Working with Strings in Python

It is somewhat difficult to define a string. In some ways, a string is text such as what is found in a book or even in this blog.  Strings are made up of characters such as letters and even symbols such as %#&@**. However, the computer does not use these characters but converts them to numbers for processing.

In this post, we will learn some of the basics of working with strings in Python. This post could go on forever in terms of what you can do with text so we will only address the following concepts

  • Finding individual characters
  • Modifying text

Finding Individual Characters

Finding individual characters in a string is simple. You simply need to type the variable name and after the name use brackets and put the number of the location of the character in the string. Below is an example

example="Educational Research Techniques"


As you can see, we created a variable called “example” the content of “example” is the string “Educational Research Techniques”. To access the first letter we use the “print” function, type the name of the variable and inside brackets put the letter 0 for the first position in the string. This gives us the letter E. Remeber that Python starts from the number 0 and not 1.

If you want to start from the end of the string and go backward you simply use negative numbers instead of positive as in the example below.

example="Educational Research Techniques"

You can also get a range of characters.

example="Educational Research Techniques"

The code above is telling python to take from position 0 to 4 but not including 5.

You can do even more creative things such as pick characters from different spots to create new words

example="Educational Research Techniques"
print(example[0:2] + example[20:25])
Ed Tech

Modifying Strings

It is also possible to modify the text in the string such as making all letters upper or lower case as shown below.


'educational research techniques'

The upper() function capitalizes and the lower() function make small case.

It is also possible to count the length of a string and swap the case with the len() and swapcase() functions respectively.



Python allows you to count how many times a character appears using the count() function. You can also use the replace() to find characters and change them.


'Educational Rqsqarch Tqchniquqs'

As you can see, the lower case letter ‘e’ appears four times. In the second line, python replaces all the lower case ‘e’s with the letter ‘q’.


Of course, there is so much more than we could do with strings. However, this post provides an introduction to what is possible.


Friedrich Fröbel

Friedrich Fröbel (1782-1852) was an influential German teacher of the 18th and 19th centuries. This post will take a look at his life and views on education.


Frobel was the son of a clergyman. At an early age, his mother dies and Frobel moves to live with his uncle at the age of ten after his father remarried. As a child, Frobel developed a lifelong love of nature, which would manifest itself in many ways.

Despite being one of the most influential educators of all-time Frobel was seen as a lazy student by his teachers. By 15, Frobel was working as an apprentice to a forest manager. However, the forest manager was not much of a teacher and had little interest in helping Frobel. This compelled Frobel to study all of the forest manager’s books on his own which allowed him to develop an extensive knowledge of plants.

In 1799m Frobel goes to college and studies science, finance, history, and architecture. After completing school he worked as an architect but was not happy with his job. At the suggestion of a friend, Frobel tried teaching and immediately fell in love with it.

From 1808-1810, Frobel was under the guidance of John Pestalozzi and studied at Pestalozzi’s school. This experience had a deep impact on Frobel’s views on education and help to shape his approach towards his innovation in education know as the kindergarten.


Frobel focused heavily on early childhood education and developed the idea of the kindergarten or “child’s garden”. Frobel created the kindergarten to help mothers with the training and teaching of their small children.

In the kindergarten, the play of the student was systematized and serves as preparation for regular school. The children learn through there play various concepts that will help them in the future.

It can not be understated how influential kindergarten has been. Virtually every state in America offers some form of kindergarten and the majority require it. Frobel has made a strong mark in his work in early childhood education.

Frobel believed that early education was critical and should follow the natural development of the child. He agreed with Pestalozzi that education needs to address physical and spiritual needs.

One point of departure between Frobel and Pestalozzi is in regards to early childhood education. Frobel supported early school training outside the home while Pestalozzi was not as enthusiastic. In many ways, Frobel brought Pestalozzi’s ideas down to the youngest of students.


Frobel mark in educational history is assured as the founder of the concept of kindergarten that is still used to this day. All though there have been changes in early childhood education as the younger ages have become more academic. The idea of kindergarten is still there at least in name throughout the world.

Introducing Google Classroom

Google Classroom is yet another player in the learning management system industry. This platform provides most of the basics that are expected in a lms.  This post is not a critique of Google Classroom. Rather, the focus here is on how to use it. It is better for you to decide for yourself about the quality of Google Classroom.

