###### September 10, 2023

### Put Your Mind To It

### How The Use of Mindfulness Can Benefit Math Students

Mindfulness encapsulates an overall state of being. Generally, it is the human capacity to be conscientious of our existence, more specifically the emotional and mental sensations we experience. This cultivates a varying amount of different skills; for instance, someone who practices mindfulness is present in the moment, intensely sensing their feelings, being reflective, and many more intuitive behaviors.

This is a specific kind of meditation many people practice. However, mindfulness in itself is a quality whereas meditation is an action. You can acquire mindfulness THROUGH meditation; all in all, the two can exist independently or together.

Having a moment-by-moment awareness with a more nurturing approach is incrementally beneficial. Rather than focusing on the future or past to gain a sense of control over your reality, practicing mindfulness relieves you of stress that your focus is entirely invested in the PRESENT. Reducing that anticipatory rumination will alleviate feelings of frustration, stress, anger, and even helplessness. Mindfulness is also especially helpful to increase metacognitive awareness, or the awareness for how you think.

Why does mindfulness matter in the first place? Because it’s an avenue one can take to overall improve their mental and/or emotional health. Mindfulness bleeds into all sorts of life experiences, like interpersonal relationships. Aside from the external benefits, mindfulness can overall better one’s relationship or perception of themselves.

There have been studies and discussions about the physical benefits of mindfulness as well, but the primary influence is within the conscious self.

**How does Mindfulness help with Math? **

By learning to address mental or emotional frustrations, you’re establishing a safe space to grow your perspective. Actively practicing mindfulness helps you to create a growth mindset, which can be helpful in times of challenge.

Due to math’s more dense and logical functionality, it’s one of those disciplines that challenges a majority of people in MANY ways. Mindfulness, especially when fused with math, can strengthen divergent thinking skills, patience, and improve many life skills.

When being faced with an obstacle, for example a challenging equation, mindfulness can be used to navigate the challenge with a more hopeful approach. If you were to fail or get the math equation wrong, you can still utilize mindfulness by removing yourself from the stressful environment, gaining clarity, then returning with a newfound approach that may attack the problem correctly (maybe even more efficiently).

Noticing the reactions you experience when partaking in mathematics can guide you to find a new attitude better suited for the task. Identifying those feelings will also pave the way to cultivate a more thoughtful, intentional response!

Younger children with less emotional regulation may find it difficult to master mindfulness during math on their own. Don’t worry, familiarizing them with the process of mindfulness can be introduced in AND out of the classroom. Implementing mindfulness at an early age can prove to be expediently helpful.

If you are a teacher or educator looking to provide a supportive environment for optimal learning, there are many ways to incorporate mindfulness! First and foremost, encourage the student(s) to be fully present and focused on what’s currently occurring! To prepare students for an engaging experience, instruct and/or guide them to calm their bodies and minds for the upcoming educational lesson.

Can you fuse mindfulness with math? ABSOLUTELY. There are a few different methods that can be integrated into a young mind’s lifestyle, whether it be during math time at school or when they experience a stressful situation at home.

**3 Practices That Blend Mindfulness With Math**

##### Count Your Breathing:

There are LOTS of specialized kinds of breathing able to sound the physiological sensations of stress or anxiety. There’s deep breathing, belly breathing, box breathing… you get the idea. Regardless of what KIND of breathing is being used, counting is a great way to control respiration!

Instruct the student or class to get comfortable in their seat(s). Count an inhale for four counts, have them hold it for another four counts, then fully exhale for the final four counts. The purpose of the counting is to bring attention to this typically involuntary action. Becoming more aware of the flow of oxygen in and out of the body will instantaneously calm the nervous system, which means the students will feel more relaxed and present for their lesson.

##### Nourish The Mind AND Body:

Cooking has proven to be a fun yet engaging task that incorporates various math techniques! The human body needs to be nourished with yummy, wholesome food to function at its best, therefore this is an exciting yet immersive way to bring a child back into their body and enjoy caring for themselves. Try including the child in fun cooking exercises that get them excited to feed their bodies (and minds).

Some fun ways to mindfully practice math is to have a child count their pieces of snacks, measure ingredients for their favorite food, time the cooking process of their highly anticipated treat, and so much more!

##### Time to Shake It Out:

Kids feel so pent up and sometimes frustrated when they cannot exert their energy in the classroom, so physical movement may help them out!

Aside from recess at school, take a few minutes at different times during school to allow children to move and wiggle their bodies. Encourage them to (safely) shake out their frustration, attune to their bodily sensations, and wiggle away any negative feelings. This can be used as a good transition or break between subjects, lessons, and used before or after a long lesson!

###### September 3, 2023

### What Makes A GREAT Math Tutor?

**What are the qualities & skills to look for when searching for an effective math tutor for your student?**

As many of us know, every student is different when it comes to learning. It’s no secret that not every student can retain or learn math easily and enjoyably. That’s quite alright! Unfortunately, it’s still something they must encounter throughout their schooling. What’s a kid to do?

