School is starting soon, and I've been thinking about how to make my classes more appealing to the children. A detailed analysis should really be done. Nowadays, kids don't seem very interested in studying, hehe... By chance, I came across this article on "Effective Teaching". It was quite enlightening, so I decided to save it and share it with everyone... What is "Effective Teaching" (effective teaching)? "Effective Teaching" means that a teacher can effectively "lecture", effectively "ask questions" (and "listen") to students, and effectively "motivate" students.
1. Effective "Lecturing"
No matter how teaching reforms, "lecturing" still stands out as a meaningful teaching method for "Effective Teaching". Its "advantages" have kept it alive in long-term teaching practices, forming its own tradition. Curriculum reform emphasizes students' autonomous learning and inquiry-based learning, seemingly not stressing the teacher's "lecturing" as much. In fact, good teachers are always those who are good at "lecturing", those who are articulate. This was true under traditional conditions, and even with modern educational technology support, the key elements of a good teacher remain largely the same. The only difference might be the amount of time a teacher spends lecturing.
Good "lecturing" always captures students' attention. This means students like the teacher, at least they like the teacher's teaching style or some details of their lectures.
Good "lecturing" always maintains a certain rhythm. Keeping a "teaching rhythm" that matches students' abilities will not only bring artistic enjoyment but also help students remember, understand certain knowledge, and form corresponding values more effectively through subtle hints. Maintaining rhythm also means letting students "grow naturally". Comenius once said, "Nature does not hurry; it moves slowly." For example, a bird doesn't put its eggs on fire to make them hatch faster, but lets them develop slowly under natural temperatures. Later, it doesn't overfeed its chicks to make them grow faster (because such methods would actually hinder their growth), but carefully selects food and feeds them gradually according to their digestive capacity. Rousseau emphasized "the natural process." He said, "The real natural process is relatively slow and gradual, blood gradually begins to boil, thoughts gradually become refined, temperaments gradually form. A smart factory worker pays great attention to making all his tools excellent before using them to manufacture things." In common terms, this is "if you rush, you won't succeed", "progress step by step", "act within your capabilities."
For those "impatient" teachers, perhaps they should be reminded, as Mr. Zhang Wenzhi suggested, that "Teaching is an art of slowness." Here, "slowness" implies a certain "rhythm", giving students time and space for independent thought.
The biggest limitation of teacher lecturing is that it may not fully engage students, putting them in a passive listening state, which can be monotonous and boring. With too much content or too long lectures, students with poor attention and memory gain little benefit. Traditional teacher lecturing struggles to inspire active student participation, often leading to teacher-centered, textbook-centered, classroom-centered teaching due to excessive, inappropriate "lecturing."
Regardless of how effective "lecturing" is, if a teacher wants to effectively motivate students to "engage" in learning, they need to ask effective "questions" and listen to students' voices, keeping teaching interactive and dialogic.
2. Effective "Questioning" and "Listening"
The basic state of effective teaching is dialogic and interactive. In such dialogic and interactive teaching, teachers can lecture, but there shouldn't always be just one voice. Whether teaching exhibits and maintains a dialogic and interactive state depends on whether the teacher can ask effective "questions."
Effective "questioning" means that the questions posed by the teacher elicit responses or answers from students, and these responses or answers make students more actively participate in the learning process. Effective questioning is a delicate teaching skill (a combination of technique and art). The effectiveness of a "question" isn't just in its wording; its effectiveness also lies in changes in tone, emphasis, word choice, and the context of the question. There are many ways to ask questions, each determining whether it will be understood by students as a question and what kind of question it will be understood as.
"Questioning" as the main form of interaction between teachers and students or among students in the classroom can shift the focus from teachers to students.
Effective "questioning" requires maintaining a certain level of openness in questions. Unfortunately, in classroom teaching, "closed" questions are most common and rampant, especially in teacher-dominated classrooms. Research shows that these types of questions account for 80% of all questions asked.
In the actual teaching process, when a teacher's questions lack basic openness, the teacher's "questioning" not only fails to invigorate teaching but also disrupts classroom teaching under the guise of "full-class questioning," "inspiration," "dialogic teaching," and "interactive teaching." After the education community repeatedly advocated "dialogic teaching" and "interactive teaching," teachers who maintained "one-man show" and "full-class cramming" habits became less common. However, after stepping out of these habits, teachers unexpectedly encountered the awkwardness of "full-class questioning."