In this post, we will learn how to set up a class in order to prepare the learning experience.

Before we begin it is assumed that you have a Gmail account as this is needed to access Google Classroom. In addition, this demonstration is from an individual account and not through the institutional account that a school would set up with Google if they adopted tGoogle Classroom.

Creating a Google Class

Once you are logged in to your Gmail account you can access Google Classroom by clicking on the little gray squares in the upper right-hand corner of your browser. Doing so will show the following.


In the example above, Google Classroom is the icon in the bottom row in the middle. When you click on it you will see the following.


You might see a screen before this asking if you are a student or teacher. In the screen above, Google tells you where to click to make your first class. Therefore, click on the plus sign and click on “create class” and you will see the following.


Click on the box which promises Google you will only use your classroom with adults. After this, you will see a dialog box where you can give your class a name as shown below.


Give your course a name and click “create”. Then you will see the following.

1.pngThere is a lot of information here. The name of the class is at the top followed by the name of the teacher below. In the middle of the page, you have something called the “stream”. This is where most of the action happens in terms of posting assignments, leading discussions, and making announcements. To the left are some options for dealing with the stream, a calendar, and a way to organize information in the stream by topic.

The topic feature is valuable because it allows you to organize information in a way similar to topics in Moodle. When creating an activity just be sure to assign it to a topic so students can see expectations for that week’s work. This will be explained more in the future.

One thing that was not mentioned was the tabs at the very top of the screen.


We started in the “stream” tab. If you click on the “students” tab you will see the following.


The “invite students” button allows you to add students by typing their email. To the left, you have the class code. This is the code people need in order to add your course.

If you click on the “about” tab you will see the following.


Here you can access the drive where all files are saved, the class calendar, your Google calendar, and even invite teachers. In the middle, you can edit the information about the course as well as additional materials that the students will need. This page is useful because it is not dynamic like the stream page. Posted files staying easy to find when using the “about” page.


Google Classroom is not extremely difficult to learn. You can set-up a course with minimal computer knowledge in less than 20 minutes. The process shared hear was simply the development of a course. In a future post, we will look at how setup teaching activities and other components of a balanced learning experience.

while statements and Nested for loops in Python

When you are unsure how much data your application may need to process it is probably appropriate to use a while statements. The while statement we keep processing until it runs out of items to process. If you remember with a traditional for loop the limit is preset by the data structure you are analyzing.

Nested for loops is another concept we will look at. They are useful when it is unclear what the conditions of execution should be.

Since they can go on forever it is possible with a while statement to create an endless loop. This is a loop that never stops processing. This will essentially crash most computers and should naturally be avoided. To avoid this you need set the environment, state the while statement, and update the condition of the environment. Below is a simple example of this.


  1. In line 1, we have the environment for the condition which is a variable called “number” set to 0.
  2. Line 2 is the while statement which states that as long as “number” is less than 10 do the following.
  3. In line 3 the variable “number” is printed.
  4. In line 4, after “number” is printed the number 2 is added to the current value
  5. This takes place until the variable “number” is equal to ten.

Below is what the output looks like if you ran this


You can see that we start with 0. This is because we set the variable “number” originally to 0. Then the value increases by just as in line 4 of the code above.

Nested for Loops

Just as with functions you can also have nested for loops. This is a loop within a loop. Below is a simple example.


  1. Lines 1-2 as for input and you can type whatever you want
  2. Line 3-4 is the first for loop at it process whatever your input is from line 1. The final result is that the loop prints this
  3. Line 5-6 are the second for loop and simply processes whatever you inputted in line 2. This loop simply prints the input from line 2.

Here is what the output would look like


You can see that the loops took turns. The first loop ran its first letter them then the second loop ran everything. Then the first loop ran its second letter and the second loop ran everything again. Therefore, nested for loops affects the timing of when the code is ran.


This post looked at the use of while statements and for loops. while statements are useful when you do not know how long you may need to process data. for loops allow you to run complex looping in which you are trying to do multiple tasks.

Pestalozzi His life and Views on Education

John Pestalozzi (1746-1827) is one of the most influential educators of the most influential educators of the early 19th century and still one of the most influential educators today. This post will examine his life and his views on education.


Pestalozzi was born Zurich, Switzerland in 1746. His father died when he was a child and Pestalozzi was raised by his mother. As a student, Pestalozzi showed no signs of greatness and his teachers accuse d him of being lazy.