To minimize the challenges that math presents, it’s a great idea to seek a potential resource outside of the child’s traditional classroom. There are various tutors available, both in-person and virtually, able to teach math in new or different ways than conventional school teachers. Not only are they outside their typical learning environment, but it’s a much more individualized and intimate setting that will give the child the attention they need to tackle their math struggles.

What should you exactly look for in a tutor? An effective and experienced tutor will encompass a wide array of useful skills and qualities to establish a worthwhile experience for the student.

Below are just a handful (of the ever-expanding) qualities of a GREAT math tutor.

**Qualities + Skills Of A Great Math Tutor**

**Great, But Growing, Knowledge of Math**: It’s important to give a young student a tutor that knows what they’re teaching. Having a prominent amount of mathematical knowledge is one of the most fundamental traits when looking for a good tutor. Not only should they have a foundational knowledge of the subject, but they should be open to expanding their perspective as math evolves with the times.

**Humility**: A humble, grounded tutor will provide an environment for your students that’s in THEIR best interest. The student is there to receive encouraging guidance on how to tackle math, not to boost the ego of the tutor. That’s why a great tutor should recognize their skills as worthwhile and useful, but utilize them for the good of others!

**Ability to Individualize Strategies for ALL Students**: Not every student is the same, especially when it comes to HOW they retain dense or difficult knowledge. Math, although very logical and quantitative, cannot be taught to everybody the same way. An experienced math tutor should take the time and care to assess the individual learning styles of every student they tutor to best plan their approach to teaching math at hand.

**Accountability**: There is a certain level of responsibility a great tutor must be able to take on. They have a wide assortment of students to educate, a schedule to maintain & update, and even families to interact with to communicate student progress. Accepting this role with an ethical and honest attitude ensures they will be able to address the unique circumstances of each tutoring relationship in a way it wholly deserves.

**Enthusiasm for Learning + Growing Math Skills**: How can you expect a young child to not get excited to learn about math if the tutor can’t be? Showing up to the tutoring session with a passion will motivate the student to TRY; the contagiousness of the enthusiasm may even get them excited to learn. An excellent math tutor will attack their job with fervor to help in any way they can, and even be excited to learn more about math themselves!

**Flexibility**: There will be times when a last-minute cancellation or rescheduling occurs, or maybe you’re a virtual tutor tackling technical obstacles. Regardless of the challenge, a great math tutor will maintain a flexible yet understanding mindset! The accessibility of a student will vary, so the tutor themselves should take as much responsibility as they can to do their part to ensure the students receive the resources they need.

**Professionalism**: In reality, the tutor isn’t just interacting with the student! There are probably guardians, parents, even fellow educators who want to be kept in the loop on the student’s progress; that can be overwhelming! An experienced tutor knows that providing an approachable, personable, and well-composed attitude so the dynamic remains beneficial and positive!

**Patience AND Positivity**: Learning is a marathon, not a sprint. Students will only learn as far as their motivation, focus, and mood can allow in various sessions. That’s why an exceptional math tutor will be patient yet challenge the student within certain boundaries. Not only that but maintaining positivity that the student will succeed in due time will rub off on them; children tend to energetically absorb what’s occurring around them. If you want the student to have a positive attitude, lead by example!

**Able to TEACH, not just lecture**: To fully retain or understand a mathematical concept, a student may need an in-depth explanation about a specific equation or concept. More likely than not, they won’t comprehend the math well if they’re just lectured to. It’s up to the math tutor to engage in discourse that fully encompasses the use, function, and steps of a math problem. Additionally, not many people learn effectively by just being talked to; they need various forms of education for their brain to absorb what’s being taught.

**Motivation**: Evidently, there will be sessions and/or weeks where the students will just not have the same determination to do the work they usually do. Despite the challenges, especially an energetic ebb and flow, a wonderful math tutor will persevere by brainstorming new yet engaging ways to teach; they will also know when to dial back on the studying to energetically match the student in the session. As long as the tutor has the drive to do the best they can to teach to the specific individual, it’ll be worthwhile.

**Reliability + Preparation**: Being a good math tutor doesn’t just mean showing up. It’s about being able to facilitate a productive session about the content the student needs to learn. That comes with showing up consistently, putting in your all, and most importantly coming PREPARED. A good math tutor will prepare for a session by outlining the lesson and its concepts whilst providing lots of exercises and reviews to effectively conceptualize the lesson.

###### August 27, 2023

### Even in Ancient Times, Women Were Breaking Barriers

### How the first recorded female mathematician Hypatia paved way for women in math and philosophy

**The Great Alexandria**

Many of us have been educated on humankind’s earliest civilizations. One of the more infamous yet mysterious communities we have collected knowledge on was Alexandria. It was a port city located in present-day northern Egypt, and one of the greatest Mediterranean cities to exist in our recorded history.