"Full-class questioning" has almost become a universal phenomenon in current classroom teaching. Teachers' new habit is to lead students to find a series of "standard answers" with pre-set "questions." Although full-class questioning involves students in teaching in form, it is essentially the same as full-class cramming, neither recognizing students as individuals capable of autonomous learning nor fundamentally changing the traditional teaching model where students passively receive information. In such "full-class questioning" classrooms, the teaching atmosphere becomes lively, even noisy, but students gain little benefit.
Classroom questioning is originally a basic classroom teaching activity. Well-designed questions can guide students' thinking and promote their learning. However, if students are led by overly trivial and meaningless questions, or if they are guided toward the same direction by questions with only one answer, they lose themselves and their direction. Such students learn from elementary school to speculate and guess others' intentions, becoming adept at reading people's expressions.
This type of full-class questioning and serial questioning teaching drowns out teaching priorities, occupies students' time for reading, thinking, and practicing, and limits their thinking.
Another problem brought by full-class questioning is that although teachers appear to be constantly paying attention to students and asking them questions, they do not "understand" students because they do not listen. Few people realize that truly effective questioning is simply "listening."
People who ruin conversations always talk incessantly, while skilled conversationalists only ask questions and listen. Once students start learning actively, the teacher's role shifts from lecturing and questioning to "listening." Skilled listeners can always turn students' "voices" into resources for effective teaching. Listening is a form of dialogue, and good conversationalists are always good listeners. This requires teachers to leave enough "waiting" time for students after "questioning," provide timely feedback for students' answers, and let students feel that the teacher is waiting and listening.
3. Effective "Motivation"
Among all the behaviors of effective teachers, the most important is whether the teacher possesses an "inspirational personality," such as enthusiasm, expectations, and trustworthiness.
(1) Enthusiasm
The "enthusiasm" shown by teachers in the teaching process has two meanings: one is being passionate about students; the other is having an "interest" and "belief" in the subject they teach.
Teachers with a passion for knowledge believe that what they do is valuable and meaningful, worth pursuing tirelessly, and convey this interest and belief in knowledge to students during the teaching process, inspiring students to take a full interest in learning. The emotional attitudes and values formed by students in the process of acquiring knowledge are closely related to the teacher's enthusiasm.
The warmth shown by teachers towards students mainly manifests through building positive, supportive relationships with them. Such a safe, relaxed, and satisfying interpersonal relationship environment promotes students' learning. Good teachers are real-life people.
Warmth means trusting, caring for, and accepting students, calling them by name affectionately, smiling frequently, etc. Warmth also means listening to students' voices, considering them important curriculum resources, and actively integrating their opinions, feelings, and ideas into their own teaching.
Good teachers are not only warm-hearted towards students but also committed and invested in their profession, motivating students to learn better through their dedication and commitment. "Enthusiastic" teachers' dedication and commitment are shown by their interest in and integration into the subject they teach; they are energetic and full of vitality. Enthusiastic teachers are often described as lively, ambitious, energetic, and expressive. Their behavior indicates their willingness to be responsible for students and the courses they teach.
"Enthusiasm" is a natural "interest," not a deliberate display or performance. Where there is exaggerated "performance," teachers' enthusiasm can cause tension and fatigue. Natural enthusiasm is preferable to quietness rather than performative "noise."
For students, a teacher's enthusiasm is hidden in the teacher's voice, tone, and body language.
(2) Expectations
Effective teachers always positively expect every learner and have high expectations for success for themselves and their students. They believe that all students can master the content taught, and they have the ability to help all students learn.
To a certain extent, students' success depends on teachers' expectations of them. If students sense from the teacher, "You're stupid and not suited for study," they will lose confidence and give up on themselves. Conversely, if students sense from the teacher, "You have the ability to learn well, you're smart, and you'll succeed if you work hard," they will double their efforts, even if they fail, believing it's temporary. Students internalize the teacher's expectations as their own, affecting their self-evaluation and effort levels. Students are highly sensitive to the teacher's expectations. If a teacher has low expectations for a particular student, not only does that student feel it, but other students can feel it as well, adjusting their thoughts and expectations accordingly.
Most students enter school confident and eager for success, but they quickly adjust their self-expectations to match the teacher's expectations. Students most easily influenced by a teacher's expectations are usually younger, poorer performers, at transitional stages (such as moving from primary to middle school), or particularly fond of the teacher.
A teacher's expectations may help students succeed, but this is only a possibility. Simply having expectations without corresponding assistance measures will not yield the desired results. Only by combining expecting students to succeed with helping them succeed can a teacher's expectations be realized in students.