Despite this, Pestalozzi goes to college to studying theology before switching to law. After completing school he tried to be a farmer but failed. After his farming venture folded did he turn to teaching by starting his own school.

Teaching during the 18th-19th century was mostly an unappreciated experience. The teachers normally lacked training and were poorly paid. In addition, many leaders did not want the general public to be educated because they believed that educated people were harder to control.

Knowing or experience all this Pestalozzi started his school anyway only for it to fail as well. The main benefit of this experience was that He discovered his love for teaching.

In 1798, Pestalozzi moves to Stanze to care for 80 orphans who had suffered from war. He ran the entire operation by himself with only help from the children. Unfortunately, he had to leave less than a year later and spends several years as an assistant teacher.

In 1805, Pestalozzi starts his second school. This school was by far more successful than his first attempt and became a leader in innovative education in Europe at the time. All the students and teachers lived, ate, and study together. This operation lasted 20 before infighting finally destroyed it. Two years later in 1827, Pestalozzi died.

Educational Views

Pestalozzi views were not so much radical as they were distinct in focusing on the individual development of the child. Teaching should follow the natural progression of the child. In addition, students learn best through repetition and learning by doing.

Combing repetition with learning by doing means that a child should do it over and over again until they are comfortable. Again, it is natural for many children to learn this way. The teacher encourages this by supporting or scaffolding the learning experience of the student

Children should be taught the literal before the abstract because this is appropriate for their senses. This also leads to inductive teaching in many instances but not necessarily always.

Pestalozzi also emphasized that human nature consisted of the physical and moral capabilities. Pestalozzi was a Christian and was convinced that a child must learn more than academics but also develop a sense of right and wrong as prescribed by religion.


Pestalozzi work continues to impact teaching today. Almost every teaching education program talks about his work in one way or another. His philosophy of the whole child approach is a summary of what many believe education should be.

for Loops in Python

The use of for loops are valuable when you need your application to do a repetitive task. Once the task is completed there is some sort of output that is returned. Understanding how to create a for loop is a critical step in utilizing the Python language.

Making for loops

Here is the basic syntax for a for loop

for item in data:
  do something

The word “for” indicates a for loop. The word “item” is an iteration variable. An iteration variable is a variable that changes value each time the loop goes through the data. It takes on the current value that is being analyzed for whatever purpose the loop has. You can name the iteration variable anything you want but a general rule is to use names that make sense for the context. Otherwise, nobody else will be able to understand your code.

After the colon is where you find “do something” here you put the command for whatever the loop is supposed to do. Below is an actual example of the use of the for loop.


Here is what happened

  1. At the top, we have our for loop. The iterator variable is “letter” and we are looping through the data of the string “education”.
  2. The next line is the action the for loop will perform. Essentially, the loop will pull each later from the string “education” and insert them one at a time into the phrase “Give me an”,. Notice how the word “letter” is at the end of our print statement. This the iteration variable that changes each time our for loop goes through the string “education.
  3. The output is several print statements each containing a different letter from the string “education”

for loops with Breaks

Breaks are used to provide conditions in which the loop will stop. In the example below, we add some code to our cheer that allows you to enter your own cheer. However, the church must be less than 10 letters otherwise you get a message that word is too long. Below is the code


Here is what it does.

  1. In line 1, you provide a word as indicated by the instructions in the parentheses.
  2. Line 2 is the for loop. letter is the iteration variable for our word in “Value”
  3. Line 3 is the if statement. The strong on “Value” is checked to make sure it is 10 characters or less.
  4. In line 4, if “Value” is greater than 10 characters you get the message that the cheer is too long.
  5. Line 5 is the break which stops the loop from continuing.
  6. In line 6, if the word is less than 10 characters you get the cheer with each letter.

Below is the output with less than 10 characters


Here is the output with more than 10 characters


Continue and for loop

The continue clause allows you to check the data and only process it based on certain conditions. In the code below, we are going to change our cheer code so that it removes spaces when making the cheer.


The code is mostly the same with a few exceptions

  • The if statement looks for blank spaces and these are left out of the cheer.
  • The continue clause tells python to keep going
  • Finally, the cheer is given

Below is what the output looks like if you ran this code


You can see that I put many blank spaces in-between the letters but these do not appear in the code. This is because of the continue clause.


for loops are a basic yet powerful tool of programming. In Python, for loops are used for the same reason as other languages and that is for completing repetitive tasks. The examples, here provide some simple ways in which this can be done.