It was founded in approximately 331 BC by Alexander the Great, a fierce Macedonian ruler and military genius. Alexander left to pursue a takeover of nearby Persia, so Alexandria was left to be ruled by the Ptolemaic Dynasty for nearly three centuries; a famous ruler within this dynasty includes queen Cleopatra VII. Alexandria was known as the greatest city to ever exist and would later become a major hotspot for early Christianity, a center for religious turmoil from clashes between faiths.

A highly regarded figure that emerged from this time was true icon Hypatia.

**Who was Hypatia?**

Hypatia (355-415 AD) was one of the first well known feminine figures in philosophy, astronomy, and math.

“First” is a loosely applicable term in this discussion since the TRUE first female mathematician was Pandrosion, but Hypatia was the first to be well recorded and depict historical accuracy about one of the world’s most prolific civilizations.

She lived during the time of ancient Alexandria, but existed amidst an incredibly disorderly and violent era in the empire’s existence. Due to the turbulent chain of events that occurred during and after her time, it greatly accentuates Hypatia’s success to defy traditional odds inflicted upon Alexandrian women.

She was absolutely set up for greatness; her father was a well known mathematician, Theon of Alexandria (335-405 AD). It was most likely that she was taught and instructed by her father, which shows through the similarities in their separate works. Theon was most known for aiding in the preservation of Euclid’s *Elements,* a thirteen book collection encapsulating mathematical theories and proofs. Much of his work molded her own, as she took great effort in preserving the historical intellect of Greek heritage, especially in the fields of math and philosophy.

A well-loved Pagan, Hypatia was quite tolerant towards those of Christian faith.This is incredibly important being that she existed in a time where the Christians, Jews, and Pagans were all experiencing conflict with one another. Her well-composed demeanor helped establish a reputable relationship with the elite upper class; this dynamic even bled into responsibilities she held later in her life.

Hypatia’s realms of expertise were heavily male dominant fields of intellect, work, and discourse. Therefore, a woman entering that space with confident and productive contributions challenged the conventionality of Alexandria’s gender roles and dynamics.

**What did she DO exactly?**

Hypatia was credited with writing commentaries for various texts. She constructed a commentary focusing on Diophantus’ *Arithmetica*. This is a partially survived thirteen volume text harping on the development of number theory through equations. Her other prominent commentary revolved around Apollonius of Perga’s *Conics*. *Conics *is a dissertation about conic sections and their influence on modern and ancient analytical geometry.

Her commentaries greatly exemplified her high level of intelligence and understanding of math as well as philosophy. In fact, she was so well-versed that she became a very well-known

teacher at the Neoplatonic school of Alexandria; she taught philosophy and astronomy. This school grounded their particular education in the teachings of infamous figures Plato and Aristotle. It catered largely to both Christian and Pagan students, and many who were of the Pagan faith became loyal pupils and friends of Hypatia.

Aside from her educational endeavors, Hypatia also spent time constructing various tools for use in her fields, such as the hydrometer and astrolabes. Even though she didn’t invent them, she showed great familiarity with their functionality.

Hypatia’s great relationships with her pupils influenced the effects of historical events on her life. The religious divide in Alexandria was very tumultuous and chaotic, and possibly led to the burning of the Great Library of Alexandria. There were books from the Library believed to be kept in the Serapeum, a temple of the Greco-Roman god Serapis, led by Saint Theophilus of Alexandria. That temple was eventually destroyed as well due to its ties to the Great Library.

Coincidentally, Theophilus was associated with one of Hypatia’s devoted pupils, Synesius. These mutual ties temporarily permitted Hypatia to continue her work until her death. Once the theologian St. Cyril ascended into his power, he continued his uncle Theophilus’s work by enabling the violence against non-Christian civilians. Hypatia was gruesomely murdered by a group of fanatical Christians; Hypatia was a well-known Pagan and fell victim to their rioting.

Despite her demise, Hypatia remains a powerful feminist icon and influential mathematician. She represented great resilience, female empowerment and a perseverance to break the mold that’s been repeatedly inflicted upon feminine figures in the past and present.

###### August 20, 2023

### Ancient Greece – Since The Beginning

**How ancient Greece birthed an entire foundation of thought for modern day technology & intellect **

Origins of Mathematical Knowledge

A multitude of classical and archaic communities paved the way for modern life and thought. Civilizations such as Rome, China, India, Egypt, Mesopotamia, Persia, and many more were able to start an array of practices- from SCRATCH. They were not privileged with many of the resources we have today, so they relied on futuristic thought and hard labor to create a life they were happy with (and proud of).

