The honest-to-goodness answer is that there is no authentic traditional Arabic saying that echoes this pedagogical principle, and there is none that even comes close. I am not even sure if such a saying exists in Chinese, although I am willing to concede that a similar concept may have been attributed to an old Chinese sage, most likely not in the exact same terms. The principle itself is universally understood. It is taught in all teach-the-teacher and train-the-trainer programs, and it makes very good sense. So the only thing left is to translate it to good Arabic from scratch. Let's try to do that, step by step.

In Arabic, rote learning is called تلقين. This is when a teacher recites something and the pupil echoes it immediately afterwards and then keeps repeating until it hopefully sticks. My mother was a Quranic teacher, and i have observed her doing exactly that. The idea behind it is not entirely senseless. The idea is that the pupil at first may not comprehend and internalize the material, but in time, the pupil matures and begins to discover the meaning behind the words, although different pupils will do so at different rates, depending on their innate intelligence, their interest, and diligence. If you have seen the movie Firelight, you will know what i mean.

With that in mind, the first part can be translated as:

Tell me and I forget
أتلقن فأنسى

The second part is fairly easy:

teach me and I may remember وأتعلم فلعلي أذكر

The last part involves the word "involve," which means to let the learner learn by doing, by participating, by experiencing and experimenting, and by making mistakes. In other words, by working first hand. Let us try:

involve me and I learn وأعمل فأتعلم

Now, let's put it together:

Tell me and I forget, teach me and I may remember, involve me and I learn.
أتلقن فأنسى، وأتعلم فلعلي أذكر، وأعمل فأتعلم

Try playing around with it and be creative. Here are some possibilities:

بالتلقين أنسى، وبالتعليم ربما أذكر، وبالعمل أتعلم
تلقنني فأنسى، وتعلمني فلربما أذكر، وتطلق يدي فأتعلم
إن لقنتني نسـيت، وإن علمتني فلربما أذكر، وإن أطلقت يدي تعلمت

And so on.