Maths Formulas: The Building Blocks of Mathematical Mastery

Maths Formulas: The Building Blocks of Mathematical Mastery

Mathematics, often regarded as the language of the universe, plays a pivotal role in various aspects of our lives. At its core, mathematics relies on formulas, concise expressions that encapsulate mathematical relationships. In this article, we will explore the world of maths formulas, delving into their significance, types, applications, and tips for mastering them.

I. Introduction

A. Importance of Mathematics

Mathematics is not merely a subject taught in schools; it is a fundamental tool that shapes our understanding of the world. From calculating daily expenses to solving complex scientific problems, mathematics is omnipresent. At the heart of this discipline lies the use of formulas, which serve as the backbone of mathematical operations.

B. Role of Formulas in Mathematics

Formulas are the key to unlocking the mysteries of mathematical problems. They provide a structured approach to solving equations, making complex calculations more manageable. Understanding and mastering formulas are essential for anyone looking to navigate the intricate landscape of mathematics.

II. Basic Arithmetic Formulas

A. Addition and Subtraction

The most elementary operations in mathematics involve adding and subtracting numbers. Basic arithmetic formulas lay the foundation for more advanced mathematical concepts.

B. Multiplication and Division

Multiplication and division are fundamental operations that extend beyond simple calculations. These operations form the basis for more intricate mathematical manipulations.

III. Algebraic Formulas

A. Linear Equations

In the realm of algebra, linear equations play a crucial role. Formulas for solving linear equations are essential for expressing relationships between variables.

B. Quadratic Equations

Quadratic equations introduce an additional level of complexity. Understanding the associated formulas is vital for solving problems involving squared variables.

C. Polynomials

Polynomials, with their multiple terms, require specialized formulas for simplification and solution.

IV. Geometry Formulas

A. Area and Perimeter

Geometry relies heavily on formulas for calculating the area and perimeter of various shapes. These formulas provide a systematic approach to measuring geometric entities.

B. Volume of Basic Shapes

Determining the volume of three-dimensional objects involves using specific formulas for different shapes.

V. Trigonometric Formulas

A. Sine, Cosine, and Tangent

Trigonometry introduces ratios and relationships between angles. Trigonometric formulas are essential for solving problems involving triangles and circular motion.

B. Applications in Real Life

Trigonometry extends beyond the classroom, finding applications in fields such as physics, engineering, and computer science.

VI. Calculus Formulas

A. Differentiation

Calculus introduces the concept of differentiation, with formulas that describe rates of change and slopes.

B. Integration

Integration formulas enable the calculation of areas under curves and the accumulation of quantities.

VII. Statistics Formulas

A. Mean, Median, and Mode

Statistics relies on formulas for summarizing and interpreting data. Mean, median, and mode formulas are fundamental in this context.

B. Standard Deviation

Standard deviation formulas provide insights into the dispersion of data points in a dataset.

VIII. Applications of Math Formulas

A. Everyday Life

Mathematics is not confined to academic settings; its formulas find practical applications in daily life.

B. Professional Fields

Professions such as finance, engineering, and science heavily rely on mathematical formulas for problem-solving and decision-making.

IX. Importance of Understanding Formulas

A. Enhancing Problem-Solving Skills

Mastering mathematical formulas enhances problem-solving skills, fostering a logical and analytical mindset.

B. Building a Strong Foundation for Advanced Mathematics

A solid understanding of basic formulas is crucial for progressing to more advanced mathematical concepts.

X. Tips for Memorizing Formulas

A. Mnemonics

Memory aids such as mnemonics can make memorizing formulas more enjoyable and effective.

B. Practical Applications

Applying formulas to real-life scenarios enhances understanding and retention.

XI. Online Resources for Learning Math Formulas

A. Interactive Websites

Online platforms offer interactive tools and resources to facilitate the learning of mathematical formulas.

B. Educational Apps

Mobile apps provide a convenient and engaging way to reinforce mathematical concepts and formulas.

XII. Common Mistakes to Avoid in Using Formulas

A. Misinterpretation

Misinterpreting formulas can lead to errors in calculations and problem-solving.

B. Lack of Practice

Regular practice is essential for retaining and applying mathematical formulas accurately.

XIII. Future Trends in Math Education

A. Technological Integration

Advancements in technology are reshaping math education, with interactive tools and digital platforms becoming increasingly prevalent.

B. Personalized Learning

Tailoring educational experiences to individual needs is a growing trend in math education.

XIV. Challenges in Learning and Applying Formulas

A. Overcoming Math Anxiety

Math anxiety can hinder the learning process, and strategies for overcoming it are crucial.

B. Bridging the Gap Between Theory and Practice

Connecting theoretical knowledge with practical application is a challenge that educators and learners face.

XV. Conclusion

In conclusion, the world of mathematics is intricately woven with formulas that unlock its secrets. From basic arithmetic to advanced calculus, understanding and applying formulas are essential skills. Embracing the challenges, utilizing resources, and recognizing the real-world applications of formulas pave the way for mathematical mastery.

