Knowledge Connectedness in Geometry Problem Solving

A cluster analysis data classification technique was used on assessment scores from 157 undergraduate nursing students who passed 2 successive compulsory courses in human anatomy and physiology. Student scores in five summative assessment tasks, taken in each of the courses, were used as inputs for a cluster analysis procedure. We aimed to group students into high-achieving (HA) and low-achieving (LA) clusters and to determine the ability of each summative assessment task to discriminate between HA and LA students. The two clusters identified in each semester were described as HA (n = 42) and LA (n = 115) in semester 1 (HA1 and LA1, respectively) and HA (n = 91) and LA (n = 42) in semester 2 (HA2 and LA2, respectively). In both semesters, HA and LA means for all inputs were different (all P < 0.001). Nineteen students moved from the HA1 group into the LA2 group, whereas 68 students moved from the LA1 group into the HA2 group. The overall order of importance of inputs that determined group membership was different in semester 1 compared with semester 2; in addition, the within-cluster order of importance in LA groups was different compared with HA groups. This method of analysis may 1) identify students who need extra instruction, 2) identify which assessment is more effective in discriminating between HA and LA students, and 3) provide quantitative evidence to track student achievement.

A group of seventh- and eighth-grade Italian students with low achievement (LA) in learning English as a foreign language (FL) was selected and compared to a group with high achievement (HA) in FL learning. The two groups were matched for age and nonverbal intelligence. Two experiments were conducted to examine the participants' verbal and nonverbal learning skills, such as native language reading accuracy, speed and comprehension, calculation, and attention and self-regulation. Both experiments showed that the LA group seemed at risk for reading comprehension difficulties, but its reading speed and accuracy were within the average range according to Italian norms. The results also excluded the possibility that FL learning difficulties of LA participants could be associated with a deficit in calculation. Furthermore, according to teachers' ratings, children with LA appeared at risk for attention-deficit disorder (ADD). The pattern of learning difficulties of seventh- and eighth-grade participants with LA appeared to be not completely comparable with that of high school students at risk of FL learning difficulties as described in the literature.

Individual and longitudinal differences among high and low-achieving, LD, and ADHD L2 learners

Equity in education is a key concern internationally; however, it is rare that this issue is examined separately for low- and high-achieving students and concurrently across different subject domains. This study examines student and school background characteristics associated with low and high achievement in mathematics and science on the Programme for International Student Assessment. Based on the results of a multilevel multinomial model of achievement for each domain, findings indicate that a greater number of the variables examined are associated with low rather than high achievement. At student level, home language, intention to leave school early, socioeconomic status, grade level, cultural capital, and books in the home are significantly associated with achievement in mathematics and science. At school level, only school average socioeconomic status is statistically significant in the models. Significant gender differences are found in the distribution of high and low achievers, which vary across the domains. In mathematics, females are more likely to be low achievers while males are more likely to be high achievers. In science, gender interacts with early school-leaving intent whereas males intending to leave school early are more likely to be in the low-achieving group than females intending to leave early. Conclusions emphasise the need for targeting resources aimed at promoting equity in outcomes at student level as well as at school level. Future work may extend the current analyses by incorporating domain-specific variables or examining cross-country differences.

Geometry problem solving is a long-standing problem in artificial intelligence. The task requires generating explainable solving sequences based on text and diagram descriptions. Existing approaches have made great progress in geometry formal language extraction and interpretable solving. However, they neglect the graph structure information in formal language. This leads to poor prediction effect of the theorem, and too long reasoning time for problem solving and affects the accuracy of problem solving. In this paper, we construct the formal language graph and use a graph convolutional network to encode structure information of formal language. We propose an improved diagram parser for better diagram relation set extraction. The experimental results show that our method achieves better performance in interpretable geometry problem solving.

Children with mathematical difficulties usually have an impaired ability to process symbolic representations. Functional MRI methods have suggested that early frontoparietal connectivity can predict mathematic achievements; however, the study of brain connectivity during numerical processing remains unexplored. With the aim of evaluating this in children with different math proficiencies, we selected a sample of 40 children divided into two groups [high achievement (HA) and low achievement (LA)] according to their arithmetic scores in the Wide Range Achievement Test, 4th ed.. Participants performed a symbolic magnitude comparison task (i.e. determining which of two numbers is numerically larger), with simultaneous electrophysiological recording. Partial directed coherence and graph theory methods were used to estimate and depict frontoparietal connectivity in both groups. The behavioral measures showed that children with LA performed significantly slower and less accurately than their peers in the HA group. Significantly higher frontocentral connectivity was found in LA compared with HA; however, when the connectivity analysis was restricted to parietal locations, no relevant group differences were observed. These findings seem to support the notion that LA children require greater memory and attentional efforts to meet task demands, probably affecting early stages of symbolic comparison.

