There's more to school and education than the three R's: reading, writing, and arithmetic. In fact, chances are that your children don't automatically gravitate to doing math in their free time, but rather something else of interest. This complex focus and interest in something not rigidly defined by a school subject is a blessing. While it can make our lives increasingly hectic to have a plethora of interests, it also helps us create a holistic life. God, our creator, is also a complex thinker with multiple interests. Think of what kind of mind it takes to create both a sea star and a moose.
Even though our interests are complex, they often have similarities - a student interested in music oftentimes sees patterns in nature, science, and mathematics relatively quickly. While generally children don't require assistance to seek extra-curricular activities, most could benefit from guidance. For example, a child struggling in mathematics may benefit from music lessons. The musical patterns, procedure, diligence, and work ethic required in learning an instrument builds lifelong skills and coincides with the skills needed to be a good mathematician.
One of the hidden benefits of encouraging our children to join an extracurricular activity is responsibility. Being accountable to different adults or groups of kids develops maturity and social skills. Few things prompt our children to complete their work like peer-pressure.
Another benefit is relational. Having a hobby, gives your child a chance to share a part of his life with you as a friend or even a student. When a child shares his love of music, robotics, art, or animal husbandry with us he is inviting us into his life as a friend. The role of friendship with your child is a unique relationship that should be encouraged as the child matures. While being our children's friend is not an ultimate goal of parenting (especially when they're toddlers) it is certainly a joy: Like the cherry on top of the ice cream - not expected, but hoped for.
Let's work together to help our children find an interest that they both; enjoy exploring and find challenging. For hobbies act as relational bridges between ultimate authority in a child's life, and fellow God-glorifier on the journey.