加速和丰富教学 → 家长资源 →高数学能力学生的特点

高数学能力学生的特点

The 威尼斯官网在线 Policy on Gifted and Talented Education states that, “从幼儿园到8年级, accelerated and enriched curricula will be provided to all students who have the capability or 动机 to accept the challenge of such a program. This curriculum will be rigorous and challenging and matched to the abilities, 成就水平, 和高能力学生的兴趣. There will be opportunities and expectations for students to learn at an accelerated pace, 深入学习, and to learn integrated themes and connections between disciplines…"

定义“数学承诺”

In order to discuss ways to identify and program for gifted and promising mathematics students, 数学承诺必须被定义. The National Council of Teachers of Mathematics (NCTM) Task Force on the Mathematically Promising defined 数学的承诺 作为——的函数

• 动机,
• 的信念,
• 经验或机会.

These variables are not fixed and need to be developed so that success for these promising students can be maximized. This definition includes the students who have been traditionally identified as gifted, 有才华的, 早熟的, 等等......, and it adds students who have been traditionally excluded from previous definitions of gifted and 有才华的 and therefore excluded from rich mathematical opportunities. This definition acknowledges that students who are mathematically promising, have a large range of abilities and a continuum of needs that should be met.(理查德·沃特海默)

Characteristics to Look for When Identifying Mathematically Gifted 学生

There are many characteristics to consider when identifying which students are mathematically gifted. The following descriptors of characteristics of highly able mathematics students should be viewed as examples of indicators of potential. Few students will exhibit all characteristics and these characteristics can emerge at different times as the child develops cognitively, socio-emotionally, 和身体上.

数学能力强的学生应该 独立 展示以下能力:

• display mathematical thinking and have a keen awareness for quantitative information in the world around them.
• think logically and symbolically about quantitative, spatial, and abstract relationships.
• perceive, visualize, and generalize numeric and non-numeric patterns and relationships.
• 分析推理、演绎推理和归纳推理.
• reverse reasoning processes and switch methods in a flexible yet systematic manner.
• 工作, 沟通, and justify matheatical concepts in creative and intuitive ways, 包括口头和书面.
• 将学习转移到新的情境中.
• formulate probing mathematical questions that extend or apply concepts.
• persist in their search for solutions to complex, "messy," or "ill-defined" tasks.
• organize information and data in a variety of ways and to disregard irrelevant data.
• 快速掌握数学概念和策略, 具有良好的留存性, and to relate mathematical concepts within and across content areas and real-life situations.
• solve 问题 with multiple and/or alternative solutions.
• 自信地使用数学.
• 用数学概念和策略去冒险.
• apply a more extensive and in-depth knowledge of a variety of major mathematical topics.
• 运用估计和心算策略.

It is important to realize that these variables are not fixed and need to be continually developed.

如何识别数学资优学生

不幸的是, there is no single method for identifying gifted and 有才华的 students nor for assessing their performance. Ways of identifying mathematically promising students include:

观察——当学生在工作的时候, particularly in problem solving situations of increasing difficulty or those designed to elicit the characteristics listed above.

投资组合—students need access to exemplars from other students and the scoring rubric should include:

• 注意和概括的模式
• 做出预测并加以验证
• 提出并调查了有趣的相关问题
• 〇衡量创造力的标准
  • 流利度(不同解决方案的数量)
  • 灵活性(解决方案的多样性)
  • 独创性(解决方案的唯一性)
  • 优雅(表达清晰)
   

Questioning—individually, in small group, or whole class:

• 学生面试
• 父母信息
• 学生兴趣/同学调查
• 正在进行的评估
• PADI diagnostic instruments, such as Rating Student Potential Teacher Checklist
• 诊断性思维任务
• 数学日志或日志

如何教数学天才学生

When planning 指令 for gifted and mathematically promising students, 有几个问题需要问:

• Do the opportunities provide for the wide range of abilities, 信仰, 动机, and experiences of students who have 数学的承诺 regardless of their socioeconomic and ethnic backgrounds, 这些机会能满足他们的连续需求吗?
• 是课程, 指令, and assessment qualitatively different and designed to meet the differing needs of promising students?
• 有资源吗?, 项目, 问题, and means of assessment that allow for differences in the level of depth of understanding and engagement?
• Are there appropriate oportunities in mathematics that have clearly defined, 全面的, integrated goals—that are not simply isolated activities?
• Are the opportunities available to all interested students and in all schools?

如…所述 英才政策; "Children with special abilities and talents are part of the human mosaic in our schools and communities. They typically learn at a pace and depth that set them apart from the majority of their same-age peers. Because they have the potential to perform at high levels of accomplishment and have unique affective and learning style need when compared to others of their age, they require 指令al and curricular adjustments that can create a better match between their identified needs and the educational services they typically receive."

节选自 培养有数学前途的学生, edited by Linda Jensen Sheffield, National Council of Teachers of Mathematics, Reston, Virginia.