One of the fundamental empires is Greece, a civilization rich with philosophical thought, groundbreaking strategy, and a jubilant social nature. They provided a historical miscellany of concepts and contraptions, which lays ground for many of the practical modalities we modernized in order to build our own civilization. Humankind embodies many Greek contributions on an intellectual basis, and we don’t even know it!

There’s so much to dive into when exploring ancient Greek culture. Despite the ecosystem of knowledge they’ve nourished, there is a core contribution that initially planted the seed of their impact + influence on modern day thought.

**Major Contributions from Ancient Greece**

One of ancient Greece’s most influential contributions primarily involves the school of thought. Logic, philosophy, and academia was one of their strong suits, for many schools of thought were born and flourished. They all lay a foundation for other areas of thought to incubate. However, one of their greatest subjects of impact is mathematics.

Math is the backbone for many other areas of knowledge we’ve used such as Science, Astronomy, Architecture & Engineering, Warfare, even Agriculture. The Greeks needed to concoct a logical methodology to formulate tools, tricks, and processes that would build their empire as efficiently as possible.

LONG before modern technology, math was a slightly more laborious process. For instance, everything was written or through word of mouth; for instance, ancient civilizations kept charts and tables on clay tablets or papyrus scripts. And because the value of thought was so potent, the exchange was that much more impactful!

**Between 685-525 BCE, (before the common era), Egypt’s ports along the Nile river opened up to Greek trade**, breaking the barrier of interaction between them. With the migration of people & goods, both verbal and written communication acted as the vehicle to carry Egyptian ideas about math. That explains how and why much of Greek mathematics was adopted from the nearby civilization.

Egypt and their neighbors, like Mesopotamia and Ionia, had some of the finest math in the world. They utilized calculations for engineering purposes, to build structures for living and business such as the Great Pyramids or boats for trade & transportation. Unlike the others, the Greeks took these mathematical calculations to create practical applications for effective life skills.

Rigor was a major characteristic of Greek math. It was meticulous, exact, and at times super specific. They spent much of their effort contemplating deeper connotations behind the math they were working on. Even the word theorem evolved from the Greek word theoreo, which translates to “I contemplate”. Therefore, Greek math was intricately rooted in the association between mathematical review and analytical scrutiny.

**Here are some of the most common contributions ancient Greek math gave to modern and even Western thought:**

**Ratios of a Triangle**: Many of us have dabbled with the Pythagorean theorem, a tool proposed by one of ancient Greece’s most impactful mathematicians, Pythagoras. The 3:4:5 triangle was easily understood as a right triangle, but the Greeks were incredibly interested in the specificities of this abstract thought unlike their Egyptian benefactors.

Eventually, they expanded on it further by trying to calculate the longest side of the triangle (the hypotenuse) by calculating the similarity between the two smaller sides. This cracked open an intellectual revolution!

**Numerical System**: One of the most popular and widely-used tools the Greek created was their base system. By picking one core number, they formulated a number system for real-life usage that was easily divisible; this helped especially with fractions and proportions.

The ancient Greeks used the base number 60, which wasn’t as difficult to apply as we think. It’s a moderately divisible number with lots of other divisible factors, which made it a pretty flexible system to work with.

**Square Root**: This was an idea concocted a tad after the Pythagorean theorem swept civilization. With the new theorem begged a new question: if two sides of a right triangle are 1 unit, and the diagonal side equates to the square root of the two sides, what is it’s exact calculation?

After trying to find the square root of 2 and realizing it was irrational, this opened a world of questions regarding the square root of all numbers and what made them rational versus irrational.

**Geometry**: This is an entire discipline with math that works with the properties and relationships between lines, points, shapes, surfaces, and higher dimensional figures. With Greek architecture and engineering came the need for deep understanding of shapes and their dimensional properties.

Because it was a time of practicality, the Greeks were really using geometry as a logistical science to calculate land measurements. This was also a practice that originated with the Egyptian mathematical perspective; how do you think they built the Pyramids so beautifully?

**Proofs**: Known as one of the most tedious and difficult techniques to master, proofs are arguments based in inference and math logic to assure the answer to a problem is correct! Other theorems and math techniques can be applied to verify the validity of the proof, encouraging the practice of deductive reasoning with logic.

The first mathematical proof was credited to another Greek math icon, Thales of Miletus. He also proposed proofs that concerned ALL mathematical shapes and figures, not just the abstract ones! His contributions kickstarted the discussion of what the Universe was made of.

###### August 13, 2023

### Math Fun

**Have Your Fun, and Learn From It Too! — Why Games Can Make for a GREAT Option to Optimize Math Review**

Let’s Have Some FUN

To sharpen learning retention in kids, it’s highly advantageous to have their full attention. And it’s even more advantageous to express the learning review in a way that’s digestible yet productive.

