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1. Categorizing student interactions with manipulatives in statics

   Rupe, K. M.; Davishahl, E. (May 2022, 2022 ASEE Zone IV Conference)

   This work in progress paper describes ongoing work to understand the ways in which students make use of manipulatives to develop their representational competence and deepen their conceptual understanding of course content. Representational competence refers to the fluency with which a subject expert can move between different representations of a concept (e.g. mathematical, symbolic, graphical, 2D vs. 3D, pictorial) as appropriate for communication, reasoning, and problem solving. Several hands-on activities for engineering statics have been designed and implemented in face-to-face courses since fall 2016. In the transition to online learning in response to the COVID 19 pandemic, modeling kits were sent home to students so they could work on the activities at their own pace and complete the associated worksheets. An assignment following the vector activities required students to create videotaped or written reflections with annotated pictures using the models to explain their thinking around key concepts. Students made connections between abstract symbolic representations and their physical models to explain concepts such as a general 3D unit vector, the difference between spherical coordinate angles and coordinate direction angles, and the meaning of decomposing a vector into components perpendicular and parallel to a line. Thematic analysis of the video and written data was used to develop codes and identify themes in students’ use of the models as it relates to developing representational competence. The student submissions also informed the design of think-aloud exercises in one-on-one semi-structured interviews between researchers and students that are currently in progress. This paper presents initial work analyzing and discussing themes that emerged from the initial video and written analysis and plans for the subsequent think-aloud interviews, all focused on the specific attributes of the models that students use to make sense of course concepts. The ultimate goal of this work is to develop some general guidelines for the design of manipulatives to support student learning in a variety of STEM topics. 

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2. Categorizing student interactions with manipulatives in statics

   Rupe K.; Davishahl, E. (May 2022, 2022 ASEE Zone IV Conference)

   This work in progress paper describes ongoing work to understand the ways in which students make use of manipulatives to develop their representational competence and deepen their conceptual understanding of course content. Representational competence refers to the fluency with which a subject expert can move between different representations of a concept (e.g. mathematical, symbolic, graphical, 2D vs. 3D, pictorial) as appropriate for communication, reasoning, and problem solving. Several hands-on activities for engineering statics have been designed and implemented in face-to-face courses since fall 2016. In the transition to online learning in response to the COVID 19 pandemic, modeling kits were sent home to students so they could work on the activities at their own pace and complete the associated worksheets. An assignment following the vector activities required students to create videotaped or written reflections with annotated pictures using the models to explain their thinking around key concepts. Students made connections between abstract symbolic representations and their physical models to explain concepts such as a general 3D unit vector, the difference between spherical coordinate angles and coordinate direction angles, and the meaning of decomposing a vector into components perpendicular and parallel to a line. Thematic analysis of the video and written data was used to develop codes and identify themes in students’ use of the models as it relates to developing representational competence. The student submissions also informed the design of think-aloud exercises in one-on-one semi-structured interviews between researchers and students that are currently in progress. This paper presents initial work analyzing and discussing themes that emerged from the initial video and written analysis and plans for the subsequent think-aloud interviews, all focused on the specific attributes of the models that students use to make sense of course concepts. The ultimate goal of this work is to develop some general guidelines for the design of manipulatives to support student learning in a variety of STEM topics. 

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3. Integrative Analysis Using Big Ideas: Energy Transfer and Cellular Respiration

   https://doi.org/10.1007/s10956-023-10040-5  

   Shemwell, Jonathan T.; Capps, Daniel K.; Fackler, Ayca K.; Coogler, Carlson H. (May 2023, Journal of Science Education and Technology)

   Big ideas in science education are meant to be interpretive frameworks that empower student learning. Unfortunately, outside of the broad conception of scientific evaluation, there are few theoretical explanations of how this might happen. Therefore, we contribute one such explanation, an instructional concept called integrative analysis wherein students use a big idea to interconnect isolated scenarios and enrich their meanings. We illustrate the characteristics and value of integrative analysis within an empirical study of student learning in 9th-grade biology. The study focused on using energy transfer as a big idea for teaching cellular respiration. Fifty-nine students were randomly assigned to one of two instructional conditions. In the “analysis” condition, students processed a set of three manipulatives representing cellular respiration molecules; then, they abstracted the deep energy transfer structure of these manipulatives as a big idea. In the “recognition” condition, students processed the same molecule-manipulatives, but without energy interpretations. Instead, they constructed additional manipulatives using novel materials. Then, students in both conditions received an identical lesson where they used their knowledge of the manipulatives to learn about one cellular respiration process, glycolysis. Specifically, students processed a sequence of three texts describing glycolysis, annotating the texts with either their deep energy transfer structure (analysis condition) or their contextualized knowledge of the manipulatives (recognition condition). A posttest showed that in the analysis condition, this process was significantly integrative as evidenced by analysis students’ advantage over recognition students in connecting glycolysis to novel phenomena and generating causal explanations about glycolysis. 

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4. Language-Guided Adaptive Perception for Efficient Grounded Communication with Robotic Manipulators in Cluttered Environments

   Patki, Siddharth; Howard, Thomas M. (July 2018, 19th Annual SIGdial Meeting on Discourse and Dialogue)

   The utility of collaborative manipulators for shared tasks is highly dependent on the speed and accuracy of communication between the human and the robot. The run-time of recently developed probabilistic inference models for situated symbol grounding of natural language instructions depends on the complexity of the representation of the environment in which they reason. As we move towards more complex bi-directional interactions, tasks, and environments, we need intelligent perception models that can selectively infer precise pose, semantics, and affordances of the objects when inferring exhaustively detailed world models is inefficient and prohibits real-time interaction with these robots. In this paper we propose a model of language and perception for the problem of adapting the configuration of the robot perception pipeline for tasks where constructing exhaustively detailed models of the environment is inefficient and in- consequential for symbol grounding. We present experimental results from a synthetic corpus of natural language instructions for robot manipulation in example environments. The results demonstrate that by adapting perception we get significant gains in terms of run-time for perception and situated symbol grounding of the language instructions without a loss in the accuracy of the latter. 

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5. Dynamic prompt learning via policy gradient for semi-structured mathematical reasoning

   Lu, P.; Qiu, L.; Chang, K. W.; Wu, Y. N.; Zhu, S. C.; Rajpurohit, T.; Clark, K.; Kalyan, A. (May 2023, International Conference on Learning Representations (ICLR 2023))

   Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TABMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TABMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TABMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TABMWP. To mitigate this, we further propose a novel approach, PROMPTPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples. 

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