Best practices for implementing effective standards

Sabean and Bavaria (2005) have synthesized a list of the most significant principles related to mathematics teaching and learning. This list includes the expectations that teachers know what students need to learn based on what they know, teachers ask questions focused on developing conceptual understanding, experiences and prior knowledge provide the basis for learning mathematics with understanding, students provide written justification for problem solving strategies, problem based activities focus on concepts and skills, and that the mathematics curriculum emphasizes conceptual understanding.

Concurrently, the following best practices for implementing effective standards based math lessons should be followed:

1.Students’ engagement is at a high level.

2. Tasks are built on students’ prior knowledge.

3. Scaffolding takes place, making connections to concepts, procedures, and understanding.

4.High-level performance is modeled.

5. Students are expected to explain thinking and meaning.

6. Students self-monitor their progress.

7. Appropriate amount of time is devoted to tasks.

                                                                            (Teaching Today, 2005b, ¶ 7)

The role of discovery and practice and the use of concrete materials are two additional topics that must be considered when developing a program directed at improving mathematics achievement. Sabean and Bavaria (2005) examined research which suggested that such a program must be balanced between the practice of skills and methods previously learned and new concept discovery. This discovery of new concepts, they suggest, facilitates a deeper understanding of mathematical connections. Johnson (2000) reported findings that suggest that when applied appropriately, the long-term use of manipulatives appears to increase mathematics achievement and improve student attitudes toward mathematics. The utilization of manipulative materials helps students understand mathematical concepts and processes, increases thinking flexibility, provides tools for problem-solving, and can reduce math anxiety for some students. Teachers using manipulatives must intervene frequently to ensure a focus on the underlying mathematical ideas, must account for the “contextual distance” between the manipulative being used and the concept being taught, and take care not to overestimate the instructional impact of their use.

Sabean and Bavaria (2005) have summarized research suggesting that the development of practical meaning for mathematical concepts is enhanced through the use of manipulatives. They further suggest that the use of manipulatives must be long term and meaningfully focused on mathematical concepts. The National Council of Teachers of Mathematics has developed a position statement which provides a framework for the use of technology in mathematics teaching and learning. The NCTM statement endorses technology as an essential tool for effective mathematics learning. Using technology appropriately can extend both the scope of content and range of problem situations available to students. NCTM recommends that students and teachers have access to a variety of instructional technology tools, teachers be provided with appropriate professional development, the use of instructional technology be integrated across all curricula and courses, and that teachers make informed decisions about the use of technology in mathematics instruction (National Council of Teachers of Mathematics, 2003).

Acknowledging and responding to the varied learning styles of students is a critical component of effective inquiry oriented standards-based math instruction. Effective strategies for differentiating mathematics instruction include rotating strategies to appeal to students’ dominant learning styles, flexible grouping, individualizing instruction for struggling learners, compacting (giving credit for prior knowledge), tiered assignments, independent projects, and adjusting question level (Computing Technology for Math Excellence, 2006). A 1998 meta-analysis of 100 research studies on teaching mathematics provided support for a three-phase instructional model. In the first phase of the model, teachers demonstrated, explained, questioned, conducted discussions and checked for understanding. Students are actively involved in discussions and responding to questions. In phase two, teachers and student peers provide student assistance that is gradually reduced while students receive feedback on their performance, corrections, additional explanations, and other assistance as needed. In phase three, teachers assess students’ ability to apply the knowledge gained while students demonstrate their ability to recall, generalize or transfer what they have learned. Effective lessons do not require students to apply new knowledge independently until they have demonstrated an ability to successfully do so (Dixon, Carnine, Lee, Wallin, & Chard, 1998).

The recent results from the Third International Mathematics and Science Study (TIMSS) have caused many teachers in the United States and Canada to take a closer look at strategies and techniques used by Japanese teachers in teaching mathematics. TIMSS results documented the advanced performance and more in depth mathematical thinking of Japanese students. A central strategy in the success of the Japanese mathematics teachers has been the use of Lesson Study, an instructional approach that includes a group of teachers developing, observing, analyzing and revising lesson plans that are focused on a common goal. This process is focused on improving student thinking and includes selecting a research theme, focusing the research, creating the lesson, teaching and observing the lesson, discussing the lesson, revising the lesson and

documenting the findings. A key element of the Lesson Study process is that it helps to facilitate teachers working together using interconnecting skills across grade levels and lessons (Teaching Today, 2006).