How to Teach Mathematics
Focus on teaching students why things work., Look for understanding in student work., Use memorization only as a tool., Create opportunities for students to explore and develop rules.
Step-by-Step Guide
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Step 1: Focus on teaching students why things work.
Teaching math is like teaching a system of procedures.
Whether you are teaching basic addition, long division, or integral calculus, you need to get your students to understand why the procedure works., When students complete homework, quizzes or tests, you should examine their work to find out what they know.
Don’t just look for the wrong answers, which show what they don’t know.
Use the student’s knowledge base of right answers to set a base for additional work.
Math is a sequential subject.
Students who do not have a strong understanding base will have increased difficulty later., Some level of memorizing is still valuable in mathematics.
Just as students learning a foreign language need to memorize basic vocabulary words, students learning math need to memorize certain basic facts.
These are things that could be worked out or solved every time, but memorizing will allow the students to focus on more advanced understanding.
Some examples, in increasing level of complexity, include:
Addition, subtraction, multiplication and division facts Squares and square roots Powers of 2 and 10 Quadratic formula Trigonometric substitutions , Rather than simply lecturing and giving students rules and definitions, give them projects that can help them discover math facts for themselves.
Students will remember rules or relationships much better if they find them through self-discovery.For example, young students can be given fraction bars or other manipulatives.
Through directed exploration, students can find certain patterns or equalities, like: 1=12+12=13+13+13{\displaystyle 1={\frac {1}{2}}+{\frac {1}{2}}={\frac {1}{3}}+{\frac {1}{3}}+{\frac {1}{3}}} 14+14=12{\displaystyle {\frac {1}{4}}+{\frac {1}{4}}={\frac {1}{2}}} Older students studying geometry, for example, can use tape measures and rulers to measure round objects and discover the relationships between circumference, diameter and radius: d=2r{\displaystyle d=2r} C/d=3.14{\displaystyle C/d=3.14} -
Step 2: Look for understanding in student work.
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Step 3: Use memorization only as a tool.
-
Step 4: Create opportunities for students to explore and develop rules.
Detailed Guide
Teaching math is like teaching a system of procedures.
Whether you are teaching basic addition, long division, or integral calculus, you need to get your students to understand why the procedure works., When students complete homework, quizzes or tests, you should examine their work to find out what they know.
Don’t just look for the wrong answers, which show what they don’t know.
Use the student’s knowledge base of right answers to set a base for additional work.
Math is a sequential subject.
Students who do not have a strong understanding base will have increased difficulty later., Some level of memorizing is still valuable in mathematics.
Just as students learning a foreign language need to memorize basic vocabulary words, students learning math need to memorize certain basic facts.
These are things that could be worked out or solved every time, but memorizing will allow the students to focus on more advanced understanding.
Some examples, in increasing level of complexity, include:
Addition, subtraction, multiplication and division facts Squares and square roots Powers of 2 and 10 Quadratic formula Trigonometric substitutions , Rather than simply lecturing and giving students rules and definitions, give them projects that can help them discover math facts for themselves.
Students will remember rules or relationships much better if they find them through self-discovery.For example, young students can be given fraction bars or other manipulatives.
Through directed exploration, students can find certain patterns or equalities, like: 1=12+12=13+13+13{\displaystyle 1={\frac {1}{2}}+{\frac {1}{2}}={\frac {1}{3}}+{\frac {1}{3}}+{\frac {1}{3}}} 14+14=12{\displaystyle {\frac {1}{4}}+{\frac {1}{4}}={\frac {1}{2}}} Older students studying geometry, for example, can use tape measures and rulers to measure round objects and discover the relationships between circumference, diameter and radius: d=2r{\displaystyle d=2r} C/d=3.14{\displaystyle C/d=3.14}
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