Active learning

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Active_learning

Classroom teaching

Active learning is "a method of learning in which students are actively or experientially involved in the learning process and where there are different levels of active learning, depending on student involvement." Bonwell & Eison (1991) states that "students participate [in active learning] when they are doing something besides passively listening." According to Hanson and Moser (2003) using active teaching techniques in the classroom can create better academic outcomes for students. Scheyvens, Griffin, Jocoy, Liu, & Bradford (2008) further noted that “by utilizing learning strategies that can include small-group work, role-play and simulations, data collection and analysis, active learning is purported to increase student interest and motivation and to build students ‘critical thinking, problem-solving and social skills”. In a report from the Association for the Study of Higher Education, authors discuss a variety of methodologies for promoting active learning. They cite literature that indicates students must do more than just listen in order to learn. They must read, write, discuss, and be engaged in solving problems. This process relates to the three learning domains referred to as knowledge, skills and attitudes (KSA). This taxonomy of learning behaviors can be thought of as "the goals of the learning process." In particular, students must engage in such higher-order thinking tasks as analysis, synthesis, and evaluation.

Nature of active learning

There are a wide range of alternatives for the term active learning and specific strategies, such as: learning through play, technology-based learning, activity-based learning, group work, project method, etc. The common factors in these are some significant qualities and characteristics of active learning. Active learning is the opposite of passive learning; it is learner-centered, not teacher-centered, and requires more than just listening; the active participation of each and every student is a necessary aspect in active learning. Students must be doing things and simultaneously think about the work done and the purpose behind it so that they can enhance their higher order thinking capabilities.

Many research studies have proven that active learning as a strategy has promoted achievement levels and some others say that content mastery is possible through active learning strategies. However, some students as well as teachers find it difficult to adapt to the new learning technique.

There are intensive uses of scientific and quantitative literacy across the curriculum, and technology-based learning is also in high demand in concern with active learning.

Barnes (1989) suggested principles of active learning:

1. Purposive: the relevance of the task to the students' concerns.
2. Reflective: students' reflection on the meaning of what is learned.
3. Negotiated: negotiation of goals and methods of learning between students and teachers.
4. Critical: students appreciate different ways and means of learning the content.
5. Complex: students compare learning tasks with complexities existing in real life and making reflective analysis.
6. Situation-driven: the need of the situation is considered in order to establish learning tasks.
7. Engaged: real life tasks are reflected in the activities conducted for learning.

Active learning requires appropriate learning environments through the implementation of correct strategy. Characteristics of learning environment are:

1. Aligned with constructivist strategies and evolved from traditional philosophies.
2. Promoting research based learning through investigation and contains authentic scholarly content.
3. Encouraging leadership skills of the students through self-development activities.
4. Creating atmosphere suitable for collaborative learning for building knowledgeable learning communities.
5. Cultivating a dynamic environment through interdisciplinary learning and generating high-profile activities for a better learning experience.
6. Integration of prior with new knowledge to incur a rich structure of knowledge among the students.
7. Task-based performance enhancement by giving the students a realistic practical sense of the subject matter learnt in the classroom.

Constructivist framework

Active learning coordinates with the principles of constructivism which are, cognitive, meta-cognitive, evolving and effective in nature. Studies have shown that immediate results in construction of knowledge is not possible through active learning as the child first goes through the process of knowledge construction, knowledge recording and then knowledge absorption. This process of knowledge construction is dependent on previous knowledge of the learner where the learner is self-aware of the process of cognition and can control and regulate it by themselves. There are several aspects of learning and some of them are:

1. Learning through meaningful reception, influenced by David Ausubel, who emphasizes the previous knowledge the learner possesses and considers it a key factor in learning.
2. Learning through discovery, influenced by Jerome Bruner, where students learn through discovery of ideas with the help of situations provided by the teacher.
3. Conceptual change: misconceptions takes place as students discover knowledge without any guidance; teachers provide knowledge keeping in mind the common misconceptions about the content and keep an evaluatory check on the knowledge constructed by the students.
4. Constructivism, influenced by researchers such as Lev Vygotsky, suggests collaborative group work within the framework of cognitive strategies like questioning, clarifying, predicting and summarizing.

Science of active learning

Active learning can be used effectively for teaching comprehension and memory. The reason it is efficient is that it draws on underlying characteristics of how the brain operates during learning. These characteristics have been documented by thousands of empirical studies (e.g., Smith & Kosslyn, 2011) and have been organized into a set of principles. Each of these principles can be drawn on by various active learning exercises. They also offer a framework for designing activities that will promote learning; when used systematically, Stephen Kosslyn (2017) notes these principles enable students to "learn effectively—sometimes without even trying to learn".

The principles of learning

One way to organize the empirical literature on learning and memory specifies 16 distinct principles, which fall under two umbrella "maxims". The first maxim, "Think it Through", includes principles related to paying close attention and thinking deeply about new information. The second, "Make and Use Associations", focuses on techniques for organizing, storing, and retrieving information.

The principles can be summarized as follows.

Maxim I: Think it through

• Evoking deep processing: extending thinking beyond "face value" of information (Craig et al., 2006; Craik & Lockhart, 1972)
• Using desirable difficulty: ensuring that the activity is neither too easy nor too hard (Bjork, 1988, 1999; VanLehn et al., 2007)
• Eliciting the generation effect: requiring recall of relevant information (Butler & Roediger, 2007; Roediger & Karpicke, 2006)
• Engaging in deliberate practice: promoting practice focused on learning from errors (Brown, Roediger, & McDaniel, 2014; Ericsson, Krampe, & Tesch-Romer, 1993)
• Using interleaving: intermixing different problem types
• Inducing dual coding: presenting information both verbally and visually (Kosslyn, 1994; Mayer, 2001; Moreno & Valdez, 2005)
• Evoking emotion: generating feelings to enhance recall (Erk et al., 2003; Levine & Pizarro, 2004; McGaugh, 2003, 2004)

Maxim II: Make and use associations

• Promoting chunking: collecting information into organized units (Brown, Roediger, & McDaniel, 2014; Mayer & Moreno, 2003)
• Building on prior associations: connecting new information to previously stored information (Bransford, Brown, & Cocking, 2000; Glenberg & Robertson, 1999; Mayer, 2001)
• Presenting foundational material first: providing basic information as a structural "spine" onto which new information can be attached (Bransford, Brown, & Cocking, 2000; Wandersee, Mintzes, & Novak, 1994)
• Exploiting appropriate examples: offering examples of the same idea in multiple contexts (Hakel & Halpern, 2005)
• Relying on principles, not rote: explicitly characterizing the dimensions, factors or mechanisms that underlie a phenomenon (Kozma & Russell, 1997; Bransford, Brown, & Cocking, 2000)
• Creating associative chaining: sequencing chunks of information into stories (Bower & Clark, 1969; Graeser, Olde, & Klettke, 2002)
• Using spaced practice: spreading learning out over time (Brown, Roediger, & McDaniel, 2014; Cepeda et al., 2006, 2008; Cull, 2000)
• Establishing different contexts: associating material with a variety of settings (Hakel & Halpern, 2005; Van Merrienboer et al., 2006)
• Avoiding interference: incorporating distinctive retrieval cues to avoid confusion (Adams, 1967; Anderson & Neely, 1996)

Active learning typically draws on combinations of these principles. For example, a well-run debate will draw on virtually all, with the exceptions of dual coding, interleaving, and spaced practice. In contrast, passively listening to a lecture rarely draws on any.