Frequently Asked Questions

  1. Q: How can I overcome math anxiety when dealing with formulas? A: Practice regularly, seek help from tutors or online resources, and approach math with a positive mindset.
  2. Q: Are there any innovative apps for learning math formulas? A: Yes, several educational apps provide interactive and engaging ways to learn and practice math formulas.
  3. Q: Why are statistics formulas important in various fields? A: Statistics formulas help in summarizing and interpreting data, guiding decision-making in fields like business and research.
  4. Q: Can I solely rely on online resources for learning math formulas? A: While online resources are valuable, combining them with traditional learning methods can enhance understanding and retention.
  5. Q: How can I ensure I don’t misinterpret mathematical formulas? A: Pay attention to details, seek clarification when in doubt, and practice applying formulas in different contexts.

Exploring Luxurious Places in China, Russia, and India

Exploring Luxurious Places in China, Russia, and India

If you’re looking for luxurious destinations, then China, Russia, and India should definitely be on your list. These countries are home to some of the world’s most opulent and lavish destinations. From grand palaces to stunning natural landscapes, these countries have it all.

In this article, we’ll look at some of the most luxurious places in China, Russia, and India. If you plan a trip to one of these countries, remember to book your air fares only with Traveloka.

Luxurious Places in China

  1. Shanghai

Shanghai is a global hub for finance, innovation, and luxury. It’s known for its stunning skyline, bustling nightlife, and high-end shopping. The city is home to some of the world’s most luxurious hotels, including the Waldorf Astoria Shanghai on the Bund and the Mandarin Oriental Pudong, Shanghai. If you’re looking for a unique and luxurious experience, then be sure to check out the Shanghai Tower, which is one of the tallest buildings in the world.

  1. Beijing

Beijing is the political and cultural center of China. It’s known for its rich history, stunning architecture, and world-class museums. The city is home to some of the most luxurious hotels in China, including the Four Seasons Hotel Beijing and the Ritz-Carlton Beijing. If you’re looking for a luxury experience, then be sure to check out the Palace Museum, which is a stunning complex of palaces, temples, and gardens.

Luxurious Places in Russia

  1. Moscow

Moscow is Russia’s capital and a city steeped in history and culture. It’s known for its stunning architecture, world-class museums, and vibrant nightlife. Moscow is home to some of the most luxurious hotels in the world, including the Ritz-Carlton Moscow and the Ararat Park Hyatt Moscow. If you’re looking for a luxurious experience in Moscow, then be sure to check out the Bolshoi Theatre, which is one of the most famous theaters in the world.

  1. St. Petersburg

St. Petersburg is a city often called Russia’s cultural capital. It’s known for its stunning architecture, world-class museums, and beautiful canals. The city is home to some of the most luxurious hotels in Russia, including the Four Seasons Hotel Lion Palace St. Petersburg and the Belmond Grand Hotel Europe. If you’re looking for a luxurious experience in St. Petersburg, be sure to check out the Hermitage Museum, one of the world’s largest and most famous museums.

Luxurious Places in India

  1. Mumbai

Mumbai is a city that’s known for its glitz and glamour. It’s home to Bollywood the Indian film industry, and is known for its high-end shopping and dining. The city is home to some of the most luxurious hotels in India, including the Taj Mahal Palace Hotel and the St. Regis Mumbai. If you’re looking for a luxurious experience in Mumbai, then be sure to check out the Gateway of India, which is a stunning monument that overlooks the Arabian Sea.

  1. Jaipur

Jaipur is a city that’s often called the Pink City due to its stunning pink architecture. It’s known for its rich history, stunning palaces, and vibrant culture. The city is home to some of the most luxurious hotels in India, including the Taj Rambagh Palace and the Oberoi Rajvilas. If you’re looking for a luxurious experience in Jaipur, then be sure to check out the City Palace, which is a stunning complex of palaces, courtyards, and gardens.

Conclusion

These are just a few of the most luxurious places in China, Russia, and India. Whether you’re looking to explore stunning natural landscapes, immerse yourself in rich culture and history, or simply indulge in a luxurious experience, these countries have it all. So why not plan your next trip to one of these stunning destinations?

LDC5: Proposed online university sparks hope of bridging education gap in least developed countries

LDC5: Proposed online university sparks hope of bridging education gap in least developed countries

Notwithstanding progress in growing enrolment costs for main education and learning, 16.2 for every cent of little ones of principal school age were out of faculty in least produced international locations (LDCs) in 2019 and virtually 50 {e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} of small children out of college all over the world are in individuals very same nations, with ladies, young children with disabilities and other kids in vulnerable circumstances disproportionately represented. 

Enrolment and completion charges for tertiary training continue being small, which has significantly-achieving implications for the structural transformation agenda of the the very least made international locations. Most of them depend on aid for their instruction budgets. At the secondary and tertiary ranges, gender disparities and disparities for the poorest and most susceptible exist.  

