There will never be a simple answer to this question. Firstly, most studies of gender differences with regards to thinking employ a dichotomous view of the human brain (male vs female), which can be problematic as there is now a general understanding that gender is not dichotomous. Yet, studies upon studies have been conducted to see if there is a such thing as a “female brain” and a “male brain”. For years, the idea that women are generally right brain thinkers and thus more emotional, empathetic, and creative, and that men are left brain thinkers, making them more logical, strategic, and risky, has dominated popular culture and scientific opinion. Thus, asserting the idea that women and men should exclusively perform better at certain tasks than others. However, recent findings have shown this idea to be more of a cultural fiction than a scientific fact.
A 2015 study conducted by Joel and colleagues tested the idea that men and women think differently by comprehensively comparing the structure of genetic female and male brains in over 1400 people. First, they measured the amount and location of gray matter, also known as “thinking matter,” in 116 different parts of the brain. This was done to find out which, if any brain areas, had sex differences. Surprisingly, only 6 in every 100 of the brains they studied could be considered exclusively male or female. Most people in the study used a mix of brain structures. The researchers took their study even further by using the same techniques to analyze more than 5,500 people's personality traits and behavior. While they found some activities to be more common in women (including scrapbooking, chatting on the phone, and keeping in touch with mom) and others in men (such as golfing, playing video games, and gambling), 98% of the people studied didn't fit a clear gender profile.
Still, there is much to be said about gender differences found in skill based tasks. For example, women generally do not perform as well in spatial tasks as men. Nonetheless, there is evidence that stereotypes have a large impact on women’s performance during spatial tasks. When primed with traditionally male traits, women are shown to perform at the same level as men (Ortner & Sieverding, 2008)! So, while it may seem that men and women have different abilities on the surface, or that they use different areas of the brain, studies are showing that this is not the case. A more likely explanation of the gender differences that we see in men and women is purely environmental and a result of social construction. Women and men are socialized to think in particular ways, and therefore, they do.
Joel, D., Berman, Z., Tavor, I., Wexler, N., Gaber, O., Stein, Y., ... & Liem, F. (2015). Sex beyond the genitalia: The human brain mosaic. Proceedings of the National Academy of Sciences, 112(50), 15468-15473.
Ortner, T. M., & Sieverding, M. (2008). Where are the gender differences? Male priming boosts spatial skills in women. Sex roles, 59(3-4), 274-281.