In the context of learning technologies, the phrase LTHC or “low-threshold high-ceiling” (also sometimes referred to as “low-threshold-no-ceiling”) originates in Seymour Papert’s description of the central design principle of the Logo programming language (Papert, 1980). Another example of a widely used LTHC platform is NetLogo, a modeling environment we use heavily in our lab. As Both in the contexts of Logo and NetLogo, as well as in the context of programming languages that we design in our lab, “Low threshold” means that new users, including those who never programmed before, should find it easy to get started, whereas “no ceiling” (or “high-ceiling”) means the language shouldn’t be limiting for advanced users. 

However, there is an additional sense in which we use the phrase “low-threshold high-ceiling”, to indicate affordances of learning environments (curricular units). An example of a LTHC learning environment is NIELS (NetLogo Investigations in Electromagnetism; Sengupta, 2009; Sengupta & Wilensky, 2005, 2008, 2009, 2010), designed in NetLogo. Here the phrase “low-threshold-high-ceiling” indicates that the same NIELS models can be used by students as young as 5th graders, as well as older students like 12th graders and undergraduates to learn and reason about the same phenomena. Since 2007, NIELS has been successfully implemented in three Chicago area middle and high schools (Sengupta, 2009; Sengupta & Wilensky, 2008, 2010), high schools in Singapore (Pathak et al., 2008, 2009; Jacobson et al., 2009), and two undergraduate classes in a major US university (Sengupta & Wilensky, 2006, 2009). From the epistemic perspective, the term low-threshold here indicates that NIELS models bootstrap learners’ intuitive knowledge that has been variously identified as natural mathematical thinking (Kaput & West, 1995; Thompson, 1995) and intuitive sense-of-mechanism (diSessa, 1993; Papert, 1980). On the “high-ceiling’ side, NIELS models enable learners to create various types of formal representations such as inscriptions (i.e., graphs, equations, algorithms) and scientific models of related concepts and phenomena, that have been traditionally the realm of only advanced learners.