Do concrete learning materials promote strong learning outcomes, or do they simply make learning tasks more initially accessible? Although concrete materials may offer an intuitive foothold on a topic, research on desirable difficulties suggests that more challenging tasks facilitate greater retention and transfer. In the approach introduced here, grounded coordination challenges (GCCs) are embedded into the design of concrete learning materials to deliberately increase the difficulty of the learning task. More specifically, these challenges are intended to promote a deliberative process of mapping between perceptual elements of the materials. In 2 experiments the GCC approach was tested in a number line estimation task by comparing training with an "incongruent ruler"--which was designed to mismatch the length of an on-screen number line--to a "congruent ruler" (both experiments), or no ruler (the 1st experiment only). In both cases participants with the incongruent ruler were more likely to transfer knowledge to spatially transformed number lines. These results indicate that desirable difficulties facilitate learning in mathematical activities. Furthermore, the difficulties should emphasize a deliberate coordination process between critical features of the learning tool and the task. Implications for the design of learning activities that balance instructional support with conceptual challenge are discussed.