At the 1976 Montreal Olympic Games, Shum was a member of the Israeli soccer team that reached the quarterfinals and finished fifth. He was a starting midfielder in all three preliminary games as Israel drew with Guatemala (0-0), Mexico (2-2) -- with Shum scoring Israel's second goal in the match -- and with France (1-1). The Israeli team finished second in the group to France with 3 points and advanced to the quarterfinals. Shum also started in the midfield and played the entire game in the quarterfinal match against Brazil, who defeated Israel, 4-1.
Shum was a member of the Israeli National team in the early 1970s. He was a starting midfielder in the 1970 World Cup, the only time in the country's history that its team advanced to the final stage. In their group, Israel lost to Uruguay (2-0), tied Sweden (1-1), and tied Italy (0-0), but did not advance past the preliminary group. He also played in the 1974 Asian Cup for Israel as they reached the final before losing to Iran, 1-0.
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