Solving olympiad geometry without human demonstrations.

Proving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1-4, owing to their reputed difficulty among the world's best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges1,5, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane geometry that sidesteps the need for human demonstrations by synthesizing millions of theorems and proofs across different levels of complexity. AlphaGeometry is a neuro-symbolic system that uses a neural language model, trained from scratch on our large-scale synthetic data, to guide a symbolic deduction engine through infinite branching points in challenging problems. On a test set of 30 latest olympiad-level problems, AlphaGeometry solves 25, outperforming the previous best method that only solves ten problems and approaching the performance of an average International Mathematical Olympiad (IMO) gold medallist. Notably, AlphaGeometry produces human-readable proofs, solves all geometry problems in the IMO 2000 and 2015 under human expert evaluation and discovers a generalized version of a translated IMO theorem in 2004.

Determinants of profiles of competence development in mathematics and reading in upper secondary education in Germany.

The registered report was targeted at identifying latent profiles of competence development in reading and mathematics among N = 15,012 German students in upper secondary education sampled in a multi-stage stratified cluster design across German schools. These students were initially assessed in grade 9 and provided competence assessments on three measurement occasions across six years using tests especially developed for the German National Educational Panel Study (NEPS). Using Latent Growth Mixture Models, Using Latent Growth Mixture Models, we aimed at identifying multiple profiles of competence development. Specifically, we expected to find at least one generalized (i.e., reading and mathematical competence develop similarly) and two specialized profiles (i.e., one of the domains develops faster) of competence development and that these profiles are explained by the specialization of interest and of vocational education of students. Contrary to our expectations, we did not find multiple latent profiles of competence development. The model describing our data best was a single-group latent growth model confirming a competence development profile, which can be described as specializing in mathematical competences, indicating a higher increase in mathematical competences as compared to reading competences in upper secondary school. Since only one latent profile was identified, potential predictors (specialization of vocational education and interest) for different profiles of competence development were not examined.

First year undergraduate nursing students' perceptions of the effectiveness of blended learning approaches for nursing numeracy.

The ability to safely calculate and administer medications are indispensable, core nursing skills in nursing education and practice. Therefore, it is imperative that nursing students are adequately prepared with the necessary numeracy skills during their undergraduate nursing studies. The focus of this study, conducted at a single multi-campus university in the western Sydney region of Australia, was to determine the effectiveness of a suite of blended learning approaches on numeracy self-efficacy from the students' perspective. Surveys were administered as part of the study and included open-ended questions. 525 students provided open-ended responses that were analysed by the research team. Four main themes were identified from the open-ended responses: (i) Self-realisation; (ii) Practice, practice, practice; (iii) Boosting confidence; and (iv) Wanting more. The themes captured students' perceptions of the benefits of having a rigorous learning design in blended learning approaches. The study showed that a structured pedagogical approach to nursing numeracy in undergraduate programs improved students' self-reported self-efficacy with mathematics and assisted students in realising the importance of learning and applying these skills as nursing clinicians.

Cognitive functions mediate the effect of preterm birth on mathematics skills in young children.

Children born preterm are at risk for cognitive deficits and lower academic achievement. Notably, mathematics achievement is generally most affected. Here, we investigated the cognitive functions mediating early mathematics skills and how these are impacted by preterm birth. Healthy children born preterm (gestational age at birth < 33 weeks; n = 51) and children born full term (n = 27) were tested at ages 5, 6, and 7 years with a comprehensive battery of tests. We categorized items of the TEMA-3: Test for Early Mathematics Abilities Third Edition into number skills and arithmetic skills. Using multiple mediation models, we assessed how the effect of preterm birth on mathematics skills is mediated by spatial working memory, inhibitory control, visual-motor integration, and phonological processing. Both number and arithmetic skills showed group differences, but with different developmental trajectories. The initial performance gap observed in the preterm children decreased over time for number skills but increased for arithmetic skills. Phonological processing, visual-motor integration, and inhibitory control were poorer in children born preterm. These cognitive functions, particularly phonological processing, had a mediating effect on both types of mathematics skills. These findings help define and chart the trajectory of the specific cognitive skills directly influencing math deficit phenotypes in children born very preterm. This knowledge provides guidance for targeted evaluation and treatment implementation.

