Exploring senior high school STEM students' critical thinking skills and metacognitive functions in solving non-routine mathematical problems

Date of Publication


Document Type

Master's Thesis

Degree Name

Master of Science in Teaching Major in Mathematics


Br. Andrew Gonzalez FSC College of Education


Science Education

Thesis Adviser

Voltaire M. Mistades

Defense Panel Chair

Minie Rose C. Lapinid

Defense Panel Member

Maricar S. Prudente
Antriman V. Orleans
Voltaire M. Mistades


The study explored the levels of critical thinking skills and patterns of metacognitive functions of Senior High School STEM students in solving non-routine mathematical problems. It sought to investigate, describe and analyze the grade 12 STEM students' (1) level of critical thinking skills in terms of (a) interpretation, (b) analysis, (c) evaluation, (d) inference, (e) explanation, (f) overall level of critical thinking skills, (2) pattern of metacognition exhibited by the students in the context of frequency of metacognitive functions, and (3) relationship between the levels of critical thinking skills and the patterns of metacognitive functioning in solving non routine mathematical problems. Data were gathered from eight grade 12 STEM students of Pitogo High School during the second semester of school year 2017-2018.

This study employed a mixed methods multiple case study approach and generated a rich account of students' level of critical thinking skills and patterns of metacognitive functions, both qualitatively and quantitatively. The students' levels of critical thinking skills were determined by a close examination and analysis of the written responses on Critical Thinking Skills Activity Sheets and transcripts of semi structured interview. A critical thinking in non-routine mathematical problem solving rubric made by the researcher and benchmarked on experts' solutions of the five non-routine problems used in the study, was also utilized in evaluating the participants' critical thinking skills. For the students' patterns of metacognitive functions, the transcripts of think-aloud problem solving sessions and the Table for Classifying Metacognitive Functions adopted from Wilson and Clarke's (2002) indicators were used.

Results of the study revealed that the grade 12 STEM students core critical thinking skills namely interpretation, analysis, evaluation, inference and explanation vary depending on the mathematical ability group the students belong. Students who have outstanding mathematical ability generally have strong critical thinking skills in solving non-routine mathematical problems. Students who belong to very satisfactory mathematical ability group exhibited moderate critical thinking skills. Students who have satisfactory and fairly satisfactory levels of mathematical ability exhibited weak critical thinking skills. The study also showed that non-routine mathematical problems can be used as a tool in assessing the students' critical thinking skills.

Furthermore, the study also showed that the grade 12 STEM students tend to be metacognitive evaluative rather than metacognitive regulative. Metacognitive awareness has relative infrequency across students and across problems. Also, the students who manifested strong level of critical thinking skills as they engage in solving non-routine mathematical problems utilized more often metacognitive regulation. The study also validated results of other researches that greater number of metacognitive strategies exhibited does not guarantee high level of performance and critical thinking skills in mathematics.

Among the major recommendations made in this study were the following: curriculum developers and administrators must incorporate the use of non-routine word problems to develop, enhance, assess the critical thinking skills of students. Further study on metacognition focusing on the unproductive aspects of metacognitive behaviors while solving mathematical problems must be done in order to contribute to an improved theory of metacognition.

Abstract Format






Accession Number


Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

1 computer disc ; 4 3/4 in.


High school students--Philippines; Mathematics--Study and teaching; Critical thinking in adolescence; Metacognition

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