Umeå University's logo

In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties.

Need-satisfying experiences corresponding to students' psychological needs of autonomy, relatedness, and competence lead to increased academic engagement and well-being. A lack of education-specific basic needs instruments validated in Swedish may inhibit basic needs research in Swedish-speaking student populations. Thus, the present study aimed to adapt the Need Satisfaction and Frustration Scale (NSFS) to the context of education in Sweden and validate this new Swedish NSFS in a sample of Swedish university students (n = 417, 59.7% women, mean age = 23.3 (SD = 4.3) years). Confirmatory factor analysis was used to investigate the dimensionality of NSFS ratings, followed by structural equation modelling of nomological networks of basic needs, academic engagement, life satisfaction, academic burnout, and perceived stress. The NSFS ratings were best described by a three-factor model with methods correction for reversed item bias. Results showed that each need uniquely contributed to perceived stress and academic burnout. Relatedness and competence, but not autonomy, were significant predictors of life satisfaction and academic engagement. The main study contribution was providing a Swedish NSFS to assess autonomy, relatedness, and competence in higher education. The results support the use of the Swedish NSFS as a three-dimensional measure of basic needs in Swedish-speaking student populations.

The current study assessed reliability and validity evidence of the shortened Swedish Mathematics Anxiety Rating Scale—Elementary (MARS-E), using data from three time points. After initial pilot tests, a total of 429 students participated in the study, completing the MARS-E twice during grade 4 and once during grade 5. Confirmatory factor analyses supported a one-factor structure at each timepoint. The scale displayed both longitudinal and gender measurement invariance across timepoints, ensuring both stability and fairness across gender and time. Factor correlations with criterion variables were examined, revealing a strong correlation between math anxiety (MA) and test anxiety (TA) (r = 0.707). However, the two constructs had distinct relationships to other criterion variables, such as math performance (rma = − 0.343, rta = − 0.110) and self-concept in math (rma = − 0.580, rta = − 0.273). Gender correlations provided evidence of girls being more strongly associated with higher math anxiety scores compared to boys. The current paper provides evidence of the Swedish MARS-E as a valid, easily interpreted, unidimensional instrument for measuring math anxiety in Swedish primary school students. Additionally, the study highlights the gender disparities concerning math anxiety as early as grades 4 and 5.

Retrieval practice is a learning strategy that has repeatedly been found to have positive effects on memory and learning. However, studies indicate that students rarely use retrieval practice on a voluntary basis. The objective of the present study was to examine students’ self-regulated use of retrieval practice, and to determine whether sex and individual differences in cognitive and non-cognitive aspects are related to optional use of practice testing. A classroom study was conducted with 146 upper-secondary school students taking courses in mathematics and Swedish. An ABAB design was used to compare students’ optional and non-optional use of retrieval practice (i.e., repeated online quizzing). Students performed cognitive tasks to assess working memory capacity and fluid intelligence and completed self-reports of non-cognitive factors related to school achievement, such as grit, need for cognition (NFC), conscientiousness and openness. Quiz use was then compared using paired- and independent-samples t-tests, and hierarchical linear regression analyses explored relations to individual differences. The results showed that students completed significantly fewer quizzes in the optional sections than in the non-optional sections, and that females completed significantly more optional quizzes than males in Swedish, but not in mathematics. Further, the results showed that conscientiousness predicted optional quiz use in mathematics, whereas sex, NFC, conscientiousness, and openness predicted quiz use in Swedish. To conclude, although the findings show a relatively low optional/self-regulated use of practice testing, in line with earlier research, they suggest that sex and non-cognitive factors, such as personality characteristics, can predict optional use of practice testing.

The experience of math anxiety can have detrimental effects on students’ math performance, and researchers have in recent years tried to design interventions aiming at reducing math anxiety. This meta-analysis aimed to examine the effectiveness of math anxiety interventions in reducing math anxiety and improving math performance. The meta-analysis comprised 50 studies and included 75 effect sizes. On average, the effect sizes were moderate (g =-0.467) for reducing math anxiety and improving math performance (g = 0.502). Interventions that focused on Cognitive support or regulating Emotions were effective both in reducing math anxiety and improving math performance. In addition, longer interventions and interventions targeting students older than 12 had the biggest decrease in math anxiety. Study quality was not related to intervention outcomes.

Background: Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR.

Methods: We employed a within-subject intervention (N=72, MAge=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high).

Results: On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups.

Conclusions: Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.

