As a part of my future career, I plan to be a prominent Math lecturer in a university. To do so, I need to obtain a good knowledge of methodologies of mathematical lecturing. In this way, I am determined to benefit from both classical proved teaching approaches as well as the modern technical facilities, technologies, and educational softwares which improves my teachings and helps my future students to understand the concepts of the mathematical courses better. So, as an expert in teaching and giving lectures, have you ever experienced an approach, used a method or applied a sort of new technology which has helped you to obtain better educational results in your Math classes? Thanks in advance for your contributions in this discussion.
This is a good question with many possible answers.
Briefly, in preparing for a lecture. it helps to think in terms of a toolbox containing the tools needed to put together each lecture. Those tools are
Notation. Work out and identify the symbols you need for your definitions and theorems.
Definitions. Identify the key terms needed to put together examples and theorems to be presented.
Sketches. Hand drawings of scenarios to be described (presented). Sketches include sets, relations between sets, mappings on sets into (onto) other sets, plots of functions of interest, surfaces of interest. Sketches are bridges between notation, definitions and theorems.
Theorems. Results important to a topic. Theorems (and their proofs) are the heart of the matter.
References. Connections between what is to be presented and results introduced by others.
Summaries: Abstracts or summaries of parts of articles or books (pertinent to a topic) are helpful.
Notes. Handwritten (not typed) notes representing a work in progress, leading up to each lecture. Your notes would contain bits and pieces of each of the above items. Here, lists are points are helpful.
LaTeX (beamer). Use LaTeX to put together a pdf file for each lecture, something you can distribute to students. That gives them a guide leading up to exams and such pdf files provide a paper trail for a set of lectures.
Dear Professor Dr. James F Peters
Many thanks for your complete explanations. I will, definitetely, benefit from your method and apply it in my future clases. Would you please also give me some hints for motivating non-interested students in mathematics?
- You can distribute flash cards at the start of your lecture to develop interest of every student in lecture.
Bset,
Dear Dr. Triq Mahmood
Thanks for your contribution. It is a good idea to use flash cards. Would you please explain more about the content of flash cards?
@Marzieh Eini Keleshteri: Would you please also give me some hints for motivating non-interested students in mathematics?
One way to make mathematics come alive for non-interested students is to incorporate some visualizations in your lectures (geometry, plots, animations, dynamically changing shapes by adjust a suite of parameters that control shape and its appearance, stories that bring home the relevance of mathematics in everyday situations). Such visualizations can be produced using Mathematica, especially the free, downloadable CDF player with 100s of beautiful demonstrations.
There is a book by Steve Krants "How to teach mathematics'. May be you would be interested in this book.(Or you had already read it?)
Regarding your statment "...motivating non-interested students..." :
there are some things in the book about how we should react on NON INTERESTING questions which are asked by students. in the classroom. How can we help them to improve such questions...etc...
Best regards
Ali Taghavi
Dear Marzieh
I would like to suggest to look at the following post, too.
https://www.researchgate.net/post/What_is_active_teaching_for_you.
@ Ali Taghavi: ... there are some things in the book about how we should react on NON INTERESTING questions which are asked by students.
Many thanks for calling attention to Krantz's excellent book.
There is a remarkable, very good commentary on Steven Krantz's book How to Teach Mathematics, that followers of this thread may find both interesting and helpful. For the pdf file for this very detailed commentary, see
Ed Dubinsky
Reflections on Krantz's How to Teach Mathematics. A Different View.
http://www.math.kent.edu/~edd/KrantzEssay.pdf
One important difference between Dubinski's approach and the one recommended by S. Krantz appears on page 24. Krantz suggests that hard copy textbooks work well [as instructional vehicles]. Dubinski takes strong exception to this suggestion by Krantz. Dubinski points out that traditional textbooks are largely unread by students. Instead, students prefer a more dynamic approach, depending on what is presented in class. Do you agree?
In the beginning you must prepare for the subject or lecture in advance.
Begin preparing the topic of the lecture and preparing and solving mathematical examples.
Preparation of all necessary tools and modern ones and the introduction of electronic means to explain the lecture.
Preparation of all necessary tools and modern ones and the introduction of electronic means to explain the lecture.
Give examples to students to involve them in solving exercises on the same subject.
5 Important Characteristics to Become a Good Math Teacher
by Stacy Zeiger; Updated July 01, 2018
Not all students like math, but a good math teacher has the power to change that. A good math teacher can help students who have traditionally struggled with arithmetic begin to build confidence in their skills. For students who are usually bored with numbers, a good math teacher can breathe new life into the subject. A good math teacher makes her class a place where students want to be.
Knowledge of Mathematics
A successful math teacher has an extensive knowledge of mathematics. She has taken multiple courses in algebra, geometry, statistics, calculus and other areas of mathematics at the college level and, possibly, even the graduate level. This knowledge allows her to confidently explain concepts and processes to her students. She is not constantly consulting the answer key in the back of the teacher's guide to help students solve problems. This confidence boosts her credibility and helps students trust in her ability to teach them what they need to know.
Teaching Strategies
Students learn in different ways, and a good math teacher understands that. She keeps up with the best practices in math education and regularly incorporates them into her instruction to help all of her students learn. She also understands there may be multiple ways to solve problems and uses those alternate strategies to help struggling students grasp difficult concepts. Her lesson plans engage students and help them feel confident in their mathematical abilities.
A Personable Approach
In the classroom, a talented math teacher does not take the "because I said so" approach or play the role of a know-it-all. Instead, she serves as a facilitator of learning, providing students with the knowledge and tools to solve problems and then encouraging students to solve them on their own. When students answer a problem incorrectly, she does not allow them to quit. She encourages students to figure out where they went wrong and to keep working at the problem until they get the correct answer, providing support and guidance where needed.
Classroom Leadership
A skilled math teacher is seen as a leader in her classroom and in the school. Her students respect her, not only for her knowledge of mathematics, but for her overall attitude and actions. Students can tell she respects them as well. She has control over the classroom, laying out clear rules and expectations for students to follow. When students misbehave, discipline is consistent and fair.
Care and Concern
As any experienced teacher knows, teaching focuses less on the content being taught than the students being taught. A good math teacher cares about her students. She recognizes when a student is having a bad day or needs some encouragement and addresses the problem to help the student refocus on the material. While she holds students to high expectations, she recognizes that occasionally life gets in the way of homework and that studying sometimes take a back seat to family obligations. Therefore, she offers students second chances when warranted and takes time out of her own schedule to help students catch up.
reference/https://work.chron.com/5-important-characteristics-become-good-math-teacher-8926.html
regards
Simplifying mathematics for students is familiar to them by solving exercises, giving homework and not using complex examples
https://www.bestvalueschools.com/lists/5-characteristics-of-a-great-math-teacher/
In lower levels some students respond to the symbolic representation. Others understand better a graphing of variables. Yet others work better with text and numbers. These differences are fundamental personality and mental characteristics. You cannot change them. Much effort is lost in trying to change things that don't need to be changed. Teaching should include the several different presentations to get the best of each student.
Math students with personalities mentality suited to higher math may choose the major and maybe graduate school. Then they might become math teachers, never realizing there is more than one way to think and work in mathematics.
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