Jump discontinuity is something my calculus students encounter when they learn about limits. They study graphs and try to determine if a function approaches a limit at distinct points along that function. Limits are a hard concept for my calculus students, as they are in life. And jump discontinuities seem to give them particular fits.
They are created by piecewise functions where a function is defined at specific points along the domain. They look like the graph above with lines jumping across the graph.
Being a math lover, they’re a wonderful way to view the graph of our lives. Each jump is a major change.
My students experience a jump between middle and high school. For a moment, they stand with one foot in each world. They dream about the future while looking at it through the lens of their past. Middle school had its own particular set of rules imposed by their friends, teachers, and parents. Those rules will change when they enter high school. So for a brief moment in their lives, they wonder about the possibilities and freedoms that will come with those new rules.
My son is navigating this process as he begins high school. There’s so much for him to learn and master, and from my perspective he’s embracing each challenge with grace and humility. I marvel at him. He’s often overwhelmed by the experience, but he doesn’t let it discourage him from the future he’s envisioned for himself.
I tried to identify all the big jumps in my life – graduating college, marriage, the birth of my children, buying a new home. The one that really sticks out was the decision to move to Bangkok, Thailand, when my kids were in elementary school. It was one of the scariest things I’ve ever done. We didn’t even have passports.
My husband was offered a one-year job in Bangkok (turned into 2), and he accepted it with about four weeks to get us there. We had very little knowledge about Bangkok, and I spent the next weeks arming myself with facts about our new home. Three weeks to go we still needed to pack up our house and transfer the kids to their new school.
When I look back on this time, I can’t believe we managed it. We jumped with both feet into the deep end. The flight to Bangkok is the literal jump between these two worlds. It was a long one, about twenty-four hours of traveling. That’s a lot of time to worry and wonder about the possibilities awaiting us. It was the unknown that I really feared. The experiences in my life couldn’t prepare me for the challenges I would face in Thailand.
Bangkok overwhelmed me in every way possible when we first arrived, but eventually I embraced my new home and grew to love it. For my kids, the experience opened their eyes to different cultures in a way they never could have experienced from the suburbs of Atlanta.
I’m learning to embrace the jumps in my life. Those moments where I can wonder about the possibilities to come while appreciating the experiences I have had in my past.