefer, L. (2010). Rubric-Referenced Assessment in Teacher Preparation: An Opportunity to Learn by Using. Practical Assessment, Research, and Evaluation, 15(1), Article 8. https://doi.org/10.7275/psk5-mf68

Samuelson, B. L., & Freedman, S. W. (2010). Language policy, multilingual education, and power in Rwanda. Language Policy, 9(3), 191–215. https://doi.org/10.1007/s10993-010-9170-7

Schneider, J. F. (2006). Rubrics for Teacher education in Community college.The Community College Enterprise, 12(1), 39-55.

Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding (Reprint). Mathematics Teaching in the Middle School, 12(2), 88–95.

Sonseca, A., Sahuquillo, O., Martinez-Casas, J., Carballeira, J., Denia, F.D., & Rodenas, J. (2015). Assessment of Oral and Written Communication Competences in the European Higher Education Area: A Proposal of Evaluation Methodologies. In 1st INTERNATIONAL CONFERENCE ON HIGHER EDUCATION ADVANCES (HEAD'15) (pp. 2-9). Editorial Universitat Politècnica de València. https://doi.org/10.4995/HEAD15.2015.485

Stevens, D.D., & Levi, A.J. (2013). Introduction to Rubrics: An Assessment Tool to Save Grading Time, Convey Effective Feedback, and Promote Student Learning (2nd Ed.). Sterling. VA: Stylus Publishing.

Tractenberg, R., Lindvall, J., Attwood, T., Via, A. (2019). The Mastery Rubric for Bioinformatics: A tool to Support Design and Evaluation of Career-spinning Education and Training. PLoS ONE, 14(11): e0225256. https://doi.org/10.1371/journal.pone.0225256.

Tupas, S. V.. (2012). Effectiveness of Problem-Based Learning Approach to the Students’ Problem Solving Performance. JPAIR Multidisciplinary Research Journal, 9(1). https://doi.org/10.7719/jpair.v9i1.4.

Vygotsky, L. S. (1978). Mind in society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.

Wilson, J. W., Fernandez, M. L., & Hadaway, N. (2011). Mathematical Problem Solving, pp. 57–78. Retrieved from http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html

Yu, Y. H., Hu, Y. N., & Zhang, J. S. (2013). A research on reading model of interactive children picture book application based on the theory of “zone of proximal development.” Applied Mechanics and Materials, 411–414(4), 2952–2956. https://doi.org/10.4028/www.scientific.net/AMM.411-414.2952

Zhou, M., & Brown, D. (2017). Educational Learning Theories: 2nd Edition. In Education Open Textbooks. Retrieved from https://oer.galileo.usg.edu/education-textbooks/1

Andrade, H. & Reddy, M. (2010). A Review of Rubric Use in Higher Education. Assessment & Evaluation in Higher Education, 35(4), 435-448, https://doi.org/10.1080/02602930902862859

Bada, O. (2015). Constructivism Learning Theory: A Paradigm for Teaching and Learning. IOSR Journal of Research & Method in Education (IOSR-JRME), 5(6), 2320-7388. Retrieved from http://www.iosrjournals.org/iosr-jrme/papers/Vol-5%20Issue-6/Version-1/I05616670.pdf

Behera, D. (2017). Assessment of Students’ Learning through Constructive Approach. Retrieved from https://www.researchgate.net/publication/331134741_Assessment_of_Students%27_Learning_through_Constructive_Approach

Bradbury, J. (2010). Why is Teaching with Problem Solving Important to Student Learning? NCTM, 13(12), 1–6.

Brookhart, S. (2013). How to Create and Use Rubrics and Why Are They Important? ASCD: Professional Learning & Community for Educators. Retrieved from http://www.ascd.org/publications/books/112001/chapters/What-Are-Rubrics-and-Why-Are-They-Important%C2%A2.aspx

Callaman, R., & Itaas, E. (2020). Students’ mathematics achievement in Mindanao context: A meta-analysis. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 148-159. https://doi.org/10.23917/jramathedu.v5i2.10282

Chowdhury, F. (2019). Application of Rubrics in the Classroom: A Vital Tool for Improvement in Assessment, Feedback and Learning. International Education Studies, 12(1), 61-68. https://doi.org/10.5539/ies.v12n1p61

Clabaugh, G. K. (2010). The Educational Theory of Jerome Bruner: A Multi-Dimensional Analysis. Retrieved from http://www.newfoundations.net/GALLERY/BrunerTheory.pdf

Cox, G., Morrison, J. &Brathwaite, Beverley. (2015). The Rubric: An Assessment Tool to Guide Students and Markers. In 1st International Conference on Higher Education Advances, HEAd’15, Universitat Politècnica de València, València, pp. 26-32. http://dx.doi.org/10.4995/HEAd15.2015.414

Creswell, J. (2014). Research Design Qualitative, Quantitative and Mixed Methods Approaches. Thousand Oaks, CA: SAGE Publications, Inc.

