Students at all levels of schooling in all countries of the world need to practice mathematical problem solving to develop competencies that they will apply in real-life scenarios. On the other hand, concerning solving, problem posing refers to both the generation of new problems and the re-formulation of given problems. Teaching mathematics from a problem posing and problem solving perspective entails more than solving non-routine problems or typical textbook types of problems. It is a way for students to exercise all aspects of problem solving: exploring, conjecturing, examining, testing, and generalizing. Tasks should be accessible and extend students’ knowledge. Even students should formulate problems from given situations and create new problems by modifying the conditions of a given problem. The quality of problems submitted to students is an issue that needs to be carefully considered. This work presents different ways to apply good practices when designing a problem solving activity with students. It is based on the experience of Digital Math Training, a project whose aim is to develop and strengthen Mathematics and Computer Science skills through problem solving activities using the ACE Maple. After initial training in the laboratories of the schools, 3 students per class - the most skilled or motivated ones - participate in online training. They are asked to solve a problem every 10 days and to submit their solution. Meanwhile, students can participate in weekly synchronous tutoring on the use of Maple and collaborate with their colleagues through forum discussions. Students are selected in an intermediate competition and a final one. In this setting it is important to carefully plan and present the activity to the students, the text of the problem should be clear, and concise, with little storytelling to enter the setting of the problem. The problems should not be too theoretical, even if they could inspect specific aspects of the related theory, and need to be solved starting by simpler requests until the most difficult ones, close to the edge of students’ knowledge, and making use of a calculator, in our case the Advanced Computing Environment Maple. Precise design principles are based on both the adoption of suitable practice and the use of Maple. These principles can be adapted to different situations. The paper describes all these features with examples, according to the literature.

Ten Tips for Successful Creation of Contextualized Problems for Secondary School Students with Maple

Sacchet, Matteo
2022-01-01

Abstract

Students at all levels of schooling in all countries of the world need to practice mathematical problem solving to develop competencies that they will apply in real-life scenarios. On the other hand, concerning solving, problem posing refers to both the generation of new problems and the re-formulation of given problems. Teaching mathematics from a problem posing and problem solving perspective entails more than solving non-routine problems or typical textbook types of problems. It is a way for students to exercise all aspects of problem solving: exploring, conjecturing, examining, testing, and generalizing. Tasks should be accessible and extend students’ knowledge. Even students should formulate problems from given situations and create new problems by modifying the conditions of a given problem. The quality of problems submitted to students is an issue that needs to be carefully considered. This work presents different ways to apply good practices when designing a problem solving activity with students. It is based on the experience of Digital Math Training, a project whose aim is to develop and strengthen Mathematics and Computer Science skills through problem solving activities using the ACE Maple. After initial training in the laboratories of the schools, 3 students per class - the most skilled or motivated ones - participate in online training. They are asked to solve a problem every 10 days and to submit their solution. Meanwhile, students can participate in weekly synchronous tutoring on the use of Maple and collaborate with their colleagues through forum discussions. Students are selected in an intermediate competition and a final one. In this setting it is important to carefully plan and present the activity to the students, the text of the problem should be clear, and concise, with little storytelling to enter the setting of the problem. The problems should not be too theoretical, even if they could inspect specific aspects of the related theory, and need to be solved starting by simpler requests until the most difficult ones, close to the edge of students’ knowledge, and making use of a calculator, in our case the Advanced Computing Environment Maple. Precise design principles are based on both the adoption of suitable practice and the use of Maple. These principles can be adapted to different situations. The paper describes all these features with examples, according to the literature.
2022
Maple Conference 2021 - Maple in Mathematics Education and Research
Online conference
2021
2
1
1
11
https://mapletransactions.org/index.php/maple/article/view/14446
Maple, Problem solving, Secondary students
Sacchet, Matteo
File in questo prodotto:
File Dimensione Formato  
Sacchet-Maple-Transactions-Ten-Tips-2022.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 564.91 kB
Formato Adobe PDF
564.91 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1875244
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact