First, it may be argued that the most important theme in Olsen's "I Stand Here Ironing" is that of the search for identity. It's a little less clear as to whom the theme most prominently applies, the mother or the daughter. While the topic of the mother's musings is the daughter,
"She’s a youngster who needs help" ... She has lived for nineteen years. There is all that life that has happened outside of me, beyond me.
the means of addressing the daughter's search for identity comes through a recollection of the mother's life during the daughter's childhood:
I was nineteen. ... I would start running as soon as I got off the streetcar ... . I found a job hashing at night so I could be with her days, ... . I had to bring her to family and leave her.
Perhaps in the end analysis, the mother's and daughter's identities are so tightly intertwined through suffering and struggle that their search for identity is a mutual one and as tightly intertwined as their personal struggles were.
The prominent theme in Tan's "Two Kinds" is also that of the search for identity. In this case, the mother has two identities to which she strongly holds: her lifelong Chinese identity and her new American identity. As may happen with immigrants, Amy's mother takes her understanding of American life from what she in a sense overhears through American television--overhears in the sense that what is presented on TV is stylized version of American life and not an authentic primer in how to be American, so she never hears the whole conversation, so to speak, about how to be an American.
In this story, the mother is overzealous in trying to mold her daughter into an American identity of her own while believing that the adage (or myth) is true that says that, in America, her daughter could be whatever she wanted to be:
My mother believed you could be anything you wanted to be in America. ... You could become rich. You could become instantly famous. ... "You can be best anything."
The daughter, talking about her own perspective from her point of view, decides that the continual disappointment of not being whatever she wants is not worth the pain of disappointment. She determines that she will resist all efforts at modification and be what she is and only what she is.
I saw only my face staring back ... I began to cry. ... I had new thoughts, willful thoughts ... I won't let her change me, I promised myself. I won't be what I'm not.
While the mother's and daughter's identities in "I Stand Here Ironing" are tightly intertwined, the mother's and daughter's identities in "Two Kinds" are separated by the gulf of cultural differences. The mother is no longer in a Chinese culture that honors her Chinese identity, but she understands only the shadow of her new American identity. The daughter knows only the silhouette of her Chinese identity but is growing up learning the sometimes painful reality of her American identity. Therefore, this thematic element of the search for identity is similar in both stories, but the theme’s dimensions are quite different in each.
In Tellie Olsen's "I Stand Here Ironing" and Amy Tan's "Two Kinds," the mothers are very different.
Olsen's story is about a woman who is reflective of her child (Emily) and her childhood—the images we receive come from the mother's perspective as she stands ironing—a seemingly endless task. The mother recalls someone at school once contacting her, worried about Emily. We learn that the child's father had abandoned them, and that for two years the mother had to leave her daughter with her in-laws before she could afford to take care of her. Another time she had to put her daughter in a convalescent home (for eight months) because Emily had measles and could not be allowed infect the family (including a new baby)—but she failed to thrive there. The mother recalls the hard years with Emily—the separations, and the mother's concern that maybe she didn't do enough...though she is adamant that she loved Emily. It was the during the Depression, and life was hard, and raising a child, harder.
And while the mother admits that Emily was hard to get close to, she recalls, too, that her daughter was a beautiful baby, and was later a gifted entertainer, winning an amateur talent contest at school.
Mother, I did it. I won, I won; they gave me first prize; they clapped and clapped and wouldn't let me go.
For all of her concern, her daughter spread her wings and took flight with her newly-realized talent. Emily has grown up and is graceful and more self-assured. The mother wonders what the caller from the school had been worried about.
However, the story ends as the mother almost prays that her daughter will realize "...she is more than this dress on the ironing board, helpless before the iron." My sense is that she hopes her daughter will not have the life the mother has had and that she will know her own self-worth, regardless—or in spite—of her mother's struggles. Or as one source states "...that she is more than the sum of her experiences."
Amy Tan's story is told from the daughter's standpoint, so the reader is only able to assemble information through the recollections of Jing-Mei (or June). This is a very different story in that the mother is married and the family lives in comfort. There is not the distance between mother and daughter her caused by poverty and endless working, but because Jing-Mei cannot share her mother's American dream for her future.
In "Two Kinds," the mother and daughter fight. Jing-Mei's mother has dreams for her daughter so that her life will be better than her own, but she pushes the child to do things that embarrass this American daughter of Chinese parents. Jing-Mei's mother believes that she can make her daughter a child prodigy by having her take piano lessons. Jing-Mei disagrees, and ends up at a recital where she really has learned nothing and has no talent to share. Both mother and daughter are embarrassed.
Here the mother does not seem to worry about the mistakes she may have made, though she does want her daughter to be successful in life. While she does not seem to worry, it does occupy her mind, but as with "I Stand Here Ironing," Jing-Mei is also able to find success in her life.
Olson's mother never seems to quite know her daughter, but Tan's Jing-Mei grows to know her mother. The piano music, years later shows that two songs she had played as a child were "two halves of the same song," much as Jing-Mei realizes that she and her mother were more connected than she could have known as a child.