How to "mount" acoustic foam ?


My main system is in my partially unfinished basement.
While I have finished the ceiling and have nice floors / rugs - I do like the industrial / rough look of the concrete walls....I just finished painting them but don't want to install any sheetrock / finishing material.
Instead I want to buy acoustic foam (2inch depth squares) and mount them to the walls - front / back and sides
And here are my questions:
1. Should I just use glue and apply the foam squares directly to the wall ?
 - IF YES - what glue should I use? I know there is the special construction glue for laying floors etc..... I now they sell it also for concrete and stone application - sold in caulk like tubes 
2. Should I first apply the foam  to a plywood / wood and anchor that to the floors ?
 - IF YES - I would imagine a few concerns: 
-  Will that wooden structure bring about sound resonance that I am actually trying to control ? (Wood isn't as bad as concrete but still....) 
-  Will I have to add a layer of caulk or similar filler between the wall and  the wooden panel? Obviously the concrete walls are not super smooth so the wood panels will not be in perfect and uniform contact. They will be held rigid with the specialty screws drilled into the walls....but still 
- What type of panels should I use....I was thinking anything from very thin cardboard like materials (to minimize any resonance from wood) to 1/2 inch plywood for rigidity.
IN SUMMARY: 

 I am leaning for the 1/8inch thick boards - In my mind it would provide smooth surface to mount the foam onto, retain the acoustic profile of the foam, and then just hold it all in place up on the wall with 4 bolts (each corner)

Anyhow....Any other tips and advice about proper installation would be appreciated.

Thank you!! 
ether
Per @slaw and @geoffkait , I removed the 4 x 24x48x2" acoustic foams I installed a few weeks ago. When first installed, there appeared to be an improvement in control of the music with better depth. However, after some further listening tests, I have to agree. While the sound is a little "wilder", it is freer. The music breathes, is louder, more dynamic. The foam basically killed the music. I have found the same effect with some mats. Damping can be deleterious. 


noromance
Per @slaw and @geoffkait , I removed the 4 x 24x48x2" acoustic foams I installed a few weeks ago. When first installed, there appeared to be an improvement in control of the music with better depth. However, after some further listening tests, I have to agree. While the sound is a little "wilder", it is freer. The music breathes, is louder, more dynamic. The foam basically killed the music. I have found the same effect with some mats. Damping can be deleterious.

>>>>>Thanks for posting your results. What I think happens is that the foam changes the nature of the acoustic wave traveling through it. Obviously the acoustic wave actually travels though the foam twice, once through the foam to the wall then back out again to the air. So any effect the foam has on the acoustic wave is doubled. As I intimated earlier ANY foam in the room has a similar deleterious effect on the sound, for example the IKEA Poang Chair that has foam seats and backing. Just when you thought it was safe to go back into the water. 🦈 Effective, non-interfering acoustic solutions such as Michael Green Echo Tunes and panels, Tube Traps, Skyline diffusers and others do not (rpt not) contain foam.

What I think happens is that the foam changes the nature of the acoustic wave traveling through it. Obviously the acoustic wave actually travels though the foam twice, once through the foam to the wall then back out again to the air. So any effect the foam has on the acoustic wave is doubled. As I intimated earlier ANY foam in the room has a similar deleterious effect on the sound, for example the IKEA Poang Chair that has foam seats and backing.

At least Geoff is "thinking" :)

The one thing Geoff doesn’t mention, *even IF his post is true* is whether or not the "deleterious effect" is worse without (correctly placed and designed) acoustic foam!

EDIT:

Besides the fact that there are numerous manufacturers of acoustic foam, and customers who report improvement in sound when using foam, this article is rather succinct and informative as to its potential benefit(s). 

https://en.wikipedia.org/wiki/Acoustic_foam
I used the term deleterious. I am not denying that the foam tamed certain aspects of the sound. It did. And extremely effectively. Bass was reduced by a significant factor while higher frequencies were "tamed". Whether foam sounds bad in itself, I do not know. All I do know is that it took the life out of the music. I tried reducing the amount of foam gradually and each reduction improved the dynamics, bass and loudness. This has been an interesting excercise. I do believe the space needs some treatment as it can be a little "live."
However despite it being in a corner of the basement, there is a lot of free space for the sound to dissipate into so reflections etc. are not as bad as might be imagined from the photos. There is some "confusion" in the upper mids when played loudly and mid bass is a little plummy on some recordings. I will look into the options mentioned. Thanks.
What we have here is simply the difference between experience and idle speculation. Of course foam seems like a good idea. That’s kind of my while point. Plus you’ve got the fact that many recording studios have been using SONEX or similar foam panels like forever. So, it’s no wonder that audiophiles get behind foam so strongly and why expectation bias is so powerful in this case. Most likely gdhal is experiencing the Backfire Effect here, more convinced than ever he must be right. 😛