Convergent Teaching Elevates Students SAT Scores and their Effectiveness in Higher Education

Convergent Teaching Elevates Students SAT Scores and Students Effectiveness in Higher Education

Abstract

Convergent teaching as a product of convergent thinking is widespread from high school to higher education. Convergent thinking and divergent thinking was coined by a psychologist Guilford in 1956. Teaching strategies responds to how learners think. Most people of the world think convergently; therefore, convergent teaching takes a great part in the education domain. Standardized exams that play a key role in college admission could be mastered through convergent learning, respectively convergent teaching. Practically, convergent teaching elevates national SAT average scores. Most of the college classes are large, as a result, most of the college professors apply convergent teaching. Students who are familiar with convergent teaching feel more comfortable with absorbing content during any session. Students who have more experience with convergent learning and teaching are most likely to graduate on time. In addition, convergent teaching equips students with a solid foundation and general tools for future jobs that are not discovered yet.

Key word: Convergent Teaching, Teacher - Centered, Formal Authority, Explicit Method, Direct Method, demonstrator method

Introduction

Convergent teaching centers on exploring new material through reasoning and problems solving and finding a single solution; consequently, elevates SAT scores and learning in high school to higher education. The cornerstone of convergent teaching is convergent thinking. Convergent thinking occurs when the solution to a problem can be deduced by applying established rules and logical reasoning (Killgore, 2010). Convergent teaching enables students to dive deeper in learning using learning strategies such as: flashcards, fact-based, following instructions, step by step, problem solving, memorization, group work, etc. Convergent teaching shows up in various forms using specific characteristics; it might appear as a teacher - centered approach in general and it might be exposed as explicit, direct, demonstrator, or formal authority teaching approach. Also, convergent teaching might take shape as a combination of the four teaching methods mentioned above. Convergent teaching enables students at least to reach the national average SAT scores, admitted in colleges or universities, and elevates students' learning in all levels, especially, high school and higher education level.

Convergent thinking is opposite of divergent thinking; the term convergent thinking was established by Joy Paul Guilford. The term means the ability to find the correct answer to questions that have a single answer and does not concern with creativity, nonetheless, oftentime convergent questions require critical thinking. The term convergent means moving closer together, especially in terms of ideas or tending to move in the direction of a point. Convergent teaching is a product of convergent thinking, which deals with convergent questions and instructions. Convergent teaching has a great impact on all learners, particularly, on the convergent thinkers.

Convergent teaching gravitates toward instructions focused on memorization, solving a problem step by step logically, listening and absorbing information, preparing for the standardized tests, etc. Memorization is a great tool for learning new vocabulary in any academic subject, learning various definitions in any subject, and learning basic formulas in any natural sciences subjects (Physics, Chemistry, Anatomy, mathematics, etc). Problem solving step by step might involve teaching through teacher - centered methods with low or high tech equips students with valuable educational information. As you can infer, it emphasizes finding the single, optimal solution to a given problem and usually demands thinking at the first or second Depth of Knowledge (DoK) (Prodigy, 2010) .

Standardized exams as a crucial ticket for students to enter gateways of great colleges or universities follow laws of convergent teaching.

Convergent teaching and several similar methods to teacher centered approaches such as explicit, direct, demonstrator, and formal authority teaching style requires strict rules to follow. In general, teachers work hard (the main performer) to apply a teacher - centered approach style. Teachers decided on the content that they intended to teach, planned how to teach this content and then assessed the content (Schreurs and Dumbraveanu, 2014). Teachers actively work throughout the whole session to cover instructions successfully.

Instructors at high school level should apply convergent teaching as a powerful tool to train students for the transition process from high school to higher education. The goal of high school teachers should focus on teacher centered instructions as a routine. The goal of the teachers and students is to create an educational environment in the long run. Being around a positive group of people who share similar goals and interests can be the single greatest catalyst to help you maintain your habit (Eatough, 2021). The good habits (teaching convergent method) in high school will assist students with being productive, absorbing information properly, and taking good notes in higher education.

