Arithmetic Reasoning Research Articles

Revealing mental representations of arithmetic word problems through false memories: New insights into semantic congruence.

What can false memories tell us about the structure of mental representations of arithmetic word problems? The semantic congruence model describes the central role of world semantics in the encoding, recoding, and solving of these problems. We propose to use memory tasks to evaluate key predictions of the semantic congruence model regarding the representations constructed when solving arithmetic word problems. We designed isomorphic word problems differing only by the world semantics imbued in their problem statement. Half the problems featured quantities (durations, heights, elevator floors) promoting an ordinal encoding, and the other half used quantities (weights, prices, collections) promoting a cardinal encoding. Across three experiments, in French and in English, we used surprise memory tasks to investigate adults' mental representations when solving the problems. After the first solving task, the participants were given an unexpected task: either to recall the problems (Experiments 1 and 2) or to identify, from memory, the experimenter-induced changes in target problem sentences (Experiment 3). Crucially, all problems included a specific mathematical relationship that was not explicit in the problem statement and that could only be inferred from an ordinal encoding. We used the presence or absence of this relationship in the participants' responses to infer the structure of their representations. Converging results from all three experiments bring new evidence of the role of semantic congruence in arithmetic reasoning, new insights into the relevance of the cardinal-ordinal distinction in numerical cognition, and a new perspective on the use of memory tasks to investigate variations in the representations of mathematical word problems. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Correctness Comparison of ChatGPT‐4, Gemini, Claude‐3, and Copilot for Spatial Tasks

ABSTRACTGenerative AI including large language models (LLMs) has recently gained significant interest in the geoscience community through its versatile task‐solving capabilities including programming, arithmetic reasoning, generation of sample data, time‐series forecasting, toponym recognition, or image classification. Existing performance assessments of LLMs for spatial tasks have primarily focused on ChatGPT, whereas other chatbots received less attention. To narrow this research gap, this study conducts a zero‐shot correctness evaluation for a set of 76 spatial tasks across seven task categories assigned to four prominent chatbots, that is, ChatGPT‐4, Gemini, Claude‐3, and Copilot. The chatbots generally performed well on tasks related to spatial literacy, GIS theory, and interpretation of programming code and functions, but revealed weaknesses in mapping, code writing, and spatial reasoning. Furthermore, there was a significant difference in the correctness of results between the four chatbots. Responses from repeated tasks assigned to each chatbot showed a high level of consistency in responses with matching rates of over 80% for most task categories in the four chatbots.

Frugal LMs Trained to Invoke Symbolic Solvers Achieve Parameter-Efficient Arithmetic Reasoning

Large Language Models (LLM) exhibit zero-shot mathematical reasoning capacity as a behavior emergent with scale, commonly manifesting as chain-of-thoughts (CoT) reasoning. However, multiple empirical findings suggest that this prowess is exclusive to LLMs that have exorbitant sizes (beyond 50 billion parameters). Meanwhile, educational neuroscientists suggest that symbolic algebraic manipulation be introduced around the same time as arithmetic word problems so as to modularize language-to-formulation, symbolic manipulation of the formulation, and endgame arithmetic. In this paper, we start with the hypothesis that much smaller LMs, which are weak at multi-step reasoning, can achieve reasonable arithmetic reasoning if arithmetic word problems are posed as a formalize-then-solve task. In our architecture, which we call SyReLM, the LM serves the role of a translator to map natural language arithmetic questions into a formal language (FL) description. A symbolic solver then evaluates the FL expression to obtain the answer. A small frozen LM, equipped with an efficient low-rank adapter, is capable of generating FL expressions that incorporate natural language descriptions of the arithmetic problem (e.g., variable names and their purposes, formal expressions combining variables, etc.). We adopt policy-gradient reinforcement learning to train the adapted LM, informed by the non-differentiable symbolic solver. This marks a sharp departure from the recent development in tool-augmented LLMs, in which the external tools (e.g., calculator, Web search, etc.) are essentially detached from the learning phase of the LM. SyReLM shows massive improvements (e.g., +30.65 absolute point improvement in accuracy on the SVAMP dataset using GPT-J 6B model) over base LMs, while keeping our testbed easy to diagnose and interpret, and within the reach of most researchers.

