A whole understanding: More on teaching fractions

According to the Principles and Standards for School Mathematics of the National Council of Teachers of Mathematics in the United States, ‘Effective mathematics teaching requires understanding what students know and need to learn, and then challenging and supporting them to learn it well.’ Having a deep and thorough knowledge of mathematics is important, but teachers also need to understand the process by which a student has arrived at a mathematical concept, or misconception, in order to build on those concepts and address any misconceptions, mindful of the typical learning capabilities, and difficulties, of students at particular ages.