An important goal of introductory physics courses is to encourage effective approaches to problem solving. To achieve this goal, many aspects of desired problem solving approach should be rewarded, e.g. via grade incentives rather than basing grades mainly or solely on correct final answers. Here we discuss findings of a study that suggests that shifting pedagogical emphasis to reward the process of problem solving approach rather than basing the grade primarily on the final answer may have an additional unexpected benefit of supporting gender equity in physics. Our study involves administering a previously-validated attitudes and approaches to problem solving (AAPS) survey in six large enrollment calculus-based introductory physics classes at a large research university in the United States. On average, women had a statistically significantly higher average AAPS score at the end of the instruction when compared with men. Moreover, on clusters of questions related to effective approaches to problem solving such as drawing diagrams and doing scratchwork, women had a significantly higher average score. Since drawing and scratchwork are part of a systematic approach to physics problem-solving, this finding suggests that women, on average, may take a more favourable approach to physics problem-solving when compared with men. Interview data with a subset of students corroborate this interpretation. Our findings suggest that awarding appropriate credit to the entire problem solving process, e.g. by giving credit for drawings and scratchwork, may support gender equity in physics. In particular, heavier reliance on open-ended questions on assessments, along with grading rubrics that are sensitive to the details of the problem-solving process, not only rewards the desired approaches to problem solving, but also supports gender equity since women are rewarded appropriately for their work. We encourage physics instructors to adopt instructional strategies that reward the problem solving process instead of only rewarding the product to ensure that students learn effective problem solving skills while also supporting a practice that is more equitable.