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.]