“Clearly, the training methods in the LDCs demand substantial growth to equip their youthful individuals with the competencies they have to have for the foreseeable future,” claimed Ms. Fatima, who is also the UN Higher Consultant for the Minimum Developed Countries, Landlocked Creating Countries and Small Island Developing States (UN-OHRLLS) at an LDC5 large-level facet occasion on the proposed on the web college for LDCs. 

Rabab Fatima, UN High Representative for the Least Developed Countries, Landlocked Developing Countries and Small Island Developing States (centre) addresses a side event on online education, held during the LDC5 Conference in Doha, Qatar.

Pandemic widens schooling gaps 

The COVID-19 pandemic has uncovered a important fault line in the training procedure, particularly in the LDCs. UNESCO‘s International Study of Bigger Education, revealed in July 2021, found that the pandemic had afflicted 220 million tertiary college students throughout the world. In LDCs, nearly all universities were being compelled to shut totally.  

Even though tutorial establishments in formulated countries ended up ready to move speedily to on line education and learning, LDCs had been not able to make the swap due to a deficiency of the needed logistics, technological resources, and expertise. 

In a environment where by technological progress is transpiring at lightning velocity, international locations chance currently being still left powering if they do not invest in the digital competencies of tomorrow’s creators. 

The greatest way to meet the increasing demand for higher education and learning at scale in an successful, charge-effective, and resilient way is to rapidly develop on the net training infrastructure in LDCs. A new UNESCO global survey on the impression of COVID-19 on better education and learning reveals that sturdy nationwide endeavours, supported by the worldwide neighborhood, are urgently desired to develop on the internet universities in LDCs. 

“That is why the Doha Programme of Action (DPoA) has a concrete focus on in this location, to undertake feasibility experiments for setting up an on line university,” reported Ms. Fatima, she stated, referring to the Conference’s agreed result, which aims at getting rid of structural obstacles to extensive expansion and sustainable growth.   

A new on the web university 

She described that the primary aims of the proposed on the net university have been to:  

  • Present plan help to advertise length instruction and open understanding for graduate and postgraduate scientific studies in science, technological know-how, engineering, and arithmetic.  
  • Make sure specific entry for the poorest and these in susceptible scenarios.  
  • Generate a virtual community of educational establishments inside of and outside of the the very least created nations.  
  • Aid program design and style and curriculum advancement. 
  • Deliver scale and sustainability to the training process, take into account all current initiatives designed by pertinent companions.  
  • And aid worldwide recognition and accreditation to intercontinental expectations. 

As asked for by the DPoA, the UN Secretary-Normal will post a report outlining the mapping of existing initiatives, feasible new modalities, source prerequisites, accreditation, and sustainable sources of funding. 

This will be submitted to the UN Typical Assembly for thought at its 78th session in September. 

“I as a result echo the Secretary-General’s contact, as he urged development companions to reverse spending budget cuts, and to devote at minimum 15 for every cent of formal progress assistance to instruction,” said Ms. Fatima. 

She added: “International financial institutions must also be on the lookout to make much more methods and fiscal area obtainable for LDCs to spend in support of high-quality instruction for all.” 

“This initiative, alongside with the other training objectives and ambitions of the Doha Programme can equip millions of young women and boys to develop into brokers of transformative transform, nevertheless newfound innovation and entrepreneurial skills.” 

Throughout the side party, Member States, worldwide companies, civil society groups, the private sector and youth reps discussed the political and economic assist wanted to build an on the internet occasion. 

A summary of the discussions was circulated and will contribute to the Secretary-General’s examine on probable options for an on-line college. 

Professor Shijian Luo, Dean of the International School of Design, Ningbo Innovation Centre, Zhejiang University, at an education-related exhibit during the LDC5 Conference in Doha, Qatar.

Instruction programmes to encourage innovation

This week at LDC5, the Qatar National Conference Centre has also hosted a amount of civil culture and academic reps, like Professor Shijian Luo from China, who spoke to UN News

Luo is the Dean of the Global College of Design and style, Ningbo Innovation Centre, Zhejiang College (ZJU-ISD). The International Style Training (IDE) programme initiated at his school is devoted to giving industrial style training to pupils from LDCs in purchase to greatly enhance the capability and competitiveness of LDCs in industrial style. 

“Each year, the programme provides up to 50 full scholarships to suitable pupils from LDCs. These scholarships, supported by the college and the governing administration, enable the students to study industrial style and cultivate their trouble-resolving expertise,” Mr. Luo said at an exhibition showcasing the students’ industrial style and design productions. 

He explained that 68 college students from 19 LDCs have been acknowledged into the 2.5-12 months programme in 2021 and 2022. “The programme also serves as an incubator to support students’ innovation and entrepreneurship by furnishing small business help, study and expert services that help turn concepts in the classroom into start out-ups in the sector,” he extra. 

