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GeoGebra was created by Markus Hohenwarter in 2001/2002 as part of his master's thesis in mathematics education and computer science at the University of Salzburg in Austria. Supported by a DOC scholarship from the Austrian Academy of Sciences he was able to continue the development of the software as part of his PhD project in mathematics education. During that time, GeoGebra won several international awards, including the European and German educational software awards, and was translated by math instructors and teachers all over the world to more than 25 languages.

Since 2006 GeoGebra is supported by the Austrian Ministry of Education to maintain the free availability of the software for mathematics education at schools and universities. In July 2006, GeoGebra found its way to the US, where its development continues at Florida Atlantic University in the NSF project Standard Mapped Graduate Education and Mentoring.

GeoGebra is a Dynamic Mathematics Software (DMS) for teaching and learning mathematics from middle school through college level. It is as easy to use as Dynamic Geometry Software (DGS) but also provides basic features of Computer Algebra Systems (CAS) to bridge some gaps between geometry, algebra and calculus.

GeoGebra was created to help students gain a better understanding of mathematics. You can use it for active and problem-oriented teaching, it fosters mathematical experiments and discoveries both in classroom and at home.

Geogebra Help
Manual https://wiki.geogebra.org/en/Manual

Tutorials

https://wiki.geogebra.org/en/Tutorials
https://www.geogebra.org/m/DmVNbn2V

http://webspace.ship.edu/msrenault/tutorial/index.html

Blog https://blog.geogebra.org/

Materials https://www.geogebra.org/materials/

YouTube https://www.youtube.com/user/GeoGebraChannel

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AZED.gov. (2009). Standards: Educational Technology.  Retrieved from https://cms.azed.gov/home/GetDocumentFile?id=56ccd13baadebe1e24c20737

Hohenwarter, M. & Preiner, J. (2007a). What is GeoGebra. The Journal of Online Mathematics and Its Applications, 7. Retrieved from https://www.maa.org/external_archive/joma/Volume7/Hohenwarter/About.html

Hohenwarter, M. & Preiner, J. (2007b). What is GeoGebra. The Journal of Online Mathematics and Its Applications, 7. Retrieved from https://www.maa.org/external_archive/joma/Volume7/Hohenwarter/History.html
ISTE. (2017). Preparing students for jobs that don't exist. Retrieved from https://www.iste.org/explore/articledetail?articleid=1002
Keeler, A. & Herrington, D. (2017). Teaching math with Google apps: 20 G suite activities. San Diego: Dave Burgess Consulting, Inc.

McGonigal, J. (2010). Gaming can make a better world. TED. Retrieved from https://www.ted.com/talks/jane_mcgonigal_gaming_can_make_a_better_world?language=en
NCTM. (2000). Principals and Standards: Executive Summary. Retrieved from https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf
Ritter, K. (2010). A constructive learning team model for secondary mathematics teachers. Published doctoral study, Walden University, Minneapolis.

Schilling, D. R. (2013). Knowledge doubling every 12 months, soon to be every 12 hours. Retrieved from http://www.industrytap.com/knowledge-doubling-every-12-months-soon-to-be-every-12-hours/3950
Willis, J. (2017). Busting math myths to create math-positive attitudes. Retrieved from https://npjscilearncommunity.nature.com/users/20252-judy-willis/posts/20852-busting-math-myths-to-create-math-positive-attitudes
Wolfram, C. (2010). Teaching kids real math with computers. [Video file]. Retrieved from https://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers

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These are some of my favorite sites. Some are utilities. Some are sites for teachers. Most are sites for students. They are in no particular order.

www.desmos.com

www.geogebra.com

www.symbolab.com

www.mathisfun.com

https://www.ck12.org

http://www.bluebit.gr/matrix-calculator/

http://matrix.reshish.com/

www.coolmath.com

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Desmos was created by Eli Luberoff. Eli began his programming life on his TI-83 graphing calculator in elementary school, culminating with a working version of Monopoly which was destroyed when he removed the backup battery by accident. Hebegan working on the software that would become Desmos.com during a year-long hiatus from Yale University in 2007, returning to graduate summa cum laude with degrees in Math and Physics in 2009. Eli was also selected by Bloomberg Businessweek as one of the top 25 entrepreneurs under 25 in 2011

Desmos's self-proclaimed "best-in-class HTML5 Desmos graphing calculator" debuted in 2011 at TechCrunch's Disrupt New Your conference. Now, millions of students around the world use Desmos for free, including students who are blind or visually-impaired. Desmos partners with educational software companies who have embedded the calculator in digital curricula and on digital assessments (including AzMERIT https://www.desmos.com/testing/arizona) .

