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Our invention sequences are designed to be used in preparation for formal instruction. They do not replace what an instructor typically does in the classroom, but are designed to prepare the students such that the subsequent instruction is more effective. This means that instructors must make time for the invention tasks. But it is our experience that there is also a return since the subsequent instruction is more efficient. Schwartz and collaborators have done research that supports our observations.
|Velocity Sequence||The velocity sequence is usually the first sequence used. The popping corn invention task introduces the students to the process of inventing an index in a fairly simple context. Next with the fastness index the students are going through the same process but in a context more closely related to the topic of subsequent instruction, namely velocity. We include the slide steepness task here because velocity is often taught using position vs. time graphs, and a facility with slope is assumed by most instructors.|
|Work Sequence||If you teach energy before momentum, then the work sequence is the students' first encounter with a product quantity. Product quantities are difficult to conceptualize; people usually focus on one of the two quantities rather than understanding that the product is DIFFERENT than the factors. Hence, students tendency to confuse work with force. The car washing invention task introduces the students to the process of inventing an index in a fairly simple context. Next with the weightlifting index the students are going through the same process but in a context more closely related to the topic of subsequent instruction, namely the work done to increase the gravitational potential energy. The job difficulty index most readily leads into formal instruction. It includes more sophisticated numbers (scientific notation and a variable). It has been shown that students often lose reasoning skills when the numbers are more complex.|