Part of growing as an intellectual is learning to understand fundamental concepts behind knowledge rather than just memorizing knowledge itself. Challenge your students to learn difficult concepts by promoting independent learning. Have them, for instance, complete a unit of math on their own without any instruction. Alternatively, break your class into groups and assign each a chapter in your textbook. Have groups learn the material on their own and teach it to the rest of the class.
To grow intellectually, students need to learn to be able to consider perspectives other than their own. Encourage this by having students write a paper arguing the opposite of what they believe, no matter what the topic is. You can also stage debates between two students on any polemical topic. Halfway through, stop the debate and have students switch sides and argue the opposing viewpoint.
Making students aware of the learning process and their own abilities is part of fostering intellectual growth. Let students evaluate their own work periodically throughout the school year. Encourage them to reflect on their own strengths and weaknesses as students. Ask them to consider what they could have done better. At the beginning of the year, have students write journal entries focused on what they hope to achieve. Have them revisit their journals later in the year and write a new entry about whether or not they achieved their goals.
You can promote intellectual growth by encouraging students to take creative approaches to problem solving. Every morning, put a logic puzzle or brain teaser on the board. Devote some time each day to allow students to try to solve it. Cross disciplines and allow students to write creative responses to their work in science or math. Encourage hands-on learning and experimenting when it comes to subjects such as natural science.