Three of the city’s public middle schools top the list to next take advantage of the new reimbursement rate for school construction, officials said. Alan Lo, Norwalk’s building and facilities manager, said the city and school district have identified Nathan Hale, Roton and West Rocks middle schools as the next buildings needing to be reconstructed or renovated. The 60 percent reimbursement rate for school construction, approved earlier this year, would benefit either option. To determine the feasibility of construction for two of the middle schools, the Land Use and Building Management committee approved $25,000 for Antinozzi Associates to provide conceptual designs and cost estimates for potential swing space at Roton or West Rocks so education can continue on-site while the existing schools are built new or renovated. Mike Faenza, project manager for Construction Solutions Group, reported to the committee that steel erection will begin in September.