To improve your child’s intrinsic motivation, help them set learning / mastery goals.
These goals place more emphasis on progress along the way and allow children to have lots of small wins on the way to their bigger goals.
This helps to keep them intrinsically engaged instead of placing all the emphasis on the end result. Think IMPROVE vs. PROVE. We don’t get to jump from step one to 100. We must make small improvements along the way to get to our goals. Often the big performance goal is overwhelming on its own. If we can find joy and engagement in each step, we are practicing our intrinsic motivation.