Catalyzes the interconversion of serine and glycine and directs the hydroxymethyl moiety of serine into the metabolic network of H4PteGlu(n)-bound one-carbon units. (6R)-5,10-methylene-5,6,7,8-tetrahydrofolate + glycine + H2O = (6S)-5,6,7,8-tetrahydrofolate + L-serine Inhibited by 5-CH3-H4PteGlu1/5 and 5-HCO-H4PteGlu1/5 in vitro. kcat is 15.8 sec(-1) with H4PteGlu1 as substrate (at pH 8.5) (PubMed:20518745). kcat is 7.6 sec(-1) with H4PteGlu2 as substrate (at pH 8.5) (PubMed:20518745). kcat is 8.7 sec(-1) with H4PteGlu3 as substrate (at pH 8.5) (PubMed:20518745). kcat is 4.3 sec(-1) with H4PteGlu4 as substrate (at pH 8.5) (PubMed:20518745). kcat is 3.5 sec(-1) with H4PteGlu5 as substrate (at pH 8.5) (PubMed:20518745). kcat is 3.5 sec(-1) with H4PteGlu6 as substrate (at pH 8.5) (PubMed:20518745). kcat is 3.8 sec(-1) with H4PteGlu7 as substrate (at pH 8.5) (PubMed:20518745). kcat is 3.3 sec(-1) with H4PteGlu8 as substrate (at pH 8.5) (PubMed:20518745). One-carbon metabolism; tetrahydrofolate interconversion. Homotetramer. Belongs to the SHMT family.