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Who is a scholar? the first reply that must be given is: He is a scholar whose whole inward intellectual and moral being has been symmetrically unfolded, disciplined and strengthened under the influence of truth. The different mental activities will always be exercised rightly when the proper equilibrium is preserved. No one faculty should be drawn out to the neglect of others. The whole inner man should be unfolded harmoniously.

Emanuel Vogel Gerhart, The Proper Vocation of a Scholar: An Address, Delivered at the Opening of the New Diagnothian Hall (July 2, 1847).


Language arts (also known as English language arts or ELA) is the study and improvement of the arts of language. Traditionally, the primary divisions in language arts are literature and language, where language in this case refers to both linguistics, and specific languages.

Language arts instruction typically consists of a combination of readingwriting (composition), speaking, and listening. In schools, language arts is taught alongside sciencemathematics, and social studies.

The Parts of Language Arts

Since we want our children to be proficient at communicating ideas through language, we want to make sure we cover all the ways language occurs. So language arts include the four main components of

  • Listening can be considered the basis for development of speaking, reading, and writing skills. It is the act of understanding spoken language, and is often paired with speaking.
  • Reading, by definition, is the ability and knowledge of a language that allows comprehension by grasping the meaning of written or printed characters, words, or sentences. Reading involves a wide variety of print and non-print texts that helps a reader gain an understanding of the material that is being read. Reading of texts that are often included in educational curriculum include fictionnonfiction, classic, and also contemporary works. Reading goes beyond calling words to understand the information presented in a written or visual context.
  • Speaking – Oration and live delivery are often key components of language arts programs. This can include dramatic interpretation, speeches, oral interpretation of poetry, and the like. Speaking is a valuable way to enhance concepts of persuasion, and develop linguistic skills.
  • Writing. Composition is defined as the combination of distinct parts or elements to form a whole and the manner in which these elements are combined or related. The following are examples of composing in language arts:
  • The art or act of composing a literary work (i.e. novels, speeches, poems)
  • A short essay, especially one written as an academic exercise. An essay is a short literary composition on a particular theme or subject, usually in prose and generally analytic, speculative, or interpretative. There are many types of short essays, including:

Compositions may also include:

Everything that relates to listening, speaking, reading, and writing in your selected language can be considered part of your language arts program.

Teachers through the years have tried to break down that big goal of “communicating ideas through language” into individual skills to work on. Most language arts programs will include these specific skills.

  • Alphabet
  • Listening Skills
  • Phonics/Beginning Reading
  • Parts of Speech
  • Rhyming Words
  • Sentence Structure
  • Handwriting
  • Punctuation
  • Reading Comprehension
  • Capitalization
  • Writing Composition
  • Public Speaking
  • Vocabulary
  • Proofreading
  • Spelling
  • Grammar
  • Reference skills (alphabetizing; using a dictionary, etc.)
  • Word study (homonyms, synonyms, prefixes, suffixes)

Social Studies

In the United States education systemsocial studies is the integrated study of multiple fields of social science and the humanities, including historygeography, political science , philosophy and psychology. One of the purposes of social studies, particularly at the level of higher education, is to integrate several disciplines, with their unique methodologies and special focuses of concentration, into a coherent field of subject areas that communicate with each other by sharing different academic “tools” and perspectives for deeper analysis of social problems and issues. The social studies aims to train students for informed, responsible participation in a diverse democratic society. The content of social studies provides the necessary background knowledge in order to develop values and reasoned opinions, and the objective of the field is civic competence.

Social studies is not a subject, instead functioning as a field of study that incorporates many different subjects. It primarily includes the subjects of historygeographyeconomicscivics, and sociology. Through all of that, the elements of ethicspsychologyphilosophyanthropologyart, and literature are incorporated into the subject field itself. The field of study itself focuses on human beings and their respective relationships. With that, many of these subjects include some form of social utility that is beneficial to the subject field itself.

Ten Themes of Social Studies

According to the National Council for the Social Studies, there are ten themes that represent the standards about human experience that is constituted in the effectiveness of social studies as a subject study from pre-K through 12th grade.


The study of culture and diversity allows learners to experience culture through all stages from learning to adaptation, shaping their respective lives and society itself. This social studies theme includes the principles of multiculturalism, a field of study in its own right that aims to achieve greater understanding between culturally diverse groups of students as well as including the experiences of culturally diverse learners in the curriculum.