Turning Dust into Gold: Distilling Complex Reasoning Capabilities from LLMs by Leveraging Negative Data

Large Language Models (LLMs) have performed well on various reasoning tasks, but their inaccessibility and numerous parameters hinder wide application in practice. One promising way is distilling the reasoning ability from LLMs to small models by the generated chain-of-thought reasoning paths. In some cases, however, LLMs may produce incorrect reasoning chains, especially when facing complex mathematical problems. Previous studies only transfer knowledge from positive samples and drop the synthesized data with wrong answers. In this work, we illustrate the merit of negative data and propose a model specialization framework to distill LLMs with negative samples besides positive ones. The framework consists of three progressive steps, covering from training to inference stages, to absorb knowledge from negative data. We conduct extensive experiments across arithmetic reasoning tasks to demonstrate the role of negative data in distillation from LLM.

Maternal prenatal paracetamol ingestion and scholastic attainments of the offspring.

Background: Fetal exposure to paracetamol (acetaminophen) has been shown to be associated with asthma and other atopic disorders, as well as behavioural problems including hyperactivity, in childhood. However, there is little information on scholastic abilities among children exposed to paracetamol in pregnancy. Objectives: To determine whether there are any differences in scholastic abilities among the offspring of women who ingested paracetamol during pregnancy compared with non-exposed children. Methods: Mothers enrolled in the Avon Longitudinal Study of Parents and Children (ALSPAC) had recorded the frequency with which they had taken the medication over two time periods during pregnancy: i) the first 18weeks and ii) 18-32weeks. The offspring have been followed up ever since. For this study we use as outcomes: a) 14 tests of ability at reading and 2 of spelling using the study's tests and the national education system test results; b) 6 of mathematical abilities including tests of arithmetic and mathematical reasoning, and c) 1 of scientific understanding. Multiple regression was used, adjusting for 15 different exposures including reasons for taking the medication as well as demographic features. Results: Almost all unadjusted and adjusted mean differences were negative (i.e., those exposed to maternal intake of paracetamol did less well), but negative associations for exposures between 18 and 32weeks of gestation were much more evident than for exposures earlier in pregnancy. Of the later exposures, after adjustment, 12 of the 23 scholastic tests were associated with prenatal exposure to paracetamol at p < 0.05. These negative effects were found in the girls (12 tests at p < 0.05) but not boys (0 tests at p < 0.05). Conclusion: Evidence from this longitudinal study suggests that maternal exposure to paracetamol is associated with disadvantages to the offspring in scholastic abilities such as mathematics and reading at secondary school ages. This raises the question as to whether there are longer-lasting effects on educational attainment from age 15years onwards, including at university level. Clearly these results should be tested in other settings, but meanwhile they add to a growing accumulation of known adverse effects of exposure to paracetamol in pregnancy.

Exploring the potential of using ChatGPT in physics education

The pretrained large language models have been widely tested for their performance on some challenging tasks including arithmetic, commonsense, and symbolic reasoning. Recently how to combine LLMs with prompting techniques has attracted lots of researchers to propose their models to automatically solve math word problems. However, most research works focus on solving math problems at the elementary school level and few works aim to solve problems in science disciplines, e.g., Physics. In this exploratory study, we discussed the potential pedagogical benefits of using ChatGPT in physics and demonstrated how to prompt ChatGPT in solving physics problems. The results suggest that ChatGPT is able to solve some physics calculation problems, explain solutions, and generate new exercises at a human level.

Interventions to improve equational reasoning: replication and extension of the Cuisenaire-Gattegno curriculum effect.