Instructors mostly use convergent teaching in colleges and universities. Students who are familiar with convergent teaching in high school get better grades in standardized exams. Students who feel comfortable with convergent teaching have a greater chance of performing well in higher education. Teachers transfer knowledge and ideas to students, and prepare them for further education (Hajesfandiari, et al., 2014). Convergent teaching equips students with general tools for future jobs too. Every job requires specific methods, approaches, and environment. Nonetheless, the general tools of education are flexible to convert in any specific tool that works in any specific job.

Method

Convergent teaching at highschool level gears up students on the right road targeting the SAT skills, the college learning style, and the graduation on time. In general, convergent thinking allocates its educational activities on a fact basis, following instructions, solving problems, memorizations, flashcards, training, and group work. Convergent teaching occurs in several methods: explicit teaching method, direct teaching method, demonstrator method, and authority method. All elements of the convergent teaching equips students with the skills that cracks down any standardized test (such as SAT or ACT exams). High scores in standardized tests open gates to study at any college or university. Many tests that are used in schools, such as multiple-choice tests, spelling tests, math quizzes, and standardized tests, are measures of convergent thinking ( Hajesfandiari at all, 2014). Convergent teaching at

Abbildung in dieser Leseprobe nicht enthalten

Figure 1. Convergent thinking - the combination of all information results with a single solution.

highschools upskills students to follow instructions in college level efficiently and dive deeper in the learning. Since most colleges and universities rely massively on convergent teaching, this method guarantees students to graduate on time with a higher grade average points.

Fact - Based

Teaching lessons obtaining fact based information usually targets linear or sequential learning in various academic subjects is a part of convergent teaching. For instance, History contains multiple relevant dates and events that happened in various times and places. Historical facts contain specific known values or specific known descriptions; facts are the cornerstone of the humanities subjects. Also facts play a crucial role in other academic subjects such as: social sciences, technical sciences, physical education, medical field, etc. Facts in technical science emerge as formulas - equations or expressions; shapes - multiple geometrical figures; description - hypothesis, lemmas, theorems, and definitions. In mathematics, solving mathematical problems and verifying proof the tendency sways on finding a single outcome. Proofs are constructed by utilizing definitions, theorems and facts (Gallian, 2008) . Any lesson or subject with the result oriented material falls in the domain of the fact based lenses. Convergent teaching concerns with the truth that we can find through the facts or evidence within a single solution.

Following Instructions

Linear instructions as a part of convergent teaching have a greater impact on students with preferences on analytical learning centered on convergent thinking. Analytic learners are best able to understand new information if it is presented in a linear, step-by-step way (Wahlig, 2017). The instructor or the teacher delivers the linear instructions for the whole class or session; therefore, all students follow and learn the same steps in order to get to the right result. Step by step instructions aim on explaining the lesson or giving students a particular task.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2. Linear instructions explained step by step.

The best way to explain the relation between convergent teaching and the linear instructions is by observing Figure 1. In Figure 1 are shown five pieces of information that converge in a single solution. Imagine a piece of information represents the first step, another piece of information represents the second step, another piece of information represents the third step, and so on. The five pieces of information can be expressed as the fifth step, which finally results with a single solution. Practically the Figure 1 converts into Figure 2 as a part of convergent teaching.

Solving Problems

Solving problems might happen in several academic subjects including social sciences, but let's reflect on solving problems in mathematics. Ploya, elaborated in detail solving problems in his book, How To Solve It, by George Polya, 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6. Even though the book is part of mathematical study,

Abbildung in dieser Leseprobe nicht enthalten

Figure 3. A general solving problems - modification of Polya ’s four step method (Malone, 2015).

it might apply in other subjects as well. The first step according to Polya involves understanding the given problem. Sometimes mathematicians in higher math incubate for a long time just to understand what they are supposed to solve. Understanding the problem right means fifty percent of the work has been done. The second step - devising the plan to solve the problem. When the plan is designed, following the third step - carry the plan out. The procedure of applying the plan generates a desired result. In order to make sure the result is right, we should check the result. Evaluating the solution, verifies the work has been done right or wrong. Polya mentions that much can be gained by taking the time to reflect and look back at what you have done, what worked, and what didn't (Ploya, n.d.). Reflecting on the result and whole plan, enables what solving strategy to use in upcoming problems, and what solving strategies are invalid. Following all Polay's steps or modifying them in terms of various conditions in a given problem compels deep learning in any given subject to extend to a larger degree.