Active learning exercises

See also: Cooperative learning § Techniques

Bonwell and Eison (1991) suggested learners work collaboratively, discuss materials while role-playing, debate, engage in case study, take part in cooperative learning, or produce short written exercises, etc. The argument is "when should active learning exercises be used during instruction?". Numerous studies have shown that introducing active learning activities (such as simulations, games, contrasting cases, labs,..) before, rather than after lectures or readings, results in deeper learning, understanding, and transfer. The degree of instructor guidance students need while being "active" may vary according to the task and its place in a teaching unit.

In an active learning environment learners are immersed in experiences within which they engage in meaning-making inquiry, action, imagination, invention, interaction, hypothesizing and personal reflection (Cranton 2012).

Examples of "active learning" activities include

• A class discussion may be held in person or in an online environment. Discussions can be conducted with any class size, although it is typically more effective in smaller group settings. This environment allows for instructor guidance of the learning experience. Discussion requires the learners to think critically on the subject matter and use logic to evaluate their and others' positions. As learners are expected to discuss material constructively and intelligently, a discussion is a good follow-up activity given the unit has been sufficiently covered already. Some of the benefits of using discussion as a method of learning are that it helps students explore a diversity of perspectives, it increases intellectual agility, it shows respect for students' voices and experiences, it develops habits of collaborative learning, it helps students develop skills of synthesis and integration (Brookfield 2005). In addition, by having the teacher actively engage with the students, it allows for them to come to class better prepared and aware of what is taking place in the classroom.
• A think-pair-share activity is when learners take a minute to ponder the previous lesson, later to discuss it with one or more of their peers, finally to share it with the class as part of a formal discussion. It is during this formal discussion that the instructor should clarify misconceptions. However students need a background in the subject matter to converse in a meaningful way. Therefore, a "think-pair-share" exercise is useful in situations where learners can identify and relate what they already know to others. It can also help teachers or instructors to observe students and see if they understand the material being discussed. This is not a good strategy to use in large classes because of time and logistical constraints (Bonwell and Eison, 1991). Think-pair-share is helpful for the instructor as it enables organizing content and tracking students on where they are relative to the topic being discussed in class, saves time so that he/she can move to other topics, helps to make the class more interactive, provides opportunities for students to interact with each other (Radhakrishna, Ewing, and Chikthimmah, 2012).
• A learning cell is an effective way for a pair of students to study and learn together. The learning cell was developed by Marcel Goldschmid of the Swiss Federal Institute of Technology in Lausanne (Goldschmid, 1971). A learning cell is a process of learning where two students alternate asking and answering questions on commonly read materials. To prepare for the assignment, the students read the assignment and write down questions that they have about the reading. At the next class meeting, the teacher randomly puts students in pairs. The process begins by designating one student from each group to begin by asking one of their questions to the other. Once the two students discuss the question, the other student ask a question and they alternate accordingly. During this time, the teacher goes from group to group giving feedback and answering questions. This system is also called a student dyad.
• A short written exercise that is often used is the "one-minute paper". This is a good way to review materials and provide feedback. However a "one-minute paper" does not take one minute and for students to concisely summarize it is suggested that they have at least 10 minutes to work on this exercise. (See also: Quiz § In education.)
• A collaborative learning group is a successful way to learn different material for different classes. It is where you assign students in groups of 3-6 people and they are given an assignment or task to work on together. To create participation and draw on the wisdom of all the learners the classroom arrangement needs to be flexible seating to allow for the creation of small groups. (Bens, 2005)
• A student debate is an active way for students to learn because they allow students the chance to take a position and gather information to support their view and explain it to others.
• A reaction to a video is also an example of active learning.
• A small group discussion is also an example of active learning because it allows students to express themselves in the classroom. It is more likely for students to participate in small group discussions than in a normal classroom lecture because they are in a more comfortable setting amongst their peers, and from a sheer numbers perspective, by dividing the students up more students get opportunities to speak out. There are so many different ways a teacher can implement small group discussion in to the class, such as making a game out of it, a competition, or an assignment. Statistics show that small group discussions is more beneficial to students than large group discussions when it comes to participation, expressing thoughts, understanding issues, applying issues, and overall status of knowledge.
• Just-in-time teaching promotes active learning by using pre-class questions to create common ground among students and teachers before the class period begins. These warmup exercises are generally open ended questions designed to encourage students to prepare for class and to elicit student's thoughts on learning goals.
• A class game is also considered an energetic way to learn because it not only helps the students to review the course material before a big exam but it helps them to enjoy learning about a topic. Different games such as Jeopardy! and crossword puzzles always seem to get the students' minds going.
• Learning by teaching is also an example of active learning because students actively research a topic and prepare the information so that they can teach it to the class. This helps students learn their own topic even better and sometimes students learn and communicate better with their peers than their teachers.
• Gallery walk is where students in groups move around the classroom or workshop actively engaging in discussions and contributing to other groups and finally constructing knowledge on a topic and sharing it.
• In a learning factory production-related subjects can be learned interactively in a realistic learning environment.
• Problem based learning or "PBL" is an active learning strategy that provides students with the problem first and has been found as an effective strategy with topics as advanced as medicine. 

Use of technology

See also: Technology-enhanced active learning

The use of multimedia and technology tools helps enhance the atmosphere of the classroom, thus enhancing the active learning experience. In this way, each student actively engages in the learning process. Teachers can use movies, videos, games, and other fun activities to enhance the effectiveness of the active learning process. The use of technology also stimulates the "real-world" idea of active learning as it mimics the use of technology outside of the classroom. Incorporating technology combined with active learning have been researched and found a relationship between the use and increased positive behavior, an increase in effective learning, "motivation" as well as a connecting between students and the outside world. The theoretical foundations of this learning process are:

1. Flow: Flow is a concept to enhance the focus level of the student as each and every individual becomes aware and completely involved in the learning atmosphere. In accordance with one's own capability and potential, through self-awareness, students perform the task at hand. The first methodology to measure flow was Csikszentmihalyi's Experience Sampling.
2. Learning styles: Acquiring knowledge through one's own technique is called learning style. Learning occurs in accordance with potential as every child is different and has particular potential in various areas. It caters to all kinds of learners: visual, kinesthetic, cognitive and affective.
3. Locus of control: Ones with high internal locus of control believe that every situation or event is attributable to their resources and behavior. Ones with high external locus of control believe that nothing is under their control.
4. Intrinsic motivation: Intrinsic motivation is a factor that deals with self-perception concerning the task at hand. Interest, attitude, and results depend on the self-perception of the given activity.

Research evidence

Shimer College Home Economics cooking 1942

Numerous studies have shown evidence to support active learning, given adequate prior instruction.

A meta-analysis of 225 studies comparing traditional lecture to active learning in university math, science, and engineering courses found that active learning reduces failure rates from 32% to 21%, and increases student performance on course assessments and concept inventories by 0.47 standard deviations. Because the findings were so robust with regard to study methodology, extent of controls, and subject matter, the National Academy of Sciences publication suggests that it might be unethical to continue to use traditional lecture approach as a control group in such studies. The largest positive effects were seen in class sizes under 50 students and among students under-represented in STEM fields.

