Instructional Strategies: Direct (or Explicit) Instruction

The direct instruction (or explicit instruction) model is based on scaffolded learning, gradually releasing the responsibility of learning from the teacher to the student, “Explicit instruction models support practice to mastery, the modeling of skills, and the development of skill and procedural knowledge” (California Department of Education, 2013, pp. 17-18).This model is particularly beneficial in teaching procedural knowledge to students regarding mathematical concepts. Typically, direct instruction begins with the teacher modeling how to perform a particular task. The teacher may utilize the think aloud strategy at this point to model how the students should reason through the task. According to Walqui (2006, p. 170), “When introducing a new task or working format, it is indispensable that the learners be able to see or hear what a developing product looks like.” Then, the teacher engages the students in guided practice, eliciting student participation in performing the next task. At first, the teacher may ask students if the steps taken to perform the task are correct. The teacher may continue with similar tasks or calculation that are progressively more difficult, eliciting greater student participating in performing the task. Following the guided practice, the teacher assigns the students an assignment or activity to complete individually. During this time, the teacher should circulate around the classroom observing student work, asking guiding questions, and offering help when needed. Throughout the lesson, the teacher checks for understanding through a variety of formative assessment techniques. These include asking the students questions, having them respond with whiteboards, or circulating and listening to their conversations as they engage in a think-pair-share. At the end of the lesson and throughout the unit, the teacher tests the students using summative assessments (i.e. quizzes, mid-chapter tests, and chapter tests).

The direct instruction model is not explicitly unique to teaching mathematics. In fact, direct instruction is easily implemented as a model for teaching reading comprehension (Gersten & Carnine, 1986) and science (Adelson, 2004). The focus of the direct instruction model is on the method or procedure used. It is a teacher-centered method that specifically addresses procedural knowledge. The benefit of direct instruction is that students acquire the skills and procedural knowledge for effectively performing certain tasks, “Teacher-centered methods of instruction are often necessary to educate students on difficult material that requires multiple steps, and for procedures which are unlikely for students to discover on their own” (Cohen, 2008, p. 4). Because the direct instruction model is teacher-centered, it does not foster the development of reasoning and metacognitive awareness that is necessary for students to think mathematically.

Rethinking the Use of Real World Examples in Mathematics

While connecting mathematics to the real world may seem like it would be a simple task, it ends up being a real challenge. I always tried to find some application to the real world that the students could use to understand the mathematics better, but it was never that easy. I realized that my struggle was not in finding the real world examples, but in what I was looking for. I usually imagined career-based real world examples. Then, if students asked why they had to learn something in mathematics, I could refer to the type of career that would need that type of mathematical background. Later, I considered re-thinking the types of examples I wanted to use. Instead of career-based real world examples, I explored real world examples that students experience day-to-day. This subtle change made it easier to think of examples. After a while, my students were even thinking of their own examples. I realized that the examples I originally presented them were far removed from anything that they could really relate to. By selecting examples that they could relate to, they were more open to working through the problem.