August Francke and Education

August Francke (1663-1727) was a Protestant minister in Germany during the 17th and 18th century. His influence on education was distinct in that he brought a distinct theological view to education. This post will examine his life and views on education.


Born in Germany in 1663 Francke studied the sciences, languages, philosophy, and theology at university. His primary complaint about his theological studies was that he understood what he studied but that he did not have a corresponding experience in his heart. In other words, Francke wanted an emotional experience about the theological concept he studied.

This search for an emotional heartfelt experience led Francke to become sympathetic towards pietism. Pietism was a theological movement that believed protestants should replace the dead orthodoxy of scholastic theology with an emotional or theology of the heart. In many ways, this was exactly what Francke was looking for and he embraces this immediately.

Around the same time circa 1687, Francke starts a school but soon leaves to become a professor at the University of Halle in 1691. It was while working at Halle that Francke reached out to the poor. Initially, his ministry was simple Bible studies. However, with time Francke and his people opened several schools and other institutions to support the poor in Germany. All this was done while he still taught at the university.

Educational Views

Francke believed that education should be linked with the future vocation of the student. This in stark contrast to the generalized education that is common in most countries today. Students destined for trades should have different education form students who are going to be merchants.

With his focus on the emotions, Francke had a lot to say in particular about classroom management. For example, he stated that a teacher should never discipline in anger. This may be because the children will think that discipline is about how people feel rather than right or wrong.

The teacher also needs to maintain discipline without being harsh and severe. Of course, this is easier said then done but it still needs to be said. On the other hand, a teacher also needs to avoid the other extreme of being too nice as this is equally detrimental. Again, this is easier said than done.

Lastly, Francke counsels teachers that they must be sure that they are not the source of the students’ behavior problems. In other words, the teacher’s poor management should not be the source of the misbehavior in a classroom. Misbehavior should originate from the student and not because of an inconsistent teacher.


Francke was a man who was looking for an emotional experience to support his theological knowledge. In reality, what he was looking for was the practical application of his theological knowledge. This is said because as Francke helped people according to his religion he also experience the emotional satisfaction he so desperately needed.

Solving a System of Non-Linear Equations

Solving a system of non-linear equations means that at least one of the equations is not linear. For example, if one equation has an exponent it may be a parabola or a circle. With this no shape that is not linear it involves slightly different expectations.

Solving a system of non-linear equations is similar to solving a system with linear equations with one difference. The difference is that with nonlinear equations you can have more than one solution. What this means is that the lines that are the equations can intersect in more than one place. However, it is also possible they do not intersect. How many solutions depends on the lines involved.

For example, if one equation is a circle/parabola and the other is a line there can be 0-2 solutions. If one equation makes a circle and the other makes a parabola there can be up to 4 solutions. Two circles or two parabolas can make a multitude of solutions

The steps for solving a nonlinear system are the same. Therefore, in this post, we will demonstrate how to solve a system of non-linear equations using the substitution and elimination methods.


The substitution method is when we plug one equation into the variable of the other equation. Below is our system of equations.


The first thing to notice is that the top equation would make a circle if you graphed it. That is why this is a non-linear system. To solve we take the second equation and substitute it for y. Below we find the values for x


Now we complete the system by finding the values for y.


THerefore are ordered pairs are (0, -3) and (1,0). These are the two points at which the equations intersect if you were to graph them.


Elimination involves making the coefficients of one of the variables opposite so that when they are added together they cancel each other out. By removing one variable you can easily solve for the other. Below is the system of equation we want to solve.


The top equation makes a circle while the bottom one makes a parabola. This means that we can have as many as four solutions for this system. To solve this system we will multiply the bottom equation by -1. This will allow us to remove the x variable and then solve for y. Below are the steps.


Now we simply solve for y.


Now we can take these values for y to solve for x.


The order pairs are as follows

  • (-2,0)
  • (2,0)
  •   (√3, -1)
  • (-√3, -1)


From this, you can see that non-linear equations can be solved using the same approaches. Understanding this is key to many other fields of math such as data science and machine learning.

elif Clause and Nested Statements in Python

This post will provide a brief introduction into the use of the elif clause and nested statements in Python.

elif Clause

The elif clause is used to add an additional set of conditions to an if statement. If you have ever used some sort of menu on a computer in which you had to make several choices it is possible that an elif clause was involved in the code.