Memorization

Memorization is a skill that enables students to remember the significant mathematical ideas (definitions, lemmas, constants, theorems, equations, etc), laws, theories, hypothesis, vocabulary, and any other educational significant information. Memorizing specific educational information goes through a process that accelerates the interrelation of the short memory and long memory. There are three memory processes of information: attention, encoding, and storage. Attention helps students to focus awareness on specific educational information and thoughts. The greater the attention to the information, the greater the possibility of remembering it. Encoding allows the educational information to be converted in a particular form in the brain temporarily. Encoding processes the information easily and saves it into a short or long memory. The act of moving information from short-term to long-term memory can be done in a variety of ways (Academic Success Center, n. d.). It is very important to learn information, but storing information in the long term memory plays a crucial role in achieving academic success in high school and higher education. In general, memorization enables students to remember fixed or specific (significant) educational information, and it is a remarkable part of convergent thinking.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4. Modified figure - According to the Atkinson-Shiffrin model of memory, information passes through three distinct stages in order for it to be stored in long-term memory (How Memory Functions, n. d.).

Flashcards

Traditionally, flashcards are used in education to memorize information in any subject. Flashcards enables all students (in any level of education) to practice with vocabulary uncommon words, practicing with multiplication tables, practicing with chemistry or physics formulas, practicing with memorizing definitions, practicing with memorizing facts and figures, etc. Flashcards are often part of spaced practice, and repetition helps you figure out what information you can remember easily and what needs additional effort (University of Southern Maine, n. d.). For instance, learning uncommon words in the English language through flashcards enables students to repeat new words, and check their progress on remembering them. In the case students experienced difficulties with memorizing a word, they might review (repeat) them more often until weaknesses transform into strengths. Flashcards make a positive change in learning uncommon words, basic formulas, definitions etc. Nonetheless, over using flashcards massively in the learning reflects a negative change in the learning outcome. Using flashcards wisely (optimally) in any subject expands learning outcomes in any academic subject.

Trainings

Training in education usually is learning by doing practical work. In a traditional in-person training situation, registration for the course, paperwork, payment, and travel arrangements (if any)-all the functions that are normally thought of as involving the organization-are completed for the most part, before classes begin.(Kim, Zene, Berge, 2002). Training with technology in education involves preparing students how to use an app or a web platform that is integrated in class. Training students how to search information, writing research papers or finding web pages with mathematical content or any other subject. Training differs from education - training is a learning process targeting a specific skill or behavior; on the other hand, education is a learning process with a target on gaining knowledge. In general, learning a specific set of skills by doing improves students' performance academically.

Group work

Group work usually is a method on student centered teaching strategy, nonetheless, group work might be effective in convergent teaching strategy or teacher centered teaching strategy. Also, group work might apply in any size of the classroom with any purpose. For instance, solving mathematical problems by using group work is a great way to get deeper in the learning. Teachers instruct students with the topic, creating groups, selecting examples and quantity of examples, and setting time to solve problems. Instructors should give clear and detailed instructions to students. Instructors cannot assume that students know how to work together, structure time, or delegate tasks (Burke, 2011). Working in groups all students can gain quick learning benefits, but some students might contribute more than others. Teachers know their students; therefore, they should give them the task that students can handle within a group. When a student thinks it is relevant to include an element as a part of the step in finding the solution, the student should justify the action to the group. Other students analyze the particular step, and then they decide whether to accept it as a part of the process in solving the problem or not. In order for the group to function rationally, the group should have a leader. There are many other significant elements that make the group effective; however, instructors know these elements in detail. Teachers address the instructions step by step in detail for effective working in groups and solving problems by using convergent teaching.

