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Turn on the truth meter (aka the metronome) ... it will tell you how fast you can really play

I also recommend you consider jazz

I've been having trouble with rhythm recently as well. It's easy when it's just quarter and half notes, but individual eighth notes or(even worse) dotted notes throw me off. I think the problem was I got lazy and never did any counting or rhythm work - I'd just 'guess' and hold quarter notes a 'reasonable' length, half notes twice that, whole notes 4x, etc. This would lead to inconsistant results - sometimes my 'guess' is correct for a peice, other times it'd be off. Even worse sometimes I'd be doing right for 90% of the peice but there'd be a measure or two that were wrong. Never enough to sound offputting, but wrong none the less. Lets put it this way, I basically added my own fermata's all over the place.

My teacher started having me right in the counting (1+2+3+4+, "one" "and" "two" "and" "three" "and" "four" "and") for every measure. Then I'm to clap, or tap, or play random chords, or hum, or however I see fit the rhythm as part of learning the piece. This felt, unessesary, at first, but I have to admit it's been helping. After a run through or two I'll identify the problem spots and be able to focus in on them. It's easier because I'm focusing on just the rhythm and not hitting the right notes. When I try to learn both at the same time it's much easier to notice hitting the wrong notes - so that gets focused on - and by the time I(or my teacher) notice the rhythm is wrong I've already got it memorized that way. Then I have to unmemorize it and re-memorize it the new way.

What I'm saying is don't be embarrased to write in the rhythm and clap your way through it a few times. I've mainly focused on learning the peices rather than purely sight-reading them, but I think this would help to both ends. If you work through the coutning on a few peices you should start to get a better feel for how long a dotted half note really is, and this will help when you see them during your sight reading. My teacher seems to be able to count while sight reading, but when I try this keeping track of both hands, fingerings, the right notes, reading the music, and counting aloud is too much - something stumbles.

Edit - I also see your question about practicing at a slower tempo. This is ussually highly recommended.

No, better results. Once you have got the notes and the rhythm figured out (perhaps just for a section of the piece,) whip out the Metronome (as previously suggested) and get it perfect (error free) at a slow tempo. Only when you can play at this tempo error free, are you ready to begin to advance the tempo. Do not let mistakes slip in. As soon as they do, go back and perfect at a slower tempo again.

This is the coaching I have been receiving and it is working wonders

Rhythm is very important. If rhythm is not good, then you ears get used to a false rhythm. Then you brain thinks that false rhythm is good and how it suppose to be. This is very bad.

If you stop everytime you make an error, then that habit will grow. So never stop, always play even when an error happens.

If you accuracy is not good, but your rythm is, then you haven't mastered the proper technique to play it at that speed. (Or your rythm is not good, but your accuracy is. That's the same.)

Slow down, until the accuracy and your rythm are both good. Speed up when you master the proper technique for doing so.

Speeding up when you're not ready for it (i.e. technical insufficient to do so), leads to less accuracy, wrong rhythm or both. Turning you, your nervous system and brain into a bad musician step by step.

That's why you should play it very slowly in the beginning, until you know how it should sound and how you know how to hit that key.

If it's not possible to play with a good accuracy and good rythm at very low speed, take a single measure and see what movement you need to play it, and remember that specific muscle movement.

If you encounter a totally new rhythm, try to clap your hands at that rhythm if you have problems. It's normal to have difficulties to learn a new rhythm. Never play a new rhythm the wrong way, otherwise it will costs you a lot of energy to correct that. (I often learned new rythms by walking. Every step was an half or quarter note, counting in my head the new rhythm and changing rythms, like 1-ne-me-te, 2-ne-me-te, 3-ne-me, 4-ne-me)

Maybe there are better ways, but that's how I learned it.

If you like Bach, try the notebook for Anna Magdalena Bach and see if something suits you. You can find it on imslp.org for free.

Edit: these rules are for learning new pieces. I don't sight read. But I think these rules could help you anyways.

Mr. Cid, I had to copy and paste your post into Notepad before I could read it comfortably. I was "bold" over by it

When sight reading it is imperative to keep going regardless of accuracy. Precision comes with practise. Of all the attributes of music, timing is the most fundamental.

When learning a piece, not sight reading, it is imperative to fix mistakes regardless of whether you go on the end of the phrase or stop immediately. Occasional fluffs are a part of playing and until you start recording, which magnifies them out of all proportion compared to live performance, can be ignored as long as you don't start getting sloppy.