Differences in measures of self-esteem and anxiety between children from three ethnic subgroups in each of three upper elementary grades, who had been divided by placing high or low on scores on tests of reading achievement, arithmetic achievement, and scholastic aptitude, were studied. In contrast to previous findings by Frerichs (1971), no self-esteem differences were noted in high vs. low reading achievement groups of Black children. Self-esteem and anxiety differences between subsamples of high vs. low achievement and of high vs. low scholastic aptitude were inconsistent across ethnic groups. Sample characteristics, differences in conditions for instrument administration, and varying child-adult relationships were suggested as possible sources of influences upon the findings.

Despite problem solving being a core skill in chemistry, students often struggle to solve chemistry problems. This difficulty may arise from students trying to solve problems through memorising algorithms. Goldilocks Help serves as a problem-solving scaffold that supports students through structured problem solving and its elements, such as planning and evaluation. In this study, we investigated how first-year chemistry students solved problems, when taught with Goldilocks Help, and whether their problem-solving success and approaches changed over the course of one semester. The data comprised of student written problem-solving work, and was analysed using frequency analysis and grouped based on the problem-solving success and the extent of the demonstrated problem-solving elements. Throughout the course of semester, students exhibited increasingly consistent demonstration of structured problem solving. Nonetheless, they encountered difficulties in fully demonstrating such aspects of problem solving as understanding and evaluating concepts, which demand critical thinking and a firm grasp of chemistry principles. Overall, the study indicated progress in successful and structured problem solving, with a growing proportion of students demonstrating an exploratory approach as time progressed. These findings imply the need for incorporation of metacognitive problem-solving scaffolding, exposure to expert solutions, reflective assignments, and rubric-based feedback into wide teaching practice. Further research is required to extend the exploration of the effectiveness of metacognitive scaffolding, in particular via think-aloud interviews, which should help identify productive and unproductive uses of the problem-solving elements.

Based on preliminary study data at Yadika 8 Jatimulya Vocational School, it was found that mathematics scores, especially in understanding and solving geometric problems, were still low. This information was obtained through documentation studies and interviews with mathematics teachers in class X majoring in AKL-1, who revealed students' difficulties in understanding and solving geometry problems. Even after the material and examples have been taught, students still experience difficulties when faced with new questions with changes in numbers and question patterns. Their ability to analyze story problems and picture questions and relate them to objects around them is also relatively low. In response to these findings, this research aims to describe the spatial abilities of students who have visual, auditory and kinesthetic learning styles. This research is entitled "Analysis of Spatial Visual Ability in Solving Geometry Problems in View of the Learning Style of Class X Students of Vocational School Yadika 8 Jatimulya" and applies descriptive research methods with a qualitative approach. Research subjects were selected using a purposive sampling technique, namely with certain considerations after giving a learning style questionnaire to all class X students at SMK Yadika 8 Jatimulya. One class was selected that had students with three different learning styles: visual, auditory, or kinesthetic. Next, students were given a written test on flat-sided spatial figures to measure their spatial abilities, and unstructured interviews were used as a data collection method. The results showed variations in students' visual spatial abilities based on their learning styles. Students with a visual learning style have good abilities in imagination, concepts, problem solving, and searching for visual patterns. Students with an auditory learning style have good abilities in concepts and problem solving, although their imagination is less strong. Students with a kinesthetic learning style seem to face difficulties in all aspects of visual-spatial abilities. In addition, the test results show that the majority of students have a moderate level of visual spatial ability. They are able to understand geometric concepts and apply them well, but there are some students who show low visual spatial abilities that require further attention. The research results also revealed a correlation between students' learning styles and their visual spatial abilities. Students with a visual learning style tend to have higher visual-spatial abilities than students with an auditory or kinesthetic learning style. This highlights the importance of understanding students' learning styles in designing effective learning strategies. Overall, this research emphasizes the importance of visual spatial abilities in solving geometric problems and the influence of students' learning styles on these abilities. This has important implications in developing learning strategies that suit individual student learning styles, especially in the context of learning geometry at SMK Yadika 8 Jati Mulya. Teachers can utilize the results of this research to design more effective learning approaches and increase the potential of each student.

Evidence on the effects of task interactivity and grade level on thinking skills involved in complex problem solving

Eight mountaineers were placed in a hypobaric chamber to simulate oxygen depletion accompanying a mountain ascent. The aim was to examine the evolution of individual and group efficiency in problem solving and anxiety according to simulated altitude. Relationships within the group, state and trait anxiety, and individual and collective performance in problem solving were repeatedly assessed at simulated altitudes of 5000m, 6000m, 7000m, and 8000m. The decrease of individual performance in problem solving, shown to be simultaneous to the increase of state anxiety, had little effect on collective performance in problem solving. These results suggest (a) that the collective success could be due to the emergence of a positive common goal and a positive appraisal of the situation and (b) that the state anxiety could act as a mediator between the variation in altitude and its effects on individual performance. The relevance of these results to real mountaineering expeditions is discussed.

