Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

Synopsis

Have you ever wondered why students too often have only a rudimentary understanding of mathematics, why even rich and exciting hands-on learning does not always result in real learning of new concepts? The answer lies in whether students have actually learned mathematical concepts, rather than merely memorizing facts and formulas. Concept-Rich Mathematics Instruction is based on the constructivist view that concepts are not simply facts to be memorized and later recalled, but rather knowledge that learners develop through an active process of adapting to new experiences. The teachers role is critical in this process. When teachers prompt students to reflect on their experiences and report and answer questions verbally, students must re-examine and even revise their concepts of reality. Meir Ben-Hur offers expert guidance on all aspects of Concept-Rich Mathematics Instruction, including
• Identifying the core concepts of the mathematics curriculum.
• Planning instructional sequences that build upon concepts that students already understand.
• Designing learning experiences that provoke thoughtful discussions about new concepts and prepare students to apply these concepts on their own.
• Identifying student errors, particularly those caused by preconceptions, as important sources of information and as key instructional tools.
• Conducting classroom dialogues that are rich in alternative representations.
• Using a variety of formative assessment methods to reveal the state of students learning.
• Incorporating problem-solving activities that provoke cognitive dissonance and enhance students cognitive competence. Concept-Rich Mathematics Instruction is grounded in the belief that all students can learn to think mathematically and solve challenging problems. If youre looking for a powerful way to improve students performance in mathematics and move closer to fulfilling the NCTM standards, look no further: this approach provides the building blocks for constructing a first-class mathematics program.

Excerpt

If we accept the centrality of Concept-Rich Instruction as highlighted in the national standard (National Council of Teachers of Mathematics [NCTM], 1989), then it is important that we develop facility in delivering that instruction. Whether we follow the most prevalent theory and research in cognitive psychology today or examine the current research emanating from mathematics educators, we will learn that teachers must play a key role in developing students' concepts and their ability to apply these concepts.

The constructivist theory that springs from Immanuel Kant's teaching tells us that the mind is an active organ and postulates that it is the teacher's responsibility to organize experiences into concepts that determine subsequent learning. Research in the field of mathematics education indicates that the teacher indeed plays a key role in meaningful learning of concepts. Without the teacher's mediation, most students do not understand the fundamental concepts, cannot make connections among the different strands within mathematics, and cannot transfer what they know beyond very particular problem situations they practiced in the classroom. Good teaching capitalizes upon the learning of core concepts. Therefore, it is . . .

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