Effects of Classroom Structure on Student Achievement Goal Orientation

Abstract

The authors assessed how classroom structure influenced student achievement goal orientation for mathematics. Three elementary school classes were assigned randomly to 1 classroom structure condition: token economy, contingency contract, or control. Students in each condition were required to set individual achievement goals on a weekly basis. The authors assessed differences in goal orientation by comparing the number of learning vs. performance goals that students set within and across classroom structure conditions. Results indicated that students in the contingency-contract condition set significantly more learning goals than did students in other classroom structure conditions. No significant differences were found for performance goals across classroom structure conditions. Within classroom structure conditions, students in the contingency-contract group set significantly more learning goals than performance goals, whereas students in the token-economy condition set significantly more performance goals than learning goals.     

What factors support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience?

There is an acknowledged gap between the theory presented in university preparation programmes and the reality of classroom practice that has resulted in many secondary mathematics pre-service teachers failing to implement university-endorsed teaching strategies. Using responses to a questionnaire and interviews, this qualitative study examined the factors that support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience. The results showed that even though the majority of pre-service teachers reported having beliefs compatible with using problem-solving tasks, the secondary students’ ability, preparation time, and the cooperating teacher were key factors that inhibited pre-service teachers’ implementation of problem-solving tasks. It is recommended that pre-service teachers regularly visit classrooms to observe the evolving implementation of problem-solving approaches. Furthermore, cooperating teachers should be required to attend professional development before the professional experience so they understand the goals of the university preparation programme and have the requisite skills and knowledge to support the implementation of problem-solving tasks in learning mathematics.     

Educational Aims,Ideals, and Activities

Abstract

The effects on student performance and student attitudes of varying the instructional locus of control between students and teachers were investigated. A 2 X 2 factorial design was used that included either teacher regulation or student regulation of 1) the setting of weekly learning goals, and 2) the evaluation of weekly work. After a 4-week period, a mathematics achievement test and a student attitude survey were administered. Results indicated that although teachers set more individual learning goals for students, students who set their own learning goals attained more of them. Students tended to evaluate their work more favorably than teachers, and work evaluations from both teachers and students were higher for students who initially set their own learning goals. In addition, students who were given the opportunity to set their own learning goals reported better goal-setting ability than those for whom goals were externally imposed by the teacher. As predicted, the self-regulated goal setting and evaluation were found to be significantly related to attitudes, but not to mathematics achievement.     

Personal best goals and academic and social functioning: A longitudinal perspective

Personal best goals (PB goals) articulate a target performance standard that matches or exceeds one’s previous best. This study examined the role of PB goals in academic and social functioning. Alongside academic and social outcome measures, PB goal items were administered to 249 high-school students at the beginning and end of their school year. Longitudinal structural equation modeling suggested, at Time 1, PB goals significantly predicted students’ deep learning, academic flow, academic buoyancy, positive teacher relationship, and favorable attitudes toward peer cooperation. Further, at Time 2, the effects of PB goals on deep learning, academic flow, and positive teacher relationship remained significant after controlling for prior variance of corresponding Time-1 factors, suggesting sustained benefits of PB goals in students’ academic and social development. These findings hold substantive, applied, and methodological implications for researchers and practitioners seeking to examine and harness PB goals in educational settings.     

Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.

     

The relation between teacher-set performance goals and students’ mathematical achievement

The relation between teacher-set performance goals for 361 individual students and these students’ mathematics achievement was investigated. High performance goals were found to strongly relate to student performance, with an effect size of d = 0.80. The performance goals were set by the teachers at the end of a step-by-step procedure, consisting of initial teacher expectations, the use of data, and team input. This procedure was expected to decrease negative expectancy bias. Higher teacher performance goals than teachers’ initial expectations, so-called positive changes, were positively associated with the performance of initially low achievers. Initially high achievers, for whom the teachers made a positive change, performed worse than comparable students for whom initial expectation and final goal were the same.     

Students’ Motivation in the Mathematics Classroom. Revealing Causes and Consequences

Students’ affective domain has been popular in the mathematics education community in an ongoing attempt to understand students’ learning behavior. Specifically, enhancing students’ motivation in the mathematics classroom is an important issue for teachers and researchers, due to its relation to students’ behavior and achievement. This paper utilized achievement goal theory—an important theoretical prospect on students’ motivation in school settings—to investigate the existence of a model presenting the relation between motivation and other affective constructs and students’ performance in mathematics. In this regard, two types of tests were administered to 321 sixth grade students measuring their motivation and other affective constructs and their performance in mathematics. Using structural equation modeling, we examined the associations among the affective constructs, motivation, and the extent to which these constructs influence students’ performance and interest in mathematics. The data revealed that students’ performance and their interest in mathematics were influenced by fear of failure, self-efficacy beliefs, and achievement goals. We discuss these findings in terms of teaching implications in the mathematics classroom.     

