Efficacy Beliefs, Problem Posing, and Mathematics Achievement

By Nicolaou, Aristoklis A.; Philippou, George N. | Focus on Learning Problems in Mathematics, Fall 2007 | Go to article overview
Save to active project

Efficacy Beliefs, Problem Posing, and Mathematics Achievement


Nicolaou, Aristoklis A., Philippou, George N., Focus on Learning Problems in Mathematics


Abstract

Perceived self-efficacy beliefs have been found to be a strong predictor of mathematical performance while problem posing is considered fundamental in mathematical learning. In this study we examined the relation among efficacy in problem posing, problem-posing ability, and mathematics achievement. Quantitative data were collected from 176 fifth and sixth grade students, and interview data from six students selected on the basis of hierarchical cluster analysis. Students' perceived efficacy to construct problems was found to be a strong predictor of the respective performance as well as of the general mathematics achievement. A strong correlation was also found between ability in problem posing and general mathematics performance. The students constructed problems of greater variety and complexity on the basis of informal tasks rather than on the basis of formal tasks. Significant differences were found in problem posing ability, between fifth and sixth grade students. The findings provide support to earlier studies indicating the predictive power of context-specific efficacy beliefs. Implications are drawn about strategies for enhancing students' efficacy beliefs and problem-posing ability.

Theoretical Background and Aims

Research on mathematics teaching and learning has recently focused on affective variables, which were found to play an essential role that influences behavior and learning (Bandura, 1997). The affective domain is a complex structural system consisting of four main components: emotions, attitudes, beliefs, and values (Goldin, 2002). Beliefs can be defined as one's subjective knowledge, theories, and conceptions and include whatever one considers as true knowledge, although he or she cannot provide convincing evidence to support it (Pehkonen, 2001). Self-beliefs can be described as one's beliefs regarding personal characteristics and abilities and include dimensions such as self-concept, self-efficacy, and self-esteem. Self-efficacy can be defined as "one's belief that he/she is able to organize and apply plans in order to achieve a certain task" (Bandura, 1997, p. 3). This study focuses on self-efficacy of primary students with respect to problem posing.

Self-efficacy is a task-specific construct and there is a correspondence between self-efficacy beliefs and the criterial task being assessed; in contrast, self-concept is the sense of ability with respect to more global goals (Pajares, 2000; Bandura, 1986), while self-esteem is a measure of feeling proud about a certain trait, in comparison with others (Klassen, 2004; Bong & Skaalvik, 2003). The task-specificity of efficacy beliefs implies that related studies are more illuminating when they refer to certain tasks, such as problem posing; the predictive power of self-efficacy is in this case maximized (Pajares & Schunk, 2002). On the other hand, the level of specificity could not be unlimited; as Lent and Hackett (1987) have rightly observed, specificity and precision are often purchased at the expense of practical relevance and validity.

The construct self-efficacy is tightly connected to motivation and plays a prominent role in human development since it directly influences behavior. According to Bandura's social cognitive theory, every individual possess a system that exerts control on his/her thoughts, emotions and actions. Among the various mechanisms of human agency, none is more central or pervasive than self-efficacy beliefs (Bandura & Locke, 2003; Pajares, 2000).

Research on self-efficacy has recently been accumulated providing among other things notable theoretical advances that reinforce the role attributed to this construct in Bandura's social cognitive theory. Several studies have indicated a strong correlation between mathematics self-efficacy and mathematics achievement (Klassen, 2004). It was further found that mathematics self-efficacy is a good predictor of mathematics performance irrespective of the indicators of performance (Pajares, 1996; Bandura, 1986) and regardless of any other variables (Bandura & Locke, 2003; Pajares & Graham, 1999).

The rest of this article is only available to active members of Questia

Sign up now for a free, 1-day trial and receive full access to:

  • Questia's entire collection
  • Automatic bibliography creation
  • More helpful research tools like notes, citations, and highlights
  • Ad-free environment

Already a member? Log in now.

Notes for this article

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
Loading One moment ...
Project items
Notes
Cite this article

Cited article

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited article

Efficacy Beliefs, Problem Posing, and Mathematics Achievement
Settings

Settings

Typeface
Text size Smaller Larger
Search within

Search within this article

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

While we understand printed pages are helpful to our users, this limitation is necessary to help protect our publishers' copyrighted material and prevent its unlawful distribution. We are sorry for any inconvenience.
Full screen

matching results for page

Cited passage

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

Cited passage

Welcome to the new Questia Reader

The Questia Reader has been updated to provide you with an even better online reading experience.  It is now 100% Responsive, which means you can read our books and articles on any sized device you wish.  All of your favorite tools like notes, highlights, and citations are still here, but the way you select text has been updated to be easier to use, especially on touchscreen devices.  Here's how:

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select.

OK, got it!

Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.

For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

Already a member? Log in now.

Are you sure you want to delete this highlight?