This module comprise two LessonSketch experiences, of the similar structure. One deals with Universal statement in  Geometry, and the second one deals with an Existential statement in Algebra. 
LessonSketch experiences:
  • What can you infer from this example? - Geometry
 This experience focuses on the role of supportive examples and counterexamples in disproving a universal statement in Geometry.
  • What can you infer from this example? - Algebra
This experience focuses on the role of supportive examples and non-confirming examples in proving an existential statement in Algebra.

Teachers' guide:
  • These two experiences, combined, cover the two possible types of quantified statements: universal (for all) and existential (there exists). 
  • The experiences highlight the different roles examples play in proving or disproving these two types of statements. Specifically: 
    • One counterexample is sufficient for proving a universal statement; 
    • Supportive examples are insufficient for proving a universal statement; 
    • One supportive example proves an existential statement;
    •  Non-confirming examples do not disprove an existential statement. 
  • The summary of these logical aspects can be found in the REP framework (Role of Examples in Proving).
Implementation suggestions: 
  • We recommend doing WCYIFTE - Geometry experience first, since it deals with universal statements, with which PSTs would be more familiar with. 
  • Follow-up with WCYIFTE - Algebra experience, which deals with existential statements.   
  • Doing the two experiences in close proximity provides an opportunity to highlight the similarities and differences in the roles of examples in proving/disproving universal and existential statements. 
Other resources:
  • Buchbinder, O., Ron, G., Zodik, I. & Cook, A. (2016). What can you infer from this example? Applications of on-line, rich-media task for enhancing pre-service teachers’ knowledge of the roles of examples in proving. In A. Leung and J. Bolite-Frant (Eds.), Digital Technologies in Designing Mathematics Education Tasks – Potential and Pitfalls. (pp. 215-235). Springer, Cham. 
This chapter describes the theoretical underpinnings of the design of the module. 
  • Buchbinder, O., & Cook, A. (2018). Examining the mathematical knowledge for teaching of proving in scenarios written by pre-service teachers. In O. Buchbinder & S. Kuntze (Eds.). Mathematics Teachers Engaging with Representations of Practice (pp. 131-154). Springer, Cham.
This chapter analyzes the scenarios written by a group of elementary and secondary PSTs following the enactment of the module in a content course on reasoning and proof. 
  • Buchbinder, O. & Zaslavsky, O. (2009). A framework for understanding the status of examples in establishing the validity of mathematical statements. In Tzekaki, M., Kaldrimidou, M. & Sakonidis, C. (Eds.). Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2, pp. 225-232). Thessaloniki, Greece. 
This paper outlines the REP (Roles of Examples in Proving) framework.