Richard Hake (1998) reviewed data from over 6000 physics students in 62 introductory physics courses and found that students in classes that utilized active learning and interactive engagement techniques improved 25 percent points, achieving an average gain of 48% on a standard test of physics conceptual knowledge, the Force Concept Inventory, compared to a gain of 23% for students in traditional, lecture-based courses.

Similarly, Hoellwarth & Moelter (2011) showed that when instructors switched their physics classes from traditional instruction to active learning, student learning improved 38 percent points, from around 12% to over 50%, as measured by the Force Concept Inventory, which has become the standard measure of student learning in physics courses.

In "Does Active Learning Work? A Review of the Research", Prince (2004) found that "there is broad but uneven support for the core elements of active, collaborative, cooperative and problem-based learning" in engineering education.

Michael (2006), in reviewing the applicability of active learning to physiology education, found a "growing body of research within specific scientific teaching communities that supports and validates the new approaches to teaching that have been adopted".

In a 2012 report titled "Engage to Excel", the United States President's Council of Advisors on Science and Technology described how improved teaching methods, including engaging students in active learning, will increase student retention and improve performance in STEM courses. One study described in the report found that students in traditional lecture courses were twice as likely to leave engineering and three times as likely to drop out of college entirely compared with students taught using active learning techniques. In another cited study, students in a physics class that used active learning methods learned twice as much as those taught in a traditional class, as measured by test results.

Active learning has been implemented in large lectures and it has been shown that both domestic and International students perceive a wide array of benefits. In a recent study, broad improvements were shown in student engagement and understanding of unit material among international students.

Active learning approaches have also been shown to reduce the contact between students and faculty by two thirds, while maintaining learning outcomes that were at least as good, and in one case, significantly better, compared to those achieved in traditional classrooms. Additionally, students' perceptions of their learning were improved and active learning classrooms were demonstrated to lead to a more efficient use of physical space.

A 2019 study by Deslauriers et al. claimed that students have a biased perception of active learning and they feel they learn better with traditional teaching methods than active learning activities. It can be corrected by early preparation and continuous persuasion that the students are benefiting from active instruction.

In a different study conducted by Wallace et al. (2021), they came to the conclusion that in a comparison between students being taught by an active-learning instructor vs. a traditional learning instructor, students who engaged in active-learning outperformed their counterparts in exam environments. In this setting, the instructor focused on active-learning was a first-time instructor, and the individual who was teaching the traditional style of learning was a long-time instructor. The researchers acknowledged the limitations of this study in that individuals may have done better because of depth in specific sections of the class, so the researchers removed questions that could be favoring one section more than the other out of this analysis.

Mathematical anxiety

From Wikipedia, the free encyclopedia

 

Mathematical anxiety, also known as math phobia, is a feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of mathematical problems in daily life and academic situations. This is, arguably, distinct from statistics anxiety where the negative state is the result of encountering statistics at any level but related to but distinct from mathematical anxiety.

Math Anxiety

Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p. 1). It is a phenomenon that is often considered when examining students' problems in mathematics. According to the American Psychological Association, mathematical anxiety is often linked to testing anxiety. This anxiety can cause distress and likely causes a dislike and avoidance of all math-related tasks. The academic study of math anxiety originates as early as the 1950s, when Mary Fides Gough introduced the term mathemaphobia to describe the phobia-like feelings of many towards mathematics. The first math anxiety measurement scale was developed by Richardson and Suinn in 1972. Since this development, several researchers have examined math anxiety in empirical studies. Hembree (1990) conducted a meta-analysis of 151 studies concerning math anxiety. The study determined that math anxiety is related to poor math performance on math achievement tests and to negative attitudes concerning math. Hembree also suggests that math anxiety is directly connected with math avoidance.

Ashcraft (2002) suggests that highly anxious math students will avoid situations in which they have to perform mathematical tasks. Unfortunately, math avoidance results in less competency, exposure and math practice, leaving students more anxious and mathematically unprepared to achieve. In college and university, anxious math students take fewer math courses and tend to feel negative towards the subject. In fact, Ashcraft found that the correlation between math anxiety and variables such as self-confidence and motivation in math is strongly negative.

According to Schar, because math anxiety can cause math avoidance, an empirical dilemma arises. For instance, when a highly math-anxious student performs disappointingly on a math question, it could be due to math anxiety or the lack of competency in math because of math avoidance. Ashcraft determined that by administering a test that becomes increasingly more mathematically challenging, he noticed that even highly math-anxious individuals do well on the first portion of the test measuring performance. However, on the latter and more difficult portion of the test, there was a stronger negative relationship between accuracy and math anxiety.

According to the research found at the University of Chicago by Sian Beilock and her group, math anxiety is not simply about being bad at math. After using brain scans, scholars confirmed that the anticipation or the thought of solving math actually causes math anxiety. The brain scans showed that the area of the brain that is triggered when someone has math anxiety overlaps the same area of the brain where bodily harm is registered. And Trezise and Reeve show that students' math anxiety can fluctuate throughout the duration of a math class.

Performance

The impact of mathematics anxiety on mathematics performance has been studied in more recent literature. An individual with math anxiety does not necessarily lack ability in mathematics, rather, they cannot perform to their full potential due to the interfering symptoms of their anxiety. Math anxiety manifests itself in a variety of ways, including physical, psychological, and behavioral symptoms, that can all disrupt a student's mathematical performance. The strong negative correlation between high math anxiety and low achievement is often thought to be due to the impact of math anxiety on working memory. Working memory has a limited capacity. A large portion of this capacity is dedicated to problem-solving when solving mathematical tasks. However, in individuals with math anxiety, much of this space is taken up by anxious thoughts, thus compromising the individual's ability to perform. In addition, a frequent reliance in schools on high-stakes and timed testing, where students tend to feel the most anxiety, can lead to lower achievement for math-anxious individuals. Programme for International Student Assessment (PISA) results demonstrate that students experiencing high math anxiety demonstrate mathematics scores that are 34 points lower than students who do not have math anxiety, equivalent to one full year of school. Besides, researchers Elisa Cargnelutti et al show that the influence of mathematical anxiety on math-related performance increases over time due to the accumulation of passive experience in the subject or other factors like more requirements on mathematics as children grow up. These findings demonstrate the clear link between math anxiety and reduced levels of achievement, suggesting that alleviating math anxiety may lead to a marked improvement in student achievement.

Anxiety rating scale

A rating scale for mathematics anxiety was developed in 1972 by Richardson and Suinn. Richardson and Suinn defined mathematical anxiety as "feelings of apprehension and tension concerning manipulation of numbers and completion of mathematical problems in various contexts". Richardson and Suinn introduced the MARS (Mathematics Anxiety Rating Scale) in 1972. Elevated scores on the MARS test translate to high math anxiety. The authors presented the normative data, including a mean score of 215.38 with a standard deviation of 65.29, collected from 397 students that replied to an advertisement for behavior therapy treatment for math anxiety. For test-retest reliability, the Pearson product-moment coefficient was used and a score of 0.85 was calculated, which was favorable and comparable to scores found on other anxiety tests. Richardson and Suinn validated the construct of this test by sharing previous results from three other studies that were very similar to the results achieved in this study. They also administered the Differential Aptitude Test, a 10-minute math test including simple to complex problems.

