A Multivariate Model of Achievement in Geometry

Abstract

Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among variables linked to successful problem solving in geometry. These variables, including motivation, achievement emotions, pictorial representation, and categorization skills, were examined for their influence on geometry achievement. Results indicated that the model fit well. Achievement emotions, specifically boredom and enjoyment, had a significant influence on student motivation. Student motivation influenced students' use of pictorial representations and achievement. Pictorial representation also directly influenced achievement. Categorization skills had a significant influence on pictorial representations and student achievement. The implications of these findings for geometry instruction and for future research are discussed.

Cognitive appraisals, achievement emotions, and students’ math achievement: A longitudinal analysis.

“…In accordance with theoretical assumptions and prior empirical evidence (e.g., Hagenauer & Hascher, 2014;Pekrun et al, 2011), our cross-sectional analyses revealed positive relations between appraisals (i.e., perceived control and perceived positive value) and enjoyment. Conversely, and also in line with previous research (e.g., Bailey et al, 2014;Pekrun et al, 2011), perceived control and perceived positive value were negatively related to anger and boredom. For anger, these results suggest that CVT could be amended by considering the relevance of lack of control for students' anger in the classroom, and by addressing the mitigating impact of positive value.…”

Teaching Geometry to Students With Learning Disabilities: Introduction to the Special Series

“…Identified cognitive factors include spatial abilities (Clements et al, 1997; Geary, 1996; Jeung et al, 1997; Kyttälä & Lehto, 2008; Purcell & Gero, 1998; Spelke et al, 2010; Verstijnen et al, 1998), fluid intelligence and reasoning skills (Battista, 1990; Dawkins, 2015; Giofrè et al, 2014), working memory (Giofrè et al, 2013, 2014), geometry content knowledge (Bokosmaty et al, 2015; Lawson & Chinnappan, 1994), and meta-cognition (Aydın & Ubuz, 2010). In addition, motivation, persistence, and student emotions (e.g., boredom and enjoyment) are frequently cited to interpret students’ geometry learning difficulties and individual differences (Bailey et al, 2014; Super & Bachrach, 1957). Some pedagogical variables also have been documented, such as the geometry curriculum (Battista & Clements, 1995; Clements & Battista, 1986; Halat et al, 2008; Oner, 2008), teachers’ instructional approaches (Kuzniak & Rauscher, 2011), and task complexity level (Hsu & Silver, 2014).…”

“…Third, female students generally have lower self-efficacy in mathematics domains, including geometry (Erdoğan et al, 2011; Erkek & Işiksal-Bostan, 2015; Louis & Mistele, 2012). Female students with lower self-efficacy are less motivated and perseverant in solving geometry problems in test settings where motivation significantly influences geometry achievement (Bailey et al, 2014).…”

Students With Specific Difficulties in Geometry: Exploring the TIMSS 2011 Data With Plausible Values and Latent Profile Analysis

“…In particular, because geometry includes considerable proof-oriented problems, it is typically considered highly related to the deductive thinking (Dawkins, 2015) and verbal logical reasoning (Battista, 1990). Geometry learning difficulties can also be related to non-cognitive factors, including motivation and persistence (Nichols, 1996), emotions (Bailey et al, 2014), meta-cognition abilities (Aydın & Ubuz, 2010), knowledge (Bokosmaty et al, 2015), and how they use knowledge (Lawson & Chinnappan, 1994). And these non-cognitive problems universally exist in all mathematical domains for struggling students, which also challenges the hypothesis that geometry difficulties should be viewed as a specific and unique subtype of math learning difficulty.…”