The phrase "seek their understanding" is correct and usable in written English.
You could use it when trying to emphasize the need for someone to appreciate or comprehend something. For example: "I implore my students to seek their understanding of the material before the exam."
"We are talking to many countries and expressing our opinion and seeking their understanding".
They underline big differences between Khan and Goldsmith in their attitudes to an important part of the job they seek and their understanding of the city they wish to lead.
We also encourage part-time enrollment of financial professionals seeking to increase their understanding of the quantitative side of finance.
For years, retailers have sought to improve their understanding of the almost mythical 'path to purchase'.
2. Committing to Learning -- In my previous Huffington Post article, "From the Front Lines of Ferguson," PICO Community Organizer Wes Lathrop directed people seeking to deepen their understanding of racism to read this article, entitled Implicit Bias as well as The New Jim Crow by Michelle Alexander.
Some participants sought to extend their understanding by asking questions but the responses they received did not always satisfy.
Given the complexity of the topic, views of the staff recruiting participants were also sought, to determine their understanding of genomics and issues arising with discussing genomics during recruitment.
Consumers can be viewed as being their own best advocates for their well-being, and many may wish to access more genomic and other personal information outside of a clinic and seek better understanding of their conditions implied by these data.
Some Native Americans, for instance, are becoming increasingly concerned with the growing desire of "outsiders" to seek understanding of their religion(s) by watching or experiencing sacred ceremonies since such observation, they believe, can trivialize these ceremonies (Kasprisin, 2003: 422).
