Construction of Concepts Images from Mathematical Models Obtained with the Tracker Software

This work aims to investigate the potential of combining the Mathematical Modeling methodology with the use of the software Tracker with undergraduate students in Mathematics in the reconstruction of physical models for the construction of function concepts. For this, a qualitative and exploratory study of bibliographic and experimental character was carried out, involving field activities. Our results point to a greater understanding in the construction of the models, since the mathematical models can be recreated from the correlation to physical models already validated. We also verified that the Tracker software enables an excellent visual perception of different concept images.

Assessing Concept Novelty Potential with Lexical and Distributional Word Similarity for Innovative Design

Generating novel design concepts is a cornerstone for producing innovative products. Although many methods have been proposed for supporting the task, their performance depends on human ability. The goal of this research is to build a method supporting designers to generate novel design concepts with the knowledge of what factors have positive effects on the novelty. Toward the goal, this research assumes that the more distant two function concepts chosen, the more novel idea would come up with by the combination of the two concepts. Based on the assumption, this paper introduces a notion of novelty potential of the combination of two function concepts, and proposes a method to assess it by the function similarity. It is calculated with the integration of a lexical database for natural language called WordNet and a distributional semantics method called word2vec. The proposed method is adapted to case studies in which students perform design concept generation for given design tasks. The correlation analysis is performed to verify the assessment performance of the proposed method. This paper discusses its possibility based on the results of the case studies.

Closing the Circuit on Function Concepts

A hands-on, project-based modeling unit illustrates how real-world inquiry deepens student engagement with function concepts.

Breaking Conventions to Support Quantitative Reasoning

Quantitative reasoning is critical to developing understandings of function that are important for sustained success in mathematics. Unfortunately, preservice teachers often do not receive sufficient quantitative reasoning experiences during their schooling. In this paper, we illustrate consequences of underdeveloped quantitative reasoning abilities against the backdrop of central function concepts. We also illustrate tasks that can perturb preservice teachers' thinking in ways that produce opportunities for quantitative reasoning. By implementing strategically designed tasks, teacher educators can support preservice teachers–and students in general–in advancing their quantitative reasoning abilities and their understanding of secondary mathematics content.