This paper describes how to use tangible interfaces for cognitive assessment and training. Assessment and training are two fundamental phases in the learning process: assessment allows to gather information in order to identify the learner starting level and monitor progresses that training can lead to. Assessment uses tests, some of which are addressed to cognitive abilities. Many tests for cognitive abilities are based on verbal materials that are not suitable for population such as young children or people with special needs, and people with hard cognitive disabilities or sensory impairment. In these cases it would be more fruitable to use physical objects. This paper illustrates a hardware-software system, LogicART, that can be used in assessment and training of cognitive abilities, such as reasoning, memory, categorization, etc. exploiting physical materials augmented by RFID/NFC Technology. These materials, employed to study cognitive abilities, offer the advantage to stimulate multisensoriality and manipulation.