“I think I can,but I'm afraid to try”: The role of self-efficacy beliefs and mathematics anxiety in mathematics problem-solving efficiency

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for mathematics, before completing an operation span task to measure working memory capacity, rating self-efficacy for mental multiplication, and then solved computer-based multiplication problems at two complexity levels. A simultaneous regression design was used to assess the unique variance associated with each variable. There were two new findings; the differential role of self-efficacy on response time and efficiency, and the potential compensatory relationship between self-efficacy and mathematics anxiety related to efficiency outcomes. Educational implications and suggestions for future research were proposed.     

The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency

A regression design was used to test the unique and interactive effects of self-efficacy beliefs and metacognitive prompting on solving mental multiplication problems while controlling for mathematical background knowledge and problem complexity. Problem-solving accuracy, response time, and efficiency (i.e. the ratio of problems solved correctly to time) were measured. Students completed a mathematical background inventory and then assessed their self-efficacy for mental multiplication accuracy. Before solving a series of multiplication problems, participants were randomly assigned to either a prompting or control group. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy and attributions to metacognitive strategy use are related to more efficient problem solving. Findings suggested that self-efficacy and metacognitive prompting increased problem-solving performance and efficiency separately through activation of reflection and strategy knowledge. Educational implications and future research are suggested.     

The effects of informational complexity and working memory on problem-solving efficiency

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of thesituational efficiency hypothesis, which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity affects problem-solving efficiency. A second prediction is that working memory capacity affects problem-solving efficiency. Students completed a working memory task and solved abstract and concrete syllogisms. Participants solved abstract syllogisms more accurately than concrete syllogisms and spent more time solving abstract syllogisms. Thus participants demonstrated greater problem-solving efficiency when solving concrete syllogisms. Results indicate that there is a trade-off between problem-solving accuracy and problem-solving time when information differs with respect to informational complexity, a phenomenon we refer to as theefficiency paradox. Working memory capacity did not affect accuracy or efficiency. The results support the conclusion that problem-solving efficiency is situational and a function of the complexity of information. Educational implications and directions for future research are suggested.     

Effects of different sequences of examples and problems on motivation and learning

Recent research has shown that example study only (EE) and example-problem pairs (EP) were more effective (i.e., higher test performance) and efficient (i.e., attained with less effort invested in learning and/or test tasks) than problem-example pairs (PE) and problem solving only (PP). We conducted two experiments to investigate how different example and problem-solving sequences would affect motivational (i.e., self-efficacy, perceived competence, and topic interest) and cognitive (i.e., effectiveness and efficiency) aspects of learning. In Experiment 1, 124 technical students learned a mathematical task with the help of EEEE, EPEP, PEPE, or PPPP and then completed a posttest. Students in the EEEE Condition showed higher posttest performance, self-efficacy, and perceived competence, attained with less effort investment, than students in the EPEP and PPPP Condition. Surprisingly, there were no differences between the EPEP and PEPE Condition on any of the outcome measures. We hypothesized that, because the tasks were relevant for technical students, starting with a problem might not have negatively affected their motivation. Therefore, we replicated the experiment with a different sample of 81 teacher training students. Experiment 2 showed an efficiency benefit of EEEE over EPEP, PEPE, and PPPP. However, only EEEE resulted in greater posttest performance, self-efficacy, and perceived competence than PPPP. We again did not find any differences between the EPEP and PEPE Condition. These results suggest that, at least when short training phases are used, studying examples (only) is more preferable than problem solving only for learning. Moreover, this study showed that example study (only) also enhances motivational aspects of learning whereas problem solving only does not positively affect students’ motivation at all.     

Understanding metacognitive inferiority on screen by exposing cues for depth of processing

Paper-and-pencil learning and testing are gradually shifting to computerized environments. Cognitive and metacognitive researchers find screen inferiority compared to paper in effort regulation, test performance, and extent of overconfidence, in some cases, with unknown differentiating factors. Notably, these studies used reading comprehension tasks involving lengthy texts, which confound technology-related and cognitive factors. We hypothesized that the medium provides a contextual cue which leads to shallower processing on screen regardless of text length, particularly when task characteristics hint that shallow processing is legitimate. To test this hypothesis, we used briefly phrased yet challenging problems for solving on screen or on paper. In Experiment 1, the time frame for solving the problems was manipulated. As with lengthy texts, only time pressure resulted in screen inferiority. In Experiment 2, under a loose time frame, the same problems were now framed as a preliminary task performed before a main problem-solving task. Only the initial task, with reduced perceived importance, revealed screen inferiority similarly to time pressure. In Experiment 3, we replicated Experiment 1's time frame manipulation, using a problem-solving task which involved reading only three isolated words. Screen inferiority in overconfidence was found again only under time pressure. The results suggest that metacognitive processes are sensitive to contextual cues that hint at the expected depth of processing, regardless of the reading burden involved.     

