### STUDENTS’ MATHEMATICS ATTITUDES AND METACOGNITIVE PROCESSES IN MATHEMATICAL PROBLEM SOLVING

#### Abstract

Mathematical problem solving is considered as one of the many endpoints in teaching Mathematics to students. This study looked into the performance in mathematics problem solving among fourth year students of Central Mindanao University Laboratory High School and their relationship with students’ attitudes towards Mathematics. The attitudes measured were Attitude towards success in Math, Mother’s mathematics attitude, Father’s mathematics attitude, Motivation, Usefulness of Math, Teacher’s mathematics attitude, Confidence in learning math, and mathematics anxiety. It also investigated the metacognitive processes of students considering varying levels of their mathematics anxiety. It used the responses of 127 students. Of the 127, (nine) 9 were selected according to their mathematics anxiety levels to determine and compare their metacognitive processes. Results showed that students consider Mathematics as useful and they have a positive attitude towards success in Mathematics. The students’ fathers, mothers, and teachers also have positive attitudes towards their mathematics learning. However, overall, the students’ performance in mathematics problem solving is considered poor. Among the eight (8) mathematics attitudes only confidence in learning Math and mathematics anxiety were correlated with performance in mathematics problem solving. Confidence in learning Math was positively correlated, while mathematics anxiety was negatively correlated with performance in mathematics problem solving. Students with high mathematics anxiety tend to confirm their solutions with their classmates. Students with moderate anxiety are test-anxious and those with low anxiety are distracted by external factors, but can readily shift their focus back to problem solving. The three (3) cases showed that students with low, moderate, and high mathematics anxiety employed mostly orientation and execution procedures. There were only few instances of verification and lesser instances of organization procedures. Self-questioning was the most observed metacognitive skill. Furthermore, students from the three (3) cases were unable to correctly answer two (2) problems, both of which are non-routine due to unfamiliarity and “experiential interference”.

** Article visualizations:**

#### Keywords

#### Full Text:

PDF#### References

FactSheets. (2007, May 8). Retrieved from National Statistics Coordination Board: http://www.nscb.gov.ph/factsheet/pdf07/FS-200705-SS2-01.asp

Alomar, B. (2006). Personal and Family Paths to Pupil Achievement. Social Behavior and Personality, 907-922.

Asparin, A. (2013). Problem Solving Abilities and Psychological Attributes of Sophomore Students: A Causal Model on Mathematics Achievement. Unpublished Master's thesis.

Brekalo, K. (2012). Attitudes toward mathematics of elementary school students and their parents. Retrieved from http://darhiv.ffzg.hr/id/eprint/2078

Brooks, A. and Schweitzer, M. (2011). Can Nervous Nelly negotiate? How anxiety causes negotiators to make low first offers, exit early, and earn less profit. Organizational Behavior and Human Decision Processes (115), 12.

Brooks, A. W. (2012). Get Excited: Reappraising Pre-Performance Anxiety as Excitement Improves Performance. . Retrieved from http://opim.wharton.upenn.edu http://opim.wharton.upenn.edu/risk/ackoff/Ackoff2012/Brooks.pdf

Bulosan, L. (2008). The Relationship of Diagnostic, National Achievement Tests, Attitudes and Academic Achievement among Grade VI Pupils at Musuan Elementary School. Central Mindanao University: Unpublished Master's thesis.

Carson, J. (2007). A Problem with Problem Solving: Teaching Thinking without Teaching Knowledge. The Mathematics Educator, 17(2), 7-14. Retrieved from http://math.coe.uga.edu/tme/issues/v17n2/v17n2_Carson.pdf

Douville, P. and Pugalee, D. (2003). Investigating the Relationship between Mental Imaging and Mathematical Problem Solving. The Mathematics Education into the 21st Century Project. Brno, Czech Republic.

Farooq, M.S. and Shah, S.Z.U. (2008). Students' Attitude towards Mathematics. Pakistan Economic and Social Review, 46(1), 75-83.

Gray, B. (2012, December). Motivation and Study, Not IQ, Are Keys to Kids' Math Success. U.S. News & World Report. Retrieved from http://search.proquest.com/docview/1272284071?accountid=139409.

