These are pieces of slate recovered from Pulau Saigon. Slate is a metamorphic rock that is composed of clay minerals that have been put under great pressure, causing fine grains of clay flakes to regrow in planes perpendicular to the compression (due to the mica in the rock). As a result it will be hard enough to "clink" when hit with a hammer, and also have a distinctive layered appearance or "foliation".
These slates are known to be slate of UK origin, brought over on a ship from the UK to Singapore to be used as a building material for (colonial) houses here. The slate may also have been used as ballast. I was unable to find a chart or guide to identifying slates, as they are technically named after the region they came from. To the untrained eye, I guess they look like the traditional grey tones of slate from Wales.
I looked for more general information about slate produced in the UK for construction, and found various information and pdf guides on the English Heritage (Officially known as the "Historic Buildings and Monuments Commission for England"):
"Stone slates were mined at Purbeck in Dorset, at Collyweston and Duston in Northamptonshire, at Stonesfield and elsewhere in the Cotswolds, in Yorkshire and occasionally in Derbyshire… At Collyweston and Stonesfield, the splitting was carried out by frost action. The raw block was either stored underground or taken to the surface where it was wetted and covered in earth until the frosts came. The frost then swelled the natural moisture within the stone and split it into slates. Frostsplit slates may be thinner and therefore lighter than those split by hand."
Source: English Heritage: STONE SLATE ROOFING: TECHNICAL ADVICE NOTE
Sidenote: When I look at this, I think all this sort of stone collecting and stone arranging must be how the romans invented crazy paving. You know, CRAZY PAVING? All broken up into all sorts of interesting shapes? (Unfortunately this joke won't be quite as funny to the majority of Singaporeans who don't get to do any of their own paving ever, owing to the fact that most people don't have landed properties to pave...)
EG: CRAZY MARBLING IN ROME!
In comparison, this is what Murai slate/schist from Singapore looks like.
I noticed these specimens at the Raffles Biodiversity Museum were casually labelled "Murai slate". But a geology enthuisiast in Singapore would have more commonly read about the "Murai Schist" (part of Jurong Formation) in reports about Singapore's geology. But this does look like slate because the characteristic of schist is that its mineral grains should be visible to the naked eye. And I don't see any conspicuous large grains of mica flakes here, so I am inclined to think this would be defined as slate.
In any case, the two types of rocks - slate and schist - can be observed to have other similar properties - apparently the Schist is metamorphosed more than the Slate, so they are very similar, except that the Schist is even harder, and the equivalent of cleavage or what we would call "slaty cleavage" is known as "schistosity".
Also, from the report "Geology of Singapore" (Published by DSTA):
"It is not proposed that the Murai Schist be recognised as a formal geological unit, but rather as a zone of well-developed cleavage in rocks otherwise recognised as sediments of the Queenstown, Jong ,and Tengah Facies. The Schist zone forms a belt up to 0.5 km wide in Ama keng, trending northeast from Tanjong Skopek to include the area originally described by Alexander (1950). A small schist zone was found on the north arm of the Pasir Laba Ridge (GR 295494) and another zone, not recorded on the map, was found in the Jong Facies in Jurong (GR332452)."So I guess the brown rock above might actually be Slate from the Murai Schist. Who comes up with all these terms anyway?
Videos of the Pulau Saigon Slate:
Slate (Top view)
Slate (Side view)
The Collectors of Pulau Saigon: Murex Trapa shells, and Pyrites (Fool's Gold)
The Chert of Pulau Saigon, a former island in the Singapore River
Bone, Metal, Wood, and Other Artefacts found on Pulau Saigon