Vectors/Basic Facts

Misconceptions or Tabula Rasa. Students are somewhat afraid of vectors, sense that there is something different about them, but don't quite know what it is. They are familiar with numbers and don't understand that vectors are different algebraic objects for which there are certain rules of composition with which these objects can be handled safely. They don't have a concept of different kinds of algebraic objects subject to specific rules of composition.

Students want to treat vectors as numbers. They are reluctant to use a different notation (with arrow) to denote vectors. Those who have seen vectors before in high school want to describe vectors in terms of magnitude and direction, not in terms of components. They usually have never heard of components. When asked to calculate a vector quantity, e.g., a force, students tend to want to calculate the magnitude only. They think they are not finished if they have found the components of the force.

Some students have difficulty with the graphical representation by vectors in terms of arrows. They don't understand in which direction the arrow points, have trouble identifying the tail and the tip of an arrow. They don't understand that the length of the arrow represents the magnitude of the vector. They don't understand the concept of magnitude of a vector.

Some students think that vectors need to be shown against axes. They don't have the notion of a vector as an absolute geometric entity. (It is true that in order to describe the direction of a vector one needs a reference line. Still the notion of axes is something separate. The notion of axes is related to the notion of basis of a vector space, which is not essential in defining the vector concept in terms of a set of objects with certain algebraic properties.)

Some students don't understand clearly that vectors can be dragged around and don't change in the process.

There are specific misconceptions related to the algebraic rules governing vectors which will be listed under Vectors/Addition, etc.

__Get a Glimpse__. Almost done. (Voice-over completed, but must still be synchronized with movie. At the end of movie, a small change is needed in the vector addition diagram.) FLASH cartoon movie involving a blimp ride from Calgary to Edmonton/Saskatoon. The point is that velocities don't add like numbers, but are vector quantities that must be added differently. The purpose of the movie is to show that there are physical quantities that are not represented by numbers.Tool Tip: "Movie of blimp ride with strong wind current".

__Explain It__. Completed. Explanation of vectors as quantities with magnitude and direction. Representation of vectors in terms of arrows. Simulation allowing manipulation of vector with variation of magnitude and angle and dragging of vector with change in either quantity. Explain It deals with the geometric (absolute) representation of a vector.Tool Tip: "Vectors as geometric quantities with magnitude and direction".

__Simulate It__. Completed. The simulation from Explain It. One page only.Tool Tip: "Magnitude and direction of vectors simulated."

__Get Information__. Done. General properties of vectors, distinguishing vectors from scalars, including notation. Graphical representation in terms of arrows. Mention of algebraic properties, but no detailed discussion of these and no mention of components.Tool Tip: "Vectors vs. scalars, notation, algebraic properties."

__Test Yourself__. Still to be done. A few questions on
notation: vectors and their magnitudes, and some basic questions
distinguishing vectors from scalars.

Tool Tip: "Vectors vs. scalars, notation, magnitude and direction."

__Vectors/Scalar Multiplication__.

This is not too difficult. Students need to learn about the fact that there is such a thing as scalar multiplication, what it does, especially the multiplication by a negative scalar. They need to learn what the negative of a vector is.

__Explain It__. Completed. With a simulation, this item demonstrates multiplication of a vector chosen by the student by any scalar and demonstrates the negative of a scalar and shows that the negative added to the original vector equals the zero vector. The rules of scalar multiplication are given.Tool Tip: "Multiplication of a vector by a scalar; negative of a vector".

__Simulate It__. Under construction. Simulation from Explain It.Tool Tip: "Multiplication of a vector by a scalar".

__Test Yourself__. Still be done. A few questions related to the Explain It item.Tool Tip: "Questions on scalar multiplication, negative of a vector".

__Get Information__. Under construction. The content of Explain It without simulation.Tool Tip: "Multiplication of a vector by a scalar, rules, negative of a vector".

__Vectors/Addition__

Misconceptions or Tabula Rasa. In adding two vectors, students ignore vector nature and add just magnitudes. Some students realize that vectors are different, but just don't know how to add them and have no intutitive feeling for what the resultant might be. Or, if they know about the tip-to-tail, they add the vectors tip-to-tail and then draw the resultant in the opposite direction, from the free tip to the free tail, so that the three vectors form a closed circuit. Or, they don't realize that there is a resultant: adding two vectors means joining them, but not drawing the resultant. Students are not familiar with the parallelogram construction. In adding more than two vectors, students are lost, don't have the understanding that they can use the associative law, first add two and then the third one to the resultant of the two.

__Get A Glimpse__. Almost done. Same as Get A Glimpse for Vectors/Basic Facts (Voice-over completed, but must still be synchronized with movie. At the end of movie, a small change is needed in the vector addition diagram.) FLASH cartoon movie involving a blimp ride from Calgary to Edmonton/Saskatoon. The point is that velocities don't add like numbers, but are vector quantities that must be added differently. The purpose of the movie is to show that there are physical quantities that are not represented by numbers.Tool Tip: "Movie of blimp ride with strong wind current".

__Explain It__. Contains three items: Explain It/Tip-to-Tail, Explain It/Parallelogram, and Explain It/Three Vectors. More information about these items under E in the row Vectors/Addition.Tool Tip: "Three items".

__Simulate It__. Contains two items: Simulate It/Two Methods and Simulate It/Three Vectors. More information about these items under S in the row Vectors/Addition.Tool Tip: "Two items".

__Get Information__. Still to be done. The essence of the three Explain It items. No simulations.Tool Tip: "Tip-to-tail and parallelogram methods, rules of vector addition".

__Vectors/Subtraction__

Misconceptions or Tabula Rasa.