scholarly journals Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm

2021 ◽  
Author(s):  
Roberto Araya
Keyword(s):  
Elementary School ◽  
Low Socioeconomic Status ◽  
Real Life ◽  
Steepest Descent ◽  
Second Phase ◽  
Mathematical Tool ◽  
School Students ◽  
Online Platform ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

scholarly journals Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm

2021 ◽  
Author(s):  
Roberto Araya
Keyword(s):  
Elementary School ◽  
Low Socioeconomic Status ◽  
Real Life ◽  
Steepest Descent ◽  
Second Phase ◽  
Mathematical Tool ◽  
School Students ◽  
Online Platform ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

scholarly journals Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1197
Author(s):  
Roberto Araya
Keyword(s):  
Elementary School ◽  
Low Socioeconomic Status ◽  
Real Life ◽  
Steepest Descent ◽  
Second Phase ◽  
Mathematical Tool ◽  
School Students ◽  
Online Platform ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

The steepest descent (or ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children’s real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development workshop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-min introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.

scholarly journals Local Search Algorithms for the Beam Angles’ Selection Problem in Radiotherapy

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Guillermo Cabrera-Guerrero ◽  
Nibaldo Rodriguez ◽  
Carolina Lagos ◽  
Enrique Cabrera ◽  
Franklin Johnson
Keyword(s):  
Radiation Therapy ◽  
Local Search ◽  
Organs At Risk ◽  
Treatment Plan ◽  
Search Algorithms ◽  
Steepest Descent ◽  
Beam Angle ◽  
Local Search Algorithms ◽  
Descent Algorithm ◽  
Steepest Descent Algorithm

One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.

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