The ability to reason about equations in a robust and fluent way requires both instrumental knowledge of symbolic forms, syntax, and operations, as well as relational knowledge of how such formalisms map to meaningful relationships captured within mental models. A recent systematic review of studies contrasting the Cuisenaire-Gattegno (Cui) curriculum approach vs. traditional rote schooling on equational reasoning has demonstrated the positive efficacy of pedagogies that focus on integrating these two forms of knowledge. Here we seek to replicate and extend the most efficacious of these studies (Brownell) by implementing the curriculum to a high degree of fidelity, as well as capturing longitudinal changes within learners via a novel tablet-based assessment of accuracy and fluency with equational reasoning. We examined arithmetic fluency as a function of relational reasoning to equate initial performance across diverse groups and to track changes over four growth assessment points. Results showed that the intervention condition that stressed relational reasoning leads to advances in fluency for addition and subtraction with small numbers. We also showed that this intervention leads to changes in problem solving dispositions toward complex challenges, wherein students in the CUI intervention were more inclined to solve challenging problems relative to those in the control who gave up significantly earlier on multi-step problems. This shift in disposition was associated with higher accuracy on complex equational reasoning problems. A treatment by aptitude interaction emerged for both arithmetic equation reasoning and complex multi-step equational reasoning problems, both of which showed that the intervention had greatest impact for children with lower initial mathematical aptitude. Two years of intervention contrast revealed a large effect (d = 1) for improvements in equational reasoning for the experimental (CUI) group relative to control. The strong replication and extension findings substantiate the importance of embedding these teaching aides within the theory grounded curricula that gave rise to them.

Ways of thinking siswa dalam menyelesaikan masalah pola bilangan non rutin: Suatu penelitian fenomenologi hermeneutik

This study was conducted with the aim of investigating and exploring students' ways of thinking (WoT) in solving non-routine number pattern problems. This study used a qualitative method with a hermeneutic phenomenological approach with grade 8 students at a junior high school in Banda Aceh. To achieve the research objectives, data collection was carried out using a written test instrument with a number pattern on a 4-digit palindrome, structured documentation, and clinical interviews. The results of the study show that students' WoT in solving non-routine number pattern problems is that there are four approaches used in solving non-routine problems, namely: first, determining the special case; second, determining the pattern; third, using a mathematical model; and fourth, using a similar problem. The subject of critical reflection uses the three WoTs above except for using similar problems. The subject of explicit reflection uses the three approaches above except for using a mathematical model. While Subjects who cannot solve the problem only use the strategy of identifying special cases. Another finding is that the subject of critical reflection tends to use different strategies from those given by the teacher, is unique, and gives reasons for algebraic forms. In contrast, explicit reflection subjects tend to be less flexible in using strategies and tend to use inductive or arithmetic reasons. To support students in their ability to pattern and think algebraically, teachers must accustom students to solving non-routine mathematical problems in various contexts of learning by using number patterns.

Relational Program Synthesis with Numerical Reasoning

Learning programs with numerical values is fundamental to many AI applications, including bio-informatics and drug design. However, current program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values from multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NumSynth, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.

Validating psychometric classification of teachers’ fraction arithmetic reasoning

Validating psychometric classification of teachers’ fraction arithmetic reasoning

Effects of a Complex Physical Activity Program on Children's Arithmetic Problem Solving and Arithmetic Reasoning Abilities.

Research has shown that higher levels of physical activity are associated with better cognitive performance in children. However, the benefits of physical activity on academic achievement and specifically on mathematics performance need to be further explored. Therefore, this study aimed to investigate the effects of a complex physical activity (CPA) intervention program, including cognitive involvement, on children’s mathematics performance. The participants were 128 children (aged 12−13 years) attending third grade in three middle schools. They were randomly allocated into a CPA intervention (n = 64) or a waitlist control group (n = 64), the latter of which was given a regular and easy-to-perform activity program. At baseline and after the intervention, students’ physical fitness was measured using a battery of standardized motor tests (20 m shuttle run test, curl-up test, push-up test, and sit and reach test). In addition, the AC-MT 11-14 test was administered to allow a standardized and comprehensive assessment of arithmetic problem-solving and arithmetic reasoning abilities. In comparison to the control, the intervention group showed significant improvements (p < 0.001) in comprehension and production (d = 1.88), arithmetic reasoning (d = 2.50), and problem solving (d = 1.32), as well as in 20 m shuttle run test (d = 1.81), push-up test (d = 1.88), curl-up (d = 3.52), and sit and reach (d = 2.52). No significant changes were found in the control group. In conclusion, findings showed that a 12-week CPA intervention program can improve mathematical performance in children in the third grade of middle school. CPA intervention may be an effective method to improve academic performance and avoid student failure.

Is Parental Mathematics Anxiety Associated with Young Children’s Arithmetical Performance?

