You have posed a thought-provoking question. Although I have never taught math, I really enjoy playing chess. My first reaction was a definite "yes" that chess would help elementary students improve math and science scores because of the problem solving and reasoning required to play the game.
I did find some old research which said: "In a 1994-97 Texas study, regular (non-honors) elementary students who participated in a school chess club showed twice the improvement of non-chess players in Reading and Mathematics between third and fifth grades on the Texas Assessment of Academic Skills."
The information included the following reasoning: "Why does chess have this impact?"
1) Chess accommodates all modality strengths.
2) Chess provides a far greater quantity of problems for practice.
3) Chess offers immediate punishments and rewards for problem solving.
4) Chess creates a pattern or thinking system that, when used faithfully, breeds success. The chess playing students had become accustomed to looking for more and different alternatives, which resulted in higher scores in fluency and originality.
5) Competition. Competition fosters interest, promotes mental alertness, challenges all students, and elicits the highest levels of achievement (Stephan, 1988).
6) A learning environment organized around games has a positive affect on students' attitudes toward learning. This affective dimension acts as a facilitator of cognitive achievement.
Chess is being taught as part of the curriculum in a number of schools in Toronto by www.chessinstitute.ca, run by Ted Winick. He ran a chess club at my sons' school for the past several years twice a week, in the mornings, and you wouldn't believe how many kids came out on a regular basis. He also has been running chess tournaments during PA days, which has been good for us.