Calculation of the Pearson product-moment correlation coefficient between the MARS test and Differential Aptitude Test scores was −0.64 (p < .01), indicating that higher MARS scores relate to lower math test scores and "since high anxiety interferes with performance, and poor performance produces anxiety, this result provides evidence that the MARS does measure mathematics anxiety". This test was intended for use in diagnosing math anxiety, testing the efficacy of different math anxiety treatment approaches and possibly designing an anxiety hierarchy to be used in desensitization treatments. The MARS test is of interest to those in counseling psychology and the test is used profusely in math anxiety research. It is available in several versions of varying lengths and is considered psychometrically sound. Other tests are often given to measure different dimensionalities of math anxiety, such as Elizabeth Fennema and Julia Sherman's Fennema-Sherman Mathematics Attitudes Scales (FSMAS). The FSMAS evaluates nine specific domains using Likert-type scales: attitude toward success, mathematics as a male domain, mother's attitude, father's attitude, teacher's attitude, confidence in learning mathematics, mathematics anxiety, affectance motivation and mathematics usefulness. Despite the introduction of newer instrumentation, the use of the MARS test appears to be the educational standard for measuring math anxiety due to its specificity and prolific use.

Math and culture

While there are overarching similarities concerning the acquisition of math skills, researchers have shown that children's mathematical abilities differ across countries. In Canada, students score substantially lower in math problem-solving and operations than students in Korea, India and Singapore. Researchers have conducted thorough comparisons between countries and determined that in some areas, such as Taiwan and Japan, parents place more emphasis on effort rather than one's innate intellectual ability in school success. By placing a higher emphasis on effort rather than one's innate intellectual ability, they are helping their child develop a growth mindset. People who develop a growth mindset believe that everyone has the ability to grow their intellectual ability, learn from their mistakes, and become more resilient learners. Rather than getting stuck on a problem and giving up, students with a growth mindset try other strategies to solve the problem. A growth mindset can benefit everyone, not just people trying to solve math computations. Moreover, parents in these countries tend to set higher expectations and standards for their children. In turn, students spend more time on homework and value homework more than American children.

In addition, researchers Jennifer L. Brown et al. shows that difference in level of mathematical anxiety among different countries may result from varying degrees of the courses. In the same culture, there is little difference in anxiety scale that is associated with gender, while the anxiety is more related with its type. Samples show greater degree of anxiety at subscale.

MEA (Mathematical Evaluation Anxiety) compared with LMA (Learning Mathematical Anxiety).

Math and gender

Another difference in mathematic abilities often explored in research concerns gender disparities. There has been research examining gender differences in performance on standardized tests across various countries. Beller and Gafni's have shown that children at approximately nine years of age do not show consistent gender differences in relation to math skills. However, in 17 out of the 20 countries examined in this study, 13-year-old boys tended to score higher than girls. Moreover, mathematics is often labeled as a masculine ability; as a result, girls often have low confidence in their math capabilities. These gender stereotypes can reinforce low confidence in girls and can cause math anxiety as research has shown that performance on standardized math tests is affected by one's confidence. As a result, educators have been trying to abolish this stereotype by fostering confidence in math in all students in order to avoid math anxiety.

While on the other hand, results obtained by Monika Szczygiel show that girls have a higher level of anxiety on testing and in total, although there is no gender difference in general learning math anxiety. Therefore, the gender gap in math anxiety may result from the type of anxiety. Tests triggers greater anxiety in girls compared with boys, but they feel same level of anxiety learning math.

Math pedagogy

The principles of mathematics are generally understood at an early age; preschoolers can comprehend the majority of principles underlying counting. By kindergarten, it is common for children to use counting in a more sophisticated manner by adding and subtracting numbers. While kindergarteners tend to use their fingers to count, this habit is soon abandoned and replaced with a more refined and efficient strategy; children begin to perform addition and subtraction mentally at approximately six years of age. When children reach approximately eight years of age, they can retrieve answers to mathematical equations from memory. With proper instruction, most children acquire these basic mathematical skills and are able to solve more complex mathematical problems with sophisticated training. (Kail & Zolner, 2005).

High-risk teaching styles are often explored to gain a better understanding of math anxiety. Goulding, Rowland, and Barber (2002) suggest that there are linkages between a teacher's lack of subject knowledge and the ability to plan teaching material effectively. These findings suggest that teachers who do not have a sufficient background in mathematics may struggle with the development of comprehensive lesson plans for their students. Similarly, Laturner's research (2002) shows that teachers with certification in math are more likely to be passionate and committed to teaching math than those without certification. However, those without certification vary in their commitment to the profession depending on coursework preparation.

A study conducted by Kawakami, Steele, Cifa, Phills, and Dovidio (2008) examined attitudes towards math and behavior during math examinations. The study examined the effect of extensive training in teaching women how to approach math. The results showed that women who were trained to approach rather than avoid math showed a positive implicit attitude towards math. These findings were only consistent with women low in initial identification with math. This study was replicated with women who were either encouraged to approach math or who received neutral training. Results were consistent and demonstrated that women taught to approach math had an implicit positive attitude and completed more math problems than women taught to approach math in a neutral manner.

Johns, Schmader, and Martens (2005) conducted a study in which they examined the effect of teaching stereotype threat as a means of improving women's math performance. The researchers concluded that women tended to perform worse than men when problems were described as math equations. However, women did not differ from men when the test sequence was described as problem-solving or in a condition in which they learned about stereotype threats. This research has practical implications. The results suggested that teaching students about stereotype threat could offer a practical means of reducing its detrimental effects and lead to an improvement in a girl's performance and mathematical ability, leading the researchers to conclude that educating female teachers about stereotype threat can reduce its negative effects in the classroom.

Common beliefs

According to Margaret Murray, female mathematicians in the United States have almost always been a minority. Although the exact difference fluctuates with the times, as she has explored in her book Women Becoming Mathematicians: Creating a Professional Identity in Post-World War II America, "Since 1980, women have earned over 17 percent of the mathematics doctorates.... [In The United States]". The trends in gender are by no means clear, but perhaps parity is still a way to go. Since 1995, studies have shown that the gender gap favored males in most mathematical standardized testing as boys outperformed girls in 15 out of 28 countries. However, as of 2015 the gender gap has almost been reversed, showing an increase in female presence. This is being caused by women's steadily increasing performance on math and science testing and enrollment, but also by males' losing ground at the same time. This role reversal can largely be associated with the gender normative stereotypes that are found in the Science, technology, engineering, and mathematics (STEM) field, deeming "who math is for" and "who STEM careers are for". These stereotypes can fuel mathematical anxiety that is already present among young female populations. Thus parity will take more work to overcome mathematical anxiety and this is one reason why women in mathematics are role models for younger women.