It has been suggested that parental mathematics anxiety may influence their children’s mathematics anxiety, attitudes, and performance. It remains an open question whether these parent-child associations differ by parental sex or parental involvement. We tested 249 Dutch-speaking Belgian participants, forming 83 (biological) mother–father–child trios. The 83 children (age: M = 5.74; SD = 0.30) attended Kindergarten. We tested their nonsymbolic comparison, symbolic numerical magnitude processing, numeral recognition, arithmetic, and matrix reasoning. We assessed both parents’ arithmetic skills, math anxiety, educational level, and division of care. More math-anxious parents tended to be less highly educated (r~0.42) and poorer at math (r~0.30). Compared to fathers, mothers had lower arithmetic, higher math anxiety, and higher educational level. Assortative mating (i.e., a significant spousal correlation) was found for educational level and arithmetic. Mothers’ (but not fathers’) educational level predicted children’s arithmetic scores (r = 0.31). Other parent-offspring correlations were non-significant. Most of the children’s test scores are intercorrelated. The parental characteristic that best predicted five- and six-year-olds’ arithmetic performance was maternal educational level rather than mathematical anxiety or performance. We discuss these findings in relation to the used measures, parental gender and involvement, children’s age, statistical power, and genetic and environmental transmission. The field is just starting to understand whether and how mathematics anxiety and the skills of parents influence those of their offspring.

Computerized working memory training in males with Duchenne muscular dystrophy: A single case experimental design study

ABSTRACT Learning disabilities (LDs) and working memory problems (WM) are common brain-related comorbidities in Duchenne muscular dystrophy (DMD). Despite growing evidence on the efficacy of computerized WM training in children with LDs, research in DMD is lacking. This exploratory study assessed whether training (1) improves dystrophin-associated WM problems in DMD, (2) effects are present at post-intervention, 3 and 8 months follow-up, and (3) improves problems that arise from their LDs. A single case non-concurrent multiple baseline across patients design evaluated the target behaviour i.e. parental reports of WM problems of four DMD participants with LDs. Additionally, participants completed cognitive tests of verbal and visual WM, academics, attention, processing speed and fluid reasoning. Parents and teachers completed behavioural questionnaires. Testing and questionnaires were administered at baseline, post-intervention (T2), 3 (T3) and 8 (T4) months follow-up. Positive effects on target behaviour were found for three of four participants, but parental bias cannot be ruled out. Short and long-term, near-and far transfer effects were found for verbal and visual WM (T2:n = 2, T3&T4:n = 1), reading (T2:n = 4,T3:n = 3,T4:n = 2), arithmetic (all T:n = 1), processing speed (all T:n = 4) and fluid reasoning (T2:n = 1,T3&T4:n = 2). Behavioural questionnaires displayed minimal changes (T2:n = 1,T3&T4:n = 2). Promising WM training results are shown in DMD that merit further research.

The dilemma of misclassifying weight in short and in historic population

Background: Clinicians often refer anthropometric measures of a child to so-called “growth standards” and “growth references. Over 140 countries have meanwhile adopted WHO growth standards.&#x0D; Objectives: The present study was conducted to thoroughly examine the idea of growth standards as a common yardstick for all populations. Weight depends on height. We became interested in whether also weight-for-height depends on height. First, we studied the age-group effect on weight-for-height. Thereafter, we tested the applicability of weight-for-height references in short and in historic populations.&#x0D; Sample and Methods: We analyzed body height and body weight and weight-for-height of 3795 healthy boys and 3726 healthy girls aged 2 to 5 years measured in East-Germany between 1986 and 1990.We chose contemporary height and weight charts from Germany, the UK, and the WHO growth chart and compared these with three geographically commensurable growth charts from the end of the 19th century.&#x0D; Results: We analyzed body height and body weight and weight-for-height of 3795 healthy boys and 3726 healthy girls aged 2 to 5 years measured in East-Germany between 1986 and 1990.We chose contemporary height and weight charts from Germany, the UK, and the WHO growth chart and compared these with three geographically commensurable growth charts of the end of the 19th century.&#x0D; Conclusion: Weight-for-height depends on age and sex and apart from the nutritional state, reflects body proportion and body built particularly during infancy and early childhood. Populations with a relatively short average height are prone to high values of weight-for-height for arithmetic reasons independent of the nutritional state.&#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D; &#x0D;