Time, Continuity, and Change

Learners examine the past and the history of events that lead to the development of the current world. Ultimately, the learners will examine the beliefs and values of the past to apply them to the present. Learners build their inquiry skills in the study of history.

People, Places, and Environment

Learners will be able to understand who they are and the environment and places that surround them. It gives spatial views and perspectives of the world to the learner. This theme is largely contained in the field of geography, which includes the study of humanity’s connections with resources, instruction in reading maps and techniques and perspectives in analyzing information about human populations and the Earth’s systems.

Individual Development and Identity

Learners will be able to understand their own personal identity, development, and actions. Through this, they will be able to understand the influences that surround them.

Individuals, Groups, and Institutions

Learners will understand how groups and institutions influence people’s everyday lives. They will be able to understand how groups and institutions are formed, maintained, and changed.

Power, Authority, and Governance

Learners will understand the forms of power, authority, and governance from historical to contemporary times. They will become familiar with the purpose of power, and with the limits that power has on society.

Production, Distribution, and Consumption

Learners will understand the organization of goods and services, ultimately preparing the learner for the study of greater economic issues. The study of economic issues, and with it, financial literacy, is intended to increase students’ knowledge and skills when it comes to participating in the economy as workers, producers, and consumers.

Science, Technology, and Society

Learners will understand the relationship between science, technology, and society, understanding the advancement through the years and the impacts they have had.

Global Connections

Learners will understand the interactive environment of global interdependence and will understand the global connections that shape the everyday world.

Civic Ideals and Practices

Learners will understand the rights and responsibilities of citizens and learn to grow in their appreciation of active citizenship. Ultimately, this helps their growth as a full participant in society. Some of the values that civics courses strive to teach are an understanding of the right to privacy, an appreciation for diversity in American society, and a disposition to work through democratic procedures. One of the curricular tools used in the field of civics education is a simulated congressional hearing. Social studies educators and scholars distinguish between different levels of civic engagement, from the minimal engagement or non-engagement of the legal citizen to the most active and responsible level of the transformative citizen. Within social studies, the field of civics aims to educate and develop learners into transformative citizens who not only participate in a democracy, but challenge the status quo in the interest of social justice. …Wikipedia

Mathematics (from Greekμάθημαmáthēma, ‘knowledge, study, learning’) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis).

Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from countingcalculationmeasurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid‘s Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Mathematics is essential in many fields, including natural science, engineering, medicinefinance, and the social sciencesApplied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.

Three leading types

Three leading types of definition of mathematics today are called logicistintuitionist, and formalist, each reflecting a different philosophical school of thought. All have severe flaws, none has widespread acceptance, and no reconciliation seems possible.

Logicist definitions

An early definition of mathematics in terms of logic was that of Benjamin Peirce (1870): “the science that draws necessary conclusions.” In the Principia MathematicaBertrand Russell and Alfred North Whitehead advanced the philosophical program known as logicism, and attempted to prove that all mathematical concepts, statements, and principles can be defined and proved entirely in terms of symbolic logic. A logicist definition of mathematics is Russell’s (1903) “All Mathematics is Symbolic Logic.”

Intuitionist definitions

Intuitionist definitions, developing from the philosophy of mathematician L. E. J. Brouwer, identify mathematics with certain mental phenomena. An example of an intuitionist definition is “Mathematics is the mental activity which consists in carrying out constructs one after the other.” A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions. In particular, while other philosophies of mathematics allow objects that can be proved to exist even though they cannot be constructed, intuitionism allows only mathematical objects that one can actually construct. Intuitionists also reject the law of excluded middle. While this stance does force them to reject one common version of proof by contradiction.

Formalist definitions

Formalist definitions identify mathematics with its symbols and the rules for operating on them. Haskell Curry defined mathematics simply as “the science of formal systems”. A formal system is a set of symbols, or tokens, and some rules on how the tokens are to be combined into formulas. In formal systems, the word axiom has a special meaning different from the ordinary meaning of “a self-evident truth”, and is used to refer to a combination of tokens that is included in a given formal system without needing to be derived using the rules of the system.