In schools

According to John Taylor Gatto, as expounded in several lengthy books, modern Western schools were deliberately designed during the late 19th century to create an environment which is ideal for fostering fear and anxiety, and for preventing or delaying learning. Many who are sympathetic to Gatto's thesis regard his position as unnecessarily extreme. Diane Ravitch, former assistant secretary of education during the George H. W. Bush administration, agrees with Gatto up to a point, conceding that there is an element of social engineering (i.e. the manufacture of the compliant citizenry) in the construction of the American education system, which prioritizes conformance over learning.

The role of attachment has been suggested as having an impact in the development of the anxiety. Children with an insecure attachment style were more likely to demonstrate the anxiety.

Math used to be taught as a right and wrong subject and as if getting the right answer were paramount. In contrast to most subjects, mathematics problems almost always have a right answer but there are many ways to obtain the answer. Previously, the subject was often taught as if there were a right way to solve the problem and any other approaches would be wrong, even if students got the right answer. Thankfully, mathematics has evolved and so has teaching it. Students used to have higher anxiety because of the way math was taught. "Teachers benefit children most when they encourage them to share their thinking process and justify their answers out loud or in writing as they perform math operations. ... With less of an emphasis on right or wrong and more of an emphasis on process, teachers can help alleviate students' anxiety about math".

Theoretical "solutions"

There have been many studies that show parent involvement in developing a child's educational processes is essential. A student's success in school is increased if their parents are involved in their education both at home and school (Henderson & Map, 2002). As a result, one of the easiest ways to reduce math anxiety is for the parent to be more involved in their child's education. In addition, research has shown that a parent's perception on mathematics influences their child's perception and achievement in mathematics (Yee & Eccles, 1988).

Furthermore, studies by Herbert P. Ginsburg, Columbia University, show the influence of parents' and teachers' attitudes on "'the child's expectations in that area of learning.'... It is less the actual teaching and more the attitude and expectations of the teacher or parents that count". This is further supported by a survey of Montgomery County, Maryland students who "pointed to their parents as the primary force behind the interest in mathematics".

Claudia Zaslavsky contends that math has two components. The first component is to calculate the answer. This component also has two subcomponents, namely the answer and the process or method used to determine the answer. Focusing more on the process or method enables students to make mistakes, but not 'fail at math'. The second component is to understand the mathematical concepts that underlay the problem being studied. "... and in this respect studying mathematics is much more like studying, say, music or painting than it is like studying history or biology."

Amongst others supporting this viewpoint is the work of Eugene Geist. Geist's recommendations include focusing on the concepts rather than the right answer and letting students work on their own and discuss their solutions before the answer is given.

National Council of Teachers of Mathematics (NCTM) (1989, 1995b) suggestions for teachers seeking to prevent math anxiety include:

• Accommodating for different learning styles
• Creating a variety of testing environments
• Designing positive experiences in math classes
• Refraining from tying self-esteem to success with math
• Emphasizing that everyone makes mistakes in mathematics
• Making math relevant
• Letting students have some input into their own evaluations
• Allowing for different social approaches to learning mathematics
• Emphasizing the importance of original, quality thinking rather than rote manipulation of formulas

Hackworth (1992) suggests that the following activities can help students in reducing and mitigating mathematical anxiety:

• Discuss and write about math feelings;
• Become acquainted with good math instruction, as well as study techniques;
• Recognize what type of information needs to be learned;
• Be an active learner, and create problem-solving techniques;
• Evaluate your own learning;
• Develop calming/positive ways to deal with fear of math, including visualization, positive messages, relaxation techniques, frustration breaks;
• Use gradual, repeated success to build math confidence in students

B R Alimin and D B Widjajanti (2019) recommend teachers:

• Never make students embarrassed in front of the class
• Build harmony and friendship between teachers and students
• Give hints to students so that they can learn from mistakes
• Encourage students not to give up when they encounter with challenges
• Teach students to help each other working on math problem

Several studies have shown that relaxation techniques can be used to help alleviate anxiety related to mathematics. In her workbook Conquering Math Anxiety, Cynthia Arem offers specific strategies to reduce math avoidance and anxiety. One strategy she advocates for is relaxation exercises and indicates that by practicing relaxation techniques on a regular basis for 10–20 minutes students can significantly reduce their anxiety.

Dr. Edmundo Jacobson's Progressive Muscle Relaxation taken from the book Mental Toughness Training for Sports, Loehr (1986) can be used in a modified form to reduce anxiety as posted on the website HypnoGenesis.

According to Mina Bazargan and Mehdi Amiri, Modular Cognitive Behavior Therapy (MCBT) can reduce the level of mathematical anxiety and increase students' self-esteem.

Visualization has also been used effectively to help reduce math anxiety. Arem has a chapter that deals with reducing test anxiety and advocates the use of visualization. In her chapter titled Conquer Test Anxiety (Chapter 9) she has specific exercises devoted to visualization techniques to help the student feel calm and confident during testing.

Studies have shown students learn best when they are active rather than passive learners.

The theory of multiple intelligences suggests that there is a need for addressing different learning styles. Math lessons can be tailored for visual/spatial, logical/mathematics, musical, auditory, body/kinesthetic, interpersonal and intrapersonal and verbal/linguistic learning styles. This theory of learning styles has never been demonstrated to be true in controlled trials. Studies show no evidence to support tailoring lessons to an individual students learning style to be beneficial.

New concepts can be taught through play acting, cooperative groups, visual aids, hands on activities or information technology. To help with learning statistics, there are many applets found on the Internet that help students learn about many things from probability distributions to linear regression. These applets are commonly used in introductory statistics classes, as many students benefit from using them.

Active learners ask critical questions, such as: Why do we do it this way, and not that way? Some teachers may find these questions annoying or difficult to answer, and indeed may have been trained to respond to such questions with hostility and contempt, designed to instill fear. Better teachers respond eagerly to these questions, and use them to help the students deepen their understanding by examining alternative methods so the students can choose for themselves which method they prefer. This process can result in meaningful class discussions. Talking is the way in which students increase their understanding and command of math. Teachers can give students insight as to why they learn certain content by asking students questions such as "what purpose is served by solving this problem?" and "why are we being asked to learn this?"

Reflective journals help students develop metacognitive skills by having them think about their understanding. According to Pugalee, writing helps students organize their thinking which helps them better understand mathematics. Moreover, writing in mathematics classes helps students problem solve and improve mathematical reasoning. When students know how to use mathematical reasoning, they are less anxious about solving problems.

Children learn best when math is taught in a way that is relevant to their everyday lives. Children enjoy experimenting. To learn mathematics in any depth, students should be engaged in exploring, conjecturing, and thinking, as well as in rote learning of rules and procedures.

Electricity generation

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Electricity_generation

Turbo generator

Electricity generation is the process of generating electric power from sources of primary energy. For utilities in the electric power industry, it is the stage prior to its delivery (transmission, distribution, etc.) to end users or its storage (using, for example, the pumped-storage method).

Usable electricity is not freely available in nature, so it must be "produced" (that is, transforming other forms of energy to electricity). Production is carried out in power stations (also called "power plants"). Electricity is most often generated at a power plant by electromechanical generators, primarily driven by heat engines fueled by combustion or nuclear fission but also by other means such as the kinetic energy of flowing water and wind. Other energy sources include solar photovoltaics and geothermal power. There are also exotic and speculative methods to recover energy, such as proposed fusion reactor designs which aim to directly extract energy from intense magnetic fields generated by fast-moving charged particles generated by the fusion reaction (see magnetohydrodynamics).