This is especially applicable and prevalent in math education, a discipline that requires a lot of practice and logistical awareness for the functionality of the techniques being taught. And hey, that can be unrealistic when you’re constantly lecturing them. Talking AT the students about math, or whatever they’re learning, doesn’t fully communicate the knowledge they need in order to understand what they’re being told. And even when you work one-on-one, instilling a two way path of communication about math, it may feel like pulling teeth with some kids. Admittedly, it isn’t the most enthralling of subjects for some young minds, and their resistance shows.

Another concern regarding communicable math review is the style in which you provide it. When addressing a class collectively, you’re catering to all kinds of learning styles. This can mean you have a cultivation of visual, auditory, kinesthetic, and even audio-visual learners. And although they each have individualized methods of retaining information, it is your job as an educator (or guardian) to mold a comprehensive yet constructive way to deliver the knowledge you need to.

Imagine being able to provide your students a tool, modality, or resource that not only TEACHES them the math they need, but grabs their attention in a positive and engaging way. Wouldn’t that be just AWESOME?

**What’s the solution, you ask?** Certainly NOT dumping a heavy review on them with no direction or energetic buffer. Instead, a better approach may be to keep it lighter in deliverance!

It’s become increasingly popular to include more lighthearted, enjoyable math reviews in the classroom through games. Yep, that’s right- games! Board games, computer games, CARD GAMES… that enjoyable pastime we highly encourage kids to participate in. And because it receives a moderately positive response from kids, it’s a prime candidate for utilization in school!

Why are they so beneficial you ask? Well, the primary appeal of games is that they’re designed to be lightly competitive but enjoyable. Not only that, they’re also easy to grasp once you play a few times (at least kid-friendly games are). If you were to find a way to incorporate math into a widely-known game structure, you create a refreshing review that actually gets the students excited to try it!

And what students love most about games is the childlike creativity or fun! If you bring a recognizable character, storyline, even movie into your classroom and use it to communicate your teaching, the students may grasp it more attentively! They naturally gravitate towards things they find enjoyable.

**What games are best to use in a classroom?** Well, that’s entirely situational.

If you have a smaller class size, you can split the class evenly and do multiple rounds of a one-on-one style game. For the larger-sized classes, team games are always a great way to instill community, teamwork, accountability, and enthusiasm! Students always receive teams well because they don’t want to feel isolated in their learning, and a few minds are always better than just one.

Ask yourself about these important factors when creating math review games:

Is this a game that is familiar to my students, or at least digestible in terms of difficulty?

If I give them the clear-cut directions and allow a few practice rounds, will they be able to effectively retain the knowledge while participating in the game?

Does this game have any offensive, discriminatory, or inappopriate content originally included that I can take out for my purposes?

Does this game ensure I can implement the exact math I’m teaching relatively easily?

What are some clear cut boundaries I need to set with my students?

After careful consideration, outline a game that you believe will deliver what you’re aiming to.

And if you’re looking for some guidance, look no further…

**Games for Inspiration**

**Trivia/Jeopardy**: Split the class into a few medium sized teams and create trivia style questions about math. You can give them whiteboards or paper to work out the problem on the screen, all the while collaborating with their classmates. Whoever has the correct answer first wins whatever reward was assigned to the question! This also broadens their knowledge of the discipline overall. A popular electronic trivia game is Kahoot!

**What’s Missing**: Memory is such an integral skill in math, and it should be exercised to the best of its ability! Present an equation, or visual representation of a problem (this is a great game for geometry-based questions) and ask the students what step or factor is missing! This helps them increase awareness for problem solving as well as formula-based questions.

**True or False**: Present a math equation or world problem (bonus if it’s on your assessments) and give the students an answer. It’s up to them to work on the problem on their own and decide if the answer you originally gave them was the correct one or a false one. This is also a great opportunity to work through the problem as a class AFTER you tell them if it’s true or false; some students may get it wrong, so if you show them the mistakes or misconceptions they’ll retain it. And this also helps them create a growth mindset!

**Match the Equation**: Matching card games are super quick, easy, and fun! You can create a deck that splits into: problems vs. answers, formulas vs. what they’re meant for, shapes vs. dimensions (size, shape, sides, etc). This is a flexible game style that’s suitable for all ages!

###### August 6, 2023

### Watering Your Money Tree: The Money Mindset

**How Implementing Basic Math Skills Can Greatly Improve Your Money Mindset**

*A Different Kind of Green Energy*

Money is boundless energy proven quite influential to our current socioeconomic systems. Everything seems to come at a price, and drives much of how we contribute to the collective with work and life.

And yet, it’s able to be solved, deciphered, even managed with the use of common math. It’s no wonder why accounting, marketing, finance, and many more industries are booming- they utilize this core piece of our earliest education to structure it!

Let’s not be blind to the similarities; math and money are both numerical, logistical, and quantitative disciplines. If we didn’t have math to help us budget our personal finances or calculate economic relations, where would we be?

