Are you about to start a unit that you know students find difficult? By starting off with an over-arching question you give students both a lens, through which to evaluate the new information, and a scale that helps them evaluate the importance of each new piece of information.
An over-arching question is a question that you would hope a student could answer at the end of the unit. It’s not a problem to be solved, or a technique to be used, but instead a question you may ask another math teacher about a topic. By posing such a question to students at the beginning, and then expecting them to answer it by the end of the unit, it puts students in a new role as learners.
Students must consider all new information as it pertains, or not, to the question. They must seek connections and draw conclusions, compress and synthesize their understanding. Because the question is one you will not answer or address until after they’ve answered it on an assessment, they’re in charge of their learning and will not be able to mimic your answer.
An over-arching question can be a conceptual question that compares various aspects of the topic at hand, can compare an older topic with the new information, can be purely conceptual focusing solely on the new topic, or any other variation. The idea is that the question gets students to think about, and relate various pieces of information and concepts together.
An example, for teaching quadratic equations, would be: How are the leading coefficient, vertex and range related?
An example for teaching radians would be: What is the difference between a radian and a degree?
There’s no magic bullet in teaching. You can’t trick kids into learning, and a question won’t make them learn either. Execution is key here. Students must be held accountable for answering the questions from their own understanding and they must perform the due diligence in seeking that understanding.
Whether they get the question correct or not is irrelevant, if they’ve made connections, considered all pieces of new information, and come away with a better understanding of the concept at hand.
In the comment box below, please let me know what your over-arching questions will be and how they worked for you.