Skewer pineapple spears, if using, and arrange on a baking sheet. Cover and freeze until firm. Meanwhile, in a large saucepan combine the apple cider, tangerine juice, and cinnamon sticks. Bring to boiling. Remove from heat. Cover and let stand 1 hour; remove and discard cinnamon sticks. Transfer to a pitcher. Cover and chill for 2 hours. Stir in the pineapple juice and rum. Serve in glasses with pineapple spears or add ice cubes.