Machine Interpretation of Students’ Hand-Drawn Mathematical Representations

2015 ◽  
pp. 49-56 ◽  
Author(s):  
Kimberle Koile ◽  
Andee Rubin
Keyword(s):  
Mathematical Representations

scholarly journals Analysis of Cooperative Perception in Ant Traffic and Its Effects on Transportation System by Using a Congestion-Free Ant-Trail Model

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2393
Author(s):  
Prafull Kasture ◽  
Hidekazu Nishimura
Keyword(s):  
Average Velocity ◽  
Transportation System ◽  
Self Organization ◽  
Model Parameters ◽  
Agent Based ◽  
Model Simulations ◽  
Mathematical Representations ◽  
Traffic Conditions ◽  
Traffic Jams ◽  
Ant Trail

We investigated agent-based model simulations that mimic an ant transportation system to analyze the cooperative perception and communication in the system. On a trail, ants use cooperative perception through chemotaxis to maintain a constant average velocity irrespective of their density, thereby avoiding traffic jams. Using model simulations and approximate mathematical representations, we analyzed various aspects of the communication system and their effects on cooperative perception in ant traffic. Based on the analysis, insights about the cooperative perception of ants which facilitate decentralized self-organization is presented. We also present values of communication-parameters in ant traffic, where the system conveys traffic conditions to individual ants, which ants use to self-organize and avoid traffic-jams. The mathematical analysis also verifies our findings and provides a better understanding of various model parameters leading to model improvements.

Supporting Mathematics Teaching Practices in Online Teacher Education

2020 ◽  
pp. 55-67
Author(s):  
David Glassmeyer
Keyword(s):  
Content Knowledge ◽  
Mathematics Teaching ◽  
Teaching Practices ◽  
Teacher Educators ◽  
Science Content ◽  
Face To Face ◽  
Mathematical Representations ◽  
Integrated Stem ◽  
Online Format ◽  
Mathematics Teaching Practices

In this chapter, the author provides an example of an integrated and collaborative activity for in-service mathematics teachers that was implemented synchronously online. While prior research details how this lesson developed middle and secondary teachers' mathematics content knowledge of logarithms and teachers' science content knowledge concept of pH, this chapter focuses on how the lesson was converted from a face-to-face format to the online format while supporting research-based essential teaching skills, specifically NCTM's Mathematics Teaching Practices (MTPs). Evidence is provided for how three MTPs were upheld using the online platform Blackboard Collaborate, followed by recommendations for other teacher educators wishing to engage teachers in online learning that supports mathematics education goals of integrated STEM education through mathematical discourse, conceptual understanding, and reasoning about mathematical representations.

Exploring teachers’ conceptions of representations in mathematics through the lens of positive deliberative interaction

Pythagoras ◽  
2012 ◽  
Vol 33 (2) ◽  
Author(s):  
Deonarain Brijlall ◽  
Sarah Bansilal ◽  
Deborah Moore-Russo
Keyword(s):  
South Africa ◽  
High School ◽  
South African ◽  
Mathematics Teachers ◽  
Classroom Environments ◽  
High School Mathematics ◽  
Teacher Conceptions ◽  
Written Responses ◽  
Mathematical Representations ◽  
Cooperation Model

This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education qualification at a South African university. Common themes in teacher conceptions of representations were investigated as part of an inductive analysis of the written responses, which were considered in terms of practices that support dialogue and negotiation. Findings suggest that these conceptions are in line with progressive notions of classroom interactions such as the inquiry cooperation model. Furthermore, the findings suggest that teachers can support the development of classroom environments that promote democratic values.

Darwin's log: a toy model of speciation and extinction

1995 ◽  
Vol 32 (02) ◽  
pp. 279-295
Author(s):  
David Aldous
Keyword(s):  
Mathematical Modelling ◽  
Stochastic Models ◽  
Genetic Type ◽  
Applied Probability ◽  
Environmental Niche ◽  
Mathematical Representations ◽  
Geographical Regions

Stochastic models for the origin and extinction of species have been rather neglected in applied probability. As an alternative to modelling speciation and extinction as intrinsically random, I shall describe and show simulations of a rulebased model. This involves mathematical representations of notions such as genetic type of species, environmental niche, fitness of a species in a niche, and adaptation. There are underlying random mechanisms for changes of niche sizes and for disconnection and reconnection of geographical regions, and these ultimately drive the evolution of species. Other approaches to mathematical modelling of evolution are briefly mentioned.

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