Gender Differences in Eye Movements in Solving Text-and-Diagram Science Problems

The main purpose of this study was to examine possible gender differences in how junior high school students integrate printed texts and diagrams while solving science problems. We proposed the response style hypothesis and the spatial working memory hypothesis to explain possible gender differences in the integration process. Eye-tracking technique was used to explore these hypotheses. The results of eye-movement indices support the response style hypothesis. Compared to male students, female students spent more time and displayed more fixations in solving science problems. The female students took more time to read the print texts and compare the information between print-based texts and visual-based diagrams more frequently during the problem-solving process than the male students. However, no gender differences were found in the accuracy of their responses to the science problems or their performances in the spatial working memory task. Implications for psychological theory and educational practice are discussed.

     

Writing in Early Adolescence: A Review of the Role of Self-Efficacy Beliefs

This review examines and summarizes 16 research studies examining the writing self-efficacy beliefs of 6th- to 10th-grade students. In the majority of the studies, self-efficacy was found to play a primary role in predicting student writing performance. Students with learning disabilities were found to over-estimate their ability to complete specific writing tasks. Several studies found gender differences, with boys rating their confidence higher than girls, although actual performance did not differ. Grade-level differences in perceived efficacy for writing were found in some studies, but not in others. Most studies emphasized that those working with young adolescents need to be aware of the importance of self-efficacy and other motivational beliefs in conjunction with academic functioning. Difficulties with specificity of self-efficacy measures, and with correspondence between measure and criterial task were found in several studies. The article concludes with suggestions for future self-efficacy research.     

Gender Differences in Eye Movements in Solving Text-and-Diagram Science Problems

The main purpose of this study was to examine possible gender differences in how junior high school students integrate printed texts and diagrams while solving science problems. We proposed the response style hypothesis and the spatial working memory hypothesis to explain possible gender differences in the integration process. Eye-tracking technique was used to explore these hypotheses. The results of eye-movement indices support the response style hypothesis. Compared to male students, female students spent more time and displayed more fixations in solving science problems. The female students took more time to read the print texts and compare the information between print-based texts and visual-based diagrams more frequently during the problem-solving process than the male students. However, no gender differences were found in the accuracy of their responses to the science problems or their performances in the spatial working memory task. Implications for psychological theory and educational practice are discussed.     

Approach to mathematical problem solving and students’ belief systems: two case studies

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between specific beliefs and problem-solving activity (or vice versa).     

The relation between students’ motivational beliefs and their use of motivational regulation strategies

The goal of this study was to investigate the relation between a set of pre-decisional beliefs including students’ task value, self-efficacy, and learning and performance goal orientations and five post-decisional, implementation strategies students use to regulate their effort and persistence for the academic tasks assigned for a specific class. A group of eighth grade students (N=114) completed a self-report survey that assessed these four motivational beliefs and the frequency that they used five motivational regulation strategies including self-consequating, environmental control, interest enhancement, and mastery and performance self-talk. Results from a series of multiple regressions indicated that the motivational beliefs, as a group, could be used to explain students’ reported use of each of the regulatory strategies examined. Further, results indicated that task value, learning goal orientation, and performance goal orientation individually explained three or more of the regulatory strategies, whereas self-efficacy was not related significantly to any of the five regulatory strategies studied. Findings are presented and interpreted in light of their significance for models specifying both motivational and volitional aspects of self-regulation.     

Inhibitory control and visuospatial working memory contribute to 5-year-old children's use of quantitative inversion

This study examined the hypothesis that general cognitive resources moderated 5-year-old children's performance differences between the Concrete Identical and the Pure Quantity conditions on inversion problems (a + b – b) but not on standard problems (a + b – c). Study 1 (N = 104) showed that children who experienced higher visuospatial working memory burden performed significantly poorer in solving the inversion problems in the Pure Quantity condition than in the Concrete Identical condition, whereas those who experienced lower working memory burden showed no such difference. Study 2 (N = 194) demonstrated that children with lower levels of inhibitory control solved significantly fewer inversion problems in the Pure Quantity condition than in the Concrete Identical condition, whereas no such difference was found in children with higher levels of inhibitory control. These findings suggest that inhibitory control and visuospatial working memory may support children's use of quantitative inversion.     