Standardized Tests

Standardized tests are the key for the entrance admission at colleges or universities in the US. According to the 2020 College Board Annual Report, the average SAT score is 1051 with a score of 528 on the Evidence-Based Reading and Writing section and 523 on the Math section (Number2 - Online Education, n. d.). Reaching National Average scores in SAT test scores takes wise and hard work on identifying single answers or solutions by selecting the right answers in multiple choice questions. Usually, students take online SAT courses or one to one SAT courses within the school districts or tutorial agencies. For instance the tutorial company, McElroy Tutoring offers fifty official SAT Pdf-s and eighty eight official ACT Pdf-s practice tests (free). Any standardized test requires a specific step by step method to solve or answer any problem or question. The greatest tool is Polya's method on SAT solving mathematical problems,, which relies massively on convergent teaching. Usually, during an SAT session teachers solve or answer around twenty questions by applying several SAT strategies on solving problems. Teachers apply step by step clear educational strategies that enable students to think like test makers and tackle the tests with great confidence. The general tool for teaching SAT classes, teachers use convergent teaching techniques.

Abbildung in dieser Leseprobe nicht enthalten

Figure 5. National Average SAT Test Scores in 2020 modified from -(NUmber 2 - Online Education, n. d. ).

Convergent Teaching Methods

Convergent teaching is based on the teacher centered method that takes the form of explicit teaching, direct teaching, demonstrator method, or authority method. Convergent teaching resonates with teaching facts, step by step teaching problem solving with a single solution. Usually, the convergent teaching starts with information or known facts and strives to find the unknown as a single solution. According to the book, Convergent Teaching: Tools to Sparkle Deep Learning in College, there are three key principles in convergent teaching - targeting, surfacing, and navigating. Principle of surfacing which includes unearthing what students know already-culturally, personally, and academically - that may offer a bridge to understanding subject-matter concepts new to them (Pallas, Neumon, 2019). Convergent

Abbildung in dieser Leseprobe nicht enthalten

Figure 6. Convergent teaching as a teacher centered method appears at least in four different methods.

Teaching as a professional practice tool is widespread in colleges and universities, and advances learning to a greater level diving deeper in the learning process. Instructors in higher education usually use a teacher centered teaching approach to deliver instructions in big classrooms. Teachers tend to use the teacher - centered method in the learning process (Yuliati, et al., 2020) . Teachers at the high school level should apply convergent teaching, preparing students passing standardized tests with at least average scores, and entering a smooth transition in higher education. Convergent teaching appears in several slightly different ways - explicit teaching, direct teaching, demonstrator teaching, and authority method. All four methods involve convergent teaching or rely massively on the teacher centered approach style. Let's take a look at the four methods below, and analyze briefly each one of them and compare or contrast one to another when necessary.

Explicit teaching

Explicit teaching is a form of convergent teaching; explicit teaching involves direct instructions toward specific learning that produces specific learning outcomes. Explicit instruction is a way to teach in a direct, structured way (Greene, n. d. ). Explicit teaching relies on some instructional teaching functions that different literature presents slightly various components of explicit teaching. Nonetheless, I will present the information from the (educational research, n.d) on the seven instructional teaching functions: Learning objective, activate prior knowledge, concept development, skill development, gilded practice, relevance, and closure.

Abbildung in dieser Leseprobe nicht enthalten

Figure 7. Explicit teaching instructions explained by four simple steps on learning a new lesson or learning material.

Explicit teaching instructions in Figure 7 - four simple steps on explicit teaching instructions. In the first step the teacher or instructor teaches or explains new material respectively the new lesson. All students pay close attention to receive the information carefully. Second step - the instructor solves the problem step by step. The third step - the whole class works in groups to solve the problem or analyze the information from the material. The fourth Step - Every student works individually by practicing on solving problems or analyzing the previous specific learning material. Also, The explicit teaching methods apply formal assessments during the addressing a lesson and checks for the students engagement.

Direct teaching

Direct teaching approach is centered teacher approach with low tech. Centered teaching approach style might incorporate low tech or high tech. Direct teaching approach signifies traditional teaching - students learn by listening and watching the lecture. The instructor delivers instructions, and the instructor might ask questions sometimes to students as measurement checking the students engagement. The definition of the direct instructions according to the National Institute for direct instruction states, “Direct Instruction (DI) is a model for teaching that emphasizes well-developed and carefully planned lessons designed around small learning increments and clearly defined and prescribed teaching tasks (Engelmann, n. d).” Direct teaching is based on clear and structured instructions that avoids misinterpretations. The explicit teaching and direct teaching might look similar but they differ a lot. Let's take a look at just one example. The Explicit teaching -Lessons are designed to meet the standards at each grade level, and are differentiated for high grades, low grades, or EL students using specific strategies (Educational Research, n. d.). The direct teaching - Students are grouped according to ability rather than age or grade (Educational Research, n. d.). The direct teaching method is also known as the natural teaching method. The direct method as a part of convergent teaching is very effective in learning a foreign language - memorizing the vocabulary and other relevant definitions. Above all, direct teaching could be demonstrated in three sub methods: formal authority, expert, and personal model.

