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"active thinking" is correct and usable in written English.
You can use it to describe the process of thinking actively or more deeply about a particular subject. For example: "We need to engage in active thinking when studying difficult topics."
Exact(14)
"The surface of our mind is the active, thinking mind.
I'm not sure if there have been any studies or anything on it, but I'm sure it's probably good brain training -- keeps your mind active, thinking and stuff like that.
Evidence reveals tight coupling of brain activity during active thinking that is mirrored to a large degree in intrinsic resting brain activity during internally driven cognitive thought processes (Smallwood et al. 2012).
This reception of the intelligible transforms the potential intellect from being a mere disposition to think to the active thinking of the intelligible; a process in which the "intellect in act" (al-'aql bi'l-fi'l) becomes its intelligible (Bouyges, 15; Hyman, 216).
In this way, thinking thinks itself as thought and is therewith active thinking, while thought, insofar as it thinks its thinking, is itself thinking, and its thinking now thought.
This could not only facilitate students' learning due to more active thinking and participation, but could make more students open their mouths to speak English.
Similar(46)
It was also much shaped by her desire to show children as they really are – active, argumentative, thinking (Little Pete Stories, 1952, and the Steep Street series illustrated by Lisa Kopper, 1987).
If the topmost layer of our most highly active and thinking material membrane, right beneath the skull, was peeled away from the rest of brain and flattened out on a sheet, it would have the shape of a winged butterfly about to fly into "blotches of odor and pulses of organs".
One must appropriate them as an active reader, thinking through the issues for oneself, so as then to genuinely assent to them (Letter 84.5 10; Wildberger 2006).
Yet despite our global energy stature, we have a sad lack of cohesive, pro-active thinking about how we should be producing, consuming and trading all our valuable energy resources, not just oil.
"In that sense, this is good pro-active thinking".
Related(20)
interactive thinking
effective thinking
aggressive thinking
intensive thinking
efficient thinking
activate thinking
dynamic thinking
energetic thinking
constructive thinking
lively thinking
active the mind
reactive thinking
active notion
active logic
active discussion
operative thinking
activist thinking
active conception
engaged thinking
active mind set
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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