Math4U meets JSXGraph
Petr Beremlijski and Pedro A. García-Sánchez
Department of Applied Mathematics, Faculty of Electrical Engineering and Computer Science, VSB-Technical University of Ostrava, Czechia, and
Departamento de Álgebra, Facultad de Ciencias, Universidad de Granada, 18071 Granada, España
petr.beremlijski@vsb.cz , pedro@ugr.es
Keywords: Digital exercises, digital assessment, mathematics, STACK
Abstract
Math4U portal helps teachers is a KA2 Cooperation Partnership supported by the European Union’s Erasmus+ program, and aims to develop the math4u.vsb.cz portal further, in particular, by expanding the TrainingGames4U, AppliedMath4U, and Math4Teacher applications. Another important goal is to prepare teacher guides to help teachers use the portal.
AppliedMath4U contains 50 detailed real-world problems, available in HTML and PDF formats for teachers and students. These real-world problems are designed to be used in the classroom and can be solved by students individually or in groups. The worksheets will be available in English, Czech, Spanish, Slovak and Polish. Each worksheet will be accompanied by a methodological guide for teachers, which will include competencies to be acquired, learning outcomes, pre-knowledge needed, timing and group distribution, potential problems encountered by the students, adaptations to different levels of students, and suggestions for further development of the topic.
The HTML versions of the worksheets will include interactive elements, so that the students can experiment, explore and check their solutions. The PDF versions will be printable and can be used in classrooms without internet access. There will be a reduced version for students and an extended version for teachers. Both static versions will include QR codes to access the interactive elements.
Most of the interactive elements appearing in the worksheets will be developed using JSXGraph. So far, we have developed applets for seven of the worksheets.
- Parabolic calculator: use of a parabola to compute the product of two numbers. Fiddle: https://jsfiddle.net/pedritomelenas/y7458Lmj/19/
- Product of two numbers with straight edge and compass. Fiddle: https://jsfiddle.net/pedritomelenas/6yf0jru9/10/
- Continuous fraction representation of a rational number. Fiddle: https://jsfiddle.net/pedritomelenas/856rwndu/4/
- Three applets to explore radioactive decay and half-life. Fiddles: https://jsfiddle.net/pedritomelenas/kx4r1f5s/2/ , https://jsfiddle.net/pedritomelenas/2c3ke1L9/5/ , https://jsfiddle.net/pedritomelenas/acuxynw8/4/
- Mean proportional between two numbers (segments). Fiddle: https://jsfiddle.net/pedritomelenas/1cfqdt9z/2/
- Golden ratio proportion of two numbers (segments). Fiddle: https://jsfiddle.net/pedritomelenas/xzL2901f/61/
- Hitting a golf ball with a given initial speed and angle, and exploring the effect of changing the initial speed and angle on the trajectory of the ball. Fiddle: https://jsfiddle.net/pedritomelenas/ncd9qt62/13/
- Carlyle circle: use of a circle to solve a quadratic equation. Fiddle: https://jsfiddle.net/pedritomelenas/L16ea498/2/
Applets will be inserted in the HTML versions of the worksheets, and QR codes will be included in the PDF versions to access standalone versions of the applets.
In our talk, we will present some examples of the worksheets for AppliedMath4U, the methodological guides, and the interactive elements.
Math4U Supports Teachers and Students is a project funded by the European Union’s Erasmus+ program (project number 2025-1-CZ01-KA220-SCH-000355317), and is running from 01-09-2025 until 31-08-2028. The European Commission’s support for the production of this abstract does not constitute an endorsement of the contents, which reflect the views only of the authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.