When a potato cooks, the starches contained in each cell are released as the cell walls break down. These starches absorb the potato’s internal moisture and swell and soften. These two processes are what transform a raw, hard potato into a cooked, softer potato fit for mashing.
If you cut your potatoes up before boiling them, the starches absorb the internal potato moisture as well as the water in which they’re being boiled. If they boil for too long, they absorb too much water and your mashed potatoes will become gummy. The difference between perfectly cooked potato pieces and soggy pieces can sometimes be as little as a minute or two.
An easy workaround is to boil potatoes whole. They’ll take a bit longer to cook but you can leave them in the hot water after boiling without undesirable effects, keeping them warm until it’s time to mash them. I start my potatoes boiling as soon as I begin cooking and mash them immediately before dinner.
If they need more moisture, you can add a bit of hot potato boiling water or another liquid. This way, you have more control of their moisture content.
I’ve never had gummy mashed potatoes, and I’ve been giving them a 1" chop for years. Takes 10 minutes to cook then drain them right away. They come out fine every time. Plus the butter melts right away when you throw everything together.
To be totally transparent, I never had gummy mash until my wife and I got together. She used to boil her potatoes, let them sit in the hot water until closer to dinner, then whip them with beaters. She’s from Ireland, I joke that the potato blight was a failed preemptive strike to prevent her from ever touching a potato.