Fractions: Work it out in Guided Math Groups
The National Math Report has a great deal to say about Fractions. First it notes that although fractions, decimals and proportions are introduced early on, many folks (adults included) still have problems problem solving with them! There should be an emphasis on “understanding and manipulating fractions.” This type of work is done in small guided math groups so you can build understanding at the concrete, pictorial and abstract level and you can work with a variety of manipulatives.
“A fraction is defined as a point on the number line, based on the concept of a part whole relation, with the unit segment [0,1] (the segment from 0 to 1) serving as a whole.”
The Report notes that to fully assess students understanding we have to distinguish between the difference of students “formal fractional notation” and “their intuitive ability to understand fractional relations and perform calculations using fractional quantities.”
Many of the mistakes regarding fractions are due to “faulty procedure. Children’s accuracy at recognizing formal procedural rules for fractions and automatic retrieval of basic arithmetic facts predicts computational skills, above and beyond the influence of intelligence, reading skills, and conceptual knowledge.”
The research shows that the more they work with fractions the more their conceptual knowledge grows. Most interestingly “motivation also has positive effects on fraction learning. Learning goals rather than performance goals may produce higher self-efficacy, skill, and other achievement outcomes in students. Performance goals with self-evaluation components may be more effective than without.”
How do you teach fractions now? How much time do you spend on building conceptual understanding? In the New Common Core, starting at 3rd grade, fractions has its own domain. I encourage everyone to talk on the grade level about the differences between learning goals and performance goals. Note what the report states. Do you have a self-evaluation piece for students as part of your performance goals?
See this great resource from the Center for Comprehensive Reform and Improvement : Beyond Slices of Pizza: Teaching Fractions Effectively