Desmos' goal is that students spend less time worrying about technology and more time thinking about math. They have built hundreds of digital activities, covering grades 6-12 and expanding quickly to other areas of math. Those activities take advantage of everything that makes computers special. They invite students to create mathematical ideas, rather than just consuming them. They encourage students to share their creations with each other, rather than with a grading algorithm. Desmos created the Activity Builder and Computation Layer to help teachers make personalized activities for their students.

Desmos Help
Learn Desmos http://learn.desmos.com/
Teacher site https://teacher.desmos.com/
Help Center https://support.desmos.com/hc/en-us/categories/201155956-teacher-desmos-com
Blog http://blog.desmos.com/
YouTube https://www.youtube.com/channel/UC_IR-dUP9trF4W8LS0_1EnA
Support https://support.desmos.com/hc/en-us

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Symbolab was developed by EqsQuest Ltd in 2011. Eqsquest is an Israeli based startup that was created with the goal of making scientific content universally accessible by expanding the searchable data space on to scientific notations, expressions, equations and formulas. The company was founded by Michal Avny, CEO, former head of AOL Relegence, Adam Arnon, chief scientist, and Lev alyshayev, CTO. On the advisory board is Professor Erez Etzion from the Physics department at Tel Aviv University , member and advisor of the Search & Discovery board of CERN. EqsQuest was founded in 2011, the company is privately held.

Symbolab is an advanced math education tool. It allows users to learn, practice and discover math topics using mathematical symbols and scientific notations as well as text. Symbolab provides automated step by step solutions to algebraic, trigonometric and calculus topics covering from middle school through college.

Symbolab offers a wealth of smart calculators including: equations, simultaneous equations, inequalities, integrals, derivatives, limits , tangent line, trigonometric equations, functions and more. The stated goal of the site is to make scientific content universally accessible by expanding the searchable data space onto scientific notations, expressions, equations and formulas. This is done by applying proprietary machine learning algorithms in order to understand the meaning and context of the queries. Symbolab strives to make math simpler.

Symbolab Help
Help Center https://www.symbolab.com/help
Support https://www.symbolab.com/user#management
Blog http://blog.symbolab.com/
YouTube https://www.youtube.com/channel/UC4BvILtjjpkcZuZ4nBkkmZg
What's New https://www.symbolab.com/whats-new

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Constructive Learning Team Model for Secondary Mathematics Teachers (Ritter, 2010).

According to employers and administrators at post-secondary institutions, high school students graduate with  deficiencies in these necessary skills: (a) reading and writing, (b) thinking and communicating, (c) forming logical arguments, (d) formulating and testing conclusions, (e) performing mathematical operations, (f) analyzing complex situations, (g) learning independently and working in teams, and (h) utilizing technology.

The constructive learning team model for secondary mathematics teachers (CLTM) was created to provide students with learning opportunities and experiences that address the aforementioned deficiencies.

Technology in the Classroom--SMILE 2016

Students who use technology demonstrate increased math performance, more so at the Middle and High School levels.

Neurologists have determined that students need to learn multiply ways to do math. Multi-sensory learning and interdisciplinary approaches. This creates the most neural pathways in short and long term memory. More use thickens those pathways; prevents pruning.

Students have 20 minutes to move from working memory to long term memory through practice. Technology can provide experiential learning to strengthen pathways. Technology allows students to perform more applied problems, more complex problems, more real world “messy” problems.

On an average school day, we collectively use 106 lifetimes by hand calculating. Students can do more problems and become more fluent when technology performs calculations.

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Knowledge Doubling Every 12 Months, Soon to be Every 12 Hours (Schilling, 2013)

http://www.industrytap.com/knowledge-doubling-every-12-months-soon-to-be-every-12-hours/3950

Buckminster Fuller created the “Knowledge Doubling Curve”; he noticed that until 1900 human knowledge doubled approximately every century.

By the end of World War II knowledge was doubling every 25 years.

Today things are not as simple as different types of knowledge have different rates of growth. For example, nanotechnology knowledge is doubling every two years and clinical knowledge every 18 months. But on average human knowledge is doubling every 13 months.

According to IBM, the build out of  the “internet of things” will lead to the doubling of knowledge every 12 hours.

Preparing Students for Jobs that Don't Exist (ISTE, 2017)

https://www.iste.org/explore/articledetail?articleid=1002

The massive shifts in technology and globalization that are expected to wreak havoc on the workplace have already begun. In many industries and countries, some of the most in-demand jobs didn’t even exist five or 10 years ago — and the pace of change will only accelerate.

“As whole industries adjust and new ones are born, many occupations will undergo a fundamental transformation,” says the World Economic Forum in its 2016 report, The Future of Jobs. “Together, technological, socioeconomic, geopolitical and demographic developments and the interactions between them will generate new categories of jobs and occupations while partly or wholly displacing others.”

