What is happening here?
For 34 + 28 your child neither works purely in their head nor yet in columns, but in steps: 30 + 20 = 50, then 4 + 8 = 12, then 50 + 12 = 62. Working in written steps means those intermediate steps get written down.
This is not a stopgap, it is the heart of place value: the 3 in 34 is not a 3, it is 30. A child who has grasped that will later also understand column arithmetic.
What helps at home
If a step is wrong, the question "Which step did you just do?" helps more than "That's wrong." Because the steps are written down, your child often finds the mistake alone. Say the tens out loud when you read along: "thirty plus twenty", not "three plus two".
Subtraction is the harder case: 62 − 28 cannot be split into 60 − 20 and 2 − 8. Here the step-by-step route is the reliable one: first 62 − 20 = 42, then take away 8, which makes 34.
What can go wrong
The most common subtraction error is doing the ones in whichever direction is easier: 2 − 8 becomes 8 − 2 = 6, giving 46 instead of 34. That is not carelessness but a misconception, and a good moment to work through small numbers (12 − 5) step by step again.
Confusion also arises when column arithmetic with carrying is shown at home too early. That comes in grade 3; two methods side by side confuse more than they help.