The professor stated that the prolonged-time period objective of the programme is to make the ability of the world’s 46 LDCs in science, technological know-how, and innovation (STI), which will lead to the achievement of the SDGs.  

“Our students are interested in bringing some of China’s practical experience in designing poverty alleviation or rural revitalization to their international locations,””Mr. Luo reported. 

The IDE programme is jointly organised by the United Nations Technology Bank for The very least Created Nations (UNTB), the Environment Eco-Structure Convention (WEDC) and ZJU-ISD given that 2021.  

The UNTB was proven in 2016 as a subsidiary entire body of the UN Typical Assembly to support LDCs strengthen their STI capacities. It at present serves 46 LDCs and former LDCs for up to five several years soon after their graduation from the category. 

Online Education Market in India to grow at a CAGR of 19.9{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} from 2022 to 2027, Driven by skill development and employment- Technavio

Online Education Market in India to grow at a CAGR of 19.9{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} from 2022 to 2027, Driven by skill development and employment- Technavio

NEW YORK, March 6, 2023 /PRNewswire/ — According to Technavio, the online education market size in India is estimated to grow by USD 3,461.93 million from 2022 to 2027. The market is estimated to grow at a CAGR of 19.9{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} during the forecast period. The growing focus on skill development and employment is notably driving the demand for the market. Working professionals across various domains focus on skill development for value addition and career growth. This is a trend that is followed by all age groups of working professionals. Working professionals prefer picking up courses on digital platforms over traditional classes due to factors such as convenience and flexibility. This trend, especially in tier 1 cities is expected to fuel the growth of the online education market in India during the forecast period.For more insights on the historic (2017 to 2021) and forecast market size (2023 to 2027) – Request a sample report

Technavio has announced its latest market research report titled India Online Education Market 2023-2027

Technavio has announced its latest market research report titled India Online Education Market 2023-2027

Leading trends influencing the market 

  • The emergence of cloud computing is a major trend driving the demand for the market in focus. This technology has helped players save significant content, data, and information on a single platform. This has also helped users to process, procure and access information at their convenience.

  • Cloud computing has also helped vendors reduce capital expenses and improve the speed of implementing SaaS-based solutions like ERP and LMS.

  • Vendors in the market are collaborating with central and state governments to popularize cloud platforms. For instance, the government has taken initiatives like the National Digital Library and the National Academic Repository to promote e-learning in institutes.

  • Hence, adopting cloud-based learning platforms in online education helps resolve several issues, thereby fueling the growth of the market in the country.

Major challenges hindering the market growth

  • The lack of infrastructure like high-speed internet, and optical fiber communication in many regions of the country may impede the growth of the market. This issue can make an otherwise economically efficient model essentially ineffective.

  • Lesser developed states and remote places in the country suffer from either lack of connectivity or are economically backward to afford the technology. Moreover, for services that offer classroom training along with e-learning, basic infrastructure like advanced hardware, software, and data centers are unavailable.

  • Hence, despite the high adoption of the internet and smartphones, insufficient infrastructure challenges the growth of the market.

Insights on Market Drivers, trends, & Challenges, historic period(2017 to 2021) and forecast period(2023 to 2027)- Request a sample report!

What’s New?

  • Special coverage on the RussiaUkraine war; global inflation; recovery analysis from COVID-19; supply chain disruptions, global trade tensions; and risk of recession

  • Global competitiveness and key competitor positions

  • Market presence across multiple geographical footprints – Strong/Active/Niche/Trivial  – buy the report!

Online Education Market in India – Segmentation Assessment
Segment Overview
Technavio has segmented the market based on End-user (Higher education and K-12), and Product (Content and Services).

  • The higher education segment is prominent in the growth of the online education market in India during the forecast period.

  • Online higher education enables time and location flexibility as well as affordability to the end-users. This has led to many ed-tech companies investing and witnessing an increase in the adoption of courses for higher education preparation.

  • For instance, Unacademy launched a dedicated platform for JEE (Joint Entrance Examination) preparation, which is one of the most competitive engineering entrance exams in India.

  • The Government of India (GoI) is further promoting online education through its Digital India initiative under the National Mission on Education through Information and Communication Technology (NMEICT).

Insights on the market contribution of various segments, historic (2017 to 2021) and forecast market size (2023 to 2027) – Download a Sample Report

What are the key data covered in this Online Education Market in India report?