The impact of penalties for wrong answers on the gender gap in test scores.

Multiple-choice examinations play a critical role in university admissions across the world. A key question is whether imposing penalties for wrong answers on these examinations deters guessing from women more than men, disadvantaging female test-takers. We consider data from a large-scale, high-stakes policy change that removed penalties for wrong answers on the national college entry examination in Chile. The policy change reduced a large gender gap in questions skipped. It also narrowed gender gaps in performance, primarily among high-performing test-takers, and in the fields of math, social science, and chemistry.

A New Objective Health Numeracy Test for Patients with Type 2 Diabetes: Development and Evaluation of Psychometric Properties.

PURPOSE: Patients with diabetes frequently need to perform certain numeric tasks such as interpreting blood glucose levels. However, there is no psychometrically sound instrument for objectively measuring diabetes-specific health numeracy. This study aimed to develop a new objective diabetes health numeracy test (DHNT) and evaluate its psychometric properties in adult patients with type 2 diabetes. METHODS: An instrument development study was conducted. Initial items were evaluated by six experts for content validity. After a pilot test, a convenience sample of 257 participants with type 2 diabetes was recruited at 2 university hospitals from May to September 2018. The structural, convergent, and criteria validity, and internal consistency of the DHNT with binary item responses were evaluated. Data were analyzed using exploratory factor analysis, Rasch analysis, tetrachoric correlation, Spearman's correlation, and the Kuder-Richardson-20 formula. RESULTS: Exploratory factor analysis yielded a single-factor solution comprising seven items. Rasch analysis confirmed that no item did not fit with the single factor and identified that the item difficulty parameters had moderate values. The convergent and criterion validity of the instrument were demonstrated, with diabetes knowledge and subjective diabetes numeracy, respectively, as was its acceptable internal consistency, by a Kuder-Richardson-20 coefficient of .81. CONCLUSION: The DHNT demonstrated satisfactory psychometric properties. The instrument with moderate levels of item difficulty may have a lower cognitive burden. The developed instrument can be applied in practice to tailor the education of diabetes self-management as per the levels of health numeracy of specific patients.

Crime and Inequality in Academic Achievement Across School Districts in the United States.

This study investigates the effect of violent crime on school district-level achievement in English language arts (ELA) and mathematics. The research design exploits variation in achievement and violent crime across 813 school districts in the United States and seven birth cohorts of children born between 1996 and 2002. The identification strategy leverages exogenous shocks to crime rates arising from the availability of federal funds to hire police officers in the local police departments where the school districts operate. Results show that children who entered the school system when the violent crime rate in their school districts was lower score higher in ELA by the end of eighth grade, relative to children attending schools in the same district but who entered the school system when the violent crime rate was higher. A 10% decline in the violent crime rate experienced at ages 0-6 raises eighth-grade ELA achievement in the district by 0.03 standard deviations. Models that estimate effects by race and gender show larger impacts among Black children and boys. The district-wide effect on mathematics achievement is smaller and statistically nonsignificant. These findings extend our understanding of the geography of educational opportunity in the United States and reinforce the idea that understanding inequalities in academic achievement requires evidence on what happens inside as well as outside schools.

Math versus meaning in MAIHDA: A commentary on multilevel statistical models for quantitative intersectionality.

