Praxis test is a gesture-based diagnostic test which has been accepted as diagnostically indicative of cortical pathologies such as Alzheimer's disease. Despite being simple, this test is oftentimes skipped by the clinicians. In this paper, we propose a novel framework to investigate the potential of static and dynamic upper-body gestures based on the Praxis test and their potential in a medical framework to automatize the test procedures for computer-assisted cognitive assessment of older adults. In order to carry out gesture recognition as well as correctness assessment of the performances we have recolected a novel challenging RGB-D gesture video dataset recorded by Kinect v2, which contains 29 specific gestures suggested by clinicians and recorded from both experts and patients performing the gesture set. Moreover, we propose a framework to learn the dynamics of upper-body gestures, considering the videos as sequences of short-term clips of gestures. Our approach first uses body part detection to extract image patches surrounding the hands and then, by means of a fine-tuned convolutional neural network (CNN) model, it learns deep hand features which are then linked to a long short-term memory to capture the temporal dependencies between video frames. We report the results of four developed methods using different modalities. The experiments show effectiveness of our deep learning based approach in gesture recognition and performance assessment tasks. Satisfaction of clinicians from the assessment reports indicates the impact of framework corresponding to the diagnosis. Keywords: Human computer interaction, Computer assisted diagnosis, cybercare industry applications, human factors engineering in medicine and biology, medical services, monitoring, patient monitoring computers and information processing, pattern recognition.