The bottom line is that there’s no way to prepare students for specific careers when we can’t even fathom what those might be. Even now, nearly half of what students learn in their first year of technical school is outdated by the time they graduate. Instead, the key to molding job-ready graduates is to teach students how to live — and learn — at the intersections.

“The most important skill is a meta-skill: the ability to adapt to changes,” says Calton Pu, professor at the Georgia Institute of Technology. “As the rate of technological innovation intensifies, the workforce of the future will need to adapt to new technology and new markets. The people who can adapt the best (and fastest) will win.”

This means students will need to become lifelong learners, and it’s up to educators to ignite their curiosity while teaching them to explore the crossroads between different subjects and disciplines.

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Busting math myths to create math-positive attitudes

(Willis, J., 2017) https://npjscilearncommunity.nature.com/users/20252-judy-willis/posts/20852-busting-math-myths-to-create-math-positive-attitudes

Math negativity often starts young, and unchecked, it builds up. Math stress and low self-expectations can come from math stereotype beliefs, parental math negativity, frequent failure to understand math concepts, or fear of making mistakes. Many early math learning is rote memorization and children become discouraged when they mistakenly believe that speed and one right answer measure math intelligence and potential.

Joy and enthusiasm are absolutely essential for learning to happen – literally, scientifically, as a matter of fact and research. Attentive focus and sustained effort are limited brain commodities. In the stress state, feelings of anxiety, confusion, and mistake fear, leave less mental effort available for cognition and taking on challenges.

Consequences of math negativity may include low participation, low challenge tolerance, falling further behind, behavior problems, and avoiding the advanced math classes needed for success in many careers after high school and college.

Teaching Math with Google Apps (Keeler and Herrington, 2018)

We are in the twenty-first century, but visitors to many math classrooms could be forgiven for thinking they had stepped back in time and walked in the Victorian era. Student often spend a lot of their mathematics classroom time watching a teacher work on mathematics, then trying to follow their steps.

We know from new brain evidence that our brains want to think visually about mathematics. When we work on mathematics, even an abstract calculation, five brain areas are involved and two of them are visual pathways. Increased mathematical understanding comes with increased communication between different areas of the brain.

We don't know what mathematical students will need in their future lives; technology is changing at such a fast pace that most of what the mathematics students are learning in school now will be obsolete when they enter the workplace.  Employers will not ever need students to calculate, as we have technological tools that can do this more effectively than any human, but they will need students to reason, to think quantitatively, and to model with mathematics.

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Teaching Kids Real Math with Computers (Wolfram, 2010)
https://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers

From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it?

Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.

NCTM and AZED.gov
https://cms.azed.gov/home/GetDocumentFile?id=56ccd13baadebe1e24c20737

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student's learning. (NCTM, 2000)

https://www.nctm.org/uploadedFiles/Standards_and_Positions/PSSM_ExecutiveSummary.pdf

The use of technology is altering the way that teachers are teaching and students are learning. Arizona students must have regular opportunities to use these tools to develop skills that encourage creativity and innovation, communication and collaboration, research and information fluency, critical thinking, problem solving and decision making, digital citizenship, and personal productivity in the classroom and in daily life.  (AZED.gov, 2009)

Jane McGonigal
https://www.ted.com/talks/jane_mcgonigal_gaming_can_make_a_better_world?language=en

Games like World of Warcraft give players the means to save worlds, and incentive to learn the habits of heroes. What if we could harness this gamer power to solve real-world problems?

In the best-designed games, our human experience is optimized: We have important work to do, we're surrounded by potential collaborators, and we learn quickly and in a low-risk environment. (McGonigal, 2010)

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Scroll left to right and also down to view all content.

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www.analyzemath.com

www.purplemath.com

http://www.wolframalpha.com

www.sosmath.com

http://mathforum.org/dr.math/

http://tutorial.math.lamar.edu/

http://www.amathsdictionaryforkids.com/

http://nlvm.usu.edu/en/nav/vlibrary.html (note this uses Java so use IE browser)

http://www.sfu.ca/~jtmulhol/calculus-applets/html/appletsforcalculus.html

https://data.world/

http://www.math-aids.com/

https://www.kutasoftware.com

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https://app.twitch.tv/download

https://discordapp.com/

https://phet.colorado.edu/en/simulations/category/physics

https://www.thatquiz.org/

http://www.onlineconversion.com/

http://wheeldecide.com/

https://kahoot.com/

http://www.socscistatistics.com/

www.dragonbox.com

https://triseum.com/variant-limits/

www.superbetter.com

www.openstax.org

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www.myopenmath.com

www.xyzhomework.com

www.mathantics.com

www.wootmath.com/

www.roomrecess.com

www.mathbits.com

www.toytheater.com

www.classcraft.com

www.mathgoodies.com

www.teachertube.com

www.kudasoftware.com

www.teacher2teacher.education