Student perceptions of the classroom environment: Relations to motivation and achievement in mathematics

This study examined the relationship of 979 middle school students’ perceptions of their mathematics classroom environment to their motivation and achievement. Structural equation modeling indicated that motivational variables (utility, personal achievement goals, efficacy) mediated the influence of perceived teacher expectations, teacher support and use of reform practices on mathematics standardised test scores. Our study provides empirical evidence that students’ perceptions that their teachers believe that they are capable of learning and understanding mathematics positively relate to their Mastery and Performance Goal orientations and mathematics Utility. Further, we found an interaction between students’ perceptions of the frequency of reform practice use in their mathematics classroom and mathematics efficacy. For students with lower mathematics efficacy, their perceptions of more frequent use of reform practices in their mathematics class related to higher standardised test performance. For students with higher mathematics efficacy, perceived use of reform practices did not significantly relate to standardised test performance. These data suggest that frequent exposure to reform practices is especially critical for students who judge themselves as being less capable in mathematics and who are lower performers. This finding differs from prior research that has suggested that reform practice use benefits higher achievers but not lower achievers. An important implication of our study is the need for coordinated, ongoing professional development that highlights reform pedagogy and beliefs while also focusing on student motivation theories and strategies.     

Classroom effect on primary school students’ self-concept in literacy and mathematics

According to the big-fish-little-pond effect (BFLP) model, high individual academic performance in a particular subject is related to high self-concept in that subject, whereas high average classroom performance has a negative effect on self-concept. In the present study, data from Finnish primary school students in grade 3 (504 students), grade 4 (487 students), and grade 6 (365 students) are used to examine whether the assumptions of the BFLP effect model hold already in primary school. Furthermore, we examined gender differences in BFLP effect. The results showed that as expected students’ high performance in literacy and in mathematics was related to high self-concept in the same subject. Support for the negative classroom effect was small and it depended on the school subject and student’s gender. That is, a high average classroom performance already in grade 3 had a negative but small effect on boys’ self-concept in mathematics. In literacy and among girls, only little support was found for the negative classroom effect.

     

An example of the use of dynamic mathematics software to create problem-solving environments that serve multiple purposes

Problem-solving is regarded as a major component of mathematical performance, and well-designed problem-solving-based learning environments have the potential to assist students in developing a meaningful understanding of mathematical concepts and procedures. In this respect, given its various features, dynamic mathematics software has been regarded by mathematics educators as a promising tool for designing such environments. This study presents an example of the use of technology to create a dynamic learning environment through a discussion of the pedagogical value of a problem selected for an activity, followed by the implementation sequence of the problem-solving activity in the classroom. The students’ experiences during the implementation of the activity are also discussed; and finally, an additional version of the problem is recommended for use in the classroom.     

中学数学协同阅读学习方略研究

通过调研可知,中学生的数学阅读、分析、解决问题的能力有待提高,可将协同阅读运用到数学阅读中来,从激活相关信息、加强迁移能力和注重整体协同三个方面定义了数学协同阅读学习策略,然后通过实验,分阶段让学生进行协同阅读的运用,由此学生学会了运用数学协同阅读,并提高了学生的分析能力、迁移能力、想象能力,以及自主学习能力与解题效率。     

Writing about personal goals and plans regardless of goal type boosts academic performance

Academic underachievement is a problem for both our education system and general society. Setting personal goals has the potential to impact academic performance, as many students realize through reflection that studying is a path towards realizing important life goals. Consequently, the potential impact of a brief (4–6 h), written, and staged personal goal-setting intervention on undergraduate academic performance (earned European Credit Transfer and Accumulation System credits) was investigated. Using a time-lagged quasi-experimental design, our model was tested with two first-year university goal-setting cohorts and two control cohorts (total n = 2928). The goal-setting cohorts (n = 698 and 711) showed a 22% increase in academic performance versus the control cohorts (n = 810 and 707). This increase depended on (1) the extent of participation in the 3-stage goal-setting intervention, (2) number of words written in the exercise, and (3) the specificity of students’ goal-achievement plans (GAP). Contrary to goal-setting theory, which necessitates goal-task specificity, the results revealed that it did not matter whether the students wrote about academic or non-academic goals, or a combination of both. Rather, it appeared to be the overall process of writing about their personal goals, the specificity of their strategies for goal attainment, and the extent of their participation in the intervention that led to an increase in their academic performance. This study suggests an important modification to goal-setting theory, namely a potential contagion effect of setting life goals, an academic goal primed in the subconscious, and subsequent academic performance.     

“Bigger number means you plus!”—Teachers learning to use clinical interviews to understand students’ mathematical thinking

This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, Human Development 52:109–128, 2009) to understand students’ mathematical thinking. This study challenged teachers’ pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students’ knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students’ ideas and connect informal or invented strategies with classroom mathematics.     