Phasing out coal-fired power stations and eventually gas-fired power stations, or, if practical, capturing their greenhouse gas emissions, is an important part of the energy transformation required to limit climate change. Vastly more solar power and wind power is forecast to be required, with electricity demand increasing strongly with further electrification of transport, homes and industry.

History

Past costs of producing renewable energy have declined significantly, with 62% of total renewable power generation added in 2020 having lower costs than the cheapest new fossil fuel option.

 

Levelized cost: With increasingly widespread implementation of renewable energy sources, costs for renewables have declined, most notably for energy generated by solar panels.

Levelized cost of energy (LCOE) is a measure of the average net present cost of electricity generation for a generating plant over its lifetime.

Dynamos and engine installed at Edison General Electric Company, New York 1895

The fundamental principles of electricity generation were discovered in the 1820s and early 1830s by British scientist Michael Faraday. His method, still used today, is for electricity to be generated by the movement of a loop of wire, or Faraday disc, between the poles of a magnet. Central power stations became economically practical with the development of alternating current (AC) power transmission, using power transformers to transmit power at high voltage and with low loss.

Commercial electricity production started with the coupling of the dynamo to the hydraulic turbine. The mechanical production of electric power began the Second Industrial Revolution and made possible several inventions using electricity, with the major contributors being Thomas Alva Edison and Nikola Tesla. Previously the only way to produce electricity was by chemical reactions or using battery cells, and the only practical use of electricity was for the telegraph.

Electricity generation at central power stations started in 1882, when a steam engine driving a dynamo at Pearl Street Station produced a DC current that powered public lighting on Pearl Street, New York. The new technology was quickly adopted by many cities around the world, which adapted their gas-fueled street lights to electric power. Soon after electric lights would be used in public buildings, in businesses, and to power public transport, such as trams and trains.

The first power plants used water power or coal. Today a variety of energy sources are used, such as coal, nuclear, natural gas, hydroelectric, wind, and oil, as well as solar energy, tidal power, and geothermal sources.

In the 1880s the popularity of electricity grew massively with the introduction of the Incandescent light bulb. Although there are 22 recognised inventors of the light bulb prior to Joseph Swan and Thomas Edison, Edison and Swan's invention became by far the most successful and popular of all. During the early years of the 19th century, massive jumps in electrical sciences were made. And by the later 19th century the advancement of electrical technology and engineering led to electricity being part of everyday life. With the introduction of many electrical inventions and their implementation into everyday life, the demand for electricity within homes grew dramatically. With this increase in demand, the potential for profit was seen by many entrepreneurs who began investing into electrical systems to eventually create the first electricity public utilities. This process in history is often described as electrification.

The earliest distribution of electricity came from companies operating independently of one another. A consumer would purchase electricity from a producer, and the producer would distribute it through their own power grid. As technology improved so did the productivity and efficiency of its generation. Inventions such as the steam turbine had a massive impact on the efficiency of electrical generation but also the economics of generation as well. This conversion of heat energy into mechanical work was similar to that of steam engines, however at a significantly larger scale and far more productively. The improvements of these large-scale generation plants were critical to the process of centralised generation as they would become vital to the entire power system that we now use today.

Throughout the middle of the 20th century many utilities began merging their distribution networks due to economic and efficiency benefits. Along with the invention of long-distance power transmission, the coordination of power plants began to form. This system was then secured by regional system operators to ensure stability and reliability. The electrification of homes began in Northern Europe and in the Northern America in the 1920s in large cities and urban areas. It wasn't until the 1930s that rural areas saw the large-scale establishment of electrification.

Methods of generation

2019 world electricity generation by source (total generation was 27 petawatt-hours)

  Coal (37%)

  Natural gas (24%)

  Hydro (16%)

  Nuclear (10%)

  Wind (5%)

  Solar (3%)

  Other (5%)

Several fundamental methods exist to convert other forms of energy into electrical energy. Utility-scale generation is achieved by rotating electric generators or by photovoltaic systems. A small proportion of electric power distributed by utilities is provided by batteries. Other forms of electricity generation used in niche applications include the triboelectric effect, the piezoelectric effect, the thermoelectric effect, and betavoltaics.

Generators

Main article: Electric generator

Wind turbines usually provide electrical generation in conjunction with other methods of producing power.

Electric generators transform kinetic energy into electricity. This is the most used form for generating electricity and is based on Faraday's law. It can be seen experimentally by rotating a magnet within closed loops of conducting material (e.g. copper wire). Almost all commercial electrical generation is done using electromagnetic induction, in which mechanical energy forces a generator to rotate.

Electrochemistry

Large dams, such as Hoover Dam in the United States, can provide large amounts of hydroelectric power. It has an installed capacity of 2.07 GW.

Electrochemistry is the direct transformation of chemical energy into electricity, as in a battery. Electrochemical electricity generation is important in portable and mobile applications. Currently, most electrochemical power comes from batteries. Primary cells, such as the common zinc–carbon batteries, act as power sources directly, but secondary cells (i.e. rechargeable batteries) are used for storage systems rather than primary generation systems. Open electrochemical systems, known as fuel cells, can be used to extract power either from natural fuels or from synthesized fuels. Osmotic power is a possibility at places where salt and fresh water merge.

Photovoltaic effect

The photovoltaic effect is the transformation of light into electrical energy, as in solar cells. Photovoltaic panels convert sunlight directly to DC electricity. Power inverters can then convert that to AC electricity if needed. Although sunlight is free and abundant, solar power electricity is still usually more expensive to produce than large-scale mechanically generated power due to the cost of the panels. Low-efficiency silicon solar cells have been decreasing in cost and multijunction cells with close to 30% conversion efficiency are now commercially available. Over 40% efficiency has been demonstrated in experimental systems. Until recently, photovoltaics were most commonly used in remote sites where there is no access to a commercial power grid, or as a supplemental electricity source for individual homes and businesses. Recent advances in manufacturing efficiency and photovoltaic technology, combined with subsidies driven by environmental concerns, have dramatically accelerated the deployment of solar panels. Installed capacity is growing by around 20% per year led by increases in Germany, Japan, United States, China, and India.

Economics

See also: Cost of electricity by source and Electricity pricing

The selection of electricity production modes and their economic viability varies in accordance with demand and region. The economics vary considerably around the world, resulting in widespread residential selling prices. Hydroelectric plants, nuclear power plants, thermal power plants and renewable sources have their own pros and cons, and selection is based upon the local power requirement and the fluctuations in demand. All power grids have varying loads on them but the daily minimum is the base load, often supplied by plants which run continuously. Nuclear, coal, oil, gas and some hydro plants can supply base load. If well construction costs for natural gas are below $10 per MWh, generating electricity from natural gas is cheaper than generating power by burning coal.

Nuclear power plants can produce a huge amount of power from a single unit. However, nuclear disasters have raised concerns over the safety of nuclear power, and the capital cost of nuclear plants is very high. Hydroelectric power plants are located in areas where the potential energy from falling water can be harnessed for moving turbines and the generation of power. It may not be an economically viable single source of production where the ability to store the flow of water is limited and the load varies too much during the annual production cycle.