Abbildung in dieser Leseprobe nicht enthalten

Figure 8. Relation of the centered-teaching method to direct instruction and types of the direct instructions.

Demonstrator Method

The demonstrator method is similar to the authority method that strives to keep the formal authority, and is known as a coaching style. A brief formal definition of the demonstrator method is as follows. The demonstrator, or coach style is the style where the teacher maintains the formal authority role, and teachers show the students what they need to learn,

Abbildung in dieser Leseprobe nicht enthalten

Figure 9. Characteristics of demonstration teaching are modified from (Unit 3, n. d,)

but used in their lesson's multimedia presentations and demonstrations (Urela, 2019). This method allows instructors to use high tech during the sessions. They might use powerpoint presentations or using videos as facts to make their point. Instructors or teachers could use videos and lecturing - they might start lecturing and they can insert some arguments well explained by the videos. Demonstration aims at several targets, and some of them could be to teach skills, concepts, or principles. Demonstration teaching method covers large classes and incorporates charts, visual art, powerpoint, or posters, as an auxiliary tool to deliver the instructions.

Authority Method

Practically the authority teaching style is lecturing style. The Authority method, also known as the lecture style, involves sitting and listening to the instructor speak about a pre-assigned topic while the students take notes and memorize to the best of their ability what is being said (Bohren, 2019). Authority teaching style you might see the teacher in the front of the class talking or giving instructions, and students absorb or write the information. You often see this style employed in higher levels of education, perhaps some middle school teachers may use it, but mainly you will see it used in high school or college (Gonzalez, 2022). This teaching style is usually seen in higher education when the classes are large and the lesson contains lots of materia that obtains data, names, facts or evidence to memorize. The formal authority teaching style is a variation of the convergent teaching method.

Results

Convergent teaching empowers students' communications skills and strengthens analytical thinking for problem solving strategies. There are several communication skills, but the purpose of the paper will center on at least nine students skills: clarity, correctness, concreteness, consciousness, courtesy, completeness, consideration, listening, non communication, etc. Communication surrounds many factors and it is not easy to define. Let's try to observe a simple definition. Communication as its simplest, is the act of transferring information from one place to another. It may be vocally (using voice), written (using printed or digital media such as books, magazines, websites, or emails), visually (using logos, maps, charts, or graphs), or non-verbal (using body language, gestures, and the tone and pitch of voice). Convergent teaching fosters logical thinking to solve problems. According to (Crescom, 2016) there are Seven Steps to an Effective - Problem Solving Process: identify the problem, analyze the problem, describe the problem, look for root causes, develop alternative solutions, implement the solution, and measure the results. Communication and problem solving skills as significant elements of convergent thinking are utilized in all academic subjects.

Abbildung in dieser Leseprobe nicht enthalten

Figure 10. Students benefit from the convergent teaching approach. Convergent teaching provides a greater range of benefits, but this paper centers on five of them.

Usually, exams with closed ended questions determine the students achievement at high school level and higher education. During an academic year high school students are exposed to various standard exams. Also, students at higher education take closed ended tests. For example, students often attend large lecture classes and must pass exams at the end of a semester (Bosch, et al.,2021) . As we elaborated in the method and discussion sections,

Abbildung in dieser Leseprobe nicht enthalten

Figure 11. Convergent teaching (Teacher - Centered) integrates Technology in the instruction in the same way as does Student - Centered approach.

convergent teaching is closely related to solving problems with a single solution. Students who have a great experience with a convergent thinking approach will have greater chances to pass standardized exams successfully.

