Rabbi Akiva said three different things. The Chachamim (the Sages) agreed with him about two of them, but disagreed with him about one of them. The first law will talk about Tumat Midras, which is when a Zav (a man with a discharge), a Zavah (a woman with a discharge), a Nidah (a menstruant), or a Yoledet, a woman who gave birth, puts their weight on an object, and it becomes Tameh (ritually impure), even if the person didn't directly touch it. For example, let's say they touched a blanket that was on top of the object but connected to it. The item would become Tameh. But all of that only works if the item itself is used to support a person. Let's say a chair, or let's say a pillow: it's used for support, so it could become something susceptible to Tumat Midras.
Rabbi Akiva said that a sandal of a lime worker, which was usually made to protect the worker's feet from burning in the lime, could become Tameh through Midras (impurity from sitting or lying). Even though the sandal's primary focus is to protect the feet of the worker from being burned, it also serves to support him, so it would be subject to Tumat Midras, according to Rabbi Akiva.
The second law we're going to talk about concerns a broken pottery oven that became Tameh. In the times of the Mishnah, the oven was like a circle with an empty bottom. That bottom would be attached to the ground; it would be cemented to the ground. In order to be considered a utensil that could become Tameh, all of the sides of the oven had to be at least four tefachim (handbreadths) high. So the Mishnah is going to talk about an oven that was split across the middle, so now it's shorter than it was before. Rabbi Akiva said that the remaining part of a broken clay oven could become Tameh only if it was at least four tefachim high. Other people had ruled earlier that three tefachim would be enough, so Rabbi Akiva had to come testify that no, four tefachim had to be required in order for it to be considered a utensil to become Tameh. The Chachamim agreed with Rabbi Akiva on both of these last two cases.
The third law we'll talk about is a little difficult to describe, but we have to imagine a box that is the frame of a chair. It's like a box with four walls and three boards side by side on top of it. That's what the person could sit on. If the two outer boards were removed, or if only the middle board was removed, a person could still sit on the chair. But if one outer board and the middle board were removed, so that only one outer board remained on one side, a person would not be able to sit. So what do we do with this type of chair in terms of Tumah (ritual impurity)? Ve'al echad lo hodu lo. One law, Chachamim did not agree to Rabbi Akiva. Al kiseh she-nitlu shenayim mechipuyav zeh betzad zeh. About a chair where two boards that were next to each other were removed, and therefore, there was only one board at the side. She-Rabbi Akiva metameh. Rabbi Akiva said that even though it can't be used as a chair anymore, it's capable of becoming tameh because it could be used as a different utensil, which is a container. So even though the original purpose of that item was to be a chair, and it no longer serves that purpose, Rabbi Akiva says it could become tameh because it has a different use now. Vechachamim metaharin. Vechachamim say no. It's tahor (ritually pure); it cannot become tameh because it doesn't fit the original purpose that it was made for, so it's not considered to be a keli, a utensil anymore.