The syntax for the elif clause is the same as for the if statement. Below is a simple example that employs the elif clause.


Here is what this code does.

  1. In lines 1-3, I print three lines of code at the beginning. These are the chouces available to the user.
  2. In line 4, the “pick” variable stores whatever number the user inputs through the “input” function. It must be an integer which is why I used the “int” function
  3. In line 5 we begin the if statemenet. If the “pick” variable is set to 1 you can see the printout in line 6.
  4. In lines 7 and 8 we use the elif clause. The settings are mostly the same as in the if statement in line 5 except the “pick” varialbe is set to different numbers with different outputs.
  5. Lastly, in line 11 we have the else clause. If for any reason the person picks somethig besides 1,2 0r 3 this message will appear.

What this code means in simple english is this

  • If the pick is 1 then print “dogs are your favorite animal”
  • or else if the pick is 2 then print “cats are your favorite animal”
  • or else if the picj is 3 then print “rabbits are your favorite animal”
  • else print “I do not understand your choice”

Here is what the code looks like when you run it


As a note, if you type in a letter or string you will get an error message. This is because our code is not sophisticated enough to deal with non-integers at this point.

Nested Statements

Just like with functions which caan be nested so can decisiion statements by nested inside each other. TO put this simply the conditions set by the first if statememnt can potentail affect the second condition. This is explained better with an example.


Here is what is happening in the code above.

  1. In lines 1 and 2 the user has to pick numbers that are saved in the variables “num1” and “num2.”
  2. Line 3 and 4 are the if statements. Line 3 and line 9 are the outter if statement and line 4-8 are the inner if statement.
  3. Line 3 shares that “num1” must be between 1 and 10.
  4. Line 4 shares that “num2” must be between 1 and 10.
  5. Line 5 is the results of the inner if statment. The results are printed using the “.format” method where the {0} and {1} are the varabiles “num1” and “num2”. After the comma is what is done to the variables, they are simply added together.
  6. Line 8 is the else clause. If someone types something diffferent form a number between 1-10 for the second number they will see this message
  7. Line 9 is the else clause for the outter if statement. This is only seen if a value different from 1-10 is inputted.

If you run the code here is what it should look like



The elif clause and nested decision statements are additional tools that can be used to empower your applications. This is some of the most basic ideas in using a langage such as Python.

Life and Educational Views of John Locke

John Locke (1632-1704) was an influential philosopher during the 17th century. Locke also had some significant views on education. This post will look at Locke’s life and his positions on education.


Locke was born in 1632 in England. He went to college at Oxford and graduated in 1655. During, his university studies Locke developed a negative attitude toward the scholastic approach to education with its heavy emphasis on rote memorization. This experience would help to shape his educational views later in life.

After completing his bachelors, Locke attended medical school. Locke was not interested so much in being a doctor as in taking better care of his own health which he had problems with. After completing medical school, Locke work as a tutor to the son of an influential nobleman.

Due to the political actions of Locke’s boss he had to leave England for a time. However,  when a new king ascended the throne in England Locke was able to return. Upon returning Locke writes one of his most famous works “Essay Concerning Human Understanding” as well as other important works.

With his return to England, Locke actually worked for the government that used to be suspicious of him. He continued to serve until his health failed him and  he died in 1704.

Educational Views

Locke primarily had a practical view of education. The learning of a student should be focused on practical. Today it is tempting to spread a child across many subjects and electives but this was not what Locke supported. Education should be simplified and to the point

Locke did not hold that education should only be academic. Reading and writing are important but they were not everything in his view. This was in stark contrast to his scholastic education experience were academics is everything.

Locke believes that character development was the ultimate purpose of education. Understanding right from wrong and showing integrity were much more important than academic prowess.

Due to his medical training, Locke also supported the idea of an education that caters to the needs of the body. Fresh air, exercise, sleep, and a plain diet were critical to successful education.

Temperance was also another key item of success as the workload of the child should be adjusted to individual needs and not all the same. For Locke, a standardized education is insensible and treats children as objects rather than as living creatures. The teacher’s job is to study the child and find what is appropriate for them.

