Diverse teaching practices with FullProof

FullProof is a computer-based system for writing geometry proofs. It holds thousands of questions covering every geometry topic, and suits grade 7 through the 4–5 unit Bagrut.

The system suits learning and practice, face-to-face and online lessons, formative assessment and learning from mistakes.

This page describes some common ways of teaching with it — only a small part of what is possible.

The system makes room for varied teaching. Many of these practices don't need a computer per student, and work with one computer for every 4 students or with no computer at all. Some examples follow. We'd be glad to hear more ideas from you.

Formative assessment

The system gives detailed feedback on every step of the proof: whether the statements and reasons are correct, which steps are missing or redundant, and whether the writing is precise and correct. Students can fix the proof and resubmit it as often as they like, until the solution is correct. Over time, students learn to write short, precise proofs.

Checking tasks and showing solutions

With FullProof you can easily see which students solved the question and how good each solution is, compare different solutions, spot common mistakes (in a question or for a student) and use the learning opportunities those mistakes create. You can address tasks individually, for example in a one-on-one lesson or a report-card comment, or with the whole class as part of the lesson.

Using solutions from the system to advance learning

Solutions written by students open many teaching opportunities, among them showing different solutions to the same question and discussing mistakes (you can hide the students' names with Hide student names in the task report). Students can present the solutions they wrote without rewriting them on the board. Students can also check other students' answers themselves (especially suited to group work, and possible without a computer by printing the solutions).

Inquiry tasks and discovering theorems

You can build tasks in which students prove one theorem or a set of related theorems. In these tasks the theorem being proved is blocked from use. You can prepare several versions in advance for different configurations in which the theorem can be proved (for example different kinds of triangles), or proofs in different ways (for example with a different auxiliary construction). You can also prove properties that aren't theorems, or build tasks around another organising idea (for example the three-games method). The theorem-proving questions are in the system under textbooks / proving theorems, and the proving theorems teaching unit (in Hebrew) explains them.

Instead of the board

You can show solutions in the system instead of writing them on the board. They can be solutions prepared in advance or a solution written together with the students in class. To invite students to present their own solutions, there's no need to rewrite the question. Especially suited to online teaching, where the presenting student can share their screen with the class.

Instead of the notebook

The system can partly replace the notebook, since students' solutions are kept in it without limit. Still, we recommend students don't give up the notebook entirely, and use it to look for a way to solve, to summarise the material, to write full handwritten solutions that don't suit the system, and to keep in practice writing without it. In particular, the system removes many barriers for students with writing difficulties.

Learning in pairs or groups

Learning in pairs or groups can encourage students to support each other. You can have only one student write the shared solution in the system, especially when computers are short. In online learning, we recommend combining it with Zoom breakout rooms.

Quiz or graded work

The teacher knows when a student asked for hints and how many attempts it took to reach the solution. You can also set a task as a Quiz: a quiz has no hints, and students don't see feedback until the teacher releases the results. You can also give summer-holiday work through the system.

Lesson plans

We've prepared lesson plans for high school (for example the grade 10 teaching units) and for middle school (for example the grade 8 teaching units), currently in Hebrew. They lay out the teaching, with suggested class and homework tasks and sample solutions to every question.