I think that you might have to focus on two particular elements in your analysis. The first would be the argument, itself. What is used to support the thesis being advocated? What facts in evidence is submitted? How cogent and coherent is the overall argument? It might require you to sketch out the basic argument and the subpoints used to defend or support it. I think that the next level you will have to undergo would be to analyze how the argument is written and how it is presented? Addressing the tone of the article, as well as the word choice and how it is presented in terms of persuasion will be involved here. I would like to suggest another source that might help with your study here. Danica McKellar has written some excellent work on the gender bias in mathematics. I would examine her arguments and study her tone and word choice in order to increase your background knowledge of the field.