  • CAGR of the market during the forecast period

  • Detailed information on factors that will drive the growth of the online education market in India between 2023 and 2027

  • Precise estimation of the size of the online education market in India size and its contribution to the market in focus on the parent market

  • Accurate predictions about upcoming trends and changes in consumer behavior

  • Growth of the online education market across India

  • A thorough analysis of the market’s competitive landscape and detailed information about vendors

  • Comprehensive analysis of factors that will challenge the growth of the online education market in India vendors

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Online Education Market In India Scope

Report Coverage

Details

Base year

2022

Historic period

2017-2021

Forecast period

2023-2027

Growth momentum & CAGR

Accelerate at a CAGR of 19.9{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf}

Market growth 2023-2027

USD 3,461.93 million

Market structure

Fragmented

YoY growth 2022-2023 ({e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf})

18.7

Regional analysis

India

Competitive landscape

Leading Vendors, Market Positioning of Vendors, Competitive Strategies, and Industry Risks

Key companies profiled

Aeon Learning Pvt. Ltd., AnalytixLabs, Coursera Inc., Educomp Solutions Ltd., Excelsoft Technologies Pvt Ltd., Indira Gandhi National Open University, Intellipaat Software Solutions Pvt. Ltd., Jigsaw Academy, Khan Academy Inc., MPS Ltd., NextEducation India Pvt. Ltd., NIIT Ltd., Reliance Industries Ltd., Simplilearn Solutions Pvt. Ltd., SMU DE, Think and Learn Pvt. Ltd., Udemy Inc, upGrad Education Pvt. Ltd., Vedantu Innovations Pvt. Ltd., Zeus Systems Pvt. Ltd., and Sorting Hat Technologies Pvt. Ltd.

Market dynamics

Parent market analysis, Market growth inducers and obstacles, Fast-growing and slow-growing segment analysis, COVID-19 impact and recovery analysis and future consumer dynamics, Market condition analysis for the forecast period

Customization purview

If our report has not included the data that you are looking for, you can reach out to our analysts and get segments customized.

Table of Contents

1 Executive Summary

2 Market Landscape

3 Market Sizing

4 Historic Market Size

5 Five Forces Analysis

6 Market Segmentation by End-user

7 Market Segmentation by Product

8 Customer Landscape

9 Drivers, Challenges, and Trends

10 Vendor Landscape

11 Vendor Analysis

12 Appendix

About Us
Technavio is a leading global technology research and advisory company. Their research and analysis focuses on emerging market trends and provides actionable insights to help businesses identify market opportunities and develop effective strategies to optimize their market positions. With over 500 specialized analysts, Technavio’s report library consists of more than 17,000 reports and counting, covering 800 technologies, spanning across 50 countries. Their client base consists of enterprises of all sizes, including more than 100 Fortune 500 companies. This growing client base relies on Technavio’s comprehensive coverage, extensive research, and actionable market insights to identify opportunities in existing and potential markets and assess their competitive positions within changing market scenarios.

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Technavio Research
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India Online Education Market 2023-2027

India Online Education Market 2023-2027

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Virtual Learning a “Critical Tool” in a Changing World

Virtual Learning a “Critical Tool” in a Changing World

During the pandemic, K-12 schools endured withering criticism for their inability to effectively educate students remotely, with many parents and lawmakers demanding a speedy return to in-person learning.

In October 2020, for instance, a Pew Research survey found that parents whose kids attended school in-person were far more likely to say they were “very satisfied” with the way school was handling instruction: 54{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} vs. just 30{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} whose kids received online instruction only.

But Patricia Brantley, who leads the 15-school network of Friendship Charter Schools in Washington, D.C., said developing and maintaining virtual learning systems will be critical to public schools going forward. Friendship began investing in virtual learning before the pandemic and has actually expanded its virtual offerings since 2021.

Related: South by Southwest Education Cheat Sheet: 23 Panels, Workshops and Screenings to See at SXSW 2023

The move is largely driven by parents, she said, who see the value of virtual learning for their kids. She noted one parent who wrote that her child requires a wheelchair to attend “a fair amount of medical appointments.” Online learning works in large part because classes are recorded for later viewing. The woman’s son, once an average student, is “now above grade” level, she wrote. Brantley also said the move has fostered “incredibly strong connections between families and with the faculty.”

Three years after the first pandemic closures, Brantley said virtual learning will also be key to attracting young teachers to the profession as other white-collar industries offer the option to work remotely. She’ll be talking about her experiences this week at South by Southwest Edu, part of a panel that explores the possibilities of online learning.

The 74’s Greg Toppo, who will be moderating the session, caught up with Brantley by email in advance of the session.

The interview was edited for length and clarity.

The 74: The panel at South by Southwest Edu asks “Is Virtual Learning the Disruptor Teaching Needs?” What’s your short answer to this question?

Patricia Brantley: Virtual learning is the solution teaching needs. There’s an age-old question: How do we best educate our young and prepare them for the world? Assuming that we can do it in the same way that it’s been done for 100 years or more, when the world has changed, is worse than naive. It is failing generations of students in ways that we may not recover.

In my opinion, the true disruptor isn’t the availability of virtual learning, it’s the convergence of factors illuminated by the pandemic. Those factors include the rise of parent-driven schooling through pods and micro schools that often rely partially on online delivery; the decline of traditional enrollment and rise in private, homeschool, online and charter options, and the flexibility now being given in other professions that make them more attractive to young college graduates than teaching. I see these factors converging in a way that is ultimately forcing changes in the way we historically have approached schooling, especially in traditional settings. Virtual learning isn’t the disruptor. It is a critical tool to support the way education must adapt to a changing world.

