Uniformization, Unipotent Flows and the Riemann Hypothesis

We prove equidistribution of certain multidimensional unipotent flows in the moduli space of genus $g$ principally polarized abelian varieties (ppav). This is done by studying asymptotics of $\pmb{\Gamma}_{g} \sim Sp(2g,\mathbb{Z})$-automorphic forms averaged along unipotent flows, toward the codimension-one component of the boundary of the ppav moduli space. We prove a link between the error estimate and the Riemann hypothesis. Further, we prove $\pmb{\Gamma}_{g - r}$ modularity of the function obtained by iterating the unipotent average process $r$ times. This shows uniformization of modular integrals of automorphic functions via unipotent flows

Engineering Childhood: Knowledge Transmission Through Parenting

Parents are the front line when it comes to the education and development of their children, and are important agents in the educational achievement of their child in a formal setting (Yun et al, 2010; Catsambis, 1995; Fan & Chen, 2001; Seyfried & Chung,2003). Parents purchase toys, read books, take children to museums, and interact with their child on a daily basis. Particular background with a subject, such as science or engineering, can affect the parent’s strategies for educating their children and subsequent understanding of main concepts (Yun et al., 2010). However, many adults and children alike have a minimal understanding of engineering (NRC, 2009). Additionally, parents have a major influence on a child’s career choice, especially those in non-dominant groups (Taylor et al., 2003; Dryler, 1998). A survey of undergraduate engineering students found that women were significantly more likely to have a parent who is an engineer and to have previously studied engineering before college (Mannon & Schreuders, 2007). Engineering parents may pass on engineering-related knowledge, interests and aspirations to their progeny. The purpose of this study is to determine what engineering parents are doing to educate their children about engineering. In this study, interviews of 24 parents who self-identified as having an engineering backgrounds and doing something to help their children learn about engineering were analyzed in order to begin to capture a variety of approaches that parents have taken in order to shape their children’s exposure to engineering. Participants were recruited in order to capture breadth in terms of engineering experiences. Participants’ backgrounds were from a diverse assortment of industry (n = 8), faculty (n = 14), and students (n =2),participating in twenty different engineering disciplines. The open-ended interviews included parents’ background, interactions with children (content, strategies and reactions), parenting ideology, and parent’s own understanding of engineering. Parents primarily reported teaching their children engineering through inquiry based learning (Q&A sessions, museum exhibits) and interactions with media (books,computers, television, and toys). While many parents stated that they don’t explicitly teach engineering concepts, several mentioned that they are explicitly encouraging a specific way of thinking about problem solving. The findings from this study provide opportunities for future research as well as educational interventions. First, we are using these findings as a baseline for research investigating differences between parents with and without an engineering background.In the future, we can also use these finding to inform the development of K-12 classroom activities. Finally, we are already using the findings to create resources for parents

Engineering Children\u27s Literature: Development of an engineering storybook for young children

While the notions of doctor, teacher and firefighter are ubiquitous in young literature,there is a lack of engagement about engineering (Holbrook et al., 2008). Picture books are a compelling medium for introducing concepts to children at a young age. Story books have the ability to present new information, increase stimulation of the imagination, and deliver messages both moral and social. In a school setting, story books have been shown to impact kindergartener’s mathematical achievement when produced in tandem with a mathematics unit (Keat & Wilburne, 2009). However, there have been little to no studies regarding the impact of engineering literature (Holbrook et al., 2008). This could potentially be affected by the lack of children’s books on the subject. Distributing correct messages about engineering to a younger age group may assist in developing a stronger perception of engineering further down the line (NAE, 2002). A marketing analysis of engineering showed that targeted audiences weren’t familiar with engineering (NAE,2008). They piloted several different taglines to market engineering, such as “engineers shape our world” and “engineers breathe life into ideas and make them reality”. However, some of the taglines were found to be more relatable to targeted audiences, such as women and underrepresented minorities, than others. Appropriate informal messages for young children include: what engineering is, what an engineer does (in terms of occupation), many types of engineering exist, engineering is all around, and anyone can be an engineer with the proper training (diversity). This poster will illuminate the process of writing a children’s book on engineering. By increasing the number of available children’s books on engineering, with age appropriate and approved messages, it may increase the early positive exposure of engineers and/or engineering to young children

