Math and Art – Functions Properties
SUMMARY
Mathematics lessons must meet the needs of students' personality development by stimulating capacities, skills and attitudes based on critical, logical, divergent and creative thinking. To achieve these, attractive and engaging mathematics lessons need to be taught using modern student-centred methods. Transforming a lesson in an agile way using the ACCED toolkit brings these benefits.
Non-violent communication is used in group work and in the warm-up activity, where students are asked to choose a mood that helps to relax the atmosphere. Moreover, the interpretation of these drawings makes the transition to the contents to be updated and applied. These activities help students to approach mathematics with love and without fear, to discover their skills for this object.
The Agile/Scrum strategy is used in Team cooperation, also in each sprint, where tasks are related to the definition of done.
In Sprint 1 the teacher makes a short revision of function properties (parity, monotony, convexity, intersection with axes) and presents them the Desmos Graphing Calculator. Integrating technology to this lesson develops the students ability to use resources (computers, Desmos, Miro, internet) for learning activities and allows the diversification of teaching strategies. Also, the graphical representation of the functions represents an useful intuitive support in studying their properties.
In Sprint 2 instead of the teacher presenting the students the properties of the four types of functions, the students are challenged to discover them in working groups by interpreting the graphs of the functions. In a group, students work according to the 1-2-4-All Liberating structure. Each of the four groups studies a type of function and then presents them to their colleagues.
PBL (project-based learning) is used in Sprint 3 to carry out the assessment. Students are asked to make a drawing related to a given topic, using at least fifty lines representing graphs of some studied functions. Completion of this project involves the comparative application of the properties of the functions, giving the student the opportunity to learn in a pleasant way.
Students can: Interpret, based on the graphic reading, the algebraic properties of the functions make a drawing on a given topic using the graph of the studied functions
OPEN DIGITAL BADGE
Badge 1 – The Drawer – uses Desmos for drawing functions graphs https://badgr.com/public/badges/-IRYL6yeRw2cAt5vAZfVKQ Badge 2 –The Interpreter - deduces some of algebraic properties of function by interpreting their graphs https://badgr.com/public/badges/0sqN5BIqSpSlMk7ygQzXYQ Badge 3 – The Analist – compares the properties of certain functions https://badgr.com/public/badges/evJiGjgVR3ybAH0xSa5tMw Badge 4 –The Artist – makes complex drawings using the graphic representation of functions Badge 1 – The Drawer – has drawn elementary functions graphs Badge 2 –The Interpreter – has deduced the parity, monotony, bijectivity, intersection of the graph with the axes using the graphs Badge 3 – The Analist – has analised the properties of certain functions depending on some parameters Badge 4 –The Artist – has drawn creative, complex drawings by using Desmos
Summary of the transformation (changes that were made in teaching)
Function properties are abstract, and their graphical representation provides useful intuitive support. Non-violent communication is used in the warm-up activity, where students are asked to choose a mood that helps to relax the atmosphere. Moreover, the interpretation of these drawings makes the transition to the contents to be updated and applied. Instead of the teacher presenting the students the properties of the four types of functions, they discover them in working groups by interpreting the graphs of the functions. In a group, students work according to the 1-2-4-All Liberating structure. PBL (project-based learning) is also used to carry out the assessment. Students are asked to make a drawing related to a given topic, using at least fifty lines representing graphs of some studied functions. The Agile/Scrum strategy is used in Team cooperation, also in each sprint, where tasks are related to the definition of done, The changes comes using exercises and methods described on the project’s website https://accedproject.org/ .
