RESOURCES FOR LEARNING ROBOTS: ENVIRONMENTS AND FRAMINGS CONNECTING MATH IN ROBOTICS

How do learning environments influence the ways that middle school students use math to engage with and learn about robotics? Data from two observational studies suggest that existing formal (scripted inquiry) and informal (competitions) learning environments in this domain are limited in their support for connecting math with robotics. In light of the evaluation of these existing learning environments, two additional studies were conducted documenting the design, implementation, and redesign of a new learning environment intended to more effectively align learning and engagement with the connection between math and robots. Pre-post assessments and analyses of student work support the hypothesis that a model eliciting learning environment can facilitate learning while maintaining interest in both disciplines, and facilitate the development of a greater sense of the value of math in robotics. Two additional studies expanded on the previous work. The first study identified two contrasting approaches for connecting math with robots in the context of the model-eliciting learning environment from the previous studies. One approach used mathematics as a calculational resource for transforming input values into desired output values. The second approach used mathematics as a mechanistic resource for describing intuitive ideas about the physical quantities and their relationships. The second study manipulated instructional conditions across two groups of students that encouraged the students to take on one of these approaches or the other. Both groups engaged in high levels of productive mathematical engagement: designing, justifying, and evaluating valid strategies for controlling robot movements with connections to mathematics. But only the mechanistic group made significant learning gains and they were more likely to use their invented robot math strategies on a transfer competition task. All six studies taken together provide a rich description of the range of possibilities for connecting math with robots. Further, the results suggest that in addition to carefully crafting environments and associated tasks to align math and robots, that instructional designers ought to pay particular attention to helping students frame their approaches to using math productively as a tool for thinking about situations

The Design Problem Framework: Using Adaption-Innovation Theory to Construct Design Problem Statements

Using Adaption-Innovation Theory to Build a Framework for Constructing Design Problem StatementsDesign problems are central to the work of practicing engineers and thus the education ofengineering students. As engineering instructors work to improve student design skills, oneoverlooked aspect could be in the way they frame and present design problems in their courses.Word choices, decisions about relevant information to include, and stated goals within thesedesign problem statements are likely to impact students’ approaches to generating solutions, aswell as the design solutions themselves.In our work, we developed a framework to assist in the development and framing of designproblem statements to encourage specific sorts of ideation behaviors. We developed the basis forthis framework by connecting literature on the structure of design problems, idea generation, taskframing, and cognitive styles. We utilized Kirton’s Adaption-Innovation (A-I) theory tounderstand the range of cognitive styles, and to create different design problem framings basedon this theory. A-I theory describes the different ways people respond to and manage structure,including the conceptual structures involved in idea generation. More adaptive individuals prefermore structure, with more of that structure consensually agreed, while more innovativeindividuals prefer less structure and are less concerned about consensus.Our review of the research suggested particular modifications in the framing of design problemstatements that would be likely to impact individuals’ natural approaches to ideation. Thosemodifications focused on varying the constraints and criteria specified in the problem. Designproblems that encourage adaptive ideation behaviors include highly specified constraints, alongwith criteria to encourage solutions that build on already existing solutions to the same or similarproblems. In contrast, design problems that encourage innovative ideation behaviors includecriteria to encourage solutions that are radically different from existing solutions and are notbound by particular constraints. We illustrate these variations by presenting a set of five designproblems, with three different versions of each problem statement, guided by the developedframework: (1) a neutrally framed version; (2) a more adaptively framed version; and (3) a moreinnovatively framed version. Additionally, we present three cases of student generated solutions,one case for each version of one of the design problems.We propose this framework as a guide for the development of design problem statements in theworkplace, instruction, and research settings. The framework can assist practicing engineers andengineering instructors to be more explicit about their own goals for the sorts of design solutionsthey aim to obtain

The Impact of Teaming and Cognitive Style on Student Perceptions of Design Ideation Outcomes

