Abrahamson, D. (2009, April). Appropriate tools: On grounding mathematical procedures in perceptual intuitions. 

Paper presented at the annual meeting of the American Educational Research Association, San Diego, April 13-17.

I report on a design-based research case study in the area of middle-school probability that served as a context for investigating whether students can build meaning for the disciplinary tools they are taught to use, and if so, what personal, technological, and interpersonal resources may support this process. The topic of binomial distribution was selected due to robust literature documenting students’ apparent ‘misconceptions’ of expected likelihoods. Li successfully built upon his event-based intuitive sense of likelihood in developing the outcome-based notion of sample space. Utilizing cognitive-science, sociocultural, and cultural–semiotic theoretical models of mathematical learning, the construct ‘semiotic leap’ is developed herein to explain Li’s insight as appropriating an available artifact as a means of warranting his intuitive inference.