Connecting Mathematical Ideas through Animated Multimodal Instruction

In this research we study the effects of instruction that links mathematical ideas in the domain of beginning algebra (i.e., in middle school). This domain is significant for several reasons. First, algebra functions as a 'gatekeeper' to more advanced mathematics, as well as future educational and employment opportunities; however, many students have substantial difficulty learning algebra.

Second, in response to growing concerns about students’ inadequate preparation and performance, algebra instruction has become a focal point of recent content standards and reform efforts in mathematics education.

Third, algebra is a domain in which connections among mathematical ideas are of central importance—it is vital for nearly all of the CCSSM standards for mathematical practice, such as reasoning abstractly, modeling, and attending to mathematical structure. Algebra instruction addresses abstract concepts (e.g., variables, generalization) and complex procedures (e.g., isolating variables, making generalizations, operating on polynomials), as well as multiple external representational systems (e.g., graphs, symbolic expressions). As such, algebra instruction involves many opportunities for making connections, and work in this area has the potential to lead to significant improvement in algebra instruction and student learning.