Which is one of the many MANY reasons why teaching math in a comprehensive way is super important. Money, and the mindset around money, has become a refreshingly popular topic of discussion these last few years. With a handful of economic crashes, loss of jobs, and the world in turmoil amidst a global pandemic, many people are coming to realize they’ve been perceiving their money all wrong.

**So, What Exactly IS a Money Mindset? **

And more importantly… WHERE does it come from?

A money mindset is your individualized collection of beliefs of money that fuel much of your attitude towards it. It forms long before you even begin to start handling your own finances, brewing inside the subconscious of your mind.

The sociologist Morris Massey theorized that there are three major periods of life in which life values, ideas, and perceptions are developed. There’s the Imprint period, Modeling period, and Socialization Period. Why is this important?

**Well, between ages zero to seven years of age (the Imprint period), the human brain heavily resembles a sponge that absorbs any information it encounters.** Much of your money mindset was developed there. You were exposed to others’ predisposed and existing money beliefs that were either expressed or inflicted upon you, especially by those who raised you.

While you may also acquire new or similar beliefs around money, the most profound influences on money occur during these years when your mind is most impressionable. And you may not even realize it, but you carry those impressions into your everyday monetary beliefs and behaviors. You subconsciously harbor an attachment style to your money, how you use it, and the emotions that arise; money is seen as a resource many use to take out their stress or success.

Essentially, the mindset you harbor and subsequently channel when making financial decisions like purchases and investments all have to do with your mindset around money itself. And you know what? It’s hard. Sometimes it can be brutal. It’s difficult to escape something that’s been conditioned in you since your earliest core memories- but you can alter them consciously to slowly assimilate or revitalize your entire view.

With the growth of knowledge through technology, it’s become significantly easier to be re-educated on how to manage your money. There are coaches, courses, media influencers, and so many more looking to enhance our financial consciousness. Because even though you live in a capitalist society with very clear-cut ideas about how money can be made and used, it may not always fit your values, needs, or background.

And even though how you use money is much more in your mind than in math, you can still incorporate mathematical skills and strategies in order to increase your awareness, and therefore your financial security.

**Bring On the Math**

On a fundamental level, using math can help you organize, plan, and allot for many different kinds of expenses! You can manage a business (if you’re an owner of one), save up for big life investments (car, house, college fund, etc.), put some money into stock, and even budget for a new item or experience you’ve been DYING to acquire.

Something critically important to remember about money is that it is an energy just as much as it is a resource. It is natural for it to come and go, and much of how you react or respond to these transactions will affect the ebb & flow of your financial wealth.

In terms of actual math skills, basic arithmetic such as addition, subtraction, multiplication, and division are practical starting methods. You can accumulate various answers for an assortment of situations; the use of arithmetic can help you calculate static or consistent numbers if you’re working with a steady income or payment.

Arithmetic is the more obvious and digestible math to use, but there are plenty of people who balance their finances with advanced strategies- and the help of technology. If you do not have access to such resources, then freshening up your mental math skills (and getting a calculator) is a great place to start.

If you’re beginning the journey to healing or bettering your money mindset, try keeping a money journal or spreadsheet (if you have access to a computer). This will be the place to record your daily and weekly expenses, which can help you craft your monthly budgets!

By keeping a detailed account of where your money goes and returns, it’ll increase your awareness. And when we broaden the scope of our awareness, we tend to feel more empowered and confident in taking aligned action.

###### July 30, 2023

### A Universe of Numbers

**How Math Greatly Affects our Daily Life and Development of Civilization**

Math has worked WONDERS for our daily lives. You may not personally enjoy the subject yourself, and that’s okay! However, it’s difficult to disregard just how influential math has become in modern society, and the development of civilization as a whole.

It’s deeply ingrained in everything we’ve built, negotiated, engineered, and modernized. It provides order in our lives and minimizes the chaos. Our statistics, logic, ethics, and deeply encoded practices all have math to thank. And whether we see it or not, math materializes into phenomena all around us.

**Math is a globally understood and utilized knowledge**, which opens us up to connecting in ways we typically couldn’t. When we encounter an opportunity to have an exchange of knowledge, we can only grow in our comprehension. That’s probably why so many of our biggest advancements came into fruition when a great discovery in math was made.

I mean, take a look at the ancient Egyptians… once they discovered how to apply their mathematical findings, the Great Pyramids came to be and, well, the rest is history.

Even when we aren’t in active math mode or solving something directly in front of us, it’s a skill we implement daily. It forges our cognitive, intellectual, and academic discipline- and yes, we use it in domestic situations as well! What do you think lays the foundation for things like cooking, telling time, even filling our homes with furniture?

