There are several of reasons why your JRT, puppy and adult alike, may be chewing.
Your JRT puppy may be cutting teeth, and the chewing helps to break the gums allowing the teeth to push through. Help your puppy with their need to chew at this time by providing them toys and such to chew on. There are some very fine toys available on the market today, geared and engineered towards helping to relieve teething discomfort.
In your adult JRT, normal chewing behavior is common. It is natures way of keeping their jaws strong, and their teeth clean. The very act of chewing helps to keep the tarter cleaned off their teeth, preventing the onset of gum disease and tooth loss.
It is normal for your JRT to chew on things: sticks, bones, what have you. They see the act of chewing as fun, a source of stimulation, a means of keeping occupied, and as a means of dealing with anxiety.
Yes, anxiety. Separation anxiety is one of the major causes of chewing in most adult JRT's. It is during this anxiety that they may be at their most destructive. They work themselves up, and get so upset, that they lash out by way of destructive chewing.
But, how do you solve the problem of your adult JRT's destructive chewing?
If your JRT is a puppy, or a newly acquired family companion, closely monitor your JRT until they learn the house rules. When you observe them chewing where and when they shouldn't, make sure you let them know they are misbehaving. Usually taking a firm tone, then moving them away from the area, or the item away from them will eventually get the point across. You must be consistent in this though, because if one time they are allowed to chew on the item, and the next they are not, then this only serves to confuse them even further.
Isolate your JRT when you are not there to monitor their behavior. When you leave the house, no matter the length of time, place your JRT in a small, closed off area, or even in a crate. Make sure that there is nothing that is chewable within their reach, thus not affording them the ability to lash out and chew, and that they have plenty of fresh water.
When choosing acceptable toys for your JRT, make sure they are easily distinguishable as toys that they are allowed to chew on. Giving your JRT an old sock or shoe only serves to confuse them. By giving them this type of chew toy, they are confused when they are corrected or scolded for chewing on the socks and shoes not designated as theirs.
"Dog Proof" your house. Any objects that you do not want them chewing on, make sure to put them up out of your JRT's reach. This will take away both the availability and temptation that the item presents.
Then, provide your JRT with chew able toys of their very own. Toys that are made for extended periods of chewing, as well as those that are of benefit to tooth and gum health are the ones that are best. To keep your JRT from getting bored with their toys, rotate in new ones about once every two to three weeks. This way, they will stay interested in their permitted chew able, and not so much the ones they are supposed to stay away from.
With those particularly persistent JRT's, it may be necessary to use a spray deterrent of some sort. The JRT will associate the item sprayer with the deterrent with an unpleasant taste and will not bother it again. Spray any items that are proving particularly difficult of breaking your JRT from.
Lastly, your JRT may be acting out and chewing because of boredom. The JRT breed needs lots of exercise, play, and stimulation. Make sure they get their needed walks as well as romping time. Being able to burn off their natural energy, will help keep them from working that energy off in other ways.