Discussion

Convergent teaching deals from lower order thinking questions to higher order thinking questions, and integrates technology from low - tech to high - tech. For instance lower order thinking questions incorporate all questions related to remembering - vocabulary, simple definitions, data, names, etc; understanding -demonstrating the facts, events, and ideas; and applying - solving simple problems in new situations based on facts and rules in different methods. Higher order thinking usually is related to critical thinking when we use analogy to solve different problems with similar properties with the same method, solving uncommon problems, solving hard problems in standardized exams, and solving problems with multiple steps. Convergent teaching involves low tech in the situation when instructors use power points or posters when they use formal authority. On the other hand, convergent teaching involves high - tech when they use direct instruction - personal model delivering instruction through Geogebra, virtual reality, Promethean, or mymath lab, etc.

Historically, development of technology in computers dictates the application or integration of technology in education. In the 1990, high wire internet changed the application of technology in education. For instance, illustrating integration of computer based teaching/learning in mathematics enhanced teaching and learning tremendously. Computer based teaching Clarifies mathematical figures; records videos with calculus, statistics, algebra, etc content so students can review the material; students can demonstrate and practice mathematical examples from different rich websites with adequate math examples for each level. Computers provide ways of teaching and learning that we did not dream of thirty years ago (Nicolas & Kaput, 1996). Computer based learning upgraded teaching and learning in a higher level that supplements students learning outcomes in the face to face teaching significantly.

The teacher centered with a high - tech platform can use cengage as an adaptive learning platform that is different from MyLabMath. Cengage does not have a very smooth transition in mathematics from an easy example to a harder one. Several years ago, examples on the quizzes or tests were harder than examples in the homework. Nonetheless, technology makes a huge leap in advancement toward sophistication. New product of Cengage guarantees that instructors can set up their course in just 10 minutes( Kelly, 2021). Companies compete with refining better products in education and surpass their competitors. The new technological invention will redefine Instructional Design and Technology more often than in the past because the volume of knowledge is doubling exponentially with respect to time. New innovation will dictate learning and teaching direction and its velocity of movement. Nonetheless, technology (Cengage or MyMath lab) has a flexibility to integrate smoothly in the convergent teaching.

Another significant technology that we can use in convergent teaching is virtual reality. Virtual reality is a computer based environment and scenes are as real. Virtual reality is a great tool to interpret geometrical figures in three dimensions where students can analyze all properties of geometrical figures with clear visual figures. Also, virtual reality can create historical events by living in the historical event that gives students the sense they experience what happened in the past. Virtual reality as a high tech has multiple benefits. The benefits of virtual reality in education go beyond academics as well to include cultural competence, the ability to understand another person's culture and values—an important skill in today's interconnected, global society (School of EDucation, 2019). Virtual reality enables students to have field trips in different parts of the world and to study cultural anthropology. High - tech devices and platforms could apply in the convergent teaching in multiple ways.

Abbildung in dieser Leseprobe nicht enthalten

Figure 12. The proof without words that shows if x • ~ = 1 then x + — > 2. The figure is taken from Math and Multimedia, 2015.

Convergent teaching can explore higher order questions by applying critical thinking and integrating high - tech during the instructions. This teaching approach could be applied in any academic subject, but let's take an example in mathematics - higher order thinking questions on proofs without words. Generally, proofs without words are pictures or diagrams that help the reader see why a particular mathematical statement may be true, and also to see how one might begin to go about proving it true (Alsina, Nelson, 2010). The best method to prove proofs without words (abstract thinking to make visible - concrete) is by using Geogebra. These proofs require deep abstract thinking (higher order thinking strategies) on how to find a single solution that proves the statement by using complex steps and great computer skills.

Abbildung in dieser Leseprobe nicht enthalten

The New Teaching Method

Educational researchers always inquire about new learning and teaching methods attaining greater and faster results. Directly or indirectly educators attempt finding better ways of teaching and they put students first, hence, their activity sways in the ethics framework. The educator strives to help each student realize his or her potential as a worthy and effective member of society (Code of Ethics, n.d.). A new teaching method, which could offer beneficial results for students is combining convergent teaching with the elements of the student centered teaching approach, respectively with the group work.

