© 2016 Elsevier GmbHA popular suggestion states that an evolutionarily grounded analogue magnitude representation, also called an approximate number system (ANS) or ‘number sense’ underlies human mathematical knowledge. During recent years many studies aimed to train the ANS with the intention of transferring improvements to symbolic arithmetic. Here we critically evaluate all published studies. We conclude that there is no conclusive evidence that specific ANS training improves symbolic arithmetic. We provide a citation analysis demonstrating that highly controversial results often get cited in support of specific claims without discussion of controversies. We suggest ways to run future training studies so that clear evidence can be collected and also suggest that data should be discussed considering both supporting and contrary evidence and arguments.