What evidence-based mathematics practices can teachers employ?
Page 4: Explicit, Systematic Instruction
Explicit, systematic instruction, sometimes simply referred to as explicit instruction, involves teaching a specific concept or procedure in a highly structured and carefully sequenced manner. Research has indicated that teaching mathematics in this manner is highly effective and can significantly improve a student’s ability to perform mathematical operations (e.g., adding, multiplying, finding the square root) as well as to solve word problems. This strategy has been shown to be effective across all grade levels and for diverse groups of students, including students with disabilities and ELLs. The key components of explicit, systematic instruction are highlighted in the table below.
During this highly structured instruction, the teacher:
During this carefully planned and sequenced instruction, the teacher:
- An influential meta-analysis of mathematics interventions indicated that explicit instruction led to large improvements in student mathematics skills.
(Gersten, et al., 2009)
- The inclusion of explicit instruction in core mathematics instruction for kindergarten students improved their achievement.
(Doabler, et al., 2015)
How does this practice align?
High-Leverage Practices (HLP)
- HLP12: Systematically design instruction toward a specific learning goal.
- HLP16: Use explicit instruction.
Although all students benefit from explicit, systematic instruction, students with mathematical disabilities and difficulties often require it if they are to learn foundational grade-level skills and concepts.
Steps in an Explicit, Systematic Instruction Lesson
Orientation to the Lesson
- Teacher gains students’ attention.
- Teacher connects today’s lesson to a previously related one.
- Teacher provides students with an advance organizer, explaining why the lesson content is important as well as how it relates to real life.
- Teacher uses essential questions to assess students’ background knowledge and to activate students’ thinking.
- Teacher reviews any previously learned important vocabulary, concepts, or procedures.
- Teacher models skill or procedure, while describing the problem-solving process (i.e., uses “think alouds”).
- Teacher leads students through several problems.
- Teacher points out difficult aspects of the problems.
- Teacher continually asks students questions to check for understanding and to keep them engaged.
- Students actively work to solve problems individually or in small groups while the teacher provides prompts and guidance or solves problems with the students.
- Teacher scaffolds instruction.
- Teacher monitors each student’s written work or small-group discussions.
- Teacher provides corrective feedback in a positive manner.
- Teacher assists students or small groups who are struggling with the skill or procedure.
- Students may discuss problems with each other.
- Students complete problems independently.
- Teacher checks student performance on independent work.
- Teacher identifies students with continuing difficulty and reteaches the skills.
- Teacher plans for opportunities to practice the skill or concept in an ongoing manner (e.g., cumulative practice).
- Teacher identifies and provides instruction for students who need reteaching or additional practice.
Source: Bender (2009), pp. 31–32; National Center on Intensive Intervention (2016)
The videos below illustrate explicit, systematic instruction being implemented during mathematics instruction, first at the elementary level and then at the high school level.
Elementary School Example (time: 3:08)
High School Example (time: 4:58)
For Your Information
Explicit, systematic instruction is critical for teaching students effective strategies for solving mathematics problems, such as the ones presented in this Module’s subsequent pages.