Cognitive Development of College Students and their Achievement in Geometry: An Evaluation using Piaget’s Theory and Van Hiele’s Levels of Thinking

Abstract

The study evaluated the cognitive development levels of college students and their achievement in Geometry using Piaget's Test of Logical Operations and Van Hiele's Levels of Thinking. The researcher employed quantitative approach to research. There were 105 respondents in which 71 of them fit the Van Hiele modified case/criterion (M3) 3 of 5 correct answers. Findings revealed that most of the college students were identified as concrete operational thinkers using Piaget's theory of concrete and formal operations who possessed the levels of classification, seriation and transitivity. Using Van Hiele's levels of thinking, most of them were classified as holistic thinkers. Students whose ages ranging from 20 years old and up were performing better in Geometry as compared to the other age brackets. It also revealed that male students were performing better than female students. In the cognitive development levels using Piaget's theory on concrete and formal operations, there is a significant difference when grouped according to age and year levels but found a non-significant difference when grouped according to sex. Significant positive relationships revealed among Van Hiele's levels of thinking, Piaget's theory of concrete and formal operations and Geometry achievement test. Van Hiele's levels of deductive and rigorous thinking and Piaget's levels of transitivity, proportionality and correlation are significant predictors in the achievement of students in Geometry. This implies further that to be successful in learning Geometry and mathematics in general, a college student must reach Van Hiele' level 3 -deductive thinking and Piaget's level 3 -transitivity.

Cognitive Skills Achievement in Mathematics of the Elementary Pre-Service Teachers Using Piaget’s Seven Logical Operations

“…With these results, the three respondents committed minor mistakes and were expected to be able to deal with and perform higher order of difficulty. The results of this study negated the study of [19], [22], [12], and [21] were the result of their studies were alarming to reveal that most of their respondents were considered at the concrete operational stage. This study apparently sounded positive since the majority (52 or 59.09%) were able to perform the logical operations.…”

A critical perspective in terms of SOLO taxonomy for reading outcomes in mother-tongue teaching curriculums (1981, 2006 and 2019) in Turkey

“…The relational level stands out for its dominance in each curriculum. All of the curriculums can be characterized by transitivity in terms of cognitive operations; however, proportionality and correlation did not seem to be included (Decano, 2017). In addition, the transitions among class levels did not show gradual advancement gradually regarding cognitive operations, as also stated by Gezer and İlhan (2015).…”

“…This taxonomy stands out among the others because it functions parallel to Piaget's cognitive development stages, is similar to the PISA reading competency levels (Li, Gao & Cao, 2011), and yields higher rates of generalizability and reliability than the revised Bloom taxonomy does in determining cognitive levels (Hattie & Purdie, 1994;Ilhan & Gezer, 2017;Meagher-Lundberg & Brown, 2001). Biggs & Collis, 1982, p.24-25;Decano, 2017;Fusco, 1983, p.55 andLi et al, 2011. As can be seen in Table 2, it can be inferred that students take the PISA exams after they have completed the late concrete stage and switched to the formal operations stage. This means that students taking this exam can perform cognitive operations such as giving names and seriation as well as identifying the relationships among components in a context-in other words, the relationships between elements that make up the whole (for example, thoughts in a paragraph, messages and supplementary messages in a text, words forming a text, word groups, and phrases), the variables that validate/do not validate an assumption, and even the proportional variations in independent texts.…”

Cognitive Abilities in Mathematical Problem Solving of Future Elementary Teachers: A Causal-Comparative Research

“…Several types of research were performed to assess mathematical cognitive abilities (Leongson & Limjap, 2003;Gamit, 2010;Pagay, 2008;Decano, 2017). In a study of cognitive abilities of college freshmen conducted by Leongson and Limjap (2003) and Gamit (2010), they discovered that freshmen fell into the concrete operational level, contrary to Piaget's belief that these college freshmen aged 16-19 years could perform logical operations with mastery.…”

“…Both studies reported a troubling finding: students had an adequate understanding of problems involving logical multiplication but an inadequate understanding of problems involving the other six logical operations. Decano (2017) also looked into the cognitive ability of college students, finding that the vast majority of them are at the concrete operational level. Furthermore, Domingo (2018) found that the results of the same analysis in Grade 12 Senior High School students were consistent with the findings of Leongson and Limjap (2003), Gamit (2010), andDecano (2017).…”