how to present math in different angles which represents depth of subject,easiness,empowerment,basics,logic,analyze,view of subject from back,view from front.Give multiple e.g.s .(just 11th & 12th)
I read a book, written in 1949, by a retiring teacher that focused on how to be an effective teacher. The four points of the book:
Know your students.
Love your students.
Know your subject.
Love your subject.
The last two are really the answer to your question. It is not enough to take a few math courses in college, you have to live math.
You can get experience in many fields: Business, architecture, engineering, science. If you do not have this experience, use your summer holidays to gain it. Professionals will happily let you tag along on projects, to learn the math applications to relate to your students. Summer workshops are another source of learning, having taught many of these, it is surprising what one can learn, and how to demonstrate/teach it.
could you tell me how and what the professionals will teach, A list of ten topics, an idea about 1 or 2 topics and a list of some angles as such....
what is the amplitude, period, and phase shift of f(x)=-3 cos(4x=Pie)+6
Alicia needs $2000 three years from now. How much should she deposit at the end of each year for the next 3 years in an account that pays 5% compounded annually?
Suppose you select 2 letters from the word {Algebra} what is the probability of sellecting a) 2 consonants b) 2 vawel c) atleast one vawel d) atmost one condonant
To present math from different angles and convey its depth, easiness, empowerment, basics, logic, analysis, and different viewpoints, you can use various strategies and techniques. Below are some examples specifically for 11th and 12th-grade math topics:
1. Depth: To present the depth of a subject, you can delve into advanced concepts beyond the basic curriculum. For example, in calculus, you can discuss the concept of limits, derivatives, and integrals in detail, exploring their historical development and applications.
2. Easiness: Mathematics can be made more approachable by breaking down complex ideas into simpler steps. For instance, in trigonometry, you can explain the relationship between the sides and angles of a right triangle using visual aids and real-life examples, making it easier for students to grasp and apply.
3. Empowerment: Show students how math empowers them by highlighting its relevance and real-world applications. For example, in statistics, you can demonstrate how data analysis and interpretation can help make informed decisions in various fields like finance, medicine, or social sciences.
4. Basics: Emphasize the importance of mastering fundamental concepts before moving on to advanced topics. In algebra, reinforce the understanding of equations, inequalities, and operations with concrete examples and problem-solving exercises.
5. Logic: Highlight the logical reasoning behind mathematical concepts and problem-solving strategies. In geometry, explore the principles of deductive reasoning through theorems and proofs, enabling students to think critically and apply logical arguments.
6. Analysis: Teach students to interpret and analyze mathematical data and information. In calculus, encourage them to analyze the behavior of functions, identify critical points, extrema, and sketch graphs to understand the relationship between variables.
7. View from the Back: Reverse the traditional approach by posing challenging problems to students and guiding them through the problem-solving process. For instance, in algebra, present a complex equation or system of equations and guide students to find the solution step-by-step.
8. View from the Front: Provide clear explanations and demonstrations of concepts while involving students in discussions and activities. For example, in probability, design experiments or simulations to help students understand the basic principles and outcomes.
Remember, these examples are merely illustrative, and there are countless other ways to present math from different angles. Adjust your teaching methods based on the specific needs and preferences of your students.