Is there a better way to learn multiplication tables besides just memorizing.

This is a good question that comes up time and time again. I reflect on an article by Daniel T. Willingham called "Is It True That some People Just Can't Do Math?" (available online) In it he writes that learning "math requires three types of knowledge: factual, procedural, and conceptual. Factual knowledge or memorized knowledge is necessary to keep working memory free when focusing on more difficult problems. Automatic retrieval of basic math facts is critical to solving complex problems because complex problems have simpler problems embedded in them."

One accepted way is to teach factual, procedural, and conceptual knowlegde in concert. "Gaining knowledge and understanding of one supports comprehension of the other."

Coming from experience in Montessori classrooms I'm aware of and I recommend her tried and true lessons for children who manipulate "beautiful objects" and over time come away with grounded conceptual knowledge.