1. In a 3- to 4-quart nonstick pan over high heat, bring 4 cups (3 3/4 cups if using quick-cooking tapioca) water to a boil. Gradually stir in tapioca; reduce heat and simmer, stirring often, until transparent, 15 to 30 minutes for pearl (5 to 8 minutes for quick-cooking). Mixture will be very thick.
2. Add 3/4 cup sugar, 1/3 cup coconut milk, and 1/2 teaspoon salt. Stir occasionally until sugar is dissolved, 2 to 3 minutes. Stir in corn, if using. Spoon into eight small bowls or ramekins (1/2 to 3/4 cup each).
3. In a 1- to 2-quart pan, mix remaining 1/4 cup sugar and the cornstarch. Add remaining 1 cup coconut milk, 1/2 cup water, and remaining 1/2 teaspoon salt. Stir over high heat until mixture is boiling, 3 to 4 minutes. Spoon equally over puddings and spread to cover tops. Chill until cool, about 30 minutes, then cover and chill until cold, about 2 hours. Just before serving, garnish with strawberries.