Well, if you practice anything, you get better at it, don't you?
I did a google search for “research arithmetic speed practice” and I found a Ed.D. thesis that studied a problem pretty close to what you're asking:
The relationship between timed drill practice and the increase of automaticity of basic multiplication facts for regular education sixth graders by Nelly P. Knowles (Walden University Ed.D. thesis, 2010). From the abstract:
This 8-week quasi-experimental quantitative study, based in cognitive development and theories of the construction of memory, used a 3-level independent variable experimental design to determine if there was a relationship between teachers’ implementation of timed drill practices and the students’ level of automaticity with regard to basic multiplication facts in 9 sixth-grade, regular education math classes. The control group received no intervention, the first treatment group received weekly timed drill practice for 3 minutes, and a second treatment group received daily timed drill practice for 3 minutes. Analysis of variance (ANOVA) procedures were used to measure the differences in pretest and posttest scores among the 3 treatment groups. Although no significant difference was found among the 3 groups’ pretest performance, a significant difference among posttest performance was
found. Scheffe’ post hoc analysis revealed that the students who were administered daily
timed practice drills performed statistically higher on the posttest than did the control
group and first treatment group. Similarly, students in the weekly timed practice drill
group had statistically significant higher gain scores than did students in the no treatment group.
The abstract doesn't mention it, but the concept of automaticity seems to measure what you're interested in: speed of recalling facts to perform arithmetic algorithms.