Notes

Vectors and vector addition is a common topic in first-year, algebra-based Physics courses. In such courses, scaled vector diagrams are often used to add vectors that are not at right angles to each other. While trigonometric methods yield more precise results, a scaled vector diagram provides a reasonably accurate answer and provides students with a feel for what is physicall happening. Even courses that avoid scaled vector diagrams and rely totally upon trigonometric methods to add vectors must have a reliance on the head-to-tail method. There are numerous student difficulties associated with the head-to-tail addition of vectors. This Concept Builder provides plenty of practice with the skill of adding vectors graphically. It makes a great pre-cursor to the actual act of creating scaled vector diagrams.

This Concept Builder is intended as an in-class activity. After some discussion, modeling, and practice with doing vector addition, allow students an opportunity to practice one or more of the activities. Questions in this Concept Builder are grouped; the grouping allows us to give students a second question from the group if the first question is missed. If a student misses a question within a group, they will eventually be presented with a different question within the same group.

There are three difficulty levels in this Concept Builder. They are referred to as the Apprentice Difficulty Level (easiest), the Master Difficulty Level, and the Wizard Difficulty Level (most difficult). Questions in the Apprentice Difficulty Level are just as difficult as those ini the Wizard Difficulty Level. But the Wizard Difficulty Level has more questions. In fact that is the only trait that makes on difficulty level different than the others. For instance, the Wizard Difficulty Level contains the same six Question Groups as the Master Difficulty Level plus three more Questiion Groups. Teachers using the Concept Builder with their classes can preview the activity (or view the Questions in the separate file) in order to judge which difficulty levels would be most appropriate for their students.

In order to complete a level, a student must correctly answer one question from each question group in that level. If a student's answer is incorrect, then the student will have to correctly answer the same or very similar question twice in order to successfully complete the level. This approach provides the student extra practice on questions for which they exhibited difficulty. As a student progresses through a level, a system of stars and other indicators are used to indicate progress on the activity. A star is an indicator of correctly answering a question from within that question group. Once a star is earned, that question group is removed from the cue of question groups to be analyzed. Each question group is color-coded with either a yellow or a red box. A red box indicates that the student has incorrectly analyzed the question and will have to correctly answer it twice before earning a star. A yellow box is an indicator that the situation must be correctly answered one time in order to earn a star. Once every question group within a level been answered, the student earns a medal which is displayed on the Main Menu. This system of stars and medals allows a teacher to easily check-off student progress or offer credit for completing assigned levels.

The most valuable (and most overlooked) aspect of this Concept Builder is the Help Me! feature. Each question group is accompanied by a Help page that discusses the specifics of the question. This Help feature transforms the activity from a question-answering activity into a concept-building activity. The student who takes the time to use the Help pages can be transformed from a guesser to a learner and from an unsure student to a confident student. The "meat and potatoes" of the Help pages are in the sections titled "How to Think About This Situation:" Students need to be encouraged by teachers to use the Help Me! button and to read this section of the page. A student that takes time to reflect upon how they are answering the question and how an expert would think about the situation can transform their naivete into expertise.