Generating equipment

Main article: Electric generator

A large generator with the rotor removed

Electric generators were known in simple forms from the discovery of electromagnetic induction in the 1830s. In general, some form of prime mover such as an engine or the turbines described above, drives a rotating magnetic field past stationary coils of wire thereby turning mechanical energy into electricity. The only commercial scale electricity production that does not employ a generator is solar PV.

Turbines

Large dams such as Three Gorges Dam in China can provide large amounts of hydroelectric power; it has a 22.5 GW capability.

Almost all commercial electrical power on Earth is generated with a turbine, driven by wind, water, steam or burning gas. The turbine drives a generator, thus transforming its mechanical energy into electrical energy by electromagnetic induction. There are many different methods of developing mechanical energy, including heat engines, hydro, wind and tidal power. Most electric generation is driven by heat engines. The combustion of fossil fuels supplies most of the energy to these engines, with a significant fraction from nuclear fission and some from renewable sources. The modern steam turbine (invented by Sir Charles Parsons in 1884) currently generates about 80% of the electric power in the world using a variety of heat sources. Turbine types include:

• Steam
  • Water is boiled by coal burned in a thermal power plant. About 41% of all electricity is generated this way.
  • Nuclear fission heat created in a nuclear reactor creates steam. Less than 15% of electricity is generated this way.
  • Renewable energy. The steam is generated by biomass, solar thermal energy, or geothermal power.
• Natural gas: turbines are driven directly by gases produced by combustion. Combined cycle are driven by both steam and natural gas. They generate power by burning natural gas in a gas turbine and use residual heat to generate steam. At least 20% of the world's electricity is generated by natural gas.
• Water Energy is captured by a water turbine from the movement of water - from falling water, the rise and fall of tides or ocean thermal currents (see ocean thermal energy conversion). Currently, hydroelectric plants provide approximately 16% of the world's electricity.
• The windmill was a very early wind turbine. In 2018 around 5% of the world's electricity was produced from wind

Turbines can also use other heat-transfer liquids than steam. Supercritical carbon dioxide based cycles can provide higher conversion efficiency due to faster heat exchange, higher energy density and simpler power cycle infrastructure. Supercritical carbon dioxide blends, that are currently in development, can further increase efficiency by optimizing its critical pressure and temperature points.

Although turbines are most common in commercial power generation, smaller generators can be powered by gasoline or diesel engines. These may used for backup generation or as a prime source of power within isolated villages.

Production

Total worldwide gross production of electricity in 2016 was 25 082 TWh. Sources of electricity were coal and peat 38.3%, natural gas 23.1%, hydroelectric 16.6%, nuclear power 10.4%, oil 3.7%, solar/wind/geothermal/tidal/other 5.6%, biomass and waste 2.3%.

In 2021, Wind and solar generated electricity reached 10% of globally produced electricity. Clean sources (Solar and wind and other) generated 38% of the world's electricity.

Energy flow of power plant

Historical results of production of electricity

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Production by country

Main article: List of countries by electricity production

See also: Electric energy consumption

The United States has long been the largest producer and consumer of electricity, with a global share in 2005 of at least 25%, followed by China, Japan, Russia, and India. In 2011, China overtook the United States to become the largest producer of electricity.

Environmental concerns

Main article: Environmental impact of electricity generation

See also: Global warming and Coal phase out

Variations between countries generating electrical power affect concerns about the environment. In France only 10% of electricity is generated from fossil fuels, the US is higher at 70% and China is at 80%. The cleanliness of electricity depends on its source. Methane leaks (from natural gas to fuel gas-fired power plants) and carbon dioxide emissions from fossil fuel-based electricity generation account for a significant portion of world greenhouse gas emissions. In the United States, fossil fuel combustion for electric power generation is responsible for 65% of all emissions of sulfur dioxide, the main component of acid rain. Electricity generation is the fourth highest combined source of NO_x, carbon monoxide, and particulate matter in the US.

According to the International Energy Agency (IEA), low-carbon electricity generation needs to account for 85% of global electrical output by 2040 in order to ward off the worst effects of climate change. Like other organizations including the Energy Impact Center (EIC) and the United Nations Economic Commission for Europe (UNECE), the IEA has called for the expansion of nuclear and renewable energy to meet that objective. Some, like EIC founder Bret Kugelmass, believe that nuclear power is the primary method for decarbonizing electricity generation because it can also power direct air capture that removes existing carbon emissions from the atmosphere. Nuclear power plants can also create district heating and desalination projects, limiting carbon emissions and the need for expanded electrical output.

A fundamental issue regarding centralised generation and the current electrical generation methods in use today is the significant negative environmental effects that many of the generation processes have. Processes such as coal and gas not only release carbon dioxide as they combust, but their extraction from the ground also impacts the environment. Open pit coal mines use large areas of land to extract coal and limit the potential for productive land use after the excavation. Natural gas extraction releases large amounts of methane into the atmosphere when extracted from the ground greatly increase global greenhouse gases. Although nuclear power plants do not release carbon dioxide through electricity generation, there are risks associated with nuclear waste and safety concerns associated with the use of nuclear sources.

Per unit of electricity generated coal and gas-fired power life-cycle greenhouse gas emissions are almost always at least ten times that of other generation methods.

Centralised and distributed generation

Centralised generation is electricity generation by large-scale centralised facilities, sent through transmission lines to consumers. These facilities are usually located far away from consumers and distribute the electricity through high voltage transmission lines to a substation, where it is then distributed to consumers; the basic concept being that multi-megawatt or gigawatt scale large stations create electricity for a large number of people. The vast majority of electricity used is created from centralised generation. Most centralised power generation comes from large power plants run by fossil fuels such as coal or natural gas, though nuclear or large hydroelectricity plants are also commonly used. Centralised generation is fundamentally the opposite of distributed generation. Distributed generation is the small-scale generation of electricity to smaller groups of consumers. This can also include independently producing electricity by either solar or wind power. In recent years distributed generation as has seen a spark in popularity due to its propensity to use renewable energy generation methods such as rooftop solar.

Technologies

Centralised energy sources are large power plants that produce huge amounts of electricity to a large number of consumers. Most power plants used in centralised generation are thermal power plants meaning that they use a fuel to heat steam to produce a pressurised gas which in turn spins a turbine and generates electricity. This is the traditional way of producing energy. This process relies on several forms of technology to produce widespread electricity, these being natural coal, gas and nuclear forms of thermal generation. More recently solar and wind have become large scale.

Solar

The 40.5 MW Jännersdorf Solar Park in Prignitz, Germany

A photovoltaic power station, also known as a solar park, solar farm, or solar power plant, is a large-scale grid-connected photovoltaic power system (PV system) designed for the supply of merchant power. They are different from most building-mounted and other decentralized solar power because they supply power at the utility level, rather than to a local user or users. Utility-scale solar is sometimes used to describe this type of project.

This approach differs from concentrated solar power, the other major large-scale solar generation technology, which uses heat to drive a variety of conventional generator systems. Both approaches have their own advantages and disadvantages, but to date, for a variety of reasons, photovoltaic technology has seen much wider use. As of 2019, about 97% of utility-scale solar power capacity was PV.