Importantly, teachers need to provide opportunities for success for each student, allowing them to experience success. This successful experience enhances students' self-confidence, helps them see their abilities, motivates them further, and leads to greater success. This is a virtuous cycle. For students struggling with learning and lacking confidence in their ability to succeed, experiencing success is even more crucial. Even if students cannot always succeed, at least ensure that each student succeeds most of the time.
Teachers express high expectations for students through "teaching behaviors." As an optimistic student perspective, teachers should regularly express their expectations for students, but to make teacher expectations promote student success, besides words, more action is needed.
Expectation and encouragement are about helping students solve problems through their own efforts, building their confidence, rather than cheap praise or incitement.
Ultimately, teachers who persistently maintain expectations and encouragement for students hold a life belief. Effective teachers are positive, centered around their and their students' success, and remain optimistic. Effective teachers have confidence and expectations for both themselves and their students. They believe they have the ability to help every student achieve academic success.
These expectations influence teachers' behaviors towards students, thereby affecting students' learning. When teachers anticipate that a student will not succeed, they tend to reduce the time and energy spent on these students, increasing the likelihood of failure. Conversely, high expectations from teachers may lead to greater teacher investment. The teacher's positive attitude and efforts also infect students, enabling them to internalize the teacher's expectations as their own, enhancing their confidence, increasing their efforts, and achieving success.
(3) Trustworthiness
Teachers build trust through candid, honest teacher-student interactions rather than through their status or academic qualifications, which only matter when recognized by students.
"Effective teachers" are always those that students feel are "trustworthy." "Trustworthiness" helps create a relaxed and safe psychological environment, making students believe that teachers can help them succeed.
Teachers' "trustworthiness" in students' minds mainly depends on two key factors: one is the teacher's knowledge; the other is the teacher's personality.
It may be relatively easier for teachers to gain students' trust in lower grades, but as students grow older and psychologically mature, it becomes harder for teachers to earn students' trust. In lower grades, teachers as adult authorities naturally command some degree of credibility from students. However, as students mature, they become less likely to automatically trust teachers. University students can judge the credibility of teachers, and these judgments partly determine the effectiveness of each teacher.
Students always expect teachers to be knowledgeable. If teachers meet students' expectations, students may admire and follow the teacher.
Besides knowledge, more importantly, it is the teacher's personal charm. As German scholar Lind said: What truly teaches students is the teacher's personality, not so-called teaching methods. Lind published "Personality Education - A Warning Against Modern Methodism," whose subtitle is worth considering for those long obsessed with "teaching methods."
Choosing and applying teaching methods is naturally important for effective teaching, but there seems to be something more important than "methods," namely the teacher's personality. The teacher's expectations, enthusiasm, and ability to win students' trust almost determine the effectiveness of teaching.
"Personality" education is the fundamental ideal of education. The ultimate concern of education always points to students' personalities, aiming to cultivate ideal personalities and pursue personality completion. To make students possess ideal personalities, teachers must first have such personalities. The German education field once saw the rise of "personality education," ignoring its biases, but it deserves attention for an education long focused on "knowledge" and indulging in "intellectualism" (including "teaching for thinking").
I. Theoretical Considerations
(1) Research on Effective Teaching by Domestic and Foreign Experts:
1. Five Key Points from Foreign Professors (Research by Gary Borich and others at the University of Texas):
(1) Clear teaching objectives;
(2) Diverse teaching methods;
(3) Clear task orientation;
(4) Student engagement;
(5) High success rate.
2. Three Key Points from Chinese Professors (Research by Huang Xiang and others at Chongqing Normal University):
(1) An active construction process based on existing knowledge and experience.
(2) Filled with rich mathematical activities such as observation, experimentation, conjecture, verification, reasoning, and communication.
(3) A personalized and multi-need learning process.
(2) My Preliminary Thoughts:
1. Preliminary Understanding of Effective Teaching:
Achieving expected and generated teaching goals, promoting students' comprehensive, harmonious, and sustainable development.
2. Theoretical Support:
(1) Holistic Principle: Emotional (motivational system) and cognitive (operating system) systems complement each other to produce overall functionality, 1+1>2.
(2) Sequential Progression Principle: From shallow to deep, from easy to difficult, continuously promoting students toward the nearest zone of mind development.
(3) Feedback Principle: Timely feedback, handling feedback information properly.
(4) Activity Teaching Theory, Constructivist Teaching Theory: Teaching itself is an activity; mathematics should be learned in mathematical activities. It is an active construction process based on existing knowledge and experience.