The weekly structure of the new teaching method starts with the convergent teaching on Monday, and continues Tuesday to Wednesday. The first three days of the week, the teacher delivers lessons step by step on explaining the mathematical concepts and solving mathematical problems. On Thursday, group work takes place - students practice on similar examples that were covered in the previous three days. During the group work students work on examples, they check their answers/solutions and compare with each other. Working in group the teacher shall not unreasonably deny the student's access to varying points of view (Ethics 11.1, n.d.). The teacher should just observe or facilitate; if students cannot solve an example completely the teacher assists them; otherwise, the teacher should respect students' way of expressing their ideas. On Friday, the teacher gives the exam to students to make sure students have learnt the content. Usually, the exam contains around eighty five percent of the concepts and examples similar to the material they explored in the class. About fifteen percent of the questions should be challenging that promotes critical thinking.

Summary

Convergent teaching could appear in various forms that apply in memorizing facts, ideas, names, events, or apply logical reasoning on solving problems with a single solution. Convergent teaching incorporates several teaching elements such as memorization, flashcards, training, standardized exams, group work, solving problems, etc. Most high school teachers and instructors in higher education utilize convergent teaching in the form of explicit, direct, demonstrator, or formal authority methods. It integrates technology from low - tech to high - tech. High school students with experience in convergent teaching have a higher chance to perform better in standardized tests, perform better academically in higher education, and graduate on time. Convergent teaching (teacher - centered approach) during the assessment could measure students learning through formative assessment and cumulative assessment. In fact, convergent teaching is a model of teaching in conservative education. The progressive education struggles to assess students effectively through the student centered method; therefore the teacher centered method has gotten a greater application in high schools and higher education. Convergent teaching might not be the greatest teaching method, but for now it does not have an appropriate substitution.

References

Aaron Pallas, Anna Neumonn, 2019, Convergent Teaching: Tools to Sparkle Deep Learning in College, John Hopkins University Press, Baltimore

Academic Success Center: Learning Center, Memory: it's a Process, Oregon State University, retrieved from, https://success.oregonstate.edu/learning/memory

Alison Burke, 2011. Group Work: How to Use Groups Effectively, The Journal of Effective Teaching, Vol. 11, No. 2, 2011, 87-95, retrieved from, https://uncw.edu/jet/articles/vol11 2/burke.pdf

Anna Bohren, March 18, 2019. Teaching Styles: Everything You need to know About Teaching Methods, retrieved from, https://blog.cognifit.com/teaching-styles/

Behnaz Hajesfandiari, Ali Gholami Mehrdad , Lotfollah Karimi, December 2014, Comparing the Effects of Convergent and Divergent Teaching Methods on Using Articles by Iranian EFL Learners, retrieved from, Comparing the Effects of Convergent and Divergent Teaching Methods on Using Articles by Iranian EFL Learners

Claudi Alsina and Roger B. Nelsen, 2010. An Invitation to Proofs Without Words, EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS Vol. 3, No. 1, 2010, 118-127 ISSN 1307-5543 - www.ejpam.com retrieved from, http://www.labjor.unicamp.br/comciencia/files/matematica/ar_roger/ar_roger.pdf

Code of Ethics for Educators, Governance Document, retrieved from https://www.nea.org/resource-library/code-ethics-educators

Crestcom, September 1, 2016. 7 Steps to an Effective - Problem Solving Process, retrieved from, https://crestcom.com/blog/2016/09/01/7-steps-to-effective-problem-solving/

Educational Research (Dataworks), Explicit Direct Instruction (EDI) vs Direct Instructions (DI), retrieved from, https://dataworks-ed.com/blog/2014/07/direct-instruction-di-vs-explicit-direct-instruction-edi/

Erin Eatough PhD, december 7, 2021. Building Good Habits in Your Life (and Ditching Bad Ones). Retrieved from, https://www.betterup.com/blog/building-habits

Ethics 11.1, SUNY ONEONTA, Foundations of Education, retrieved from, https://courses.lumenlearning.com/suny-oneonta-education106/chapter/ethics/

Eva Bosch, Eva Seifried, and Birgit Spinath, October, 2021, What successful students do: Evidence-based learning activities matter for students' performance in higher education beyond prior knowledge, motivation, and prior achievement, retrieved from, https://www. sciencedirect.com/science/article/abs/pii/S1041608021000935