Mathematics can, broadly speaking, be subdivided into the study of quantity, structure, space, and change (i.e. arithmeticalgebrageometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty

See also: Areas of mathematics and Glossary of areas of mathematics …Wikipedia


Biology, study of living things and their vital processes. The field deals with all the physicochemical aspects of life. The modern tendency toward cross-disciplinary research and the unification of scientific knowledge and investigation from different fields has resulted in significant overlap of the field of biology with other scientific disciplines. Modern principles of other fields—chemistrymedicine, and physics, for example—are integrated with those of biology in areas such as biochemistry, biomedicine, and biophysics.

Biology is subdivided into separate branches for convenience of study, though all the subdivisions are interrelated by basic principles. Thus, while it is custom to separate the study of plants (botany) from that of animals (zoology), and the study of

the structure of organisms (morphology) from that of function (physiology), all living things share in common certain biological phenomena—for example, various means of reproductioncell division, and the transmission of genetic material. …Encyclopedia Britannica



Empirical sciencesFormal science
Natural scienceSocial science
earth science, and space science
political science,
human geography, and psychology
mathematics, and statistics
agricultural science,
medicine, and materials science
Business administration
public policy
pedagogy, and international development
Computer science

Thomas B. FORDHAM Institute


Six principles for high-quality, effective writing instruction for all students

CAO Central

Getty Images/DragonImages

Editor’s note: The Thomas B. Fordham Institute recently launched “The Acceleration Imperative,” a crowd-sourced, evidence-based resource designed to aid instructional leaders’ efforts to address the enormous challenges faced by their students, families, teachers, and staff over the past year. It comprises four chapters split into nineteen individual topics. Over the coming weeks, we will publish each of these as a stand-alone blog post. This is the eighth. Read the firstsecondthirdfourthfifthsixth, and seventh.

Explicit writing instruction not only improves students’ writing skills but also helps build and deepen their content knowledge, boosts reading comprehension and oral language ability, and fosters habits of critical and analytical thinking. The process of planning, writing, and revising can be taught in intentional, sequential steps. In following this process, students can improve their skills and overall comprehension and retention of information.[1] It’s imperative that schools not scrimp on writing instruction as they help students recover from the pandemic.

To be effective, writing should be embedded in the content of the core curriculum and begin at the sentence level. As Judith Hochman and Natalie Wexler describe in The Writing Revolution: A Guide to Advancing Thinking Through Writing in All Subjects and Grades, “Writing and content knowledge are intimately related. You can’t write well about something you don’t know well. The more students know about a topic before they begin to write, the better they’ll be able to write about it. At the same time, the process of writing will deepen their understanding of a topic and help cement that understanding in their memory.” They go on to establish six key principles of the Hochman method, which include explicit skills instruction, the infusion of grammar in practice, and an emphasis on planning and revising. These form a strong basis for high-quality, effective writing instruction for all students.


  • Adopt and implement a high-quality English language arts curriculum (see the section on “Reading”).
  • Select a writing curriculum and activities that feature explicit, carefully focused instruction and connect to a variety of content areas, including building writing time into all subjects. To date, “The Writing Revolution,” also known as the Hochman method, is the only curriculum that combines these two elements.
  • Writing activities should start at the sentence level. Tasking young students with longer assignments will overtax them and short-circuit learning. Sentences are the building blocks for all writing.
  • Expand teachers’ awareness and enthusiasm for the role that frequent sentence-level writing, sentence expansion and combining, and even note-taking activities can play in enhancing any kind of instruction. A school-wide study of The Writing Revolution can serve as a sound starting point.
  • Invest in ongoing curriculum-based professional learning for leaders, instructional coaches, and teachers to build expertise and fully leverage the power of high-quality writing instruction.


Content and cognitive science

There is a robust body of research indicating that writing has the potential to boost comprehension and retention, extending back to the 1970s.

In a landmark study, undergraduates were given five minutes to read an article. They then were randomly assigned to one of four tasks: reading the article once; studying it for fifteen additional minutes; creating a “concept map” or bubble diagram of the ideas in the article; or writing what they could remember from the passage, known as “retrieval practice.” When tested a week later, the group that had engaged in writing had a clear advantage in recalling information and making inferences.[2]

Writing about a topic is akin to preparing to teach something you have learned, which has also been shown to improve recall, a phenomenon called the “protégé effect.”[3] Essentially, writing requires students to recall something they have slightly forgotten (the mechanism at work in retrieval practice) and explain it in their own words (the mechanism at work in the protégé effect). A recent meta-analysis found that writing about content in science, social studies, and math reliably enhances learning in all three subjects.[4]

But most existing approaches to writing instruction fail to take full advantage of these potential benefits. Instead, they ask students to write about their own experiences or about random topics, without providing much background information.

