I think you're reading too much out of the story. She didn't learn math from the computer, but she developed her skills. The computer didn't teach; it augmented.
I believe I have correctly identified the thesis of the story. My evidence for believing this is the following:
1) The laptop is analogized to the condom balloons, which were an instructional technique to "open [students'] minds to a subject they previously wouldn't let in". One way we can see the author is analogizing computers to condoms is the title: "Computers as Condoms", which is a simile.
2) The student was identified as both hating math and having no substantial skills prior to the computer intervention.
3) The computer intervention "led her to allow herself to think about these previously horrible things".
4) After the computer intervention, she was described as having marked objective improvement in scores.
The above points, taken together, do not support the conclusion that the article is claiming "the computer merely augmented an existing understanding of mathematics". They do support the conclusion that the student had no demonstrable understanding of mathematics, and that through using the computer, she gained a demonstrable understanding of mathematics.
I don't want to rant too much here about pedagogy, but the above exercise in "identify the thesis and then support your identification with textual evidence" is another crucial skill which can be effectively taught by, well, teaching it.
There are some pedagogical theories that focus instead on something closer to "Hey, how does this text make you feel?" For example, you hypothetically may feel that the author thinks laptops are a nice extra to have in support of a traditional mathematics curricula. If you hypothetically feel this way, you are wrong. Your conclusion is not supported by the text.
The phrase "you are wrong" is highly controversial is many pedagogical schools these days. That is a shame.
[Edit: I apologize for sounding like a lecturing English teacher. It may be related to me having taught English.]
In my view, this points to the thought that education requires two components: first, the presentation of materials by a teacher; and second, willingness to receive those materials by the student. In some places, such as Japan and South Korea, the latter is accomplished by fostering intense competition. This article presents an alternative. Perhaps the merits of these and other alternatives for creating a willingness to learn are debatable, but it seems rather dismissive to suggest, as the initial comment does, that more teaching is the whole answer.
I do sympathize with the initial's commenter's complaint that teaching has too much moved to what are essentially therapy sessions for children. The problem does seem to be a lack of balance, with a focus too strong on making children willing to open their minds, without providing anything to put inside.
She was a fifth-grade student at a public school in Boston. This indicates that she had a sufficient understanding of mathematics to reach that grade level, and had previously been instructed by the traditional method. The result being low test scores.
We're not talking tabula rasa here, we're talking about a regular student with a poor grasp of the subject matter.
Additionally, the text you've placed in quotes is meaningfully different from the post you're replying to.
They do support the conclusion that the student had no demonstrable understanding of mathematics, and that through using the computer, she gained a demonstrable understanding of mathematics.
This contradicts your earlier post, which implied that this was (for unspecified reasons) not an effective method of teaching math skills.