The Impact of Teaming and Problem Solving Style on Student Perceptions of Design Ideation Out comes The importance of idea generation (ideation) within the engineering design process is recognized in academic and industrial settings alike. The collaborative nature of engineering design is also well-established, with individuals of differing personalities, technical backgrounds, and levels of experience coming together to meet shared design objectives. Engineering educators routinely put students in design teams to complete both simple and complex projects, with the assessment of students’ individual differences becoming increasingly common. Our goal for this study was to explore the extent to which teaming and problem solving style, respectively, impact the perceptions of students about the creativity, diversity, and elaborateness of their ideas, as well as their perceptions of the relative difficulty of generating ideas alone or with another person.To this end, a study was conducted with 122 students participating in a variety of engineering-related programs across three Midwestern universities. Student academic level ranged from high school students participating in a pre-engineering program to undergraduate and graduate students enrolled in engineering and design degree programs. All students engaged in two separate ideation sessions (one individually and one in pairs) and completed a problem solving style inventory (KAI®). For the first session, students were asked to generate solutions to adesign problem individually using words and sketches. After this first ideation exercise, students were asked to generate ideas for a new problem in a two-person team, recording their ideas separately on their own individual worksheets. For each idea generated in the paired session,students were also asked to indicate which person of the two first verbalized each idea, as well a show much each person contributed to the idea’s generation and development.Following each ideation session, students completed a short reflection survey (individually) to provide insights into how they perceived their own ideation during the session. In particular, the students were asked to evaluate how creative, diverse, and elaborate their ideas were, along with the level of difficulty they experienced generating ideas under each condition. These student perceptions were analyzed for differences between the individual and paired ideation sessions. In addition, correlations between the students’ perceptions (from both sessions) and their individual problem solving styles were examined to determine whether perceptions differed between the more adaptive (more structured) and the more innovative (less structured) problem solvers, as measured by KAI ®. Preliminary results suggest that student perceptions of both the diversity and the elaborateness of their ideas are influenced by teaming and/or problem solving style. This paper will report on the details of our experimental procedure, the results of our analyses, and the implications of these results in the engineering classroom

Evaluating the Impacts of Different Interventions on Quality in Concept Generation

Producing ideas of high quality has great importance in engineering design. Although concept generation is sometimes one of the shorter phases of a project, concept generation that leads to viable and unique solutions can greatly contribute to a product’s final outcomes. Concept generation also has importance as a tool for engineering education and academic research. Because the quality of solutions can vary from individual to individual and from circumstance to circumstance, it would be useful to better understand how different interventions influence the outcomes of the ideation process in the concept generation stage of engineering design. In this work, we investigated the impacts of the problem context and three specific interventions designed to increase the ideation flexibility for the outcomes of concept generation. The three interventions were problem framing, design tools, and teaming. Our results show that both problem framing and teaming impact several aspects of quality, while design tools only impact the quantity of ideas produced

Impact of Problem Contexts on the Diversity of Design Solutions: An Exploratory Case Study

Impact of problem contexts on the diversity of design solutions: An exploratory case study he role of ideation in design is to generate design solutions that have the potential for further development. Having many diverse ideas increases the potential for successful design out comes by increasing the number of possibilities available during concept evaluation and selection phases. How do we define the problems that would allow for the most diverse solution space?The purpose of this study was to gain an understanding of how different contexts impacted the variety of solutions generated within the solution space, by a diverse group of students. In this exploratory case study, we report on (1) how we identified a set of design problems with diverse contexts appropriate for students with varied backgrounds, and (2) how we explored the impact of these problem contexts on the size of the solution space, aiming to select the contexts with the most diverse pool of ideas for our ongoing studies [1]. Our results show that diversity judged by multiple raters was consistent and provided us with evidence to support the decision of which design problems to use in our further studies

Variance in Centrality within Rock Hyrax Social Networks Predicts Adult Longevity

BACKGROUND: In communal mammals the levels of social interaction among group members vary considerably. In recent years, biologists have realized that within-group interactions may affect survival of the group members. Several recent studies have demonstrated that the social integration of adult females is positively associated with infant survival, and female longevity is affected by the strength and stability of the individual social bonds. Our aim was to determine the social factors that influence adult longevity in social mammals. METHODOLOGY/PRINCIPAL FINDINGS: As a model system, we studied the social rock hyrax (Procavia capensis), a plural breeder with low reproductive skew, whose groups are mainly composed of females. We applied network theory using 11 years of behavioral data to quantify the centrality of individuals within groups, and found adult longevity to be inversely correlated to the variance in centrality. In other words, animals in groups with more equal associations lived longer. Individual centrality was not correlated with longevity, implying that social tension may affect all group members and not only the weakest or less connected ones. CONCLUSIONS/SIGNIFICANCE: Our novel findings support previous studies emphasizing the adaptive value of social associations and the consequences of inequality among adults within social groups. However, contrary to previous studies, we suggest that it is not the number or strength of associations that an adult individual has (i.e. centrality) that is important, but the overall configuration of social relationships within the group (i.e. centrality SD) that is a key factor in influencing longevity

Engineering in and for Science Education

Chapter in: The Journey From Child to Scientist: Integrating Cognitive Development and the Education Science