Neil Stuart Lennie - once headmaster at prestigious Caulfield Grammar School - admitted that in 2014 he taught at a secondary college when unregistered.

Melbourne Magistrates Court heard on Tuesday that Lennie, 67, had repeatedly refused for years approaches by the Victorian Institute of Teaching to produce his qualifications to be registered.

Magistrate Franz Holzer, who heard Lennie described as a "maths genius", said his conduct was "cavalier" if not arrogant.

Lennie, of Box Hill North, also pleaded guilty to a charge of holding himself to be a registered teacher.

Prosecutor Rodney Hepburn said Lennie was advised in 2007 that all teachers were required to renew their registration every five years and that six months later he applied to renew his teacher registration which was approved in May, 2008.

Mr Hepburn said a month later, after the institute decided to hold a formal hearing into Lennie's "conduct in obtaining his registration", he advised that he wished to withdraw his application for renewal and so from May, 2009, he ceased to be registered.

In July of that year Lennie further advised that he had retired in May, 2008, as principal of the Melbourne Senior Secondary College, but as he remained only in a voluntary and honorary capacity he was not required to be registered with the institute.

Mr Hepburn said Lennie was told that his interpretation was wrong and that it was a criminal offence to teach while unregistered.

The chair of the college board and members of its teaching staff later confirmed that Lennie had been continuously employed as its principal from 2004 until his employment was terminated in April last year.

Defence barrister Steven Lowry said that Lennie also had been deputy principal at Mount Scopus, a chief examiner in physics and had appeared on national TV in China during a lifelong career in education in which he had made a "huge contribution" to the community and the profession and positively influenced thousands of students.

Mr Lowry said the chair of council at Caulfield Grammar School, where Lennie introduced the coeducational program, praised him as a person of high integrity and moral and spiritual values.

He said his client had a prior court appearance in 1997 over a tie he took from Myer, which Mr Hepburn revealed had involved Lennie having taken an item and then return to the outlet to claim a refund, a circumstance Mr Holzer regarded as a "foolish error of judgement he no doubt regretted".

In his sentencing submissions, Mr Hepburn noted that Lennie, between 2004 and last year, received about $600,000 in "benefits" and had been warned numerous times to produce his qualifications but had "refused to do so".

Mr Holzer acknowledged Lennie's significant contributions to education and the benefit he gave to many students over generations, but noted his lack of compliance and adherence to his regulatory obligations.

He said of concern was having confidence in the education system and that there was "sufficient concern" to warrant the recording of convictions.

Lennie, who offered to pay the fine "within a few days", was given 28 days and also was ordered to pay $113 costs.