An Engineering Tale: Using Storybooks to Analyze Parent–Child Conversations About Engineering (Fundamental)

Envisioning a larger workforce of engineers, with broad participation from a diverse set of workers, is one of the central concerns of engineering education research. While many current K-12 programs focus on engineering thinking and design, there is still a need to promote aspiration and understanding of engineering as an occupation, especially in out-of-school environments where children spend a majority of their time. Career aspirations and expectations of children have already started to develop prior to entering formal schooling. Several studies has shown that parents play a significant role in the development of occupational awareness in their children, but the process by which this occurs is not well understood. In engineering and other fields it is common for children to follow in the career footsteps of their parents in a phenomenon called occupational inheritance. It is hypothesized that parents socialize their children through the social norms, personal knowledge, attitudes and beliefs that they share through everyday activity.This study investigated the strategies that engineering parents conduct when reading a story about engineering to their children. Conversation analysis was used to distinguish the knowledge, attitudes and beliefs that were shared during the interaction. Twenty-four participants that self-identified as engineers (through a degree conferred or job association or other) video-recorded themselves in their own home, reading a provided story book to their young children, aged 3 to 5 years. The storybook centered on two kids on a mission to deliver an odd shaped package to an engineer. Along the way they ponder who an engineer is, what they do, and where they work before eventually meeting up with a team of engineers. The storybook also contained imagery of potential misconceptions (e.g. only work on trains, similarity to mechanics) as well as messages from “Changing the Conversation” (e.g. engineers make the world a better place).Several of the results told an interesting tale: while engineering parents are expected to have a high degree of understanding about their field, they had difficulty in expressing occupational knowledge, and in some cases even had difficulty correcting misconceptions that the child held. Also, several parents expressed astonishment when their child did not recognize that they too were engineers. Engineering parents also provided additional engineering knowledge during the storybook reading.The results of this study will be used to develop materials to inform parents (as well as the general public) of strategies with which to engage conversations about engineering,and can be extended to other non-familiar occupations as well

Integrating Children’s Literature into Occupational Learning about Engineers

At a very young age, a child has the ability to formulate ideas regarding the occupation of a lawyer, a nurse or even a doctor. However, studies have shown that most children have limited information regarding engineers, and the lack of knowledge can often perpetuate into adulthood(Cunningham et al., 2005; NAE, 2002). Augur et al. (2005) found that “occupational aspirations and expectations of children undergo dramatic development changes during the elementary years, as well as resisting change in other respects.” This means prior to school education,children have already formed their perception of occupations and that stereotypical attributes have already been firmly established. Therefore, it is important to introduce occupations, such as engineering, at a very early age typically before a child enters school. Few studies have looked at the influence of media on the career development of children,though it has been implied as the primary source of occupational learning (Watson & McMahon,2005). Media in the case of children includes the influence of television, toys, and literature(books, newspaper, magazines, etc.). Fictional story books are a compelling medium for introducing concepts to children at a young age, as it can present new information in an engaging way, increase the stimulation of the imagination and deliver messages. However, while the notions of doctor, teacher and firefighter are ubiquitous in young literature, there is a lack of engagement about engineers (Holbrook et al., 2008). A search of children’s literature, using multiple methods, found six books pertaining to engineering, four narrative storybooks, an autobiography, and a tradebook (non-fiction). These books were analyzed for (1) common misconceptions in engineering, (2) thematic analysis of messages, (3) integration of problem-solving ability, and (4) implications for learning in and out of classroom. The misconceptions observed were derived out of the author’s lack of knowledge regarding engineering, and often were associated with mismatched identities (i.e. an engineer operates a train). Messages included the application of math and science as tools for engineers and the concept that engineers impact the world around them. Problem solving ability was evidenced through main character interaction when faced with a challenge. A broader approach looking at children’s narrative stories investigated embedded engineering themes in popular stories. This examination revealed that many popular children’s stories communicated concepts relevant to engineering, although engineering was not explicitly described or discussed. These concepts included problem solving, multiple alternatives, and spatial conceptualization. Integrating children’s books with either direct engineer references or even using popular books containing implicit engineering concepts has implications for learning in both formal and informal environments

