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Motivating is a big part of inspiring students. If they aren't motivated to learn, there's probably not a lot you can do to inspire them. Take some time to consider student motivations. First, think about intrinsic motivations.  Intrinsic motivations are basically internal. They are personal to each student. For example, intrinsic motivations might include a passion for the subject, or a desire to challenge themselves by mastering a skill. In an English class, you might have students intrinsically motivated by a love of books. Extrinsic motivations are also important to consider. These motivations come from outside sources. For example, parental expectations are an external motivator.  Another example is meeting the required GPA to keep a scholarship. It is important to learn what motivates each of your students. You can then use those personal goals to help encourage and inspire them. Each individual learns in different ways. Some students are visual learners, while others do best hearing information. Try mixing up your lessons so that you incorporate different styles each class.  Maybe you are teaching about World War II. You could play a popular song from the era, show a video clip of an important battle, and provide a letter from a soldier for students to read. Some students are collaborative learners. Others work best on their own. Try to provide a balance of group projects and individual learning. A great way to inspire students is by treating them as individuals. Once they see that you are interested in them, they are more likely to respond positively to learning. Take some time to learn something interesting about each student.  With very young students, Show and Tell can be a great way to get to know kids. Make sure to follow up on what you've learned. For example, you could say, "Teddy, you told us last week you have a new baby sister. How's that going?" With high school or college students, take an interest in their academic or career goals. You could say, "Tom, you're doing really well in my class. Have you considered majoring in Psychology?" Make sure to maintain boundaries. It's never a good idea to get too personal with your students. Sometimes it can be hard to connect learning to real life applications. For example, students might not understand how studying history can help them in their "real life". Inspire and motivate by giving them effective examples of how each lesson applies to them. Show your history students that your class can help them achieve  future career goals. For example, you can say, "In this class, we'll learn to analyze primary source documents. This will help you no matter what career you choose. If you're a lawyer, you'll have to analyze testimony, for instance. If you're in finance, you'll need to perhaps analyze stock reports." Students can feel unmotivated and uninspired if they are having trouble in the class. A student who is struggling to understand certain concepts might need some extra help. Take time to give some extra time to students who need it.  You could say, "Tina, I noticed you're having trouble with fractions. Maybe during free time, we could sit together and I'll give you some pointers." Ask questions. For example, "Mark, you seem to be having some issues coming up with a thesis statement. Is there something about the assignment that is confusing to you? How can I help?"
Consider intrinsic motivations. Understand extrinsic motivations. Appeal to different learning styles. Get to know your students. Use effective examples. Help struggling students.