The Enactment and Perception of Mathematics Pedagogical Values in an Elementary Classroom: Buddhism,Confucianism, and Curriculum Reform

The purpose of this case study was to investigate the values demonstrated by an elementary school teacher in her mathematics teaching and what values her students perceived. This research adopted the valuing theory (Raths, Harmin & Simon, 1987) and used classroom observations and interviews to document the teacher’s mathematics pedagogical values and a questionnaire, interviews, and instructional artifacts to document the students’ perceptions of these values. The results of this research identified two educational values and three mathematics pedagogical values that were influenced by the teacher’s personal beliefs about Buddhism, Confucianism, and curriculum. Her goals for education were to reinstate the students’ original enlightenment and the students’ respect for ethics and experts when dealing with people and life; and her values about mathematics learning were that it depends on individual efforts and personal understanding, her central purposes for teaching were to make students understand the mathematics content and to cultivate their problem-solving methods, and her purposes for evaluation were to understand students’ learning and to encourage students to correct their errors. The students’ awareness of these goals and values did not parallel the teacher’s personal priorities. The implications of teachers’ pedagogical values on teacher professional development and curriculum reform are discussed.     

数学课堂教学中数据分析核心素养的培育

培养学生数据分析素养是新时代教学变革对数学教学提出的新要求,同时,在数学课堂教学中培育学生的数据分析核心素养也是新时代教师面临的挑战。21世纪初各国提出的核心素养之一即包括数学与科学技术素养,我国数学课程标准也明确将数据分析列入数学学科核心素养。因此,数据分析的数学课堂教学应突破传统、单一的教学理论与方法,创设新维度的课堂教学及模式。数据分析知识体系是数学课堂教学及其建构的重要载体,建构的基本框架包括问题与情境、材料与数据、活动与经验、知识与技能、理论与方法五个维度。教师应通过数学问题解决教学、数据情境教学、案例式教学、探究式教学与开放式教学、数学思想方法的教学等多元化路径培育学生的数据分析核心素养。     

Students’ Emotions in the High School Mathematical Class: Appraisals in Terms of a Structure of Goals

Little research in the field of Mathematics Education is directed towards emotions of students beyond their emotions in problem-solving. In particular, the daily emotions of students in a mathematics class have been sparsely studied in the field of mathematics education. In order to fill this gap, this qualitative research aims to identify high school students’ emotional experiences in the mathematics classroom and identify the appraisal structures that support such emotional experiences. Focus group interviews were carried out until theoretical saturation of the data was achieved (N = 53 in nine focus groups interviews). Data analysis is based on the theory of cognitive structure of emotions, which specifies eliciting situations for each emotion and the variables that affect intensity. The emotional experiences in this structure are as follows: satisfaction, disappointment, hope, fear, joy, distress, boredom, interest, pride, reproach, self-reproach, like and dislike. These results show that the emotional experiences of students are based on their appraisals of events, objects and agents in terms of a structure of goals.     

浅谈小学数学课堂教学中问题意识的培养

数学既是小学阶段就开始接触的学科,也是对小学生数学思维运用和解题能力要求较高的学科,没有问题可“问”的小学数学课堂无疑是枯燥和无趣的,难以真正实现对小学生思维能力的培养,因此,本文结合目前小学数学课堂出现的问题,探究怎样在小学数学教学中将学生问题意识培养起来。     

Heterogeneity of student perceptions of the classroom climate: a latent profile approach

Student perceptions are a pivotal point of measurement for understanding why classroom learning environments are effective. Yet there is some evidence that student perceptions cannot be reliably aggregated at the classroom level and, instead, could represent idiosyncratic experiences of students. The present study examines whether heterogeneity in student perceptions of the classroom climate has implications for student achievement. We use data from 1428 seventh grade students in 75 mathematics classrooms from the Michigan Study of Adolescent and Life Transitions. Three dimensions of student perceptions of the classroom were measured: emotional support, autonomy support and performance focus. To obtain a measure of heterogeneity, we first reduced the data using latent profile analysis to describe profiles of students’ perceptions of the classroom. Next, we quantified the heterogeneity of student perceptions within classrooms using Simpson’s D. Classroom-level heterogeneity (Simpson’s D) of students’ perceptions was negatively associated with students’ mathematics achievement, even after controlling for individual- and classroom-level previous achievement, student’s prior perceptions and other variables. Findings suggest that measures of heterogeneity in student perceptions might be important for understanding classroom- and teacher-level effects on student outcomes.     

四大能力统领下的高中数学高效课堂构建研究

改变传统的教学观念,创新教学方法、教学模式,构建高效课堂成为当务之急。文章以构建高中数学高效课堂为目的,从培养学生的认知能力、创新能力、合作能力、职业能力等方面,探究构建高中数学高效课堂的有效途径,以培养学生的数学素养和数学能力,提升高中数学课堂教学的质量与效率。