Here are some useful tips and key ideas in teaching mathematics to primary level or secondary level students. Teaching math to young children is a play game if your can build their interest in the subject.
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:
·
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.
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).
