In a method of operating a memory controller, a decoding status flag is received from a memory module including a plurality of data chips and at least one parity chip. Each of the plurality of data chips and the at least one parity chip may include an on-die error correction code (ECC) engine. The decoding status flag is generated by the on-die ECC engines. A first number and a second number may be obtained based on the decoding status flag. The first number represents a number of first chips including an uncorrectable error that is uncorrectable by the on-die ECC engine. The second number represents a number of second chips including a correctable error that is correctable by the on-die ECC engine. At least one of a plurality of decoding schemes is selected based on at least one of the first number and the second number. A system ECC engine may perform ECC decoding on at least one of the first chips and the second chips based on the selected decoding scheme.