Catalyzes the reversible interconversion of serine and glycine with tetrahydromethanopterin (H4MPT) serving as the one-carbon carrier. Cannot use tetrahydrofolate (THF or H4PteGlu) instead of H4MPT as the pteridine substrate. Also probably exhibits a pteridine-independent aldolase activity toward beta-hydroxyamino acids, producing glycine and aldehydes, via a retro-aldol mechanism. 5,10-methylenetetrahydromethanopterin + glycine + H2O = 5,6,7,8-tetrahydromethanopterin + L-serine Optimum pH is 8.1. Optimum temperature is 60 degrees Celsius. Amino-acid biosynthesis; glycine biosynthesis; glycine from L-serine: step 1/1. Homodimer. Belongs to the SHMT family. Extended N-terminus.