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Discover Ludwig"show improvement" is correct and usable in written English.
You can use it when discussing a situation that has changed positively over time. For example, "Sarah's grades have really shown improvement since she started studying with a tutor."
Exact(60)
He began to show improvement immediately.
Their teams need to show improvement.
Test scores are starting to show improvement as well.
Moreover, indexes of poverty seem to show improvement.
Within several months, Reeve began to show improvement.
The task now is to show improvement on the field.
This last area is usually the slowest to show improvement.
"She began to really show improvement," he said.
Results show improvement of the various yield measures.
Recent studies also show improvement in effective coverage.
"The first four, five, six weeks of the season, we need to show improvement.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com