Explicit instruction

Explicit instruction has been found to be one of the key elements in teaching children with learning difficulties (Gersten, 2009). The guidelines of explicit instruction have also been used in ThinkMath materials. Explicit instructoin means that a teacher models a strategy (e.g. a calculation strategy or a procedure) step-by-step for children. Here, based on suggestions by Forbringer and Fuchs (2014), a lesson example is given to model a strategy for addition facts that exceed 10 (e.g. 8 + 4).

  1. Introduction/Warm-up
  • Connection to everyday life: Examples from everyday life are given, in which children need to calculate beyond ten, e.g. how much do their purchases cost; how many sweets they have altogether, etc. At this point, children employ different strategies to solve problems, for example, using their fingers and counting verbally.
  • Do children possess the required skills and concepts: Do children know the bounds of ten by heart (e.g. 4 + 6 = 10, 7 + 3 = 10)? Do children know the facts of 10 + 1, 10 + 2 ? These are requirements for learning a calculation strategy that exceeds ten. Some children may require more repetition in these skills.
  1. Introducing new strategy
  • Modelling new strategies and procedures: The teacher introduces an effective way of calculating sums that exceed ten. For example, 8 + 5 –> 8 + 2 + 3 –> 10 + 3 –> 13
  • The teacher thinks aloud
  • Examples are presented with concrete materials
  • Students are actively involved.
  1. Guided practice
  • Children practice under teacher guidance, receiving feedback from the teacher
  • Concrete and visual materials are used to make abstract concepts more understandable
  • Children discuss and share their ideas
  • Before moving to independent practice, the teacher evaluates that a child has understood the new strategy.
  1. Independent practice
  • Many calculation problems using the same strategy are solved
  • Including some exercises that have been used before in guided practice may give children greater self-confidence.
  1. Ending of lesson
  • Ask children: ‘What was the main topic you learned?’ or ‘What did you learn in this session?’
  • The teacher tells the children the next topic to be covered in the subsequent lesson



  • Forbringer, L. L., & Fuchs, W. W. (2014). RtI in math. Evidence-based interventions for struggling students. New York: Routledge.
  • Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060).Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Educational Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/practiceguides/