Acquisition of a skill in a Physics course is demands repeated practice with as much feedback as possible. Many teachers of Physics spend time on the skill of graphically adding vectors using the head-to-tail vector addition method in order to determine the resultant. This Concept Builder is intended to provide students multiple practice opportunities of visually rearranging the given vectors into a head-to-tail arrangement and identifying the resultant vector as extending from the tail of the first vector to the head of the last vector. Feedback is immediate and opportunities to repeat missed questions are plentiful.

This Concept Builder is intended for use near the early to middle stages of a learning cycle on vector addition. Its strength is in helping students acquire the habit of using the head-to-tail vector addition method to add 3, 4, or 5 vectors. The vectors are displayed on a background grid of adjoining squares with each vector extending from one corner to another corner of a square on the grid. While the vectors cannot be physically moved about the screen, a student can easily use a pencil or a pen cap on the screen and place it on the grid at the corner where the second, third, fourth, or fifth vector ends. They can then visually identify the length and direction of the resultant vector.
 

This Concept Builder is intended as an in-class activity. After some discussion, modeling, and practice with adding vectors, allow students an opportunity to practice one or more of the three levels of difficulty. Questions in this Concept Builder are grouped, with questions in the same group being nearly identical. If a student misses a question within a group, they will eventually be presented with a different question within the same group. Teachers using the Concept Builder with their classes should preview the activity (or view the Questions in the separate file) in order to judge which levels would be most appropriate for their students.

Our summary of the three levels is as follows:

We can imagine it being profitable to allow students to make judgements as to what level to begin with and to progress from easier to more difficult levels. 

In order to complete a level, a student must correctly answer one question from each question group at 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 level. 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 que 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 at a level has 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.