Jeanne Scheurs , Roza Dumbraveanu, 2014. A shift from teacher centered to learner centered approach, International Journal of Engineering Pedagogy (iJEP), ACADEMIA Accelerating the world's research, retrieved from,

https://www.academia.edu/19683308/A Shift from Teacher Centered to Learner Centered Approach?from=cove r page

Joseph Gallian, January 25, 2008. Advice for students learning Proofs, retrieved from, https://www.d.umn.edu/~jgallian/Proofs.html

Hannah Wahlig, April 18, 2017. Analytical Learning Style, retrieved from, https://howtoadult.com/analytical-leaming-styles-8346827.html

How Memory Functions - Storage, retrieved from, https://opened.cuny. edu/courseware/lesson/51/student/?task=8

Kim Greene, What is Explicit Instruction, Understood - School Support, retrieved from, https://www.understood.org/en/articles/what-is-explicit-instruction

Qiqi Yuliati Zaqiah, Aam Hasanah, Din Wahyudin, As'ari Djohar, 2022. Implementation of Brain - Based Learning Capability to Improve Students Critical Thinking Skills, Journal of positive School Psychology http://jpornalppw.com 2022, Vol. 6, No. 8, 2922-2931

Math and Multimedia, September 16, 2015. Proof Without Words: If x >0, x + 1/x >=2, retrieved from, http://mathandmultimedia.com/2015/09/16/proof-without-words-if-x-0-x-1x-2/

Nicolas Balacheff, James J. Kaput, 1996. Computer based Learning in Mathematics, retrieved from https://link.Springer.com

Number 2 - Online Education, What is an Average SAT Score And How Do SAT Scoring Percentiles Work? Average SAT Score, retrieved from, https://www.number2.com/average-sat-score/

Prodigy, September 10, 2020, How to teach Convergent and Divergent Thinking: DEfinitions, Examples, Templates, and More, retrieved from, https://www.prodigygame.com/main-en/blog/convergent-divergent-thinking/

Ploya's Problem Solving Techniques, retrieved from, https://math.berkeley.edu/~gmelvin/polya.pdf

Rick Gonzalez, 2022. What is Authority Teaching Style? Go2Tutors, retrieved from, https://go2tutors.com/authority-teaching-style/

Rhea Kelly, october 25, 2021. New Cangage Product Embeds Course Material into Learning Management System, retrieved from, https://campustechnology.com/articles/2021/10/25/new-cengage-product-embeds-course-materials-into-learning-ma nagement-system.aspx

Siegfried Engelmann, Basic Philosophy of Direct Instructions, National Institute for Direct Instructions, retrieved from, https://www.nifdi.org/15/index.php?option=com_content&view=article&id=52&Itemid=27

School of Education, 12/16/2019. Virtual Reality in education:Benefits, Tools, and Resources, retrieved from, https://soeonline.american.edu/blog/benefits-of-virtual-reality-in-education

Skills You Need, Communication Skills, retrieved from, https://www.skillsyouneed.com/ips/communication-skills.html

Soomyung Kim Cho and Zane L. Berge, February 8, 2002. Overcoming Barriers to Distance Training and Education, retrieved from (PDF) Overcoming Barriers To Distance Training And Education

Synthia Malone, 2015. The Art of Problem Solving, Pearson, the image is retrieved from, https://slideplayer.com/slide/13255766/

University of Southern Maine, Academic Gains Through Improved Learning Effectiveness (Agile), retrieved from, https://usm.maine.edu/agile/using-flashcards

Unit 3, Methods of Teaching Pakistan studies, retrieved from, https://slidetodoc.com/unit-3-methods-of-teaching-pakistan-studies-week/

Urea, I. R. (2019). The influences of teacher' teaching style upon the pupils' well-being. New Trends and Issues

Proceedings on Humanities and Social Sciences. [Online]. 6 (7), pp 172-179. Available from: www.prosoc.eu

William DS Killgore, 2010. Effects of Sleep Deprivation on Cognition, Progress in Brain Research, 2010, retrieved from, https://www. sciencedirect.com/science/article/abs/pii/B9780444537027000075

[...]