Standards-Based Instruction in Mathematics|
Standards-based instruction in any content area is designed to help establish what students should learn at each grade level. Standards are more than curriculum frameworks, however. They stipulate the skills, concepts, and knowledge that are achievable. They should be used, in turn, to build criterion for assessments and establish goals for learning. Additionally, standards provide educational communities in each state with expected outcomes.
To successfully integrate a standards-based approach, teachers need to:
Characteristics of a Standards-Based Mathematics Classroom
- Understand the rationale for using standards as a basis for instruction.
- Know the math standards in his or her state and level and plan to incorporate them into the instructional plan for the year.
- Implement best practices instructional strategies into math lessons to maximize effectiveness.
To begin, there are several essential characteristics of a successful standards-based classroom. They include:
Working with Standards
- Each lesson is designed to address specific concepts or skills identified by the standards.
- Learning activities are student-centered.
- Lessons emphasize inquiry and build problem-solving skills.
- Activities require students to think critically and apply their knowledge.
- The learning environment is structured to give students adequate time, space, and materials to complete tasks.
- Assessment is a varied, on-going process, designed to evaluate both student progress and teacher effectiveness.
There are a variety of approaches that you can take to understand the standards and integrate them into your instruction. Some teachers take a straightforward approach by breaking down the standards into skills and concepts to be learned. Some feel this approach to be limiting and too literal.
Others set about looking with standards from the perspective of the higher level thinking skills that can be engaged and the inquiry processes that can occur. This process is sometimes called teaching for understanding, as described by authors Grant Wiggins and Jay McTighe in Understanding By Design.
Whatever approach you choose, you will need to obtain the standards for students at the levels that you teach. Next, identify the specific objectives that you see indicated by your reading of each standard.
Best Practices Instructional Strategies for Math Lessons
The process of addressing math standards can be eased by implementing best practices instructional techniques and strategies for the grade level you teach. Effective math lessons that implement these best practices have the following characteristics:
Keep these best practices in mind as you plan your lessons: they will help you address math standards and will help your students take on the greater challenges that this content presents.
- Students' engagement is at a high level
- Tasks are built on students' prior knowledge
- Scaffolding takes place, making connections to concepts, procedures, and understanding
- High-level performance is modeled
- Students are expected to explain thinking and meaning
- Students self-monitor their progress
- Appropriate amount of time is devoted to tasks
It is helpful for teachers to look for common themes and interconnected concepts among the standards. For example, noticing and making connections between algebra and geometry standards is a worthwhile pursuit. It is possible to address multiple standards in the same lesson this way.
Along with the strategies and suggestions discussed above, teachers can help their students meet math standards by helping them develop the following skills:
This article was contributed by Heidi Janzen, a former classroom teacher and mathematics specialist, and Jennipher Willoughby a writer and former science and technology specialist for Lynchburg City Schools in Lynchburg, Virginia.
- Foster Students' Reasoning Abilities
The reasoning abilities of students should be fostered at all times. Math teachers can help improve their students reasoning abilities and address math standards by conducting lessons that provide them ample opportunity to question, examine, conjecture, and experiment. Additionally, teachers should expect their students to explain their thinking and reasoning throughout every math activity. Math teachers should try to incorporate the use of conjectures and proving or disproving these conjectures in almost every lesson.
- Expand Students' Abilities to Represent Mathematical Information
All students need multiple opportunities to explore various ways to represent mathematical information. Students should be comfortable using symbolic (formulas, equations, expressions), tabular, and graphical representations. Students should also be able to use coordinate graphs to represent and to analyze a variety of relationships. They should gain experience using variables to represent numerical relationships and to show the interdependence of quantities. As with conjectures, try to incorporate the use of symbolic and graphical representations in as many lessons as possible.