With the increase in prominence of the investigative approach in Hong Kong science curricula from the primary to the senior secondary level, there is urgency for local science educators including primary school teachers to gain a better understanding of pupils' existing cognitive understanding and reasoning ability for performing science investigation. This is to allow teachers to see where pupils stand in relation to investigation so as to seek a better way to nurture the investigative approach. This paper reports the preliminary findings of a pilot project aiming to reveal the existing cognitive understandings of primary pupils which may facilitate or hinder them to conduct scientific investigation. Using an investigation task on heat conduction as a probe, the study reveals that Primary 4 and 5 pupils, though limited in their understanding and ability to design a reliable and valid investigation, were quite ready to maneuver through the process and were able to evaluate their design by reflecting on their experiences. It was also found that the Primary 5 pupils exhibited a better understanding and reasoning ability than their Primary 4 counterparts in these aspects.