RATIONALE: Intersectionality has been increasingly adopted as a theoretical framework within quantitative research, raising questions about the congruence between theory and statistical methodology. Which methods best map onto intersectionality theory, with regard to their assumptions and the results they produce? Which methods are best positioned to provide information on health inequalities and direction for their remediation? One method, multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA), has been argued to provide statistical efficiency for high-dimensional intersectional analysis along with valid intersection-specific predictions and tests of interactions. However, the method has not been thoroughly tested in scenarios where ground truth is known. METHOD: We perform a simulation analysis using plausible data generating scenarios where intersectional effects are present. We apply variants of MAIHDA and ordinary least squares regression to each, and we observe how the effects are reflected in the estimates that the methods produce. RESULTS: The first-order fixed effects estimated by MAIHDA can be interpreted neither as effects on mean outcome when interacting variables are set to zero (as in a correctly-specified linear regression model), nor as effects on mean outcome averaged over the individuals in the population (as in a misspecified linear regression model), but rather as effects on mean outcome averaged over an artificial population where all intersections are of equal size. Furthermore, the values of the random effects do not reflect advantage or disadvantage of different intersectional groups. CONCLUSIONS: Because first-order fixed effects estimates are the reference point for interpreting random effects as intersectional effects in MAIHDA analyses, the random effects alone do not provide meaningful estimates of intersectional advantage or disadvantage. Rather, the fixed and random parts of the model must be combined for their estimates to be meaningful. We therefore advise caution when interpreting the results of MAIHDA in quantitative intersectional analyses.

Gender gaps in cognitive and social-emotional skills in early primary grades: Evidence from rural Indonesia.

This paper examines the magnitude and source of gender gaps in cognitive and social-emotional skills in early primary grades in rural Indonesia. Relative to boys, girls score more than 0.17 SD higher in tests of language and mathematics (cognitive skills) and between 0.18 and 0.27 SD higher in measures of social competence and emotional maturity (social-emotional skills). We use Oaxaca-Blinder decomposition to investigate the extent to which gender differences in early schooling and parenting practices explain these gender gaps in skills. For cognitive skills, differences in early schooling between boys and girls explain between 9% and 11% of the gender gap whereas differences in parenting practices explain merely 3%-5% of the gender gap. This decomposition result is driven largely by children living in villages with high-quality preschools. In contrast, for social-emotional skills, differences in parenting styles toward boys and girls explain between 13% and 17% of the gender gap, while differences in early schooling explain only 0%-6% of the gender gap.

Multi-institutional study of GRE scores as predictors of STEM PhD degree completion: GRE gets a low mark.

The process of selecting students likely to complete science, technology, engineering and mathematics (STEM) doctoral programs has not changed greatly over the last few decades and still relies heavily on Graduate Record Examination (GRE) scores in most U.S. universities. It has been long debated whether the GRE is an appropriate selection tool and whether overreliance on GRE scores may compromise admission of students historically underrepresented in STEM. Despite many concerns about the test, there are few studies examining the efficacy of the GRE in predicting PhD completion and even fewer examining this question in STEM fields. For the present study, we took advantage of a long-lived collaboration among institutions in the Northeast Alliance for Graduate Education and the Professoriate (NEAGEP) to gather comparable data on GRE scores and PhD completion for 1805 U.S./Permanent Resident STEM doctoral students in four state flagship institutions. We found that GRE Verbal (GRE V) and GRE Quantitative (GRE Q) scores were similar for women who completed STEM PhD degrees and those who left programs. Remarkably, GRE scores were significantly higher for men who left than counterparts who completed STEM PhD degrees. In fact, men in the lower quartiles of GRE V or Q scores finished degrees more often than those in the highest quartile. This pattern held for each of the four institutions in the study and for the cohort of male engineering students across institutions. GRE scores also failed to predict time to degree or to identify students who would leave during the first year of their programs. Our results suggests that GRE scores are not an effective tool for identifying students who will be successful in completing STEM doctoral programs. Considering the high cost of attrition from PhD programs and its impact on future leadership for the U.S. STEM workforce, we suggest that it is time to develop more effective and inclusive admissions strategies.

Interdisciplinarity research based on NSFC-sponsored projects: A case study of mathematics in Chinese universities.

