A Journey from Memorization to Understanding

Even though the students in Jessica Milton’s resource room had memorized most of their multiplication facts, they knew very few of their division facts. Jessica, a teacher at West Smiths Station Elementary School in Alabama, discovered the reason: the students lacked a conceptual understanding of the relationship between the two operations.

Interested in building this understanding, Jessica decided to simultaneously use the Strategic Math Series Multiplication Facts 0-81 and Division Facts 0-81. Following the suggested scripts in the manuals, she first taught Lesson 1 of multiplication and then Lesson 1 of division. She then continued to alternate between manuals across all lessons. Through this innovative approach, students solved both types of problems using manipulatives and drawings. The result: students could more easily understand that multiplication and division were inverse operations.

Jessica also changed the problems on the learning sheets to the facts that were not mastered. She assessed students’ mastery with un-timed tests as well as fluency with timed tests. Jessica asked students to explain their computation processes to her verbally to assess how their understanding of the operations changed. Jessica provided 20 minutes of instruction during a portion of students’ time in the resource room several days per week. After six weeks of instruction, students could explain how to solve multiplication and division problems. Students reached 100% mastery and their fluency increased to over 30 correct digits per minute (proficiency). Now students have the prerequisite understanding and skills to engage in grade level instruction related to division which includes computation as well as explanation of one’s work.

Margaret Flores
Professor, Auburn University
Auburn, AL