ABSTRACT
Mathematics difficulties (MD) are widespread. Higher mathematics achievement is associated with college success and greater job opportunities. In this chapter, we address the intersection between cognitive research on the science of learning and the education of students with MD. First, a conceptual framework for mathematics learning is provided, including consideration of individual differences in domain general and domain specific learning processes. Next, learning principles that promote successful learning in mathematics are described, along with examples of how the principles can be translated into educational practice for students with MD. We argue that in addition to providing developmentally appropriate instruction in content knowledge, such as whole number and fraction knowledge, application of more general learning principles validated by research will lead to deeper and more durable learning for struggling students. These learning principles include studying and comparing correct as well as incorrect worked out problem-solutions; using integrated visual and verbal models to reduce splitting attention; interleaving or varying practice with problems of different types; providing frequent cumulative practice or review that is spaced out over time; connecting and integrating concrete and symbolic representations; presenting arithmetic problems in different formats; using physical movements and gestures to promote learning; and incorporating activities with number lines to increase learning of whole numbers and fractions.