We investigate the interdisciplinarity of mathematics based on an analysis of projects sponsored by the NSFC (National Natural Science Foundation of China). The motivation of this study lies in obtaining an efficient method to quantify the research interdisciplinarities, revealing the research interdisciplinarity patterns of mathematics discipline, giving insights for mathematics scholars to improve their research, and providing empirical supports for policy making. Our data set includes 6147 NSFC-sponsored projects implemented by 3225 mathematics professors in 177 Chinese universities with established mathematics departments. We propose the weighted-mean DIRD (diversity of individual research disciplines) to quantify interdisciplinarity. In addition, we introduce the matrix computation method, discover several properties of such a matrix, and make the computation cost significantly lower than the bitwise computation method. Finally, we develop an automatic DIRD computing system. The results indicate that mathematics professors at top normal universities in China exhibit strong interdisciplinarity; mathematics professors are most likely to conduct interdisciplinary research involving information science (research department), computer science (research area), computer application technology (research field), and power system bifurcation and chaos (research direction).

The moderating role of intrinsic value in the relation between psychological needs support and academic engagement in mathematics among Chinese adolescent students.

This study was to assess the moderating roles of intrinsic value in the relation of basic psychological needs support to academic engagement in mathematics. We recruited 246 middle school students by using the Basic Psychological Needs Support Scale, the Intrinsic Value Scale and the Academic Engagement Scale. This study found that both basic psychological needs support and intrinsic value had significant predictions on the three aspects of academic engagement. Moreover, the interaction item between basic psychological needs support and intrinsic value could significantly affect emotional and cognitive engagement, but not behavioural engagement. The findings indicated that except for behavioural engagement, the associations between basic psychological need support and emotional or cognitive engagement could be moderated by intrinsic value. This study provides a special perspective for educators and researchers to recognise the role of intrinsic value in promoting adolescents' higher levels of involvement in mathematics class.

Predictors of developing mathematics anxiety among middle-school students: A 2-year prospective study.

While there is an abundance of research pertaining to the development of anxiety disorders, there is still a dearth of knowledge regarding the development of anxiety in the general population. The objective of this study was to longitudinally explore the development of mathematics anxiety among normative middle-school students, and to identify the moderating role of gender, school transition and scholastic achievements on these trajectories. Subjects included 413 sixth grade students (53.3% females, mean age 11.27 ± 0.38 years). Participants were evaluated for their level of anxiety in the context of mathematics, using the Value of Education scale, in four time-points with a 6-month gap between each time-point. Data regarding subjects' grades and school transition were also collected. A growth curve analysis using hierarchical linear modelling revealed that girls, students who transitioned between schools and high achievers (each independently) reported a significant increase in mathematics related anxiety towards the end of sixth grade, which later decreased during seventh grade. The findings of this prospective study on factors affecting the development of mathematics anxiety among normative adolescents may be important in planning focused primary prevention school-based strategies.

Brief Report: Investigating Relations Between Self-Concept and Performance in Reading and Math for School-Aged Children and Adolescents with Autism Spectrum Disorder.

A typically developing student's perceptions of his or her own capabilities (academic self-concept), is predictive of later academic achievement. However, little is known about academic self-concept in youth with autism spectrum disorder (ASD). To understand whether students math self-concept and reading self-concept predicted their performance, 44 school-aged children and adolescents with ASD and 36 age-matched individuals with typical development (TYP) rated their perceived math and reading abilities and were administered standardized achievement measures. Results showed self-concept was predictive of performance in math and reading in the TYP group. For youth with ASD, there was agreement between self-concept and performance only in math. These findings suggest that educators should be cautious when interpreting the self-assessments of reading ability in students with ASD.

Performance in grade 12 mathematics and science predicts student nurses' performance in first year science modules at a university in the Western Cape.