MOTIVATIONAL BELIEFS AND LEARNING STRATEGIES IN ORGANIC CHEMISTRY

Students enter college chemistry courses with different sources of motivation, appropriate or inappropriate assumptions about their probability of success and how to study. This study is theoretically aligned with self-regulated learning research. Clearly, academic performance is closely related to student motivational beliefs and learning strategies. This study investigated the motivational beliefs and learning strategies of 2 years of college students in the second semester of organic chemistry. Responses to the Motivational Beliefs and Learning Strategies Questionnaire indicated that student self-efficacy was highly correlated with academic performance (semester grades). Gender differences were quite pronounced. Male academic performance was associated with intrinsic motivation as well as the importance placed on the learning task. Test anxiety was negatively associated with male grades. Extrinsic motivation was negatively correlated with female grades. Responses to students’ sense of control over learning, the value of the learning task, and self-efficacy were significantly higher for males compared to females. Faculty who attend to these different patterns may influence beliefs as well as learning strategies. Correcting erroneous assumptions about how to learn chemistry may help students shift both their attitudes and their learning practices. The notable gender difference suggests that female chemistry students may especially profit from focused faculty intervention.     

Prediction of learning and comprehension when adolescents read multiple texts: the roles of word-level processing, strategic approach, and reading motivation

Sixty-five Norwegian 10th graders used the software Read&Answer 2.0 (Vidal-Abarca et al., 2011) to read five different texts presenting conflicting views on the controversial scientific issue of sun exposure and health. Participants were administered a multiple-choice topic-knowledge measure before and after reading, a word recognition task, and a reading motivation inventory that included two dimensions: Science reading self-efficacy, focusing on readers’ beliefs about their capabilities to comprehend what they read in science, and science reading task value, focusing on readers’ beliefs about how important, useful, and interesting it is to comprehend science texts. In addition, strategic reading pattern was assessed in terms of the degree of non-linear reading behavior. Multiple regression analysis showed that word recognition skills strongly predicted learning from the texts, as assessed by participants’ increase in topic knowledge. However, when multiple-text comprehension indicated by performance on open-ended short-essay questions was the dependent variable, not only word recognition but also strategic reading pattern and science reading self-efficacy emerged as unique predictors when topic knowledge was controlled for. Science reading task value was not related to performance. This study provides new evidence that new literacy competencies needed in a knowledge society, such as synthesizing or integrating across multiple conflicting sources of information, still largely involve word-level, strategic, and motivational processes that may profitably be targeted through systematic instruction.     

Influence of motivational beliefs and strategies on recall task performance in elementary, middle and high school students

In the present study, we propose a model describing how motivational beliefs and strategies influence study performance of students at three different school levels: elementary (age 8-10), middle (11-14), and first year high school (15). Participants were administered the AMOS 8-15 instrument (Cornoldi et al. 2005) designed for measuring the influence of motivational beliefs and strategies on recall task performance. Results of multigroup analysis confirmed the relations proposed in our model between motivational beliefs and strategies for all three groups, the largest difference being in how these aspects influenced performance on recall tasks: in elementary and middle school, motivational beliefs have direct influence on performance, whereas in high school they influence performance through strategy use.     

Construction play and cognitive skills associated with the development of mathematical abilities in 7-year-old children

Construction play is thought to develop logico-mathematical skills, however the underlying mechanisms have not been defined. In order to fill this gap, this study looks at the relationship between Lego construction ability, cognitive abilities and mathematical performance in 7-year-old, Year 2 primary school children (N = 66). While studies have focused on the relationship between mathematics performance and verbal memory, there are limited studies focussing on visuospatial memory. We tested both visuospatial and verbal working memory and short term memory, as well as non-verbal intelligence. Mathematical performance was measured through the WIAT-II numerical operations, and the word reading subtest was used as a control variable. We used a Lego construction task paradigm based on four task variables found to systematically increase construction task difficulty. The results suggest that Lego construction ability is positively related to mathematics performance, and visuospatial memory fully mediates this relationship. Future work of an intervention study using Lego construction training to develop visuospatial memory, which in turn may improve mathematics performance, is suggested.     