In addition, most instructional approaches vastly underestimate how difficult it is to learn to write.[5] Young students may be juggling everything from letter formation and spelling to putting their thoughts in a logical order. Yet virtually all strategies expect inexperienced writers, including kindergartners, to write multiple-paragraph essays. The theory is that students need to develop their voice, fluency, and writing stamina from the earliest stages. But writing at length only increases cognitive load, potentially overwhelming working memory and depriving students of the cognitive capacity to absorb and analyze the information they’re writing about, much less acquire target skills.[6]

The Institute of Education Science’s Practice Guide on elementary writing cites twenty-five studies finding a variety of positive effects that follow from paying close attention to the writing process. It also recommends that one hour a day be devoted to students’ writing beginning in the first grade, and acknowledges that this is unlikely to be achieved unless writing practice occurs in the context of non-ELA content area instruction.[7]

Starting at the sentence level

Studies have shown the positive effects of interventions such as sentence combining and sentence expansion and teaching sentence-construction skills generally.[8] The IES Practice Guide recommends that students be taught to construct sentences. There are also indications in the literature on “writing to learn” that shorter writing assignments, including poems, yield larger benefits.[9] In addition, focusing on learning to construct sentences before moving on to paragraphs lightens the load on students’ working memory, freeing up cognitive space for absorbing and analyzing the content they’re writing about.

And yet for some reason, there appears to have been no studies testing whether there are greater benefits from an approach that explicitly teaches students to write sentences before asking them to embark on lengthier writing.

In the meantime, it’s best to begin writing at the sentence level. Sentence-level instruction not only lightens cognitive load, it also makes instruction in the conventions of written language—such as grammar, punctuation, etc.—far more manageable. Teachers confronted with page after page of error-filled writing often don’t know where to begin, and they don’t want to discourage students by handing back a sea of red ink. And if students can’t write a good sentence, they’ll never be able to write a good paragraph or a good essay.

Many students don’t easily absorb the mechanics of constructing sentences from their reading, as most approaches to writing instruction assume. Rather, they need to practice how to use conjunctions, appositives, transition words, and so forth. Activities that teach these skills, when embedded in the content of the curriculum, simultaneously build writing skills, content knowledge, and analytical abilities.

For example, students learning about the Civil War might be given the sentence stem “Abraham Lincoln was a great president _____________.” and then asked to finish it in three different ways, using “because,” “but,” and “so.” This kind of explicit instruction can also familiarize students with the syntax and vocabulary that are found in written but not spoken language, and can boost reading comprehension. Once you have learned to use a word like “despite” or a construction like the passive voice in your own writing, you’re in a much better position to understand it when you encounter it while reading.

Example: The Writing Revolution

The potential of explicit writing instruction that is embedded in the content of the curriculum and begins with sentence-level strategies is enormous. As far as can be determined, the Writing Revolution method is currently the only approach to writing instruction that combines these two features. It rests on six key principles:

  1. Students need explicit instruction in writing, beginning in the early elementary grades.
  2. Sentences are the building blocks of all writing.
  3. When embedded in the content of the curriculum, writing instruction is a powerful teaching tool.
  4. The content of the curriculum drives the rigor of the writing activities.
  5. Grammar is best taught in the context of student writing.
  6. The two most important phases of the writing process are planning and revising.

Once students are ready for lengthier pieces, the Writing Revolution focuses considerable attention on teaching students to construct clear, linear outlines. When students transform their outlines into finished pieces of writing, they are able to construct coherent, fluent paragraphs and essays by drawing on the sentence-level strategies they have been taught.

Reading List

Arnold, K., Umanath, S., Thio. K., Reilly, W., McDaniel, M., Marsh, E. (2017). Understanding the cognitive processes involved in writing to learn. Journal of Experimental Psychology: Applied. 23(2), 115-127.

Bangert-Drowns, R., Hurley, M. and Wilkinson, B. (2004). The Effects of School-Based Writing-to-Learn Interventions on Academic Achievement: A Meta-Analysis. Review of Educational Research. 74(1), 29-58.

Graham, S., and Hebert, M. A. (2010). “Writing to Read: Evidence for how Writing Can Improve Reading. Carnegie Corporation Time to Act Report.” Washington, D.C.: Alliance for Excellent Education.

