Notes on a Journal Critique: Mathematics self-efficacy of college freshman

Hall, M. J. & Ponton, M. K. (2005). Mathematics self-efficacy of college freshman. Journal of Developmental Education, 28(3), 27-33.


No topic sentence.

No mention of the statistics used.

No mention of the hypothesis.

Implications mentioned: Focus on developmental maths (DM) teaching test teaching methods --> improved instruction and learning.

Statement of purpose made.

Literature Review

Comprehensive literature review; relevant studies mentioned.

Some studies mentioned were over 10 years old = old data, perhaps not relevant nowadays.

Ability to learn maths --> success --> major chosen--> degree obtained.

Enrolments in developmental classes increasing past 30 years.

Trusty & Niles (2003): High math score high school--> likelihood to obtain Bachelors.

Dorner & Hutton (2002): Supports above: Math most essential to choose major.

Hackett et al. (1990): Math performance + perceived ability (efficacy) --> academic success.

Bandura (1986): Accomplishments + verbal persuasion + vicarious learning + physiology and affect = SE.

Institutions investing money; complementary courses, teachers, resources etc.

Definition of developmental class given, though not near the beginning --> left wondering + vague - function to expand academic skills.

Quality instruction is a priority.

Provided a clear definition of self-efficacy (SE): Personal belief in capability to organise and take action to achieve outcomes.

SE --> choice of academic strategies --> degree of perseverance, effort and achievement in maths.

Thus, low SE --> lack of requisite skills to accomplish maths tasks.

Statement of the Problem

Stated clearly: Large amounts of institutional money invested in developmental courses, how effective are they?

Arendale (2003): Legislation + tertiary boards want to increase accountability.

Significance of the Study

Educators who understand how students cognitively process info --> more effective teaching.

Students believing they cannot control some factors of learning.

Educating students to understand how they learn --> awareness of their potential --> gain confidence in maths to make mistakes and persevere --> success --> more effective professionals in the wider community.

Improve student abilities to identify factors that limit their success in math --> agentic problem-solving --> success in maths.

Student perceptions of ability to excel are critical to their future professional roles.

As motivation + SE increase for students --> success in maths class.

Better teaching and learning practices will support student motivation and development of SE.

Research Questions

Is there a relationship between biopsychosocial development and self-efficacy?

Wheland & Butler (2003): Relationships found between + academic self-concepts + attitudes for success.

Higbee & Thomas (1999): Relationships between maths outcomes + internal factors (e.g., attitudes) and stigma (--> embarrassment).

Not enough known about SE as a mediating factor in student engagement and success with academic maths.


Clear hypothesis: Personal beliefs of ability will inhibit success of students in maths classes.


Self-report questionnaire, the Mathematics SE Scale (MSES; Betz & Hackett, 1983): Measures 2 domains: Using mathematics in everyday tasks, and obtaining a B or more grades in their mathematics course. 34 items, Likert scale 0 - 9, construct validity (r= .56).

Population and sample. Sample reflects important characteristics of the population to be generalised to. A random selection from intact classes --> large sample of calculus and algebra freshman classes; N = 185, females = 100 and males = 85. Selection criteria was not adequately explained, though it was based on ACT scores (Al = <16; Cal = >25).

Research design. Between groups survey design. Independent t-test was suitable because two independent groups completed the survey and the total scores of the survey was a continuous level of measurement.


Normality and homogeneity of variance assumptions were met. Algebra mean = 5.33 and calculus mean = 7.08. Appropriate tests were chosen to test the hypothesis. Significant difference in maths self-efficacy was found, t = 8.902, p<.001. No significant differences were found between genders. Two-way ANOVA using sub-scale scores; no gender main effects or interaction between gender and course enrolment, F = .007, p = .936). A Pearson’s correlation found a moderate positive relationship between maths SE scores and ACT scores (r = .580). Limitations of Study

A limitation section was not included. May be that the the maths classes are different to each other and not comparable. The study did not mention ethnicity of the sample, yet the literature review had noted that minority groups (and females in general) are affected by stigma (Green, 1990).

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