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"higher levels of knowledge" is correct and usable in written English.
You can use this phrase when you want to refer to a greater understanding of a certain topic. For example: "John has achieved higher levels of knowledge in mathematics through his rigorous studies."
Exact(57)
Results indicated that experimental group participants reported higher levels of knowledge than controls and knowledge gain in certain areas.
It was hypothesised that learners in a redesigned 'Optima' environment would reach higher levels of knowledge construction due to clearer scaffolding.
But, of course, this may just be a sad commentary on the gap that exists between the quality of the qualifications that young people in Britain now leave school with, and the higher levels of knowledge and skill that they find the workplace now demands.The OECD report only serves to remind everyone in the field of education and training how bad the current situation is.
Certainly the participants in this study had higher levels of knowledge and acceptance of biological evolution than those in other study populations.
The next example reveals that in some cases not even first-order knowledge is sufficient to trigger action, and higher levels of knowledge are necessary.
The value of ITS appears to increase along with the need to deal with the complexity, multi-level interactions, and abstract concepts that are required for higher levels of knowledge and technical skill.
They also exhibit higher levels of knowledge and acceptance of biological evolution compared to previously studied groups (Rutledge and Sadler, 2007; Moore et al., 2009; Moore and Cotner, 2009a; Moore and Cotner, 2009b).
As people develop higher levels of cognitive ability, they will also tend to achieve relatively higher levels of knowledge.
Similar(3)
It included language the defense had sought, requiring the higher level of knowledge.
If it's more complicated, the caller gets bumped up to a second level to an employee who has a slightly higher level of knowledge.
EPs must strive for a higher level of knowledge for themselves and for future generations.
More suggestions(16)
higher degrees of knowledge
higher levels of sophistication
higher levels of intelligence
higher levels of familiarity
higher levels of background
higher levels of comprehension
higher levels of recognition
higher levels of science
higher levels of fluency
higher levels of information
higher levels of competence
higher levels of awareness
higher levels of expertise
higher rates of knowledge
higher levels of research
greater levels of knowledge
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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