II. Operational Considerations
(1) Deeply Study the Textbook, Carefully Analyze the Learning Situation (Establish Clear and Reasonable Teaching Goals):
1. Deeply Study the Textbook, Discover Your Unique Insights (Creatively Use the Textbook)
(1) Fully understand key difficulties, find entry points.
(2) Cultivate growth points, stimulate innovation points.
2. Carefully Analyze the Learning Situation.
(1) Analyze students' existing knowledge base, thinking characteristics, and physiological/psychological conditions.
(2) Empathize, consider the students' perspectives: where do they start learning this knowledge? Where do their thoughts get blocked? What methods can open their minds and overcome thinking obstacles?
(2) Positive Interaction (In a Sense, the Essence of Teaching Is Teacher-Student Interaction):
1. Teachers: Act as good organizers, guides, collaborators, present but not overstepping.
2. Students: Actively Participate in Learning Activities, Participation Has Three Levels.
(1) Behavioral Participation (External Manifestation: Do they use their hands when required, speak during discussions, write during practice?)
(2) Emotional Participation (Facial Expressions, Especially Eyes, Indicate Attention Level: Are They Enthusiastic, Active?)
(3) Cognitive Thinking Participation (Deep-Level Participation: Are They Highly Focused, Actively Thinking, Generating Sparks of Thought, Making Unexpected Yet Reasonable Comments?)
Student participation should not only be in quantity but also in quality.
(3) Improve Learning Methods (Cultivate Inquiry Awareness and Practical Abilities):
Discovery, acceptance, exploration, imitation, practical operation, and practice are all learning methods, scientifically and reasonably applied based on content, target audience, and environment.
1. Autonomous Exploration
(1) Start with directed exploration (in critical areas, explore and exchange), not all math knowledge needs to be explored by students.
(2) Make autonomous exploration complementary to meaningful acceptance, mutually reinforcing.
(3) Handle the relationship between inheritance and development.
Mathematics teaching in China and abroad does not have absolute superiority; instead, they should learn from each other and complement each other's advantages. Mathematics curriculum reform cannot be entirely westernized; it should integrate Eastern and Western methods to construct an effective teaching approach that is both theoretically sound and practically useful. China's good traditions should be carried forward, innovated upon, developed, and reflected upon.
2. Collaborative Exchange (Not Just Formalities).
(1) First think independently, then collaborate and exchange, creating a need for collaboration.
(2) Organize well, assign clear roles, and evaluate the effectiveness of collaboration.
3. Hands-On Practice
(1) Emphasize hands-on experimental validation in the teaching process and practical assignments inside and outside the classroom. Multimedia and traditional teaching methods should complement each other; multimedia should not replace hands-on experiences and sensory insights.
(2) Effectively conduct integrated mathematics practice classes.
(4) Appropriate Evaluation and Motivation:
1. Purposes of Evaluation:
(1) Stimulate enthusiasm, enhance self-confidence;
(2) Correct mistakes;
(3) Experience the joy of progress and success.
2. Some current evaluations do not achieve these purposes and have two issues:
(1) Excessive cheap praise makes students arrogant and unable to handle setbacks.
(2) Reluctance to point out problems leads to students being unable to distinguish right from wrong, affecting their lifelong development.
3. Solutions:
Evaluate students:
① Pay attention with heart;
② Experience with emotion;
③ Express appropriately, evaluations need sincerity and personalized feedback: demonstrate guidance and motivation.
(5) Gradual Improvement in Exercises:
1. Mathematical exercises generally go through three levels:
Basic exercises or targeted single-item exercises → Comprehensive exercises or variant exercises → Developmental exercises with higher comprehensiveness.
2. Reflect four characteristics: hierarchical, targeted, practical, open-ended.
3. Emphasize variant exercises:
(1) Variant exercises: These refer to exercises that change non-essential attributes of concepts in different forms to highlight essential attributes.
(2) Function: Help students recognize the essential attributes of things from various representations and different scenarios, thus understanding concepts more broadly, accurately, and deeply. They play a crucial role in cultivating students' profound, flexible, critical, and creative thinking.
(6) Integrated Three-Dimensional Teaching Effect:
While implementing dual foundations (basic knowledge and skills), allow students to experience processes, learn methods, and form correct attitudes, emotions, and values. Let students' personalities develop; improve upper, middle, and lower-level students based on their original foundations.
Relevant Link: "Concepts and Strategies of Effective Teaching" http://reading.cersp.com/Teacher/School/200605/1491.html
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