Perspectives on the problem-posing activity by prospective teachers: A cross-national study

There is an ongoing research interest to disclose factors that influence problem-posing performance by involving cross-national backgrounds. This research extends that effort by conducting a comparative analysis on the performance of Indonesian and Hungarian prospective teachers in a problem-posing task. A total of eighty-three prospective teachers from Indonesia and Hungary were asked to pose a problem based on the current calendar. For more in-depth insights, an interview was conducted with a representative participant. The obtained data were analysed quantitatively using Fisher's exact test and qualitatively in nature. Their mathematical background seems to influence the characteristic of their proposed problem and the solution approach they utilized. The typical tasks proposed by Indonesian prospective teachers are exercise and mostly related to arithmetic operations, while those by Hungarian prospective teachers are challenging problems and generally connected to arithmetic sequences. Moreover, in solving their problems, Indonesians tend to show arithmetic reasoning while Hungarians often denote algebraic reasoning. These disparities might be attributed to the types of problems that each group typically encounters during their mathematics lessons.

The relationship betweens math anxiety and arithmetic reasoning: The mediating role of working memory and self-competence

The complex interplay between cognitive and emotional factors at the base of maths achievement started to be evaluated and quantified in the last few years. Only a few studies, anyway, examine at the same time, the role of working memory (visuospatial and verbal subsystem) and maths anxiety together with self-competence, on maths attainment. To investigate the specific link between these three factors, in a large developmental sample, we enrol 335 students from the 3rd, 5th, and 7th grades. In respect to emotional and motivational factors, data indicates a direct influence of maths anxiety on maths performance. Furthermore, the results highlight that maths anxiety differently impacts working memory subsystems. In fact, we observe a significant and indirect effect of MA, through the visuospatial system, on maths achievement. Our results provide further support to the hypothesis that maths anxiety is a special type of anxiety, most likely impacting the visuospatial rather than the verbal working memory subsystem. Data is discussed in terms of a possible mechanism underlying maths anxiety and visuospatial working memory at the base of this specificity, and in relation to the role of self-competence in this interplay.

Nurse Education and Mathematical Competency: Implementation of an Online, Self-Directed, Prerequisite Model.

Mathematical competency in the profession of nursing has increasingly become a central focus as more nursing students appear to struggle with basic concepts of arithmetic, mental estimation, and critical reasoning. This paper highlights how one School of Nursing in Ontario, Canada implemented a Dosage Calculation Competency Test model which involved an online, self-directed, prerequisite approach to improve student mathematical competency and confidence. The purpose of this research case study was to document, through shared participant perceptions, the creation, implementation, and subsequent modifications to a Dosage Calculation Competency Test model in light of student needs and advances in online learning and assessment. The research design combined a quantitative survey of Year 1–4 nursing students, followed by a series of qualitative, semi-structured interviews with nursing students and program instructors. The study took place within a School of Nursing undergraduate program in Ontario, Canada. Forty-four participants, including students from all four years of the nursing program, completed the survey, followed by individual interviews with nine students and six faculty instructors. Survey (the open-response items) and interview data were analyzed thematically using ATLAS.ti (ATLAS.ti, Berlin, Germany). The authors recount the new DCCT model’s development, implementation, and subsequent modifications and further discuss student/instructor perceptions of learning types, math confidence, and competency. The paper concludes with a series of seven key recommendations for nursing programs.

Ordinality: The importance of its trial list composition and examining its relation with adults' arithmetic and mathematical reasoning.

Understanding whether a sequence is presented in an order or not (i.e., ordinality) is a robust predictor of adults’ arithmetic performance, but the mechanisms underlying this skill and its relationship with mathematics remain unclear. In this study, we examined (a) the cognitive strategies involved in ordinality inferred from behavioural effects observed in different types of sequences and (b) whether ordinality is also related to mathematical reasoning besides arithmetic. In Experiment 1, participants performed an arithmetic, a mathematical reasoning test, and an order task, which had balanced trials on the basis of order, direction, regularity, and distance. We observed standard distance effects (DEs) for ordered and non-ordered sequences, which suggest reliance on magnitude comparison strategies. This contradicts past studies that reported reversed distance effects (RDEs) for some types of sequences, which suggest reliance on retrieval strategies. Also, we found that ordinality predicted arithmetic but not mathematical reasoning when controlling for fluid intelligence. In Experiment 2, we investigated whether the aforementioned absence of RDEs was because of our trial list composition. Participants performed two order tasks: in both tasks, no RDE was found demonstrating the fragility of the RDE. In addition, results showed that the strategies used when processing ordinality were modulated by the trial list composition and presentation order of the tasks. Altogether, these findings reveal that ordinality is strongly related to arithmetic and that the strategies used when processing ordinality are highly dependent on the context in which the task is presented.