Online or face-to-face learning? Exploring the personal factors that predict students' choice of instructional format

Notwithstanding the growth of online learning, little is known about the personal factors that predict student decisions to enroll in online courses. This study examined the relations between several personal factors and students' choice of instructional format. After completing an online course, service academy undergraduates (N = 564) completed a survey that assessed their motivational beliefs (task value and self-efficacy), achievement-related emotions (enjoyment, boredom, and frustration), and satisfaction with the course. Results indicated that students who preferred to take future courses in an online format (as opposed to face-to-face) also reported greater confidence in their ability to learn online (self-efficacy) and greater satisfaction with their recent online learning experience. Logistic regression analysis confirmed and extended these findings, indicating that membership in the online preference group was predicted by higher self-efficacy and satisfaction, and lower task value beliefs. Taken together, results from this study provide researchers and practitioners with a better understanding of how several personal factors relate to students' choice of instructional format.     

Testing interest and self-efficacy as predictors of academic self-regulation and achievement

We examined whether individual interest, as an affective motivational variable, could predict academic self-regulation and achievement, above and beyond what academic self-efficacy predicted. We tested the relationships between academic self-efficacy, individual interest, grade goals, self-regulation, and achievement of Korean middle school students (N = 500) in four different subject areas. Consistent with previous findings, self-efficacy predicted achievement both directly and indirectly via grade goals. Self-efficacy also predicted self-regulation, but only when grade goals mediated the relationship. Supporting our hypothesis, individual interest functioned as a correlated yet independent and direct predictor of self-regulation. It also predicted achievement, but only when self-regulation mediated the relationship. We thus suggest that academic self-regulation could be encouraged through the promotion of two distinct motivational sources, academic self-efficacy and individual interest. We further suggest that the pathways linking individual interest to academic self-regulation and achievement may differ from those linking academic self-efficacy to the same variables.     

Working memory performance of Italian students with foreign language learning difficulties

It has been suggested that the ability to learn a foreign language is related to working memory. However, there is no clear evidence about which component of working memory may be involved.Two experiments investigated working memory problems in groups of seventh and eighth grade Italian children with difficulties in learning English as a second language. They were compared with control groups of children matched for age, education, school, and intelligence who differed for foreign language learning ability.Experiment 1 focused on clarifying how modality-specific the memory problem of children with a foreign language learning difficulty (FLLD) is. Verbal working memory tasks (forward and backward digit span) were proposed together with visuospatial working memory (VSWM) tasks. Groups showed a significant difference only in the more passive verbal working memory task, that is, the forward digit span.Experiment 2 focused on clarifying how central the verbal working memory problem of students with an FLLD is. A nonword repetition task and an Italian version of the listening span test were proposed. Groups differed significantly in both tasks. However, differences in the listening span test disappeared when nonword repetition performance was partialed out. It was concluded that a difficulty in learning a foreign language is mainly related to the more passive aspects of verbal working memory, typically associated with the articulatory loop.     

Self-efficacy, task complexity and task performance: Exploring interactions in two versions of vocabulary learning tasks

The present study aimed for better understanding of the interactions between task complexity and students?? self-efficacy beliefs and students?? use of learning strategies, and finally their interacting effects on task performance. This investigation was carried out in the context of Chinese students learning English as a foreign language in a university in China. The participants were 78 second-year university students (mean age?=?20.9?years). This study used a repeated-measures design with task complexity as the within-participants factor, and task sequence as the between-participants factor. Results indicated a significant task effect for self-efficacy beliefs and task performance, and a significant interaction effect of sequence with task complexity for learners?? self-efficacy beliefs in learning for both task versions, learners with higher self-efficacy beliefs had better task performances than learners with lower self-efficacy beliefs. The results also revealed a strong correlation between self-efficacy and the use of learning strategies for both tasks.     

Doubling mental rotation scores in high school students: Effects of motivational and strategic trainings

Achievement in mathematics, science, biology, chemistry, and other school subjects requiring abstract reasoning on spatial relationships is favored by mental rotation abilities, that is by the capability to mentally manipulate objects in space. This suggests the need to develop effective trainings aimed at improving mental rotation performance. Previous research focused mostly on practice with spatial tasks. Since motivational beliefs, gender stereotypes and self-confidence can affect performance, this research tested the hypothesis that a training including motivational aspects will be effective as well. Two intervention studies with high school students (n = 122 and n = 70 respectively) confirmed that a three-session-training based on allowing practice in adopting a holistic strategy to solve the mental rotation items or on fostering effective motivational beliefs increased the mental rotation scores up to 1 SD. The discussion focuses on the characteristics of effective trainings aimed at improving mental rotation abilities in high school students.