  • Teaching sentence-construction skills has improved reading fluency and comprehension.

Graham, S. and Perin, D. (2007). “Writing Next: Effective Strategies to Improve Writing of Adolescents in Middle and High Schools – A report to Carnegie Corporation of New York.” Washington, D.C.: Alliance for Excellent Education.

Graham, S., Kiuhara, S.A., and MacKay, M. (2020). The effects of writing on learning in science, social studies, and mathematics: A meta-analysis. Review of Educational Research. 90(2), 179-226.

  • Embedding writing instruction in content and having students write about what they are learning in English language arts, social studies, science, and math has boosted reading comprehension and learning across grade levels.

Hochman, J. and Wexler, N. (2017). The Writing Revolution: A Guide to Advancing Thinking Through Writing in All Subjects and Grades. Jossey-Bass.

Graham, S., Bollinger, A., Booth Olson, C., D’Aoust, C., MacArthur, C., McCutchen, D., and Olinghouse, N.(2012). “Teaching elementary school students to be effective writers: A practice guide (NCEE 2012-4058).” Washington, D.C.: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

 Karpicke, J., and Blunt, J. (2011). Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping. Science. 331(6018) 772-775.

Mueller, P. A., and Oppenheimer, D. M. (2014). The Pen Is Mightier Than the Keyboard: Advantages of Longhand Over Laptop Note Taking. Psychological Science, 25(6), 1159–1168.

  • Two key takeaways: the benefits of writing for information retention are strongest with writing by hand rather than on the computer; and the act of writing solidifies students’ knowledge of a subject.

Naka, M., & Naoi, H. (1995). The effect of repeated writing on memory. Memory & Cognition, 23(2), 201–212.

  • Demonstrates the crucial link between writing about something and remembering the content involved.

Panero, N.S. (2016). Progressive mastery through deliberate practice: A promising approach for improving writing. Improving Schools, 19(3), 229-245.

  • Summarizes the research on improving writing quality as well as writing strategies that improve reading comprehension, and connects those to practices taught in The Writing Revolution.

Seven, S., Koksal, A.P., Kocak, G. (2017). The Effect of Carrying out Writing to Learn Activities on Academic Success of Fifth Grade Students in Secondary School on the Subject of ‘Force and Motion. Universal Journal of Educational Research. 5(5), 744-749.

Tindle, R. and Longstaff, M.G. (2015). Writing, Reading and Listening Differentially Overload Working Memory Performance Across the Serial Position Curve. Advances in Cognitive Psychology. 11(4), 147-155.

Wexler, N. (2019). “Writing and cognitive load theory,” ResearchED, Issue 4,

  • “Writing can impose such a heavy burden on working memory that students become overwhelmed, unable either to improve their writing skill or to benefit from the positive effects that writing can have on reading comprehension and learning in general.”

Willingham, D. (2003). Students remember … what they think about. American Educator, 27(2), 37–41.

  • Writing can facilitate students’ thinking about what they are supposed to learn.

[1] From Brian Pick: I think it is important here to address both the writing process and the writing mechanics. Both matter but sometimes schools focus almost exclusively on only one or the other.

[2] From the editors: See “Retrieval Practice Produces More Learning than Elaborative Studying with Concept Mapping.” For more about writing and retrieval, see “The effect of repeated writing on memory,” which compares memorization among Japanese and American students using writing as a memorization strategy.

[3] From the editors: For example, in a study by Muis et al., elementary students who were solving complex math problems used more metacognitive strategies when preparing to teach those strategies compared to a control group. In a study by Nestojko et al., participants who were told they would be teaching a passage had better recall than those who were told they would be tested on the passage.

[4] From the editors: See “The Effects of Writing on Learning in Science, Social Studies, and Mathematics: A Meta-Analysis.

[5] From the editors: Research shows that writing imposes a heavier cognitive load on working memory than reading. See “Writing, Reading, and Listening Differentially Overload Working Memory Performance Across the Serial Position Curve.”

[6] From Jamila Newman: I think it’s important that schools see writing as gateway to student independence and agency. Reading and listening often position students as consumers, but writing and speaking position students as producers of argument, opinion, and ideas.

[7] From the editors: See “Teaching Elementary School Students to Be Effective Writers.”

[8] From the editors: See both “Writing Next” and “Writing to Read,” two Carnegie Corporation of New York reports published by the Alliance for Excellent Education.

