This paper outlines an initiative in mathematics education research that aims to augment qualitative methods of research into mathematical cognition and learning with quantitative methods of psychometrics and psychophysiology. Background and motivation are provided for this initiative, which is coming to be referred to as educational neuroscience. Relations and differences between cognitive and educational neuroscience are discussed. This is followed by descriptions of methods, along with some of the kinds of expertise required for educational researchers to use such methods more effectively. Overall, this paper points to new horizons and opportunities for research in mathematics education, with some associated pitfalls in areas that appear to be particularly ripe for opening up with these new methods. [This paper was published in: J. Novotna, H. Moraova, M. Kratka, & N. Stelikova (Eds.) Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (vol. 2; pp. 257-264). Prague, Czech Republic: Charles University.]