How Do Children Learn Mathematics

Editor's Notes

• #3: 1. Chinese proverb: I hear and I forget, I see and I remember, I do and I understand. This principle is based on the premise that students will have greater understanding if they “do” the mathematics. 2. Children have different developmental levels. We will be looking at some theories that give you windows for what’s appropriate, but the teacher plays a critical role in judging the development stage of the student. 3. Math builds on previous learning. We see this in the NCTM standards. Students focus on the same 10 standards regardless of grade level. This is known as a “spiral approach.” Teachers need to make sure, however, that the level of sophistication changes as students progress through the grades. A spiral curriculum should not just be there for review. 4. Manipulatives and real-world examples provide many opportunities for talking about math. Communication in a math classroom make take the form of student-to-student communication or student-to-teacher communication. 5. Teachers need to know when to ask questions and what kinds of questions to ask. (Bloom’s taxonomy?) Sometimes low-level questions are appropriate, other times open-ended questions are necessary.
• #4: 6. Manipulatives - Because math, by its very nature is abstract, students need models to help make sense of math. 7. Metacognition affects learning. Metacognition refers to what one knows or believes about oneself as a learner and how one controls and adjusts one’s behavior. Metacognition is a form of looking over your own shoulder. 8. Teacher attitudes are vital - Research has shown that teachers who enjoy teaching math and are enthusiastic about their subject matter tend to produce students who like math. Teachers need to have high expectations for all students regardless of their race or gender. 9. Gender Aptitudes are equal - Research suggests that teachers may treat boys differently than girls. (less likely to praise girls for correct responses, less willing to prompt girls, ask lower level questions of girls, attribute boys’ failure to a lack of motivation where girls is a lack of ability. Girls are particularly susceptible to learned helplessness, the belief that one cannot control outcomes and is destined to fail. Teachers need to dispel myths such as “only white males do math” and have equally high expectations for both boys and girls. Teachers should also call attention to female role models in math and science and communicate to parents the importance of encouraging and supporting their daughters to persist in nontraditional fields. 10. Rentention-Because math is cumulative, retention is critical. 11. Math Anxiety -next slide
• #6: Math anxiety is a clear-cut, negative, mental, emotional, and/or physical reaction to mathematical thought processes and problem solving.
• #8: 1. Panic - Students have a feeling of helplessness. They feel that a brick wall has come down and they will never do better and have reached their limit in math. 2. Paranoia - Students have a feeling that everyone knows the answer except them. They feel they have been faking math for years and everyone knows it. 3. Passive - They have an attitude that either they have a math mind or they don’t. There is nothing they can do to become better in math. They sit back and don’t take action. 4. Lack of Confidence - They don’t trust their intuition. They rely on memorizing rules instead of understanding the concepts.