Assessing numerical reasoning provides insight into financial literacy

Financial literacy is linked to financial well-being and decision making. While financial literacy and numeracy skills are strongly related, the relevance of different aspects of numeracy (mental arithmetic, math achievement, and numerical reasoning) for financial literacy has not yet been examined. Data were collected from 88 cognitively healthy adults, mean age = 50 years (SD = 15); mean education = 15 years (SD = 2); 61% females; with 56% Caucasian, 36% Black, and 90% non-Hispanic. Financial literacy was measured with the widely used Big Three scale, and numeracy was measured with the Wechsler Adult Intelligence Scale-III, Arithmetic subtest; the Wide Range Achievement Test-IV, Math Computation subtest; and the Weller’s Abbreviated Numeracy Scale (WANS). Regressions analyses were conducted with financial literacy as the outcome variable and each numeracy measure along with demographics (age, sex, and education) as the predictors. In all the models, only the numeracy measures were significant as individual predictors, with numerical reasoning holding the strongest association with financial literacy, followed by mental arithmetic and math achievement. The current study supports the existing literature that numeracy is important for financial literacy, and provides empirical evidence for the specific contributions of individual numeracy measures that clinicians may use to garner impressions about financial skills.

Sözel Soruların Matematik Diline Dönüştürülmesi Becerisinde İki Öğrenci Grubunun Karşılaştırılması

Bu çalışmada; Öğrencilerin sözel olarak verilen bir matematik problemini matematik diline dönüştürürken ne tür yöntemleri kullandığını ve bu yöntemleri doğru kullanıp kullanmadığı araştırılmıştır. Bu araştırmada ortaokul 6.sınıfta okuyan iki ayrı öğrenci grubunun karşılaştırılması yapılmıştır. Bu öğrenci grubu seçilirken Iğdır ilindeki ortaokullardan iki tanesi seçilmiştir. Bu okullardan biri merkezde ve genelde kamu görevlisi orta-yüksek sosyo-ekonomik duruma sahip ebeveynlerin öğrencilerinden oluşmakta, diğeri ise biraz daha merkeze uzak olan ve genelde esnaf ve dar gelirli sosyo-ekonomik duruma sahip ebeveynlerin öğrencilerinden oluşmaktadır. Lee ve Chang (2012); Van Ameron, (2003); Akkan ve ark. (2012) tarafından kullanılan ve Bal ve Karacaoğlu (2017) tarafından geliştirilen veri toplama aracı olarak Öğrencilerin Cebirsel Sözel Problemleri Çözme Stratejilerini ve Hatalarını Belirleme Formu kullanılmıştır. Her iki okuldan da 30’ar öğrenciye 5 adet açık uçlu soru sorulmuş öğrencilerin verdikleri cevaplar SPSS paket programı vasıtasıyla Aritmetiksel Akıl Yürütme, Cebir Öncesi Akıl Yürütme ve Cebirsel Akıl Yürütme başlıklarında incelenmiştir. Araştırmanın sonucunda ortaokul altıncı sınıf öğrencilerinin cebirsel sözel problemler için sonucun doğruluğuna ve çözüm yoluna karar verme, çözüme ilişkin mantıklı tartışmalar yapma, sözel problemi çözme, genelleme yapma ile uygun muhakemeyi belirleme ve kullanma boyutlarındaki beceri düzeylerinin arzu edilen seviyede olmadığı belirlenmiştir. Ebeveynlerin öğrenim düzeyinin yüksek olması ve sosyo-ekonomik durumunun iyi olması, akademik olarak öğrencinin başarısına katkı sağladığı görülmüştür.