Department of Education. (2019). PISA 2018 National Report of the Philippines. Retrieved from https://www.deped.gov.ph/wp-content/uploads/2019/12/PISA-2018-Philippine-National-Report.pdf.

Donlan, K. (2014). The Usefulness of Rubrics. ESSAI, 12, Article 15. Retrieved from https://dc.cod.edu/essai/vol12/iss1/15/

Francis, J.E. (2018). Linking Rubrics and Academic Performance: An Engagement Theory Perspective. Journal University Teaching & Learning Practice, 15(1). Retrieved from http://ro.uow.edu.au/jutlp/vol15/iss1/3

Gallego-Arrufat, M. J., & Dandis, M. (2014). Rubrics in a secondary mathematics class. International Electronic Journal of Mathematics Education, 9(1-2), 75-84. Retrieved from https://www.iejme.com/download/rubrics-in-a-secondary-mathematics-class.pdf

Garofalo, C., Holden, C. J., Zeigler-Hill, V., & Velotti, P. (2016). Understanding the connection between self-esteem and aggression: The mediating role of emotion dysregulation. Aggressive Behavior. 42(1), 3-15. https://doi.org/10.1002/ab.21601

Gleason, B. L., Gaebelein, C. J., Grice, G. R., Crannage, A. J., Weck, M. A., Hurd, P., Walter, B., & Duncan, W. (2013). Students’ Critical-Thinking and Problem-Solving Abilities across a 6-Year Doctor of Pharmacy Program. American Journal of Pharmaceutical Education, 77 (8), Article 166. https://doi.org/10.5688/ajpe778166

Gulikers, J., & Oonk, C. (2019). Towards a Rubric for Stimulating and Evaluating Sustainable Learning. Sustainability, 11(4), 969. https://doi.org/10.3390/su11040969

Gurat, M. G. (2018). Mathematical problem-solving strategies among student teachers. Journal on Efficiency and Responsibility in Education and Science, 11(3), 53–64. https://doi.org/10.7160/eriesj.2018.110302

Darling-Hammond, L., Flook, L., Cook-Harvey, C., Barron, B., & Osher, D. (2020). Implications for educational practice of the science of learning and development. Applied Developmental Science, 24(2), 97-140, https://doi.org/10.1080/10888691.2018.1537791

Jeong, H. (2015). Rubrics in the classroom: do teachers really follow them?. Language Testing in Asia, 5(1), 6. https://doi.org/10.1186/s40468-015-0013-5

Jönsson, A. (2014). Rubrics as a way of providing transparency in assessment. Assessment & Evaluation in Higher Education. 39(7), 840-852. https://doi.org/10.1080/02602938.2013.875117

Kinne, L., Hasenbank, J, & Coffey, D. (2014). Are We There Yet? Using Rubrics to Support Progress Toward Proficiency and Model Formative Assessment., Grand Valley State University. EJ1052581, XI, 109–128. https://files.eric.ed.gov/fulltext/EJ1052581.pdf

Kumar, R. (2014). Research Methodology: A Step-by-step Guide for Beginners Fourth Edition. London, UK: SAGE Publications LTD.

Malang, O. (2016). Effectiveness of Rubric as a Learning Tool in Teaching Mathematics of Investment.College of Education. (Unpublished master’s thesis).University of Southeastern Philippines. Philippines.

Manikandan, S. (2011). Measures of Central Tendency: Median and mode. Journal of pharmacology and pharmacotherapeutics, 2(3), 214.

McKenzie, J. E. (2019). Randomisation is more than a coin toss: The role of allocation concealment. BJOG: An International Journal of Obstetrics & Gynaecology, 126(10), 1288-1288. https://doi.org/10.1111/1471-0528.15559

Muhammad, A., Lebar, O., Mokshein, S.E., Mohamed, R., Ridzwan, S., & Khairil, L. (2018). Assessing Student Teachers’ Soft Skills Using Rubrics in E-portfolio. International Journal of Academic Research in Business and Social Sciences, 8(10), 1245-1255. http://dx.doi.org/10.6007/IJARBSS/v8-i10/5295

OECD. (2017). How does PISA for Development measure mathematical literacy? PISA for Development Brief, I (February 2014), 0-1. Retrieved from https://www.oecd.org/pisa/aboutpisa/9-How-PISA-D-measures-math-literacy.pdf

Oliveros, J. C. (2014). Adversity Quotient and Problem-solving Skills in Advanced Algebra. JPAIR Multidisciplinary Research Journal, 17(1). Retrieved from http://ejournals.ph/form/cite.php?id=12385

Palmay, A. (2015). Improving the Problem Solving Performance of Struggling Learners in Mathematics. Retrieved from https://www.semanticscholar.org/paper/IMPROVING-THE-PROBLEM-SOLVING-PERFORMANCE-OF-IN-P%C3%A1lmay/17def322cbbaaddcf689f8a9ebf9f287307c7c5a.

