Teaching Modules

Teaching and learning

The sketchometry teaching modules provide a comprehensive teaching and learning concept that individualizes learning processes and promotes inquiry based learning. It can be used on a modular basis, particularly in geometry and calculus classes at secondary level.



The concept of the sketchometry teaching modules enables the transition from passive-receptive teaching to active discovery learning.

The content is not presented as a “ready-made system”. In a construction phase learners first get instructions on paper worksheets on how to construct objects and configurations with sketchometry. In the subsequent exploration phase work assignments are given that encourage learners to experiment independently and then to document the results by handwritten notes.

Structure of a teaching module

A teaching module consists of the following elements:

  • Information sheet (for teachers)
  • Students’ worksheet
  • Result sheet
  • Exercise sheet (optional)
  • Video to accompany the students’ worksheet

Information sheet

Each sketchometry teaching module contains an information sheet for teachers with the following components:

  • Learning prerequisites and objectives
  • sketchometry gestures and actions
  • Further exploration and tasks

Learning prerequisites and objectives

A teaching module adds a digital component to traditional teaching. The information sheet first lists the learning prerequisites and objectives of the respective module topic. This allows an easy inclusion into your own lesson script.

sketchometry gestures and actions

The sketchometry gestures and tools required to work on the teaching module are presented. Only very few (three to four) tools are necessary. This means that a teaching module can be used even if the students have little experience in using sketchometry.

Further exploration and tasks

Finally, further topical suggestions and differentiation options are provided.

Students’ worksheet

The core of a teaching module is a (printable) worksheet that guides the students.

This is done in two phases, a construction phase and an exploration phase.

Construction phase

The students’ worksheets contain some construction assignments. These are short instructions for developing their own construction with sketchometry. The students are actively involved.

Exploration phase

In the subsequent exploration phase instructions on the worksheet encourage learners

  • to experiment with their construction,
  • to make conjectures,
  • to take handwritten notes and sketches.

In addition to the construction the focus is on intensive engagement with the mathematical problem.

Result sheet

The individual formulation of conjectures and reasons requires practice and experience. To make it easier to keep one’s own records during the exploration phase, each teaching module includes a result sheet. The predefined structure of the result sheet allows to present the expected entries clearly – especially in the initial phase.

Handwritten notes, also in the study journal

With increasing experience students will be able to document their observations and results more independently and without a predefined structure. They then write down their ideas, sketches, assumptions and results in their exercise book or study journal. This can also include constructions with compass and ruler.

Handwritten notes and revisiting the interactive content initiate a further, deeper learning process and support sustainable learning success.

Exercise sheet

Exercise sheets serve as an optional component for deepening and clarifying the topic and can be used for individualizing lessons.

Understanding & practicing

The exercise sheets also contain tasks that can be completed both with and without digital tools. They are the connection to the traditional lesson script.

The exercise sheets are also suitable for homework.


Explanatory videos are an additional motivation for many students to engage in the relevant content.

The videos are suitable

  • for repeating the content,
  • to catch up learning material if the relevant lessons have been missed,
  • for working in inverted/flipped classroom settings.

Advantages of the sketchometry teaching modules

  • The content is not presented as a “ready-made system”.
  • Constructing independently makes students more familiar with the task at hand.
  • A self-created construction gives a sense of achievement.
  • “Slowing down” the learning process.
  • Intensive engagement with the respective topic.
  • Students have to be active.
  • Students work autonomously.
  • Their own notes force students to reflect and structure their thoughts.
  • Students determine their own learning pace.
  • No previous technical knowledge required.

Think – Pair – Share

Teaching with sketchometry teaching modules according to the “Think - Pair - Share” method supports inquiry-based teaching and learning.

Teaching and learning with sketchometry teaching modules according to the “Think-Pair-Share” method.

The aim of this approach is a combination of active, independent work phases of the students (guided by assignments to construct, explore, document, and discuss) and a presentation and results assurance phase moderated by the teacher.


First, the students work independently on the worksheet. They work on the respective construction task and then carry out the investigation tasks. At the same time, they write down their observations and assumptions on the result sheet. The teacher provides help for self-help if necessary or on request.


The students compare their results with those of their neighbors or within their learning group. If necessary, they add comments to their notes. The teacher observes the individual learning groups and is again available for advice (help for self-help). In doing so, the teacher finds out which assumptions or solutions are produced and thus gains an overview of the results achieved.


The results are discussed with the whole class. This can be done based on a completed result sheet of a learning group. In this more teacher-centered phase the teacher guides the discussion, corrects – if necessary – the results presented and makes any necessary additions. New terms can also be introduced in this phase.

Together with the students a sample result sheet can be created, which is then made available to the whole class, electronically or as a printout.

This approach is recommended rather than a result sheet prepared by the teacher. Otherwise, there is a danger that the students will not contribute enough themselves, because they know that they will receive a finished result sheet from the teacher.