Practising at a slower tempo does not have the same results as practising at normal tempo - they're much better than that!

Daily practising should be done below recital tempo and pieces only brought up to tempo infrequently or for performance. It is also important that when mistakes are introduced at recital tempo you should always finish your practise with a tempo that allows a high level of accuracy.

Tempo is a strange beast. Fast pieces I practise at two speeds, one that is high quality but fluffs do occur and one at which I can be flawless. Only occasionally do I bring them up to tempo, maybe once or twice a year for a week or two. Moderate pieces I tend to keep around recital speed unless there's a difficult area that requires isolated slow practise, e.g. the first episode in Für Elise. Very slow pieces I typically practise slightly faster than recital speed.

Don't buy Bach books for technique, buy Bach for pleasure. The technique comes as a bonus.

For six months I think you're ahead of the game.

For me it works best to alternate between full tempo, slow practice and playing through the whole piece, practicing larger chunks and practicing just small fractions with difficult stuff. I don't have any fixed practice routine, but I am beginning to feel quite well what works and what doesn't at a given time, so I change when I feel I am not getting anything out of what I am doing.

Sight reading is a good skill to learn, but I don't think it's very useful for learning the pieces and playing in general at the beginning stages. One needs to be able to concentrate on difficulties without the pressure of going on...

I must say that I have trouble gauging your level of musical experience. On the one hand you say that you can read music around level 2 or 3 (either RCM or ABRSM, I assume).

Do you mean with that that you understand the signs and musical symbols and you understand what they are about? Or do you actually mean them in the sense that I would understand "read" in that context, meaning that with little practise (like a couple of repetitions) you're able to play them well.

If the later, colour me green with envy - that I think would be a tremendous achievement in roughly 6 months.

The fact that you're struggling with the rhytm might mean one of several things: you might be able to easily play pieces of level 2 and 3 and are trying to sight read pieces on the same level. In that case you're demanding too much of it. More experienced sight readers tell me that you usually sightread two or the most one level below you current level. If you're on 3 and try to sightread at level three, chances are you won't succeed.

On the other hand it might be that while you can play pieces at level three as in hitting the right notes in the right order, but you haven't mastered them. Mastered as in correct timing, clear dynamics, expressive touch and rhytmic certainty. In that case you might still want to sightread pieces at level 1 or 2 the most, while practising rhytm with other means.

I definitely understand the musical terms and symbols, I have the notation memorized (some of the ledger lines.) I can read most grade two sheet music but some I have to slow down.
Yes, I have recently tried classical grade 3 music, and I do find it immensely difficult to sight read with minuscule errors.

So I should level down a notch in order to get better at the things I'm not particularly good at?

So long as you recognize that sight-reading is a completely different discipline than memorizing repertoire for performance (and thus recognize the different rules for practicing), then you can practice it. You should pick a slow enough tempo (and easy enough material) that you can maintain at least a 95% accuracy (the minimum percentage required for building fluency in reading determined by Language Arts guidelines based on research) and avoid stopping or interrupting the steady flow of rhythm at all costs. As such, you must also learn to FEEL the rhythm while playing (unless you use a metronome) – be it by tapping the left foot, counting the beats aloud, etc. – if expressive playing is the desired result.

Mr.Cid: You appear to be doing very well as a self taught beginner. One book that I would highly recommend to you is Playing the Piano for Pleasure: The Classic Guide to Improving Skills Through Practice and Discipline by Charles Cooke. This book was first published over 40 years ago but has been re-published in 2011. It was recommended elsewhere on these boards and I can confirm it is a brilliant book and one well worth adding to your reading material. You can check it out on Amazon.

Excellent suggestions. My piano teacher recommended this book for me. I've never regretted purchasing it.

Isn't sight-reading partly memorizing your repertoire. In a sense of remembering passages and its fingering from previous pieces we have played and applying it to the piece we are playing now? I may not have made any sense but hopefully you know what I am talking about.
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Not really -- sure there may be similarities between songs but each reads differently. To me, sight-reading is more like transcribing what you see on the page to what you play, note-wise, then after time you work on the nuances, etc.

Everything you said is right, but assuming one works on level-relevant material for increasing their repertoire, they can only approach and memorize so much repertoire material over a certain period of time. Assuming that a similar type of memorization (or perhaps, experience) - as discussed - is gained through successful sight-reading of material, then the latter quantity has the opportunity to be significantly greater.