Active Mathematics for Homeschooling Families


Hans Ruegg

Soy suizo-peruano, padre educador de dos hijos adolescentes. Vivo en la sierra peruana y he trabajado como maestro teológico, como profesor de inglés, como capacitador de colaboradores en el ministerio con niños, y en un proyecto de refuerzo escolar y educación alternativa. - - Formación profesional: - Certificado suizo de Madurez en Matemática y Ciencias Naturales - Magíster en Teología (Basilea, Suiza) - Diplomado en Educación Cristiana (Antorcha Ministerios Educativos, Perú) - Asesoramiento por la Fundación Moore para educación en casa - Diversos cursos a distancia en las áreas de Matemática, Educación, y las TIC. - - - I am a Swiss-Peruvian, homeschooling father of two teenagers. I live in the Peruvian Highlands and have worked as a teacher of Theology and English, as a trainer of staff for Children's Ministry, and pioneering a project of remedial classes and alternative education (K-12).

Reviews (1)

Margaret Wilson


A free online course for homeschooling families who wish to improve their children's math learning experience.

In parallel, this course is also offered in Spanish.

Note: This course is now self-paced. You can enroll, start and finish any time you wish.

If you enrolled already in this course at an earlier date, enter with that same account and continue.
(In case you forgot your password, on the login page click on "Forgot your Password?". You will then have to indicate your email address - the same you used for creating your account.)


Course Description

In this course we will explore several creative ways of learning and teaching mathematics, corresponding to children's needs. Course participants (parents and teachers) will review and adjust their own concept about mathematics, and will practice mathematical thinking. At the same time they will realize some practical math projects with their children. So the course includes also the children's math classes. The methods applied here are mostly based on the concept of "Active School". The most important goals of the course are that participants:

  • Overcome fear of math, and discover a new approach to mathematics based on concrete materials, own investigations, and games.
  • Become capable of designing and realizing practical mathematical activities with their children.
  • Acquire an understanding of the mental development of children, in order to design their activities accordingly.
  • Begin to practice mathematical thinking, together with their families.


For whom is this course?

This course is mostly designed for homeschooling families. This surrounding provides the best opportunities and the greatest freedom for practicing the projects suggested in this course. But other families, school teachers, students, and other interested participants may also benefit from this course, adapting the projects to their specific situation.

The projects are optimized for children from 6 to 12 years old; but you will also receive some hints of how to adapt them for smaller or older children.


Course Structure and Workload:

The course consists of five modules. Each module requires:

  • Studying some short instructional texts and videos
  • Answering some questions of review and reflection about the theory lessons
  • Realizing a math project with your own children, or with another comparable group of children. (This will be the most important part of the course.)
  • Submitting a written report about the project, which will be peer-reviewed by other course participants.

Additionally, it is much recommended to participate in the discussion forums related to the course.

The recommended total time required for completing each module is 15 hours distributed over two weeks. About half of this time will be invested into the practical project with the children.


Summary of Course Contents

Module 1: Let's start with a concrete activity
We will begin to acquire a new perspective about math; we will talk about the importance of concrete activities for learning; and we will realize our first practical project (Estimating and measuring quantities).

Module 2: Mathematics is understanding and applying principles
We will learn about principle-based math teaching, and we will realize a practical project about the principles which govern the decimal system, using an abacus and other related materials.

Module 3: Doing mathematics is creating, investigating and discovering.
How does the child's own investigative activity help to learn math? - The practical project of this module encourages children to discover mathematical properties by themselves.

Module 4: Continue thinking mathematically
We will go deeper into some elements of mathematical thinking, and we will realize another mathematical investigation.

Module 5: Your own project
We will talk about how to build a positive relationship with mathematics. - In this module, participants design a project based on their own ideas.

Some of the course videos are publicly accessible at


Prerequisites for participants:

A disposition for changing your views about math, and for practicing new ways in learning and teaching math.
Opportunity for realizing the practical projects with your own children or with a comparable group.
No special mathematical knowledge is necessary.

Note: This is an introductory course. Other more advanced courses which build upon this one are planned for the future.

Course content

  • Module 0: Enter into our circle, introduce yourself, get accustomed to this course.

  • 0.1. Some values and attitudes which will help you to succeed in an online course

  • 0.2. Course Structure and Time Requirements

  • 0.3. Some questions and answers about this course

  • 0.4. Getting used to the Eliademy website

  • 0.5. Additional readings

  • Module 1: Let's start with a concrete activity

  • 1.1. Hints for the practical realization of the projects

  • 1.2. How to write your Project Report

  • Module 2: Mathematics is understanding and applying principles

  • 2.1. Worksheets related to the projects of Module 1

  • Module 3: Doing mathematics is creating, investigating and discovering

  • 3.1. Worksheets related to the projects of Module 2

  • 3.2. Hints for writing your project report (Modules 3 and 4)

  • Module 4: Continue thinking mathematically

  • 4.1. Worksheets related to the projects from Module 3

  • Module 5: Your own project

  • 5.1. Worksheets related to the projects from Module 4

  • 5.2. Hints for writing your project report (Module 5)

  • The last week: Will the adventure continue?

Interested? Enroll to this course right now.

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