6:37 Does this mean that God chooses who will be saved and that it is not the personal choice of the individual, as some teach?

No! This simply reflects the fact that all believers are the Father's gift to the son who died for them (CP Psa 2:7-8; 33:12; Ro 8:29).

Everyone who listens to and learns from God, will come to and believe in Jesus (CP Jn 6:44-45, 64-65). Jesus quotes Jer 31:34 in Jn 6:45 (CP Jer 31:31-34).

It is plainly evident from those scriptures that Jn 6:37 does not teach that God acts sovereignly in the matter of salvation, choosing whom He will to save and damning the rest to eternity.

If that were so, then Jn 3:16 and all the other scriptures which teach that salvation is the personal choice of the individual, are meaningless (CP De 30:11-19; Josh 24:15; 2Chr 15:2; Isa 45:22; 55:1-7; Eze 18:20-30; 33:10-20; Joel 2:32; Mt 11:28-30; 12:47-50; Jn 3:14-17, 36; 5:24; 6:35,47; 7:17,37-39; Ac 2:21,37-39; 10:34-35,43; 13:47-48; 16:30-34; 17:30-31; Ro 1:16-18; 4:5-25; 10:8-17; 1Cor 1:21; 8:3; Ga 3:7-9; 1Ti 2:1-6; He 5:9; 2Pe 3:9; 1Jn 2:2; Rev 21:6; 22:17).

Those scriptures all clearly teach that God's call to salvation is an open invitation to all who hear the call. God has not already determined for or against any man's salvation (CP Jn 3:36). This proves that individuals choose for themselves whether or not they want to be saved.

The word believeth here is from the Greek word pisteuo, which means to place confidence in, to trust, to be persuaded of. It implies obedience to as a moral choice. Believeth not is from the Greek word apeitheo, which means refuse to be persuaded, refuse to believe, refuse to obey.

Thus "he that believeth" is he that chooses to believe, whereas "he that believeth not" is he who chooses not to believe or who refuses to obey.

This is irrefutable proof that salvation is the personal choice of the individual and that God does not intervene in any way (see also comments on Mt 11:28-30, 13:10-11, 20:16; Jn 3:14-15, 3:36, 12:37-40, Ac 2:37-38, 13:48, 28:23-29, Ro 3:24-26(A), 8:28-30, 9:7, 9:10-13, 9:14-18, 9:19-21, 10:14-17, 11:2 11:4, 11:7-10; Eph 1:3-6, 1:11-14, 2:8-10, 1Th 1:4; 2Ti 1:8-9; 1Pe 1:2, and author's studies Salvation - A Free Will Choice or Predestiated? and Chosen by God? in his book Advanced Studies in the Christian Faith (Volume 1)).