We investigated the types of help that students request while solving math problems under the tutelage of an adult. One hundred eighteen third and sixth graders, classified as high, medium, and low math achievers and working under one of two academic goal conditions (i.e., either learning or performance goals), were asked to solve inductive reasoning problems. Students were encouraged to request whatever information they felt they needed. We found that sixth graders, in comparison with third graders, were more likely to ask for process-related hints and less likely simply to ask for the answer or express a vague lack of understanding. Students given learning goals, in comparison with those given performance goals, were more likely to request confirmation of an answer and less likely to show maladaptive patterns of questioning. Performance goals had a strong, detrimental effect on the number of problems that low achievers solved. Relations among goals, prior math achievement, help seeking, and problem-solving performance were examined.

This paper presents an end-to-end deep learning method to solve geometry problems via feature learning and contrastive learning of multimodal data. A key challenge in solving geometry problems using deep learning is to automatically adapt to the task of understanding single-modal and multimodal problems. Existing methods either focus on single-modal or multimodal problems, and they cannot fit each other. A general geometry problem solver should obviously be able to process various modal problems at the same time. In this paper, a shared feature-learning model of multimodal data is adopted to learn the unified feature representation of text and image, which can solve the heterogeneity issue between multimodal geometry problems. A contrastive learning model of multimodal data enhances the semantic relevance between multimodal features and maps them into a unified semantic space, which can effectively adapt to both single-modal and multimodal downstream tasks. Based on the feature extraction and fusion of multimodal data, a proposed geometry problem solver uses relation extraction, theorem reasoning, and problem solving to present solutions in a readable way. Experimental results show the effectiveness of the method.

Close links between children's capacities to store and manipulate information over brief periods have been found with achievements on standardised measures of vocabulary, language comprehension, reading, and mathematics. The study aimed to investigate whether working memory abilities are also associated with attainment levels in the national curriculum assessments at 7 years of age. Eighty-three children aged 6 and 7 years attending local education authority schools participated in the study. Working memory skills were assessed by a test battery designed to tap individual components of Baddeley and Hitch's (1974) working memory model. Children were assigned to normal and low achievement groups on the basis of their performance on national curriculum tasks and tests in the areas of English and mathematics. Children with low levels of curriculum attainment showed marked impairments on measures of central executive function and of visuo-spatial memory in particular. A single cut-off score derived from the test battery successfully identified the majority of the children failing to reach nationally expected levels of attainment. Complex working memory skills are closely linked with children's academic progress within the early years of school. The assessment of working memory skills may offer a valuable method for screening children likely to be at risk of poor scholastic progress.

본 연구는 종합적 사고력과 지식탐구역량이 대학생의 학업성취에서 차이를 보이는지 확인하고자 하였다. 이를 위해 충청북도 소재 K대학교 재학생 349명을 대상으로 학업 고성취집단과 저성취집단을 구분하고, 집단 간 잠재평균의 차이를 검증하였다. 종합적 사고력과 지식탐구역량 요인들(목표설정, 학습몰입, 과제수행, 학업성찰, 학습전략)을 잠재변인으로 하여 구조방정식모형의 잠재평균분석을 실시하였다. 분석 절차에 따라 측정모형의 형태 동일성, 측정 동일성, 절편 동일성 등을 검증한 결과, 학업 고성취집단과 저성취집단의 측정모형은 모두 적합도가 수용 가능한 수준으로 나타났다. 동일성 검증에 따라 학업 저성취집단을 참조집단으로, 고성취집단을 측정집단으로 잠재평균을 비교하였다. 그 결과, 학업 고성취집단은 6가지 요인 모두 저성취집단과 유의한 차이를 보였다. Cohen의 효과크기를 보면 과제수행과 학습몰입은 .90 이상으로 차이가 컸으며, 학습전략, 학업성찰, 종합적 사고력 등은 .60 이상을, 목표설정은 .49로 중간수준의 효과크기를 나타냈다. 이러한 연구결과를 바탕으로 대학생의 학업성취에 필요한 학습 방안을 제언하고, 후속 연구에 대한 제언을 논의하였다.The purpose of this study was to determine whether the comprehensive thinking ability and knowledge exploration capability showed differences in the academic achievement of college students. For this purpose, 349 students at K University in Chungcheongbuk-do were divided into high and low achievement groups, and the difference in latent mean among the groups was examined. The latent mean analysis of the structural equation model was conducted with the factors of comprehensive thinking ability and knowledge exploration capability(target setting, learning commitment, task performance, academic reflection, learning strategy) as latent variables. According to the analysis procedure, the model identity, measurement identity, and section identity of the measurement model were verified. According to the test of equality, latent mean were compared with the low achievement group as the reference group and the high achievement group as the measurement group. As a result, all six factors showed significant difference from the low achievement group. According to Cohen s effect size, task performance and learning commitment differed more than .90, and learning strategy, academic reflection, and comprehensive thinking were above .60, and goal setting was .49. On the basis of these findings, the study suggested a study plan for college students’ achievement and discussed suggestions for subsequent research.