Dpi is a meaningless value without referencing the dimensions an image should be printed at.
If your multitone colour or grayscale image is supposed to be printed at 50% DIN A4 format, that means the image must have a minimum resolution of 2480px by 1754px (plus a bit of bleed if running off the page, but let's leave that out of the conversation for now).
PPI (Pixels Per Inch) is used to denote image resolution, DPI when the image is printed.
8.267" x 300px = 2480px
5.847" x 300px = 1754px
Now you know how to calculate the minimum required resolution.
Your image should have that resolution and the ppi (not dpi) embedded parameter should be set to 300ppi (DO NOT resample after the right resolution requirements are met in your image editor - only change the internal PPI parameter!).
PPI by itself has no impact on resolution - only pixels do. What the PPI parameter does is tell layout software (such as InDesign) at what size it should be placed on the paper. That is it.
I could save a single pixel at 10.000 PPI and it wouldn't change the actual resolution of that one pixel. I could save a 10.000px square image at 1PPI and it again wouldn't make a difference to the actual resolution.
The single pixel with 300ppi embedded would be placed at exactly 1 inch square dimensions when imported into InDesign. (It translates to a printed 1dpi - 1 dot per inch).
This is why InDesign distinguishes between actual PPI and effective PPI: what is the PPI value embedded in an image file, and what is the actual ppi calculated by checking the image's resolution against the size that image is placed in the layout. The effective resolution should always be more or less 300PPI for colour and grayscale images.
For academic work often black and white imagery is placed as well. In that case the image should ideally have a minimum effective PPI resolution of 1200ppi - the above 1/2 A4 image would then have a resolution of 9920px by 7016px resolution. The reason for this is that black and white only does not need to be rasterized to simulated tints and hues by introducing dot patterns. These images should in principle ALWAYS be saved as TIFF. JPG is NOT suitable for these type of images.
So for black and white 1bit scans and images:
8.267" x 1200px = 9920px
5.847" x 1200px = 7016px
In short: never rely on DPI or PPI only - it is a useless unit to measure the actual effective resolution of a placed image. Always calculate the actual required pixel resolution at the size it will be printed at.
If unsure, inquire about the publication's layout/print size, and deliver images with an effective max resolution at the max size that these could be placed in the publication.
And
@MacGizmo is correct in stating that many people working in the layout business have themselves utterly confused about what PPI/DPI means.
If someone asks you for 300dpi images, they have no clue indeed. They need to provide more information for you to decide what effective resolution your images should be delivered at. Which is why you need AT LEAST the final print size of the layout and how your images will be scaled and positioned on the page.