Thanks, candela and Pallas I have time-guru on my phone. But I must admit I never used it, because the internal metronome is easier to use, and I get the clicks via headphones. I will involve this app into my next lesson.
I was thinking, if there is a mental trick to retain the tempo. I tried with constantly slowing down at every new phrase. Actually it feels like I am slowing down, but it seems it is more of a constant speed in reality. Works sometimes well, sometimes so la-la, and sometimes not.
Alfred Adult All-in-One Course Level 2 and 3
I think it's just one of those things you need to notice yourself... because eventually we have to be able to pace ourselves without metronome. Though I would imagine that tools such as that fading metronome would be a good aid. And recording ourselves, to notice all the things we're blind to when playing.
When I find out I did it, I give myself a very stern warning to pay more attention next time. One example was blues lesson 7. Remember how I went back to it to work on staccato left - legato right hand?
I recorded it again, slower so I could concentrate on that. To my horror I heard it speed up throughout. The two recordings are still there for all to notice 
My solution is to try and be more aware of it. When a piece should be played slower than I can (rare, but happens), I try to remind myself not to rush, keep it steady... and it seems to keep me in line for at least a little while 
WieWaldi If your digital piano doesn't have a built-in one, get a smartphone app. Even the free ones are good enough to do the job.
Ha ha, you clearly don't understand what a dinosaur you're dealing with - I don't have a smartphone and have no desire to get one! 
I'm old fashioned, I have a basic phone which has just two functions; calls and texts. I deliberately chose a basic piano with no extras, because I like to keep things simple and also I never used the extras on my previous instrument. I once tried to use the built in metronome but the process to set it up and adjust the speed was confusing as the Casio did not have a screen/display attached so there was no visibility of whether it was on the desired speed or not. Tech stuff confuses me!
"Don't let's ask for the moon, we have the stars." (Final line from Now,Voyager, 1942)
Nightowl Dinoraurs didn't have internet and computers... Maybe try this: https://www.musicca.com/metronome
If you get a stand-alone metronome, I strongly suggest one with a different sound for the down-beat. Mechanicals often don't provide this, and if they do, they are starting to get expensive.
WieWaldi Ah, thanks so much, that is a really easy tool to use! I might give that a try later. 
@Sophia Yep, that looks dinosaur friendly! I do like those old fashioned metronomes and it would go nicely with the cherry wood effect of my piano cabinet.
Two great options for me to consider, so no excuses for me now!
"Don't let's ask for the moon, we have the stars." (Final line from Now,Voyager, 1942)
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Hahaha I wish! That was just the photographer making us pose at the hotel where our wedding pictures were taken. In fact I completely forgot this picture even existed (it was close to two decades ago), and came across it again just the other day. Since our blues "teacher" graduated me to "lovely beginner", I decided it was time to change the little girl to a lovely (or so my husband seems to think) bride instead 
WieWaldi I was thinking, if there is a mental trick to retain the tempo.
For some people it works better to embody the beat by tapping the free foot or even just a toe. There's something with the physical movement that can make it easier to keep a steady pulse compared to just thinking about it.
About the apps. If your digital piano has bluetooth audio in, you can set it up to hear your phone's metronome in your piano's headphones or speakers. I much prefer the sound and interface of apps compared to my piano's built-in metronome.
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candela If your digital piano has bluetooth audio in
Unfortunately not. Not even Line-in. 
The successor model has BT audio, now. If I'd give any digital piano shopper a tip, it would be this.... Drum-computer, backing-track player, and a sophisticated metronome. All easy and without cables.
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I put my phone away when practicing piano. A standalone metronome is much less distracting. It is also quite a bit easier to use, whether changing tempo in small or large steps. This one by Seiko is what I have. Highly recommend it.
Speed comes from working at speed so that your brain can begin to process and recognize what's going on.
Race car drivers do not practice driving slowly so that they don't bump into each other. They train to drive fast with control of the car. They push themselves and expect a little rubbing while racing.
In the same vein, you will not get faster by playing slowly and carefully. You must push the speed limit of your fingers and expect to fumble. This is how the human brain works and you will begin to correct the fumbles automatically. Eventually you will stop fumbling and can control the speed at which you play.
Just like a race car driver controls the speed at which he drives..
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Well, it's interesting that you mentioned a race car driver though - because of all people, a racer can't afford to fumble at all. He fumbles, he dies. So although I agree with what you're saying (we need to push ourselves to go a little faster than our comfort zone), it's no use speeding it up to the point of fumbling. I think the trick is to stay just within the "no-fumble" zone until it becomes the "whoa I feel like a tortoise" zone and then crank up the speed a notch. Rinse, repeat
By doing that my current piece is now at the 70bpm "fumble? what the heck is that?", 80bpm "here are my fumble zones" and 100bpm "are these weirdly flailing objects moving in the general direction of the correct keys really my fingers controlled by my brain?" But give it a week or two and I will probably be able to give a different report 
Would it be an idea to split these last few posts into your new thread?
5 days later
Well, I'm happy to say I am moving on from A Classy Rag because I got a recording done today - practice pays off There were a few pieces I got up to about 60-80% okay-ish (I will polish those later), so that means I'm now ready to move on to the unfinished symphony (Schubert). I'm looking forward to that one - it's like the classical version of a boogie woogie or ragtime piece
Sophia, you are really zooming through book 3! I'm still moving through book 2 at snail speed, but I think this is quite common at this stage. I have been working on the Elgar piece for a few days, and have made a tentative start with Dark Eyes, but both pieces are stretching my skills as they include fiendishly tricky two part writing for the right hand. The Chopin piece is next, and I've briefly attempted RH notes, but I'm not ready to properly tackle it yet.
I really don't think I'll progress further than grade 2 or 3 - I don't think my old brain is up to the level of multi-tasking involved beyond that level. I foresee that complex pieces probably involve 2 part writing for BOTH hands - the thought is terrifying! I will play for pleasure at an intermediate[ish] level but not become a slave to piano.
"Don't let's ask for the moon, we have the stars." (Final line from Now,Voyager, 1942)
Nightowl I really don't think I'll progress further than grade 2 or 3
Well, you say that now, but remember when we were in book 1? I listened to some people perform pieces from the second book and I thought I'd NEVER be able to play that. And here we are today - playing them. Sure, not as well as the professionals, but then again they once were where we are now. I agree with not becoming a slave to piano but I do think that as long as we keep at it regularly, we have no choice but to become better at it
I think the real fun starts when we allow ourselves to get away from Alfred dictating what we play and start picking music that we LIKE to play. Every now and then Alfred has such a piece, but nowhere near often enough. Though this third book is a little more pleasant than the first two - and I'm allowing myself to gloss over over pieces that I don't care for a little more often now. As long as I'm able to keep up with what the book is trying to teach, I'm okay with it now.