Friendship is D.C.’s first public, tuition-free online education provider. Can you talk a little about what you’ve built and what your enrollment trends are?

We began investing in online education years before the pandemic, opening Friendship Online Academy in 2015 for grades K to 8 and expanding to high school in 2019. Our original families knew that traditional settings weren’t serving their children well. The truth is we followed them to online learning as the solution. We were proud of our very specialized, small virtual community that featured incredibly strong connections between families and with the faculty.

Inline pull quote: “You can’t lose human relationships in the shift to online learning. Despite what some may think, a high-quality online learning environment is still centered on people and relationships, not technology.” — Patricia Brantley

Then, as many families were hesitant or unable to return to in-person schooling during the 2021-2022 academic year, our enrollment exploded. We went from barely 200 students to 700. Our staff grew from four full-time teachers to a staff of 40, with a faculty that includes master teachers, guidance counselors, social workers, parent liaisons and resident artists that are leading students through deep experiences in the fine arts. Our growth is an indication of the effectiveness and appeal of online learning environments.

Part of our success here is likely due to our intentional approach to design. Since 2015, our priority has been to design an online program with the learner at the center.  Interestingly, by centering the learner, we also designed a new experience for the teacher, one that creates flexibility and evolves the profession. By doing this, we saw significant interest from teachers to take on this role and high satisfaction rates from those who did. This experience gives us reason to question the prevailing idea that there is a shortage of people who want to teach. Rather, what we see is that many teachers want the freedom and flexibility to evolve. In that way, virtual learning can be as attractive and impactful for educators as it is for students and families.

Related: Many Remote Learning Options Shutting Down as School Reopens for Fall 2022

What have some of your early successes been?

While our enrollment trends are strong indicators of our program’s success, I’m even more pleased with the academic results we continue to achieve. Ensuring access to effective small learning environments and robust online options for students and families are absolute priorities for us. That’s why we are so proud to see results like those from the spring 2021 study from (educational consultants) EmpowerK12, which found that Friendship Online students previously deemed “at-risk” for academic failure outpaced citywide growth in both English and Math during the pandemic.

I also consider it a success that we haven’t gotten locked into one way to meet families’ needs. As we’ve continued to grow and learn, we’re piloting other learning environments that push the limits on traditional school. Our microschools and hubs, which also emerged as part of the need created by the pandemic, were a game changer for many of our families. When we looked at the data, kids who were in those pods achieved larger academic gains than their peers who were not. Some even progressed faster than they did before the pandemic.

I understand you’re using an AI system that listens to kids’ reading and reports back to teachers. What other innovations are you able to bring to the table?

We are constantly driven by the question: “What do families, students, and teachers need right now, today?” We are always asking ourselves this question and we push ourselves to remain open-minded about where the answers might lead us. Over the course of the past few years, this has certainly included expanding our online options and microschools, but it’s also included innovations that aren’t necessarily connected to technology.

For example, since the pandemic taught us that learning can happen anywhere, we’ve made investments in more experiential learning for our students. Partnering with Capital Experience Lab at Friendship Blow Pierce Academy has made the entire city part of our students’ learning journey. We’ve also developed a career coaching program for students to help them prepare for the future and discover career paths they never knew existed. In addition to their teachers and peers, our students are also learning from members of their community.

Friendship Charter Schools CEO Patricia Brantley said the small network is expanding its virtual options at the request of families. (Courtesy of Friendship Charter Schools)

Friendship Charter Schools CEO Patricia Brantley said the small network is expanding its virtual options at the request of families. (Courtesy of Friendship Charter Schools)

During the pandemic, we heard so much about how online learning was problematic. Yet your work suggests there’s huge interest from families. What does the conventional wisdom miss about online learning in 2023?

The first thing that’s missed is the idea that you can paint family and student needs with a broad brush. Does online learning work for everyone? Certainly not. But for those families and students who gravitate towards online learning, it can be a game changer. The pandemic forced all of us to adopt online learning, so of course there were going to be plenty of situations where that wasn’t the ideal learning environment. Now that we can integrate choice into the equation, you start to see that those families and students who opt in to this kind of learning are usually the ones who have great success with it. The idea here is that families need to be empowered to choose the best learning environment for them and we need to be prepared with diverse options to meet their needs.

“Does online learning work for everyone? Certainly not. But for those families and students who gravitate towards online learning, it can be a game changer.”

Patricia Brantley

The other thing that was missed in the urgency created by the pandemic is that you can’t lose human relationships in the shift to online learning. Despite what some may think, a high-quality online learning environment is still centered on people and relationships, not technology. If you leverage technology — and the flexibility it affords — to allow the student-teacher relationship to thrive, that’s when you see the kind of success we’ve been able to achieve over time.