Hembe Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety. Journal for Research in Mathematics Education, 21(1), 33-46. Retrieved May 2013, from http://www.jstor.org/stable/749455 Jaszdzewski, K. (2011). Attitudes about Mathematics: Compare and Contrast Boys and Girls from High and Low Socio-Economic Status. California State University, Chico: Master's thesis. Kadijevich, D. (2008). TIMSS 2003: Relating Dimensions of Mathematics Attitude to Mathematics Achievement. Зборник Института за педагошка истраживања, 40(2), 327-346. doi:10.2298/ZIPI0802327K

Kalder, R. and Lesik, A. (2011, December). A classification of attitudes and beliefs towards mathematics for secondary mathematics pre-service teachers and elementary pre-service teachers: An exploratory study using latent class analysis. IUMPST: The Journal, 5. Retrieved from www.k-12prep.math.ttu.edu

Kelley, T. and Hill, R. (2007, January 1). Cognitive Processes of Students Solving Technical Problems. Retrieved from http://digitalcommons.usu.edu: http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1008&context=ncete_cstudies

Kelley, T. and Hill, R. (2007). Cognitive Processes of Students Solving Technical Problems. DigitalCommons@USU. Retrieved January 9, 2013, from http://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=1008&context=ncete_cstudies

Kidd, J. (2003). The Effects of Relational Teaching and Attitudes on Mathematics Anxiety. Retrieved January 9, 2013, from http://repository.lib.ncsu.edu/ir/bitstream/1840.16/973/1/etd.pdf

Kleanthous, I. and Williams, J. (2010). Perceived parental influence on students’ mathematical achievement, inclination to mathematics and dispositions to study further mathematics. In M. a. Joubert (Ed.), British Congress for Mathematics Education.

Lowrie, T. (2004). Authentic problem solving: The influence of cultural artefacts on sense making. Problem solving in mathematics education. Refereed Proceedings of the Problem Solving Topic Study Group (TSG, 18) of the International Congress of Mathematics Education. Copenhagen, Denmark.

Lowrie, T. and Clancy, S. (2003). Multimodal texts: Numeracy development in naturalistic learning contexts. Referred Proceedings of the Annual Australian Association for Research in Education Conference, Auckland, New Zealand.

Lyons, I.M. and Beilock, S.L. (2012). When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math. doi:10.1371/journal.pone.0048076

Ma, X. and Kishor, N. (1997). Assessing the Relationship between Attitude toward Mathematics and Achievement in Mathematics: A Meta-Analysis. Journal for Research in Mathematics Education, 28(1), 26-47. Retrieved from http://www.jstor.org/discover/10.2307/749662?uid=3738824&uid=2129&uid=2&uid=70&uid=4&sid=21101752854197

Martin, R. (2002). Math Attitudes of Gifted Students: A Focus on Gifted Girls in the Elementary Grades. Virginia Beach, Virginia. http://scholar.lib.vt.edu/theses/available/etd-11302002-174715/unrestricted/Dissertation-Martin.pdf

Middleton, J.A. and Spanias, P.A. (1999). Motivation for Achievement in Mathematics: Findings, Generalizations, and Criticisms of the Research. Journal for Research in Mathematics Education, 30(1), 65-88.

Milne, L. (1992). Bridging Mathematics Students: Attitudes, Autonomous Learning Behaviours, and Problem Solving. La Trobe University College of Northern Victoria.

Miserandino, M. (1996). Children Who Do Well in School: Individual Differences in Perceived Competence and Autonomy in Above-Average Children. Journal of Educational Psychology, 88(2), 203-214.

Molleker, J. (2000). Parent attitudes and student attitudes toward mathematics. Retrieved from http://www.fhsu.edu/: http://contentcat.fhsu.edu/cdm/singleitem/collection/thesis/id/2040/rec/2

NCTM. (n.d.). Retrieved from www.nctm.org: http://www.nctm.org/standards/content.aspx?id=26860

Nicolaidou, M. and Philippou, G. (2003). Attitudes towards Mathematics, Self-Efficacy, and Achievement in Problem-Solving. Retrieved January 23, 2013, from http://www.dm.unipi.it: http://www.dm.unipi.it/~didattica/CERME3/proceedings/Groups/TG2/TG2_nicolaidou_cerme3.pdf

Norton, S. and Rennie, L. (1998). Students' Attitudes towards Mathematics in Single-Sex and Coeducational Schools. Mathematics Educational Research Journal, 10(1), 16-36.

Orongan, R. (2007). Structural Model of Cognitive, Affective and Demographic Factors on Tertiary Students' Performance in Introductory Statistics at Central Mindanao University, Bukidnon, Philippines. Central Mindanao University, Musuan, Bukidnon: Unpublished Dissertation.

Oszoy, G. and Ataman, A. (March 2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education.

Ozsoy, G., Memis, A. and Temur, T. (2009, October). Metacognition, study habits and attitudes. International Electronic Journal of Elementary Education, 2(1). Retrieved from http://www.iejee.com/2_1_2009/ozsoy.pdf

Pradeep, R. (n.d.). A Study of Mathematics Anxiety Amongst Primary Pre-service Teachers enrolled in a Dutch Teacher Training Program. Universiteit Van Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.

