The secretary of the school board or board of education of each Class I, II, or III school district shall, within ten days after any regular or special meeting of the board, publish one time in a legal newspaper published in or of general circulation in such district a list of the claims, arising on contract or tort, allowed at the meeting. The list shall set forth the name of the claimant and the amount and nature of the claim allowed, to consist of not more than ten words in stating the nature of each such claim. The secretary shall likewise cause to be published a concise summary of all other proceedings of such meetings. Publication of such claims or proceedings in a legal newspaper shall not be required unless the publication can be done at an expense not exceeding the rates provided by law for the publication of proceedings of county boards.