What are the benefits of math in daily life? Oh, let us count some (of the infinite) ways…

**Daily Benefits of Math**

**Builds Mental Discipline**: It’s no secret that math is an incredibly rigorous topic to learn and master, which we’ve been exposed to from very young ages. The numbers, equations, formulas, proofs, measurements, shapes… they are all intricately designed with their unique set of rules and methods. When we are presented with a problem to solve or decipher, it’s on us and our discipline to consistently show up and remain engaged. In order to get the answers we need to understand the math, that involves discipline and perseverance to get it done.

**Can Help Build a Growth Mindset**: This is especially useful for young minds & students, since they don’t have as much emotional or mental regulation. Our brains naturally react to a roadblock in two ways: find another solution or give up. When math presses us with a similar kind of obstacle, it gives us the option to learn the technique effectively by trying an improved strategy or settle for the wrong answer. Encouraging younger students or those starting out in math to find a new means of solving the problem helps stretch and grow their brain by LEARNING from prior mistakes. If we don’t learn, how can we be expected to do better?

**Logical + Quantitative Reasoning**: These are two fundamental elements to developing an argument. Providing the logical explanation or function combined with quantitative approaches can establish necessary evidence to prove the validity! Combining these both will cultivate inductive, deductive, even statistical methods. When applied to math, this can aid in analyzing the deeper meanings that the math insinuates.

**A Language of Science + Technology**: Although Science and Technology are their own innovative fields, math helps to organize and communicate their information. When math is applied to technology, it can help people such as scientists and engineers create systemic and productive practices to transmit useful knowledge. It also helps specify what is necessary to construct the tools and advancements making our daily lives that much easier.

**Foundation for MANY fields**: Aside from the obvious, math lays a strong infrastructure for many other fields. For instance, math is utilized in cooking, architecture, politics, economics, accounting, finance, mass production, and so many more fields. Jobs in ALL of these fields most likely require a background in math, being that they all use different disciplines within math to find what they’re looking for.

**Paves Way for Invention**: Obviously humanity would not be where it is without math to help them modify their inventions. With the use of math (and even a growth mindset), we can find new ways to strengthen or improve an idea or physical creation. If you read early Greek works revolving around the understanding of the Universe, they resorted to math to support their philosophical discoveries.

**Helps Us Understand The Universe**: Yes, math pervades all forms of universal matter. Even quantifiable amounts of sub particles can alter the impact of a singular atom. Things such as sacred geometry, quantum physics, and mathematical structure that explains all things discoverable (and still not discovered) in our Universe.

**Encourages Critical Thinking**: When it comes to math, critical thinking implies there is a reasonable decision or judgment needed to be made to execute the problem. In other words, the person doing the math must make thought-out decisions given the information and mathematical criteria at hand.

###### July 23, 2023

### Introducing… Euclid!

**How the Contributions of One Alexandrian Mathematician Influenced the Course of Human Thought**

**What Started As A Thought…**

Soon blossomed into an entire movement of thought and education.

We’ve all been taught about ancient Greece as well as their intellectually rich culture. They birthed and molded so many foundational leaders of thought in realms such as math, philosophy, religion, even art and architecture.

One of the most contributors to the evolution of math is Euclid. Euclid was known and referred to as the “father” or “founder” of Geometry. Geometry is a very distinct field within mathematics responsible for explaining the relationships of planes and objects. We all start to integrate geometrical knowledge when we learn the properties of shapes, points, lines, and the connection between them all!

Euclid is the namesake of Euclidean geometry, which is the basis of plane geometry like his published works allude to. But we’ll get into that later!

**About Euclid**

What we know of Euclid derives from a summary of famous mathematicians contrived by Greek philosopher Proclus (410-485 CE). Very little detail is actually known about Euclid’s life, however, has been hypothesized and framed by key events: his birth, death, and prominent mathematical contributions.

Euclid was born approximately 325 BCE and hails from the great Alexandria, a prominent civilization in Egypt. It is believed he passed there as well about 265 BC.

He taught in Alexandria at the time of Ptolemy I Soter (367/366-283/282 BC), the Macedonian ruler of Egypt.

In the summary procured by Proclus, it describes Euclid stating:

Not much younger than these [pupils of Plato] is Euclid, who put together the “Elements”… for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry…

Euclid of Alexandria is typically mistook for Euclid of Megara, who lived 100 years before he was even born! And even though much of his existence remains in question, there is absolutely no doubt that he provided one of the most revolutionary pieces of work for math to evolve in the following 2000 years.

**Euclid’s Contributions + Euclidean Geometry**

What did Euclid ultimately contribute to math?

He wrote a collection of work known as the Elements. Euclid’s Elements is a compilation of postulates, proposals, and rules of geometry. There are five postulates introduced at the beginning of this collection, assuming the existence of points and lines and how they relate to one another.

**The five postulates state:**

– A straight line segment can be drawn to connect any two points.

– Any straight line segment can extend indefinitely in a straight line.

– Given any straight line segment, a circle can be drawn having the segment as a radius and one endpoint (of the segment) as the circle’s center.