Prado, N. (1995). An Evaluation of the Fourth Year Secondary School Mathematics Program in Mindanao. University of the Philippines, Diliman, Quezon City: Unpublished dissertation.

Preston, P. (1986, June). Math Anxiety: Relationship with Sex, College Major, Mathematics Background, Mathematics Achievement, Mathematics Performance, Mathematics Avoidance, Self-Rating of Mathematics Ability, and Self-Rating of Mathematics Anxiety as Measured by the Revised Math. Retrieved from http://trace.tennessee.edu: http://trace.tennessee.edu/utk_graddiss/1252

Pritchard, R. (2004). Investigating Parental Attitudes and Beliefs in Mathematics Education. Mathematics education for the third millennium: towards 2010: proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia.

Pugalee, D. (2004). A Comparison of Verbal and Written Descriptions of Students' Problem Solving Processes. Educational Studies in Mathematics, 55(1/3), 27-47. Retrieved from http://www.jstor.org/stable/4150301.

Raghunathan, R. and Pham, M. (1999, July). All Negative Moods Are Not Equal: Motivational Influences of Anxiety and Sadness on Decision Making. Retrieved from http://www.columbia.edu: http://www.columbia.edu/~tdp4/OBHDP1999A.pdf

Scarpello, G. (2005). The Effect of Mathematics Anxiety on the Course and Career Choice of High School Vocational-Technical Education Students. Retrieved January 12, 2013, from http://dspace.library.drexel.edu/bitstream/1860/492/8/Scarpello_Gary.pdf

Skaalvik, S. and Skaalvik, E.M. (2004, February). Gender Differences in Math and Verbal Self-Concept, Performance Expectations, and Motivation. Sex Roles, 50(3/4).

Stankov, L. Morony, S. and Ping, L.Y. (2011). Confidence and Self-monitoring. SingTeach, 5-7. Retrieved May 2013, from http://s3.amazonaws.com/academia.edu.documents/30683277/SingTeach_Issue29_Web.pdf?AWSAccessKeyId=AKIAIR6FSIMDFXPEERSA&Expires=1368259265&Signature=agfySfotj1138h9Z61dOHINTkSw%3D

Stillman, G. and Galbraith, P. (1998, July). Applying mathematics with real world connections: metacognitive characteristics of secondary students. Educational Studies in Mathematics, 36(2), 157-194. Retrieved May 2013, from http://link.springer.com/article/10.1023%2FA%3A1003246329257

Tan, DA and Limjap, AA. (2018). Filipino Students’ Use Of Metacognitive Skills In Mathematical Problem Solving: An Emergent Model. International Journal for Development Research, 8(5), 20430-20439.

Tocci, C. a. (1991, May - June). Achievement, Parental Support, and Gender Differences in Attitudes toward Mathematics. The Journal of Educational Research, 84(5), 280-286.

Visser, D. (1987). The Relationship of Parental Attitudes and Expectations to Children's Mathematics Achievement Behaviour. The Journal of Early Adolescence, 1-12.

Vygotsky, L. (1987). Thinking and speech. In R. R. Carton, The Collected Works of L.S. Vygotsky (pp. 39-243).

Widmeyer Research & Polling. (2009). Attitudes toward Math and Science Education among American Students and Parents: Summary of Findings. Widmeyer Research & Polling.

Yara, P. (2009). Students Attitude towards Mathematics and Academic Achievement in Some Selected Secondary Schools in South-western Nigeria. European Journal of Scientific Research, 36(3), 336-341. Retrieved from http://www.eurojournals.com/ejsr.htm

Yee, L. (2010). Mathematics Attitudes and Achievement of Junior College Students in Singapore. Retrieved January 25, 2013, from http://www.merga.net.au: http://www.merga.net.au/documents/MERGA33_Lim.pdf

Yeo, J. (2004). Do High Ability Students Have Mathematics Anxiety? Journal of Science and Mathematics Education in S.E. Asia, 27(2), 135-152. Retrieved from http://www.recsam.edu.my/R%26D_Journals/YEAR2004/jour04no.2/joseph(135-152).pdf

Yong, H.T. and Kiong, L.N. (n.d.). Metacognitive Aspect of Mathematics Problem Solving. MARA University of Technology, Malaysia. Retrieved from http://www.ccs.neu.edu/home/lieber/courses/material s/MetaCognitive.doc

DOI: http://dx.doi.org/10.46827/ejes.v0i0.1814

### Refbacks

- There are currently no refbacks.

Copyright (c) 2018 Conrado Ares Duque Jr, Denis Abao Tan

This work is licensed under a Creative Commons Attribution 4.0 International License.

Copyright © 2015-2021. **European Journal of Education Studies** (ISSN 2501 - 1111) is a registered trademark of **Open Access Publishing Group**. All rights reserved.

This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).