BACKGROUND: The demand for highly qualified and skilled nurses is increasing in South Africa as well as around the world. Having a background in science can create a significant advantage for students wishing to enrol for an undergraduate nursing qualification because nursing as profession is grounded in scientific evidence. AIM: The aim of this study was to investigate the predictive validity of grade 12 mathematics and science on the academic performance of first year student nurses in science modules. METHOD: A quantitative research method using a cross-sectional predictive design was employed in this study. The participants included first year Bachelor of Nursing students enrolled at a university in the Western Cape, South Africa. Descriptive and inferential statistics were performed to analyse the data by using the IBM Statistical Package for Social Sciences versions 24. Descriptive analysis of all variables was performed as well as the Spearman's rank correlation test to describe the relationship among the study variables. Standard multiple linear regressions analysis was performed to determine the predictive validity of grade 12 mathematics and science on the academic performance of first year student nurses in science modules. RESULTS: The results of this study showed that grade 12 physical science is not a significant predictor (p > 0.062) of performance in first year science modules. The multiple linear regression revealed that grade 12 mathematics and life science grades explained 37.1% to 38.1% (R2 = 0.381 and adj R2 = 0.371) of the variation in the first year science grade distributions. CONCLUSION: Based on the results of the study it is evident that performance in grade 12 mathematics (ß = 2.997) and life science (ß = 3.175) subjects is a significant predictor (p < 0.001) of the performance in first year science modules for student nurses at the university identified for this study.

Reading, Mathematics and Fine Motor Skills at 5 Years of Age in US Children who were Extremely Premature at Birth.

Objectives The prevalence of extreme prematurity at birth has increased, but little research has examined its impact on developmental outcomes in large representative samples within the United States. This study examined the association of extreme prematurity with kindergarteners' reading skills, mathematics skills and fine motor skills. Methods The early childhood longitudinal study-birth cohort, a representative sample of the US children born in 2001 was analyzed for this study. Early reading and mathematics skills and fine motor skills were compared among 200 extremely premature children (EPC) (gestational age <28 wks or birthweight <1000 g), 500 premature children (PC), and 4300 term children (TC) (≥37wks or ≥2500 g). Generalized linear regression analyses included sampling weights, children's age, race, sex, and general health status, and parental marital status and education among singleton children. Results At age 5 years, EPC were 2.6(95 % CI 1.7-3.8) times more likely to fail build a gate and were 3.1(95 % CI 1.6-5.8) times more likely to fail all four drawing tasks compared to TC (p values <0.001). Fine motor performance of PC (failed to build a gate, 1.3[95 % CI 1.0-1.7]; failed to draw all four shapes, 1.1[95 % CI 0.8-1.6]) was not significantly different from TC. Mean early reading scale score (36.8[SE:1.3]) of EPC was 4.0 points lower than TC (p value < 0.0001) while mean reading score (39.9[SE:1.4]) of PC was not significantly different from TC (40.8[SE:1.1]). Mean mathematics scale score were significantly lower for both EPC (35.5[SE:1.0], p value < 0.001) and PC (39.8[SE:0.8], p value = 0.023) compared to TC (41.0[SE:0.6]). Conclusions for Practice Extreme prematurity at birth was associated with cognitive and fine motor delays at age 5 years. This suggests that based on a nationally representative sample of infants, the biological risk of extreme prematurity persists after adjusting for other factors related to development.

Physically active Chilean school kids perform better in language and mathematics.

We examined the association between the engagement in regular physical activity (PA) and the academic performance (AP) of school-age children from Santiago Metropolitan Region. In a random sample of 1271 students (13.3 ± 2.3 years old) we measured regular PA, accounting for hours of weekly scheduled exercise, and AP, using national standardized tests scores in Language and Mathematics. Bivariate and multivariate regression analyses were used to model the relation between academic and health-related behaviors. Two outcomes were considered: (i) sufficiency according to the Ministry of Education and (ii) discretionary sufficiency (tests z-scores ≥50th percentile). About 80% of students were poorly engaged in scheduled exercise (<2 h per week). Devoting more than 4 h per week to scheduled exercise significantly increased the odds of reaching the official and discretionary sufficiency in both Language and Mathematics. Moderate engagement (2-4 h per week) just improved the odds of reaching the discretionary sufficiency standard. These results confirm the poor engagement in regular exercise at the school level. School kids with the highest allocation of time to scheduled exercise have better AP in Language and Mathematics. Our findings support the notion that academic and health-related behaviors are linked and, similarly, that school health programs may have positive effects on educational outcomes.