A large portion of mathematics education centers heavily around imitative reasoning and rote learning, raising concerns about students’ lack of deeper and conceptual understanding of mathematics. To address these concerns, there has been a growing focus on students learning and teachers teaching methods that aim to enhance conceptual understanding and problem-solving skills. One suggestion is allowing students to construct their own solution methods using creative mathematical reasoning (CMR), a method that in previous studies has been contrasted against algorithmic reasoning (AR) with positive effects on test tasks. Although previous studies have evaluated the effects of CMR, they have ignored if and to what extent intrinsic cognitive motivation play a role. This study investigated the effects of intrinsic cognitive motivation to engage in cognitive strenuous mathematical tasks, operationalized through Need for Cognition (NFC), and working memory capacity (WMC). Two independent groups, consisting of upper secondary students (N = 137, mean age 17.13, SD = 0.62, 63 boys and 74 girls), practiced non-routine mathematical problem solving with CMR and AR tasks and were tested 1 week later. An initial t-test confirmed that the CMR group outperformed the AR group. Structural equation modeling revealed that NFC was a significant predictor of math performance for the CMR group but not for the AR group. The results also showed that WMC was a strong predictor of math performance independent of group. These results are discussed in terms of allowing for time and opportunities for struggle with constructing own solution methods using CMR, thereby enhancing students conceptual understanding.

Purpose: Learning new vocabulary has been identified as a challenge for students with (developmental) language disorder ((D)LD). In this study, we evaluate the effects of two active learning methods, (a) retrieval practice (RP) and (b) rich vocabulary instruction (RVI), in a group of students with (D)LD in secondary school.

Method: A quasi-experimental counterbalanced within-subject design was used to compare and evaluate the effect of RP and RVI on learning Tier 2 vocabulary, with target and control words as dependent measures. Eleven students with (D)LD (Mage = 14.9 years) attending a language unit participated. RP and RVI were implemented in regular classroom activities during 16 lessons (eight lessons/instructional condition). Learning was assessed by comparing performance on a pretest session 1–2 weeks prior, with posttest performance 1 week after each instructional condition.

Results: The learning gain for RP was superior to that for RVI, both with respect to the Bayesian probabilistic estimations for target words relative to control words and in direct comparison with RVI. Only weak evidence was found for RVI with respect to the Bayesian probabilistic estimations for target words relative to control words.

Conclusions: All participants showed positive learning gains following RP,whereas the outcome for RVI was more diverse. This initial work suggests that RP promotes larger learning gains relative to RVI and promotes learning across language profiles. This study extends previous studies by exploring the implementation of RP in regular classroom activities and by using more complex to be-learned material (Tier 2 words).

There is an emerging consensus that retrieval practice is a powerful way to enhance long-term retention and to reduce achievement gaps in school settings. Less is known whether retrieval practice benefits performance in individuals with low intrinsic motivation to spend time and effort on a given task, as measured by self-reported need for cognition (NFC). Here, we examined retrieval practice in relation to individual differences in NFC by combining behavioral and functional magnetic resonance imaging (fMRI) data. Using a within-subject design, upper-secondary school students (N = 274) learned a language-based material (Swahili-Swedish word-pairs), with half of the items by means of retrieval practice with feedback and half by study only. One week later, the students were tested on the word-pairs either in the classroom (n = 204), or in a fMRI scanner (n = 70). In both settings, a retrieval practice effect was observed across different levels of NFC (high or low). Relatedly, comparable fMRI effects were seen in both NFC subgroups. Taken together, our findings provide behavioral and brain-imaging evidence that retrieval practice is effective also for individuals with lower levels of NFC, which is of direct relevance for educational practice.

It is well established that math anxiety has a negative relationship with math performance (MP). A few theories have provided explanations for this relationship. One of them, the Attentional Control Theory (ACT), suggests that anxiety can negatively impact the attentional control system and increase one's attention to threat-related stimuli. Within the ACT framework, the math anxiety (MA)—working memory (WM) relationship is argued to be critical for math performance. The present meta-analyses provides insights into the mechanisms of the MA—MP relation and the mediating role of WM. Through database searches with pre-determined search strings, 1,346 unique articles were identified. After excluding non-relevant studies, data from 57 studies and 150 effect sizes were used for investigating the MA—MP correlation using a random-effects model. This resulted in a mean correlation of r = −0.168. The database search of WM as a mediator for the MA—MP relation revealed 15 effects sizes leading to a descriptive rather than a generalizable statistic, with a mean indirect effect size of −0.092. Overall, the results confirm the ACT theory, WM does play a significant role in the MA—MP relationship.