Shouldn't the direction of electric field be opposite to that of the flow of electron? 
Above is the picture of the path taken by an electron in a conductor which is connected to a circuit. It was drawn by my teacher. Now, I know that the direction of flow of electron is opposite to that of the Electric field. But as you can see in the picture, he told the class that this is the path taken by an electron. He was actually trying to explain to the class why the average speed of an electron is much much greater than its average velocity when connected in a circuit. And he had also warned that he might interchangably use the terms electron and positron, which he had warned are not the same. So does the above path taken by an electron and it being finally displaced x units in the direction of the electric field make sense ?
 A: Qualitatively, think of the overall motion of electrons as having two components.
One component involves the random motion of free electrons. That is the very rapid random motion of the individual electrons in a conductor due to thermal energy, for which there is no net collective motion of the electrons in any particular direction. It's the motion your teacher describes as the "path taken by an electron". It exists whether or not an electric field is present.
The second component occurs when an electric field is introduced. The electrons now collectively move in a direction opposite to the direction of the electric field in the conductor. It is simply by convention that the direction of the electric field is the direction of the force (and movement) that a positive charge would experience if placed in the field.
The collective motion of the electrons is called the drift velocity and is directly related to the current in the conductor. This velocity is very slow compared to the random velocities of the electrons that occur with or without the electric field present.
It is also useful to note that electric current through a surface is defined as the rate of electric charge transport through that surface. Note it says "charge" without specifying whether the charge is positive or negative. The "charge" may be electrons, positive ions, positive "holes" in semiconductors, etc. So in some  cases the charge will move in the direction of the electric field and in others (electrons) it will move in the direction opposite to the field.
Hope this helps.
A: In the classical model, electrons in a conductor are bouncing around at random in thermal equilibrium with the atoms.  In the presence of an electric field the path between each bounce becomes a curve, with each deflection being opposite to the direction of the field.
A: Think about a pinball or pachinko game. Overall the force on the back due to gravity is downward. But on its way down the ball interacts with the bumpers, so it spends most of its time bouncing around semi randomly. Ultimately it always ends up at the bottom of the game board though.
The electron is similar. It interacts with the atomic nuclei, causing its motion to be mostly random. But in the end it ends up moving overall in the direction of the one uniform force on it, due to the electric field.
