No, more tests should not be given to students as tests and exams are not the best way of measuring intelligence and retention of studied material. Tests and exams are often biased toward students who are more well off financially, as financially well off students do not have to do with stressers such as hunger which can impede performance.
Many studies suggest that more tests don't improve academic performance, as teachers are forced to teach to the test by rote memory rather than actually applying principles on the various subject-matter. These studies reflect the same results in schools from various areas, both rural and urban. The US does more testing than most countries, yet our school system often isn't as good as those countries.