Joseph Lancaster's Improvements has this to say on the matter http://www.constitution.org/lanc/practical.htm
On a repeated or frequent offence, after admonition has failed, the lad to whom he presents the card has liberty to put a wooden log round his neck, which serves him as a pillory, and with this he is sent to his seat. This machine may weigh from four to six pounds, some more and some less. The neck is not pinched or closely confined — it is chiefly burthensome by the manner in which it encumbers the neck, when the delinquent turns to the right or left. While it rests on his shoulders, the equilibrium is preserved; but, on the least motion one way or the other, it is lost, and the logs operate as a dead weight upon the neck. Thus, he is confined to sit in his proper position.
It makes for good reading and he goes on to say ....
Few punishments are so effectual as confinement after school hours. It is, however, attended with one unpleasant circumstance. In order to confine the bad boys in the school-room, after school-hours, it is often needful the master, or some proper substitute for him, should confine himself in school, to keep them in order. This inconvenience may be avoided, by tying them to the desks, in such a manner that they cannot untie themselves
So the log is like a smaller portable 'stocks' http://en.wikipedia.org/wiki/Stocks.
I find a slightly different description at https://iainmavrocoggins.wordpress.com/tag/victorian-england/ (Ian Mavro Coggins) which says
More stringent was “the log”, a four to six pound chunk of wood that was fixed by a rope about neck in response to “a repeated or frequent offence”. Lancaster notes that its effect is “chiefly burthensome”
However I can find no other evidence, yet, to back up the claim that it was a chunk of wood hung by a rope
There is also a slightly different description of 'the log' here, The Union Charity School in Brighton http://www.middlestreet.org/mshistory/punish.htm, which was a 'Lancaster' school. An ex-pupil describes the possible punishments:
Mr. John George Bishop, an old-boy of the school described the first headmaster as follows:
“Mr. Sharp – a man of sterling worth – was the first Master of this school. He was however a strict disciplinarian, and some of his modes of punishment were decidedly original. In addition to the orthodox ‘strap’ and ‘birch’, the ‘dunce’s cap’ and the ‘red tongue’ for talkers, there was for the incorrigibles a ‘wooden collar’ – an unpleasant necklet; and for the truant, a ‘log’ – this latter a veritable log of wood some 3 ft long, which, chained to the leg, had to be dragged by the truant several times around the school, amid the ill-concealed scoffs and jeers of his fellows.
If we accept that 'a wooden collar' and 'the log' may have been the same thing Lancaster intended it may have looked something along the lines of this image (from http://www.oocities.org/westhollywood/heights/9417/other.html StocksMaster)