If you don't know what the discovery method is, let me give you a quick summary of the basics. With the discovery method teachers create an opportunity for students to DISCOVER mathematics (formulas, algorithms, connections, etc...). This is basically opposite of a teacher standing in front of the classroom and TELLING the students the mathematics. The discovery method leads to a greater understanding of mathematics and also builds students' confidence. Here are 4 tips to implements the discovery method in your classroom.

1. Open-Mindedness Environment: Since students are discovering what works and what doesn't work failure is bound to happen. In fact, you want failure to happen, because students will learn what does not work. However, students hate failing, because they do not want to look inferior to their classmates. This is especially true once students hit middle school, where students protect their image fiercely. If you don't set up an open-minded classroom, many students will rather not try than try and fail.

Setting up an open-minded classroom needs to start from day 1. It's a culture you need to establish and live in your classroom. Talk to your students about how mistakes are opportunities for growth. Even displaying student's mistakes (without names) and taking time to learn what mistakes were made is a great strategy, because your students will see how learning really does happen from mistakes.

2. Guided Task: You need to give your students a guided task. Guided tasks often have more than one answer, are approachable for all levels and have room for continued challenge. A simple example might be, "Create a prism with a volume of more than 230 cubic meters and less than 200 cubic meters." A challenge you could add on to this question is a condition of surface area as well. Let your students have a productive struggle.

3. Teacher Assistance: Teacher assistance is absolutely essential for successful discovery. Teacher assistance is NOT lecturing nor is it telling students what to do. Teacher assistance IS walking around the room and asking questions to the students. The questions may look like "Explain to me what you are thinking." "Explain to me this step that you did right here." If students are stuck, "Tell me what you do understand" or "Tell me what part you don't understand." Guide your students but do not spoil the discovery process.

4. Conclusion: Since the point of the discovery method is that students discover something you need to make sure to bring it all together to verify that ALL students have actually discovered what they need to discover. Also, if your guided tasks have multiple solutions or multiple ways to arrive at the solution you need to discuss this. One way that I have done this in my classroom, is when students are working and I'm walking around I make notes of the different ways students are solving the problem. I then have groups present different aspects of their process. I usually don't have time, nor is it necessary, to have groups make a huge presentation of their whole process. You just want to highlight the important points with the goal that all students make the discovery that you need them to make, such as an algorithm or formula.

Once I implemented the discovery method in my classroom, retention of the material increased because students could connect the mathematics to experiences.

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