In some countries, the nameplate capacity of photovoltaic power stations is rated in megawatt-peak (MW_p), which refers to the solar array's theoretical maximum DC power output. In other countries, the manufacturer states the surface and the efficiency. However, Canada, Japan, Spain, and the United States often specify using the converted lower nominal power output in MW_AC, a measure more directly comparable to other forms of power generation. Most solar parks are developed at a scale of at least 1 MW_p. As of 2018, the world's largest operating photovoltaic power stations surpassed 1 gigawatt. At the end of 2019, about 9,000 solar farms were larger than 4 MW_AC (utility scale), with a combined capacity of over 220 GW_AC.

Most of the existing large-scale photovoltaic power stations are owned and operated by independent power producers, but the involvement of community and utility-owned projects is increasing. Previously, almost all were supported at least in part by regulatory incentives such as feed-in tariffs or tax credits, but as levelized costs fell significantly in the 2010s and grid parity has been reached in most markets, external incentives are usually not needed.

Wind

The San Gorgonio Pass wind farm in California, United States.

The Gansu Wind Farm in China is the largest wind farm in the world, with a target capacity of 20,000 MW by 2020.

A wind farm or wind park, also called a wind power station or wind power plant, is a group of wind turbines in the same location used to produce electricity. Wind farms vary in size from a small number of turbines to several hundred wind turbines covering an extensive area. Wind farms can be either onshore or offshore.

Many of the largest operational onshore wind farms are located in China, India, and the United States. For example, the largest wind farm in the world, Gansu Wind Farm in China had a capacity of over 6,000 MW by 2012, with a goal of 20,000 MW by 2020. As of December 2020, the 1218 MW Hornsea Wind Farm in the UK is the largest offshore wind farm in the world. Individual wind turbine designs continue to increase in power, resulting in fewer turbines being needed for the same total output.

Because they require no fuel, wind farms have less impact on the environment than many other forms of power generation and are often referred to as a good source of green energy. Wind farms have, however, been criticised for their visual impact and impact on the landscape. Typically they need to be spread over more land than other power stations and need to be built in wild and rural areas, which can lead to "industrialization of the countryside", habitat loss, and a drop in tourism. Some critics claim that wind farms have adverse health effects, but most researchers consider these claims to be pseudoscience (see wind turbine syndrome). Wind farms can interfere with radar, although in most cases, according to the US Department of Energy, "siting and other mitigations have resolved conflicts and allowed wind projects to co-exist effectively with radar".

Coal

Bełchatów Power Station in Bełchatów, Poland

Frimmersdorf Power Station in Grevenbroich, Germany

Coal-fired power station diagram

Share of electricity production from coal

A coal-fired power station or coal power plant is a thermal power station which burns coal to generate electricity. Worldwide there are over 2,400 coal-fired power stations, totaling over 2,000 gigawatts capacity. They generate about a third of the world's electricity, but cause many illnesses and the most early deaths, mainly from air pollution.

A coal-fired power station is a type of fossil fuel power station. The coal is usually pulverized and then burned in a pulverized coal-fired boiler. The furnace heat converts boiler water to steam, which is then used to spin turbines that turn generators. Thus chemical energy stored in coal is converted successively into thermal energy, mechanical energy and, finally, electrical energy.

Coal-fired power stations emit over 10 billon tonnes of carbon dioxide each year, about one fifth of world greenhouse gas emissions, so are the single largest cause of climate change. More than half of all the coal-fired electricity in the world is generated in China. In 2020 the total number of plants started falling as they are being retired in Europe and America although still being built in Asia, almost all in China. Some remain profitable because costs to other people due to the health and environmental impact of the coal industry are not priced into the cost of generation, but there is the risk newer plants may become stranded assets. The UN Secretary General has said that OECD countries should stop generating electricity from coal by 2030, and the rest of the world by 2040. Vietnam is among the few coal-dependent fast developing countries that fully pledged to phase out unbated coal power by the 2040s or as soon as possible thereafter.

Natural gas

Natural gas is ignited to create pressurised gas which is used to spin turbines to generate electricity. Natural gas plants use a gas turbine where natural gas is added along with oxygen which in turn combusts and expands through the turbine to force a generator to spin.

Natural gas power plants are more efficient than coal power generation, they however contribute to climate change but not as highly as coal generation. Not only do they produce carbon dioxide from the ignition of natural gas, but also the extraction of gas when mined releases a significant amount of methane into the atmosphere.

Nuclear

Nuclear power plants create electricity through steam turbines where the heat input is from the process of nuclear fission. Currently, nuclear power produces 11% of all electricity in the world. Most nuclear reactors use uranium as a source of fuel. In a process called nuclear fission, energy, in the form of heat, is released when nuclear atoms are split. Electricity is created through the use of a nuclear reactor where heat produced by nuclear fission is used to produce steam which in turn spins turbines and powers the generators. Although there are several types of nuclear reactors, all fundamentally use this process.

Normal emissions due to nuclear power plants are primarily waste heat and radioactive spent fuel. In a reactor accident, significant amounts of radioisotopes can be released to the environment, posing a long term hazard to life. This hazard has been a continuing concern of environmentalists. Accidents such as the Three Mile Island accident, Chernobyl disaster and the Fukushima nuclear disaster illustrate this problem. 

Electricity generation capacity by country

The table lists 45 countries with their total electricity capacities. The data is from 2022. According to the Energy Information Administration, the total global electricity capacity in 2022 was nearly 8.9 terawatt (TW), more than four times the total global electricity capacity in 1981. The global average per-capita electricity capacity was about 1,120 watts in 2022, nearly two and a half times the global average per-capita electricity capacity in 1981. Iceland has the highest installed capacity per capita in the world, at about 8,990 watts. All developed countries have an average per-capita electricity capacity above the global average per-capita electricity capacity, with the United Kingdom having the lowest average per-capita electricity capacity of all other developed countries.

Country	Total capacity (GW)	Average per capita capacity (watts)
WORLD	8,890	1,120
China	2,510	1,740
United States	1,330	3,940
European Union	1,080	2,420
India	556	397
Japan	370	2,940
Russia	296	2,030
Germany	267	3,220
Brazil	222	1,030
Canada	167	4,460
South Korea	160	3,130
France	148	2,280
Italy	133	2,230
Spain	119	2,580
United Kingdom	111	1,640
Turkey	107	1,240
Mexico	104	792
Australia	95.8	3,680
Saudi Arabia	85.3	2,380
Iran	83.3	977
Vietnam	72.2	721
South Africa	66.7	1,100
Poland	64	1,690
Thailand	63	901
Ukraine	62.2	1,440
Egypt	61.1	582
Taiwan	58	2,440
Netherlands	53.3	3,010
Sweden	52.1	5,100
Argentina	51.9	1,130
Pakistan	42.7	192
Norway	41.7	7,530
United Arab Emirates	40.7	4,010
Malaysia	37.9	1,110
Chile	37	1,930
Venezuela	34.1	1,210
Kazakhstan	29.6	1,600
Switzerland	27.8	2,960
Austria	26.7	2,890
Algeria	25.9	590
Greece	24.4	2,400
Israel	23.7	2,520
Finland	22.2	3,980
Denmark	21.3	3,710
Ireland	13.3	2,420
New Zealand	11.6	2,320
Iceland	3.24	8,990