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Authoring of help content within educational technologies is labor intensive, requiring many iterations of content creation, refining, and proofreading. In this paper, we conduct an efficacy evaluation of ChatGPT-generated help using a 3 x 4 study design (N = 274) to compare the learning gains of ChatGPT to human tutor-authored help across four mathematics problem subject areas. Participants are randomly assigned to one of three hint conditions (control, human tutor, or ChatGPT) paired with one of four randomly assigned subject areas (Elementary Algebra, Intermediate Algebra, College Algebra, or Statistics). We find that only the ChatGPT condition produces statistically significant learning gains compared to a no-help control, with no statistically significant differences in gains or time-on-task observed between learners receiving ChatGPT vs human tutor help. Notably, ChatGPT-generated help failed quality checks on 32% of problems. This was, however, reducible to nearly 0% for algebra problems and 13% for statistics problems after applying self-consistency, a "hallucination" mitigation technique for Large Language Models. [ABSTRACT FROM AUTHOR]

Large language models such as ChatGPT have been shown to excel in solving complex math problems. However, they cannot solve basic arithmetic problems such as 758*639 = 484,362. This makes us ponder if LLMs have been trained to solve math and science problems in the right way. When a student learns math at school, she or he starts with arithmetic, then moves to word problems, polynomials, and calculus. Each skill she or he acquires will be used in the next stage to solve more advanced problems. In this paper we propose Scaffolding Learning for LLMs, which imitates how a student learns a subject in a step-by-step manner. For example, we first train an LLM to perform highly specific operations such as multiplication and division, and then apply such "skills" in a more generic task such as solving word problems. This is related to Curriculum Training, which trains a model on tasks following a specific order, such as training on easy tasks first and then gradually increases the difficulty. Our proposed approach goes from specific tasks to generic ones, which can be considered as a special case of Curriculum Training. Our empirical studies show that when an LLM has "mastered" a specific skill, only a small amount of training is required to teach it to apply the skill to a more generic application., Competing Interests: NO authors have competing interests., (Copyright: © 2024 Yin, Yin. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

In this paper, we examine q-Bernstein-Bézier surfaces in Minkowski space- R13 with q as the shape parameter. These surfaces, a generalization of Bézier surfaces, have applications in mathematics, computer-aided geometric design, and computer graphics for the surface formation and modeling. We analyze the timelike and spacelike cases of q-Bernstein-Bézier surfaces using known boundary control points. The mean curvature and Gaussian curvature of these q-Bernstein-Bézier surfaces are computed by finding the respective fundamental coefficients. We also investigate the shape operator dependency for timelike and spacelike q-Bernstein-Bézier surfaces in Minkowski space- R13 , and provide biquadratic and bicubic q-Bernstein-Bézier surfaces as illustrative examples for different values of the shape controlling parameter q. [ABSTRACT FROM AUTHOR]

Substantial progress has been made in understanding the neurocognitive underpinnings of learning math. Building on this work, it has been hypothesized that declarative and procedural memory, two domain-general learning and memory systems, play important roles in acquiring math skills. In a longitudinal study, we tested whether in fact declarative and procedural memory predict children's math skills during elementary school years. A sample of 109 children was tested across grades 2, 3 and 4. Linear mixed-effects regression and structural equation modeling revealed the following. First, learning in declarative but not procedural memory was associated with math skills within each grade. Second, declarative but not procedural memory in each grade was related to math skills in all later grades (e.g., declarative memory in grade 2 was related to math skills in grade 4). Sensitivity analyses showed that the pattern of results was robust, except for the longitudinal prediction of later math skills when accounting for stable inter-individual differences via the inclusion of random intercepts. Our findings highlight the foundational role of early domain-general learning and memory in children's acquisition of math. [ABSTRACT FROM AUTHOR]

Past research has shown that growth mindset and motivational beliefs have an important role in math and science career interest in adolescence. Drawing on situated expectancy-value theory (SEVT), this study extends these findings by investigating the role of parental motivational beliefs (e.g., expectancy beliefs, utility values) and parent growth mindset in math on adolescent career interest in math-intensive fields (e.g., mathematics, computer science, statistics, and engineering; MCSE) through adolescent motivational beliefs in math. Structural equation modeling was used to test the hypothesized model using data from 290 adolescents (201 girls, 69.3%; Mage = 15.20), who participate in informal STEM (science, technology, engineering, mathematics) youth programs, and their parents (162 parents, 87.7% female) in the United Kingdom and the United States. As hypothesized, adolescent expectancy beliefs, utility values, and growth mindset in math had a significant direct effect on MCSE career interest. Further, there was a significant indirect effect of parental expectancy beliefs in math on MCSE career interest through adolescents' expectancy beliefs. Similarly, there was a significant indirect effect from parental utility values in math to MCSE career interest through adolescents' utility values. The findings suggest that parents' math motivational beliefs play a critical role in adolescent math motivational beliefs and their career interest in math-intensive fields. [ABSTRACT FROM AUTHOR]