Deborah Stipek

Teachers’ beliefs and practices related to mathematics instruction

Abstract Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners.

Children's Beliefs about Intelligence and School Performance.

The study was designed, first, to explore associations among childrens beliefs about intelligence and effort, goal orientations, self-reported learning strategies, and academic achievement. Assessments of all variables were conducted twice over 1 school year on 319 children in Grades 3-6. Results indicated that the belief that intelligence is relatively fixed was associated with the beliefs that performance is relatively stable and that intelligence is global in its effects on performance. This set of beliefs was differentiated from the belief that effort has positive effects on intelligence and performance. Childrens beliefs in intelligence as fixed and affecting performance were negatively associated with academic achievement, but a path analysis provided only modest support for the hypothesis that the effect of such beliefs would be mediated by a performance goal orientation and accompanying superficial learning strategies.

Perceived Personal Control and Academic Achievement

Perceived control of events is one motivational variable that appears to affect children’s academic achievement. In this review the conceptualization and measurement of the control dimension is discussed from three theoretical perspectives: social learning theory, attribution theory, and intrinsic motivation theories. For each of these three perspectives evidence on the relationship between achievement and perceptions of control is summarized, and possible explanations for the relationship are discussed. Throughout this review similarities and differences among these orientations are pointed out. Specific recommendations are made for research which will advance our understanding of this relationship and which will provide the most useful information to educators.

Economically Disadvantaged Preschoolers: Ready to Learn but Further to Go.

Cognitive competencies and motivation were assessed in 233 preschool and kindergarten children in the fall and again in the spring. Cognitive assessments were given again in the spring of the following year (kindergarten or 1st grade) to a subsample of 88 children. The results revealed much poorer performance among the economically disadvantaged children compared with advantaged children on all 8 of the cognitive tests. For most cognitive measures, gains were roughly equal and the socioeconomic status (SES) differences at the end of 1 or 2 years in school were similar to the differences at the beginning of the year. Only a few SES differences were found on the motivation measures assessing childrens self-confidence, attitude toward school, expectations for success, dependency, and preference for challenge; they did not systematically favor either disadvantaged or advantaged children. Classroom observations revealed some differences in disadvantaged and advantaged childrens classroom behavior.

Gender differences in children's achievement-related beliefs and emotional responses to success and failure in mathematics.

A sample of 194 3rd graders and 279 junior high school students completed questionnaires measuring achievement-related beliefs before and after they took a regularly scheduled mathematics exam. Girls rated their ability lower, expected to do less well, were less likely than boys to attribute success

Promoting Conceptual Thinking in Four Upper-Elementary Mathematics Classrooms.

Informed by theory and research in inquiry-based mathematics, this study examined how classroom practices create a press for conceptual learning. Using videotapes of a lesson on the addition of fractions in 4 primarily low-income classrooms from 3 schools, we analyzed conversations that create a high or lower press for conceptual thinking. We use examples of interactions from these fourth- and fifth-grade lessons to propose that a high press for conceptual thinking is characterized by the following sociomathematical norms: (a) an explanation consists of a mathematical argument, not simply a procedural description; (b) mathematical thinking involves understanding relations among multiple strategies; (c) errors provide opportunities to reconceptualize a problem, explore contradictions in solutions, and pursue alternative strategies; and (d) collaborative work involves individual accountability and reaching consensus through mathematical argumentation.

Competence, contingency, and the development of perceived control.

In an effort to learn how perceived internal control changes with age, 33 developmental studies using 12 different locus of control (LOC) scales are surveyed. A few studies show developmental declines in perceived control, about half show consistent developmental increases, and about half show mixed results or no significant developmental differences. A critical examination of the LOC scales reveals that some developmental findings may be artifacts of scale characteristics, and that others may reflect developmental effects on constructs other than perceived control. Most importantly, the scales and the LOC literature fail to distinguish clearly betwen two dimensions of perceived control that may show quite different patterns of developmental change. These dimensions are perceived contingency of outcomes and perceived competence of self; combined, they form a simple but potentially powerful conceptual framework for theory and research on the development of perceived control. The explanatory power of this framework is briefly illustrated, relevant evidence is surveyed, and embryonic proposals are advanced for the study of perceived contingency and competence independently and in interaction.

Good Beginnings: What difference does the program make in preparing young children for school?

Cognitive competencies and motivation were assessed at the beginning and the end of the year for 228 preschoolers and kindergartners and again at the end of the next year (kindergarten or first grade) for 93 of the participants. Participants were in classrooms classified as either emphasizing basic skills in a less positive social climate or de-emphasizing basic skills in a more positive social climate. Cognitive competencies were assessed with two achievement tests (one for letters/reading and another for numbers/math) and six subscales from the McCarthy test. Motivation (perceptions of competence, attitudes toward school, anxiety, affect, risk taking, expectations for success, independence, and persistence) was assessed in an experimental setting and by observing childrens behavior in their classroom. The results showed primarily negative effects on both cognitive and motivation outcomes of preschool programs emphasizing basic skills using structured, teacher-directed approaches in a relatively negative social climate. For kindergartners both positive and negative achievement and motivation outcomes were associated with both types of classrooms.

Self-Concept Development in the Toddler Years.

This study was designed to determine groupings of behaviors asociated with self-concept development in toddlers and the sequence in which groups of behaviors appear. Mothers of 123 toddlers of ages 14 to 40 months reported on the presence of 25 behaviors associated with the self.

No Child Left Behind Comes to Preschool

In this article I examine recent policy initiatives related to early childhood education that can be traced either directly to No Child Left Behind (NCLB) or to the emphasis on standards and accountability that produced NCLB, including the development of standards and assessments and moving the birth date for kindergarten eligibility to require children to be older when they enter school. I also discuss instructional and assessment issues that need to be considered if new pressures to teach academic skills in preschool benefit rather than do harm to young children.