[9] From the editors: See “The Effects of School-Based Writing-to-Learn Interventions on Academic Achievement” and “The Effect of Carrying out Writing to Learn Activities on Academic Success of Fifth Grade Students in Secondary School on the Subject of ‘Force and Motion’.”POLICY PRIORITY: HIGH EXPECTATIONSTOPICS: EVIDENCE-BASED LEARNINGCURRICULUM & INSTRUCTIONTEACHERS & SCHOOL LEADERS



Forensic Science



Technology, Engineering and Robotics






is a diverse range of (products of) human activities involving creative imagination to express technical proficiency, beauty, emotional power, or conceptual ideas.

There is no generally agreed definition of what constitutes art, and ideas have changed over time. The three classical branches of visual art are painting, sculpture, and architectureTheatredance, and other performing arts, as well as literaturemusicfilm and other media such as interactive media, are included in a broader definition of the arts. Until the 17th century, art referred to any skill or mastery and was not differentiated from crafts or sciences. In modern usage after the 17th century, where aesthetic considerations are paramount, the fine arts are separated and distinguished from acquired skills in general, such as the decorative or applied arts.

The nature of art and related concepts, such as creativity and interpretation, are explored in a branch of philosophy known as aesthetics. The resulting artworks are studied in the professional fields of art criticism and the history of art.

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The arts 

refers to the theory, human application and physical expression of creativity found in human cultures and societies through skills and imagination in order to produce objectsenvironments and experiences. Major constituents of the arts include visual arts (including architecture, ceramicsdrawingfilmmakingpaintingphotography, and sculpting), literary arts (including fictiondramapoetry, and prose), performing arts (including dancemusic, and theatre), and culinary arts (including cookingchocolate making and winemaking).

Some art forms combine a visual element with performance (e.g. cinematography), or artwork with the written word (e.g. comics). From prehistoric cave paintings to modern-day films, art serves as a vessel for storytelling and conveying humankind’s relationship with the environment.


(from Greekμάθημαmáthēma, ‘knowledge, study, learning’) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis). It has no generally accepted definition.

Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of such by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from countingcalculationmeasurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid‘s Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

Mathematics is essential in many fields, including natural scienceengineeringmedicinefinance, and the social sciencesApplied mathematics has led to entirely new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics (mathematics for its own sake) without having any application in mind, but practical applications for what began as pure mathematics are often discovered later.


Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmeticalgebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The oldest mathematical texts from Mesopotamia and Egypt are from 2000 to 1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (additionsubtractionmultiplication and division) first appear in the archaeological record. The Babylonians also possessed a place-value system and used a sexagesimal numeral system which is still in use today for measuring angles and time. Wikipedia

2 to 4 hours (or more) per day

Education is the process of facilitating learning, or the acquisition of knowledgeskillsvaluesbeliefs, and habits. Educational methods include teachingtrainingstorytellingdiscussion and directed research. Education frequently takes place under the guidance of educators, however learners can also educate themselves. Education can take place in formal or informal settings and any experience that has a formative effect on the way one thinks, feels, or acts may be considered educational. The methodology of teaching is called pedagogy.

Progressive education

Progressive education, movement that took form in Europe and the United States during the late 19th century as a reaction to the alleged narrowness and formalism of traditional education. One of its main objectives was to educate the “whole child”—that is, to attend to physical and emotional, as well as intellectual, growth. The school was conceived of as a laboratory in which the child was to take an active part—learning through doing. The theory was that a child learns best by actually performing tasks associated with learning. Creative and manual arts gained importance in the curriculum, and children were encouraged.

Special education

Special education, also called special needs education, the education of children who differ socially, mentally, or physically from the average to such an extent that they require modifications of usual school practices. Special education serves children with emotional, behavioral, or cognitive impairments or with intellectual, hearing, vision, speech, or learning disabilities; gifted children with advanced academic abilities; and children with orthopedic or neurological impairments. See also deafnessblindnessspeech disordermental disordergifted childchildhood disease and disorderlearning disabilities.



Pre-K/K Reading

Elementary School Reading

Middle School Reading

High School Reading


What’s Up –

You can catch up on all of NASA’s current and future missions at nasa.gov.

I’m Preston Dyches from NASA’s Jet Propulsion Laboratory, and that’s What’s Up for this month.View all Videos

Hey parents and kids, share your thoughts and ideas (comments are open at the end of the page) ⬇




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