Capturing the Design Thinking of Young Children Interacting with a Parent

Children have often been labeled as “natural engineers” whose curiosity about the world around them evokes comparisons to skills used by professional engineers and taught to undergraduate engineering students. Building towers out of blocks, taking things apart and figuring how things work are a part of childhood and have been considered to be precursors to engineering thinking.However there has been considerable debate around what engineering looks like for young children. Can young children engage in design and if so, what does that look like? How can we differentiate “design” (especially “modeling” or “create”) activity from normal everyday play?Several design models have taken into account the developmental stages of young children, but they often are based on assumptions and have minimal evidence.In the GRADIENT (Gender Research on Adult-child Discussions within Informal ENgineering environmenTs) study, a collaboration between researchers at a museum and university, we looked at how parents with young girls engage in two different engineering activities in informal settings. The first setting is a Preschool Play dates program for children 3-5 years old, where the parent-daughter dyads were asked to build a tower first out of familiar materials (foam blocks)and then out of unfamiliar materials (dado squares). The second setting is a pneumatic ball run that is part of an engineering exhibit at the museum and was focused on children 6-11 years old.In each setting, 30 dyads were video recorded, and the verbal and non-verbal segments were open and axially coded for engineering talk and action.We found that children engage in the engineering design process in ways that are similar to other models of the engineering design, that include problem scoping, idea generation, modeling,testing, evaluation and revision. We also found that children engage in both predictive and reflective behavior, and often add context to the problem. However, we want to acknowledge that the way children engage in engineering thinking is different from the way that adults do(especially with idea generation and revision) and we will discuss this further in the paper. This work lays a foundation for future research, as understanding how children engage in the design process can help us understand how children learn engineering design skills, and how people develop engineering design skills across pre-college, undergraduate, and professional practice.The work also has implications for the development of learning experiences in both school and out-of-school settings

Engineering Together: Context in Dyadic Talk During an Engineering Task (K-12 Fundamental)

Exploring how children develop early interest and understanding in engineering canprovide useful information for the ongoing efforts to increase the access of women inengineering careers. Drawing on occupational choice theories, girls and women havetended to place a high value on helping others in their work, but do not often realize thatcareers in engineering can lead to these types of endeavors. Adding layers of socialcontext that highlight the connections between engineering endeavors and improving thelives of others may create a more engaging experience for girls and women, andpotentially lead to increased development of girls’ engineering interest and understanding.Additionally, informal learning environments are positioned to become a pivotal role in inspiring today’s youth to pursue careers in STEM. These contexts have already been shown to be important avenues in which children can develop lifelong interest and understanding of broad range of STEM topics. Moreover, informal learning environments often allow for parents and children to work together to foster interest and engagement within STEM.Parent-child dyads who were visiting a metropolitan science museum as part of it\u27s program for preschool-aged children were asked to participate in a study that explores parent-child engineering conversations through a conversation analysis methodology. Dyads consisting of a parent with their daughter (aged 3-5 years) were video-recorded while engaged in two different engineering tasks: building a tower out of familiar materials and constructing a second tower out of unfamiliar materials. In the preliminary phase, participants (n = 25) were asked to build a tower with a specified goal, whereas participants in the follow-up phase (n = 25) were given the same directions though infused with a social context (i.e. building for someone, for a specified purpose).This paper will examine the differences in the use of context between fathers and mothers within the preliminary and follow-up phases, including the frequency and type of context used towards the design of the towers. Four case studies were evaluated to highlight key findings such as the addition of context to the preliminary phase and the involvement of social context in the follow-up. It was found that in the preliminary phase that both parents and the children added context to the task – a finding that resonates with the research that girls are more interested in socially relevant activities. When given a more detailed background, children integrated the given context within design decisions and explanations even going so far as to expand on the original information.By examining the dyad’s interaction, we hope to identify recommendations we can make to other parents on how to foster engineering interest in their children, as well as contribute ideas for activities for K-5 classrooms to reach a wider range of children

