Altogether 1,285 Finnish children were followed up from the end of kindergarten through Grade 1. All were nonreaders at school entrance. The aim was to delineate predictors of resistance to treatment that are evidenced as little or no reading progress during Grade 1. On the basis of reading achievement in Grade 1 spring, four subgroups were formed. These were fast, average, and slow reading acquisition and slow progress in both reading and math. Kindergarten spring scores in phonological awareness, letter knowledge, rapid naming, and number skills differentiated well among the groups, the latter two being more robust predictors. Task avoidance added to the prediction over and above cognitive skills. Its effect disappeared when parental history of reading and math difficulties was included in the equation. The present results depict poor response to instruction as a general learning problem rather than a specific reading difficulty. Poor response to instruction differs from dyslexia also in that treatment resisters start school with cognitive prerequisites that do not indicate severe reading and math problems.