If the condom your partner is using is too small, it would probably break while being put on. So there's probably another reason why the condom is breaking, and it could be one or a combination of many things.
If you're using old condoms or if the packaging was broken, they can become dried out and deteriorate, and therefore more easily split or tear. Make sure the condom package has not broken and that it hasn't expired.
If there is not enough lubrication during sex, pressure builds up on the condom, which could cause it to break. To ensure sufficient lubrication, use water-based personal lubricants such as YES, a natural lubricant, or KY products. Avoid using oil-based lubricants as they can cause latex condoms to deteriorate. Also, don't use body lotion, petroleum jelly (both oil-based), or other items not intended for intercourse because they are not vagina-friendly.
Be sure the condom is applied properly and that there is a 'nipple' at the end of the condom (a space for the semen). The condom should roll up the penis easily and quickly. There is no need to pull or stretch the condom if it's properly applied and the right size.
If you are experiencing prolonged penetration, meaning penetration without pulling out for more than about three minutes, check the condom to be sure it's still in place. Intensity of movement can also dislodge a condom.
Most condoms these days come with a reservoir tip, if not, leaving space to collect the semen is useful. However, when you or your partner are rolling the condom on, be sure to pinch this tip, and smooth any air down the shaft towards the rim so it escapes. If you don't do this, the condom can definitely burst.