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"show good progress" is correct and usable in written English
You can use it when you want to express that someone is making improvements in a particular area. For example, "The students have been showing good progress in their reading skills this year."
Exact(12)
Jorma Ollila, Nokia's chief executive, said, "Despite the more difficult market conditions, we have been able to show good progress".
Many schools stumbled while adjusting to the more challenging tests for reading, writing and maths but with many still managing to show good progress among their pupils.
'The second quarter results show good progress in our downstream businesses [refining and retailing], with operational performance improvement, increasing volumes and strong marginssaid Jeroen van der Veer, the group chairman, said.
Nolan added: "While today's figures show good progress, the market is not as competitive as we would like". Nolan said savings of around £230 were available to some switchers "so we would urge everyone to shop around for a better deal, especially if their supplier announces a price rise".
The preliminary experimental results presented in this work, although limited in number and constrained by actuator problems and design limitations, as it will be reported, show good progress towards routine current profile control in DIII-D and leave valuable lessons for further advancements in the field.
Our Q2 results show good progress in monetization, but we are not satisfied with our growth in audience.
Similar(48)
We are showing good progress as a team and everyone is looking forward to getting out racing again".
"They're showing good progress in the business, particularly in terms of advertising and electronic commerce revenue," said Conan Laughlin, an analyst at Deutsche Banc Alex. Brown.
There is no way to guarantee they are going to be employed for life". He said that while the success rate is not "astounding," it shows good progress for many people.
But the EEA warned that although on areas such as industrial pollution, air pollution and waste management the EU was showing good progress, the outlook for two decades from now was increasingly grim on all environmental fronts.
Algorithm development at SRON using the UV and visible part of the solar spectrum for ozone profile retrieval and the near infrared for carbon monoxide and methane retrieval has shown good progress.
More suggestions(15)
show positive progress
show good achievements
show better progress
show significant advances
show satisfactory progress
show significant progress
show good accuracy
show racial progress
show enough progress
show promising progress
show insufficient progress
show steady progress
show remarkable progress
show good scaling
show immediate progress
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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