The 10 most innovative companies in education of 2023

The 10 most innovative companies in education of 2023

After the upheaval of the pandemic—and the sweeping experiment in online learning that it forced on schools—this year’s most innovative education companies are finding new, inventive ways to build on the explosive growth of online education. Companies like edX and Multiverse are focused on making tech bootcamps and apprenticeships more accessible to underrepresented communities, while InStride is creating customized workforce development initiatives alongside corporate partners such as Amazon. Purdue University is tackling the nationwide shortage of semiconductor engineers head-on, by creating a suite of dedicated degrees and partnering with executives from leading chip companies.

Other companies are looking to empower educators as they navigate a crowded landscape of ed tech solutions: LearnPlatform runs evaluations for schools and districts that are trying to evaluate the efficacy of their digital tools and now works directly with ed tech companies as well. TPT (formerly known as Teachers Pay Teachers) continues to be a resource for more than seven million educators across the world and is doubling down on content moderation to ensure quality and cultural competency in its teaching materials.

1. Purdue University

For training the next generation of semiconductor engineers

2. LearnPlatform

For making it cheaper and faster for edtech companies to prove their products work

As schools have adopted more and more edtech products during the pandemic, educators are looking for evidence that they actually work. LearnPlatform is helping administrators and districts do just that, by analyzing the efficacy of their edtech tools and conducting evaluations more quickly and at a lower price point. As of last year, LearnPlatform had run more than 1,200 evaluations for its school customers, who serve nearly 10 million students and teachers.

With the launch of its new evidence-as-a-service subscription program in February 2022, LearnPlatform is also enabling edtech companies to prove their products are effective—and that they comply with the requirements outlined by the Every Student Succeeds Act, which mandates that federal funding is used for “evidence-based services.” More than 60 companies now use LearnPlatform’s subscription service, including such popular edtech providers as Age of Learning and Varsity Tutors. In December 2022, LearnPlatform was acquired by Instructure, the $3.6 billion market-cap maker of digital learning and assessment systems.

Read more about LearnPlatform, honored as No. 38 on Fast Company’s list of the World’s 50 Most Innovative Companies of 2023.

3. edX

For making tech bootcamps low-cost and accessible to underserved communities outside of tech hubs

Originally a joint venture between Harvard and MIT to host online courses, edX grew to attract 45 million learners and was acquired by edtech giant 2U in 2021. 2U has largely bet the company’s future on the edX platform, investing heavily in edX tech bootcamps that run the gamut from web development to cybersecurity. In October 2022, edX partnered with Google Cloud to introduce a cloud-computing professional certificate. In December, it teamed up with UC Davis to offer one in search engine optimization.

In an effort to better reach underserved communities, edX also introduced the Access Partnerships program, which brings together local workforce organizations and educational institutions to offer those bootcamps for a nominal fee—or free of charge—and also provide financial support for wraparound services like childcare and transportation. After pilot programs with the University of Oregon and the University of Birmingham in the U.K., edX expanded in 2022 to eight additional states and Canada, with a focus on burgeoning tech hubs such as Denver, Orlando, Tulsa, and Utah’s Silicon Slopes region.

Access Partnerships have already shown signs of success: Graduates in Oregon secured jobs at Microsoft and Nike—with a majority of students finding jobs within 30 days—while the U.K. program saw high rates of enrollment from women and non-white students, who made up well over 40{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} of bootcamp participants. In the fourth quarter of 2022, 2U introduced more than 150 new edX courses from 57 distinct institutions, and the company credits edX with driving 37{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} of organic leads, lowering the company’s cost of acquiring new customers.

4. Babbel

For expanding its language-learning empire

Since getting its start in Berlin, the language-learning app Babbel has gone global, racking up 10 million paid subscriptions. In 2022, Babbel made significant inroads into the United States—selling more than 1 million subscriptions during Q1—while bolstering its app-based language lessons with new offerings, including live classes and B2B services. Babbel for Business, which has 1,000 corporate partners across the world, launched in the U.S. in 2022 and already counts companies like Airbnb and McDonald’s as clients.

In response to the war in Ukraine, Babbel created free language courses in Polish, German, and English for people who were displaced, along with resource guides to help refugees and hosts communicate. More than 400,000 Ukrainians are now learning a language through Babbel.

5. InStride

For enabling employers to invest in their workers

Since launching in 2019, InStride has served more than 57,000 employees through 2,300 workforce education programs designed alongside corporate partners and academic institutions. Employees who participate in InStride’s programs have a retention rate of 92{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} (compared with 63{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} for those who don’t), and they’re also three times as likely to be promoted. In 2022, InStride partnered with Amazon to create the Next Mile program, a $19 million investment from the tech giant that gives 275,000 eligible delivery partners—who are third-party contractors—the opportunity to participate in employer-sponsored upskilling programs. Other companies such as Labcorp have created programs that aim to help frontline workers move into more senior roles. Beyond its work with corporate partners, InStride has also introduced ancillary services like the Career Education Paths program, which maps out the courses and degrees that employees need to qualify for specific tech jobs.