Parents as Critical Influence: Insights from Five Different Studies

Parents play a number of roles in engineering education: they can motivate children’s interest in engineering in early childhood, as well as later when their child is in the process of selecting a major at college, they can provide support in learning engineering concepts and thinking skills, and can serve as role models if they themselves are engineers. Several empirical studies have shown that parents play a significant role in the occupational aspiration and career goal development of their children. In addition,parents’ own beliefs and aspirations have been found to be important factors in children’s career and academic aspirations. In recent reviews regarding children’s career development, parents were highlighted as crucial and important figures in developing occupational awareness in their children. Additionally children have more understanding of the parents’ occupations than other occupations. Retrospective studies have also revealed that parents are a significant motivator, especially for low socio-economic students to enter into engineering. Finally, parents can provide scaffolding and other support as children learn engineering concepts and skills.Using multi-case analysis, this paper will examine the role of parents in engineering education through five distinct studies. The first study, GRADIENT, looks at how parents engage in an engineering activity with girls aged 3-11 within two different informal settings and how parent gender has an impact on their interactions. The Informal Pathways to Engineering (IPE) project investigates how informal engineering programs support engineering-related learning over time with middle school students and their support system of parents, teachers and other informal educators. The INFUSE study looks at conversations between engineering parents and their children while reading an engineering storybook. A fourth study examines how intersectionality influenced the experiences of nine female students in high school engineering where the interview data from the students and their parents reveal that institutions of race, class, and gender within their families play a significant role in these young women\u27s interest in and entry into engineering. The last study investigates the different ways that parents with an engineering background help their children to learn about engineering via interviews with the parents.The collection of these five studies provides unique insights into and a more comprehensive understanding of the ways that parents can and do play roles in PreK-12th grade students’ engineering education

Using Puppets to Elicit Talk During Interviews on Engineering with Young Children

Interviewing can be tricky at best, but with a younger audience (\u3c 5 years) there are some additional barriers that inhibit the interview process such as shyness, short attention span,lack of vocabulary, and level of parental guidance (Clark, 1999). When in an interview, a child may try to ‘second guess’ what the researcher wants them to say, especially if they believe that the interviewer may already know the answer (Gallop, 2000). Additionally young children tend to give monosyllabic answers to open ended questions (Tizard &Hughes, 1984), and might require more prompting than adults.One aide that has been recently investigated is the use of puppets to elicit children’s talk for research (Epstein et al., 2008). Puppets have been shown to: • Decrease children’s fears of the interview process • Lower anxiety levels • Help assess children’s knowledge • Help children to adjust to environment • Provide effective communication and teaching tools. Most research focuses on puppets within clinical contexts, but recently the use has been extended towards other applications such as qualitative interviews (Epstein et al., 2008),mathematical lessons (Cauley, 1988), promoting science engagement (Naylor et al,2007), and teaching phonics (Johnston & Watson, ???). However, there has not been any documented use of this research approach within engineering education.There are three common interview techniques involving puppets in practice: the Alien Puppet Interview (API) (Krott and Nicoladis, 2005), the Puppet Interview (PI) (Cassidy,1988; Verschueren, Buyuk and Marcoen, 2001) and the Berkeley Puppet Interview (BPI) (Measelle et al., 1998; Ablow et al., 1999). Each technique has a different strategy depending on how the child interacts with the puppet.As part of a larger project, children ages 3-5 were interviewed about an engineering task that they had just completed with their parents during a museum event. The interview was a hybrid mix of the Alien Puppet Interview and the Puppet Interview, depending on the way in which the child interviewee chose to interact with the puppet. Thirty interviews were analyzed for children’s interaction, quality of answers, and behavior toward the puppet.In the paper, we will provide more details about the specific interview approach used for our study (as well as insights into how children responded to this interview approach) in addition to a larger discussion of the three interview techniques in order to provide a research methodology resource for other pre-college engineering education researchers to use

Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis

We study asymptotic relations connecting unipotent averages of $Sp(2g,\mathbb{Z})$ automorphic forms to their integrals over the moduli space of principally polarized abelian varieties. We obtain reformulations of the Riemann hypothesis as a class of problems concerning the computation of the equidistribution convergence rate in those asymptotic relations. We discuss applications of our results to closed string amplitudes. Remarkably, the Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring in perturbative closed string theory.Comment: 15 page