Panadero, E., & Jonsson, A. (2016). Chapter 7 The Use and Design of Rubrics to Support

January 1–14. https://doi.org/10.1007/978-981-10-3045-1

Philominraj, A., Bertilla, M., Ramirez-Muñoz, B. & Fuentealba, A. (2018). The Interconnectedness between Experience and Intelligence to English Language Teaching. English Language Teaching, 11(5), 68-73. https://doi.org/10.5539/elt.v11n5p68

Pongsakdi, N., Laine, T., Veermans, K., Hannula-Sormunen, M., & Lehtinen, E.(2016). Improving Word Problem Performance in Elementary School Students by Enriching Word Problems Used in Mathematics Teaching. Nordic Studies in Mathematics Education, 21(2), 23-44.

Raposo, M., Cebrian-de-la-Cerna, M., Martinez-Figueira, E. (2014). Electronics Rubrics to Assess Competences in ICT Subjects. European Educational Research Journal, 13(5), 584-594. https://doi.org/10.2304/eerj.2014.13.5.584

Raymond, R., Alkrisat, M., & Hebda, T. (2018). Improving Students through Rubric Redesign. Corpus ID: 117226503. Retrieved from https://www.semanticscholar.org/paper/Improving-Student-Outcomes-through-Rubric-Redesign-Raymond-Alkrisat/470253cc597d00e791cf17e32eafc61c378892f5

Reitmeier, C. A., Svendsen, L. K., &Vrchota, D. A. (2004). Improving Oral Communication skills of students in Food science courses. Journal of Food Science Education, 3, 15-20. https://doi.org/10.1111/j.1541-4329.2004.tb00036.x

Reynolds-Keefer, L. (2010). Rubric-Referenced Assessment in Teacher Preparation: An Opportunity to Learn by Using. Practical Assessment, Research, and Evaluation, 15(1), Article 8. https://doi.org/10.7275/psk5-mf68

Samuelson, B. L., & Freedman, S. W. (2010). Language policy, multilingual education, and power in Rwanda. Language Policy, 9(3), 191–215. https://doi.org/10.1007/s10993-010-9170-7

Schneider, J. F. (2006). Rubrics for Teacher education in Community college.The Community College Enterprise, 12(1), 39-55.

Skemp, R. R. (1976). Relational Understanding and Instrumental Understanding (Reprint). Mathematics Teaching in the Middle School, 12(2), 88–95.

Sonseca, A., Sahuquillo, O., Martinez-Casas, J., Carballeira, J., Denia, F.D., & Rodenas, J. (2015). Assessment of Oral and Written Communication Competences in the European Higher Education Area: A Proposal of Evaluation Methodologies. In 1st INTERNATIONAL CONFERENCE ON HIGHER EDUCATION ADVANCES (HEAD'15) (pp. 2-9). Editorial Universitat Politècnica de València. https://doi.org/10.4995/HEAD15.2015.485

Stevens, D.D., & Levi, A.J. (2013). Introduction to Rubrics: An Assessment Tool to Save Grading Time, Convey Effective Feedback, and Promote Student Learning (2nd Ed.). Sterling. VA: Stylus Publishing.

Tractenberg, R., Lindvall, J., Attwood, T., Via, A. (2019). The Mastery Rubric for Bioinformatics: A tool to Support Design and Evaluation of Career-spinning Education and Training. PLoS ONE, 14(11): e0225256. https://doi.org/10.1371/journal.pone.0225256.

Tupas, S. V.. (2012). Effectiveness of Problem-Based Learning Approach to the Students’ Problem Solving Performance. JPAIR Multidisciplinary Research Journal, 9(1). https://doi.org/10.7719/jpair.v9i1.4.

Vygotsky, L. S. (1978). Mind in society: The Development of Higher Psychological Processes. Cambridge, MA: Harvard University Press.

Wilson, J. W., Fernandez, M. L., & Hadaway, N. (2011). Mathematical Problem Solving, pp. 57–78. Retrieved from http://jwilson.coe.uga.edu/emt725/PSsyn/PSsyn.html

Yu, Y. H., Hu, Y. N., & Zhang, J. S. (2013). A research on reading model of interactive children picture book application based on the theory of “zone of proximal development.” Applied Mechanics and Materials, 411–414(4), 2952–2956. https://doi.org/10.4028/www.scientific.net/AMM.411-414.2952

Zhou, M., & Brown, D. (2017). Educational Learning Theories: 2nd Edition. In Education Open Textbooks. Retrieved from https://oer.galileo.usg.edu/education-textbooks/1

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