6. One League

For democratizing access to a top business school

One League was founded by Umaimah Mendhro, a Harvard Business School alum who grew up in Pakistan and Saudi Arabia with limited access to formal education. Mendhro’s goal was to make a top business school education more accessible to people from different countries and underrepresented backgrounds. One League, a part-time digital MBA program inspired by Harvard Business School’s curriculum, was developed in partnership with Harvard, and many of its instructors previously taught there.

In 2022, One League launched with a 60-person group of fellows who received full scholarships. (The fellows hailed from 30 different countries and included refugees and first-generation college graduates.) One League has introduced tracks focused on data science as well as innovation and entrepreneurship with MIT and Stanford, respectively, for fellows who’ve completed its core MBA curriculum. The organization’s mentorship board includes more than 50 industry leaders from Harvard and other top institutions, to help graduates of the program establish a network and find work opportunities.

7. SchooLinks

For taking aim at the college and career readiness market

As a college and career-planning platform for students, SchooLinks is betting that it can improve upon existing solutions in the college readiness space. Over one million students are now using SchooLinks, along with 150 schools and districts, and a number of its clients have switched over from Naviance, the major player in the space. Alongside career exploration and internship listings, SchooLinks offers features such as virtual-reality campus tours and financial-aid calculators. For counselors, SchooLinks provides a suite of administrative tools to track applications and oversee course planning.

In 2022, SchooLinks introduced career exploration tools for elementary students, expanding on its use as a K–12 tool. Through its industry partner portal, the company is helping local businesses reach high school students to offer internships and other opportunities. SchooLinks also recently launched the Pulse program, which seeks to give counselors a more well-rounded view of their students by collecting social-emotional data across schools and districts.

8. Multiverse

For using salaried apprenticeships to give underrepresented tech workers a foot in the door

Multiverse is positioning its apprenticeships—which have placed more than 10,000 students in salaried tech roles at such companies as Cisco, Citi, and Verizon—as a proxy for a traditional college degree or workplace training (and a tuition-free one at that). The U.K.-based company, which was founded in 2016 by Euan Blair, entered the U.S. market in 2021 after a rebrand and now boasts a roster of more than 500 employers, who foot the bill for its services. (Even amid the pandemic and layoffs across the tech industry, Multiverse has seen its client base increase ninefold since 2020.) Nearly all Multiverse apprentices—more than 90{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf}—end up staying with their employers, and a majority of them identify as women or BIPOC.

In September 2022, Multiverse formalized a partnership with the OneTen coalition of Fortune 500 CEOs, committing to place thousands of Black workers without four-year degrees into apprenticeships at OneTen companies such as Cisco and Intermountain Health. The company is also reimagining how to assess and train prospective apprentices to make the application process more equitable, rather than relying solely on grades or other traditional criteria. With an additional $220 million in funding last year, Multiverse is expanding its footprint in the U.S., where the company already receives about 5,000 apprentice applications each quarter.

9. TPT

For helping teachers adapt to digital classrooms through peer-to-peer exchange

Since its humble origins as the brainchild of a New York City public school teacher, the online marketplace TPT (formerly Teachers Pay Teachers) has become a hub for millions of educators who rely on it to exchange—and monetize—their instructional content. Its user base of 7.5 million now includes 85{e4f787673fbda589a16c4acddca5ba6fa1cbf0bc0eb53f36e5f8309f6ee846cf} of teachers in the U.S. and educators across 170 countries. As downloads on TPT have crossed one billion, with teachers having earned a cumulative total in excess of $1.5 billion, the platform has faced challenges with quality control and plagiarism. To address those issues, in April 2022, TPT created the Content Moderation Advisory Board, a group of third-party experts who advise the company on diverse imagery, historical accuracy, and cultural competency in its teaching resources. As schools were forced to adapt to remote and hybrid models, TPT introduced Easel, a collection of interactive digital tools. The company added Easel into its subscription offering for schools in 2022. Since launching last year, Easel has been adopted by 1.4 million teachers and nearly 5 million students.

10. Disco

For giving industry experts an easy way to build live learning communities

Disco is courting creators and industry experts with a platform that makes it easy for them to build and monetize live online courses and foster community-based learning. Since launching in 2021, Disco has attracted such notable instructors as author Margaret Atwood and renowned strategic advisor and author Roger Martin, whose course had been on pace last fall to generate seven-figure revenue in 2022. In March 2022, Disco raised a $15 million series A round led by edtech investor GSV Ventures. A key differentiating aspect of Disco is that it serves not only individuals but also communities that want to take advantage of Disco’s tools to run their own online academies. Examples include the design portfolio platform Dribbble, the entrepreneurial incubator On Deck, and the battery sciences–focused BatteryMBA. In keeping with its mission, Disco is investing in its own live learning community, DiscoU, and an accelerator program to help its creators most effectively use the platform.