– All right angles are congruent (equal).

– If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.

**
The fifth postulate defines what’s known as a parallel postulate**, and it has not been proven yet despite many attempts.

You’ll probably find many of these postulates as basic rules introduced to you when you learned what geometry was! Elements essentially highlights the fundamentals of Euclidean geometry, which is taught in secondary education.

There are thirteen books in total, highlighting definitions and propositions revolving around the theory of geometry, proportions, circles, number theory, geometric algebra, and solid figures. Euclid dives into great detail for each subject he accentuates with his writing to ensure the comprehension of how they all correlate to one another.

It’s one of the oldest surviving mathematical publications known to humankind, which is why it’s been carried into our prevalent education today.

**Why Is It Important?**

Subcategories of math such as geometry and number theory help us develop a wide array of applications. For instance, geometry helps us develop and understand spatial awareness as well as relationships. This helps us create modern structures that hold up, and it also helps us find shapes for functional inventions. Without the fundamental knowledge of circles, polygons, and solid shapes, we wouldn’t have half the stuff we use on a daily basis!

###### July 16, 2023

### Calling In Some Tutoring Help

**Here’s why YOU Should Consider a Tutor for That Extra Push **

**School Of Thought**

We all need support. There are times where we’ll need it more than usual, but needless to say community is an incredible resource. Support is a way to surrender to our vulnerability and seek a little comfort.

And when it comes to education, support is not just a resource but a NECESSITY.

Everybody is adept in different fields of knowledge, so stepping into areas of unknown can be quite frustrating. It’s especially uncomfortable for young kids, who get frustrated much easier when they don’t receive instant gratification (or understanding).

If they’re in traditional schooling, they’re probably learning multiple subjects at a time- and that can get overwhelming! It’s difficult to expect perfection in EVERY area they embark on, so what’s a kid to do?

That’s why it’s super important to consider any and all resources available to them! Outside of a regular classroom setting, there’s a multitude of ways to incorporate extra care to supplement education. One of the more personalized experiences is hiring or finding a tutor!

Tutors can explore ANY subject, from writing to science to math and even to test preparation. They’re especially useful for math education since so many kids are not naturally affluent in this dense discipline.

But what REALLY makes a tutor so enthralling? Oh, let us list the ways!

**Why Tutors Are Worthwhile**

Tutors are personable, malleable, and considerate people able to provide a refreshing perspective to a learning experience. They may bring new and even revolutionary approaches to comprehending the fundamentals or machinations of an educational area.

**What are the biggest benefits of hiring a tutor?** Here are some core benefits just to name a few!

**Provides an Intimate Experience**: Tutors not only provide a unique learning experience but it’s a direct exchange between an educator and student; that constitutes a nurturing atmosphere! You can find tutors that work one-on-one or in smaller group volumes, which can make the actual environment less distracting or intimidating! There are going to be private educators that will work with your needs or goals, and may even introduce new ideas to broaden your tool kit.

**Have An Individual Approach**: Every tutor is going to bring something different to the table. What’s so inspiring about tutors is their unique perspective and teaching styles! While traditional teachers & educators do the same- they do have to follow institutionalized rules and regulations. Tutors show up to their containers bringing a lifetime of experience, knowledge, OTHER resources, and more to cultivate a one-of-a-kind experience.

**Easily Accessible**: With the age of technology comes more and more ways to access what we need- especially amidst a global pandemic! One of the coolest things about seeking a tutor is the various platforms you can discover them on! Aside from the usual in-person options, you can find a virtual tutor as well! This goes to show how flexible and accommodating tutors can be, and it doesn’t limit you to a certain proximity! Tutors can be found anywhere and passionate about helping you achieve your desired outcomes.

**Primarily There to HELP You**: Although this is a full-time or part-time profession for these people, they’re all there to help YOU. Tutors are passionate about bringing new and refreshing ways to learn into someone’s space, which is what makes each and every encounter with them so amazing! Regardless of the amount of students they teach at a time or the subject at hand, the tutor is there to give that extra push of support and accountability you need to level up your learning!

**What To Consider**

Aside from ALL the benefits of hiring a tutor, there are a multitude of things for YOU to consider so you know what exactly to look for.

**Here are some powerful questions to help you get started:**

– What are you looking to learn more about, or master? This is going to help you niche the content demographic for your future educator.

– If you’re looking for someone else (i.e. a child you interact with or student you teach), what seems to be their biggest setback?

– What ACTUALLY needs to be broadened: the understanding of the content, or methods to better execute it? Some people have harder times understanding the functions of what they’re learning rather than the content itself.

– What are some qualities and characteristics you want to experience with your tutor?

– Are there any other learning accommodations you need to consider?

– Do you learn better in-person, virtually, or a mix?

– What kind of learner are you (visual, auditory, kinesthetic, audiovisual)?