Locke also had much to say about language. He boldly claimed that the learning of Latin was overrated and really an activity for the upper class and not really for everybody. Locke also said that the best way to learn a language was through practice and not through the study of theoretical rules of language use.  In many ways here, Locke is laying the foundation for modern beliefs in TESOL.


John Locke was a highly influential philosopher of the 17th century who had unique views on education at his time. His ideas on wholistic education are still relevant today and his thoughts on language acquisition are perhaps the main view in that discipline today.

Life and Educational Views of John Comenius

John Comenius (1592-1670) was a Czech educator who has had a tremendous influence on education. This post will take a look at his life and educational philosophy.


Comenius was born in 1592. Early in life lost his parents and was raised by guardians. Due to this chaos, there were some delays in Comenius education as he did not study Latin until he was 16, which was considered late during this time.

Comenius late exposure to Latin allowed him to observe with a critical eye how it was taught compared to if he had studied as an uncritical small child. This would lay the foundation for his views towards language teaching and education in general.

Comenius would later go on to college and would graduate and take the position of minister in his church. These first few years were peaceful as he would work and marry. In addition, Comenius continues to nourish his views on education. However, were would soon break out and Comenius would lose all of his property in the process.

From here, Comenius goes fully into education and teaches and writes. Comenius would work in several countries writing about education as well as teaching. He focused a great deal on reforming how language was taught in particular Latin. In addition, he produced several highly influential books such as”The Gate of Tongues Unlocked” which may be one of the first language teaching books ever and “Didactic Magna” which may be one of the first books on teaching methods. In 1670, Comenius died at the age of 77.

Educational Views

Comenius believed that education should not only improve the main but should be focused on the development of the whole man which means physical, mental, and social development. The teaching should be inductive and based on examples. this means that you teach by using examples and have the students make conclusions.

The focus on inductive teaching and observation made Comenius critical of rote memorizing. Instead, understanding should be the primary goal. Lastly, Comenius was a support that everyone should be educated and not just males. This idea was somewhat ahead of its time.

Comenius is most famous for proposing grade levels. His system had four levels.

  1. Level 1 Domestic school-Home with mother
  2. Level Proper School-Basic reading and writing
  3. Latin School-College Preparation
  4. University

Comenius also had views on specifically teaching language. He supported teaching the mother tongue first until mastery. His point was that comprehension of the language must move in step with the tongue.  Comenius claimed there was no benefit to teaching a language without understanding. Of course, this is in strong contrast to Audiolingualism which is a strong support of nonsense repetition.

He also believed that learning by doing was the most appropriate way to learn a language. After the students do it you can teach them the rules. This allows the students to build on their strengths.


The life work of Comenius is an example of practical Reformation of educations. Many of his ideas and views are still influencing education to this day.

Logical Flow in Python

Applications often have to make decisions and to do this they need a set of conditions to him them decide what to do. Python, like all programming languages, has tools that allow the application to execute various actions based on conditions. In this post, we will look at the use of if statements.

If Statement Define

An if statement is a statement used in Python that determines when an action should happen. At a minimum, an if statement should have two parts to it. The first part is the condition and the second part is the action that Python performs if the condition is true. Below is what this looks like


This is not the most beautiful code but this is the minimum for a if statement in Python.

If Statement 

Below is the actual application of the use of an if statement

if number ==5:

In the code above we created a variable called number and set its value to 5. Then we created the if statement by setting the condition as “if number equals 5” the action for this being true was prin the string “correct”, which Python does at the bottom.

Notice the double equal sign used in the if statement. The double equal sign is used for relational equality while the single equal sign is used for assigning values to variables. Also, notice the colon at the end of the if statement. This must be there in order to complete the code.

There is no limit to the number of tasks an if statement can perform. In to code above the, if statement only printed “Correct” however, we can put many more print functions or other actions as shown below.

if number ==5:

All that is new above is that we have two print statements that were executed because the if statement was true.

Multiple Comparisons

In the code above python only had to worry about whether number equaled 5. However, we can have Python make multiple comparisons as well below is an example.

if (number>0) and (number<10):

Now for the print functions to execute the number has to be greater than 0 but less than 10. If you change the number to something less than 0 or greater than 10 nothing will happen when you run the code because the conditions were not met. In addition, if you type in a letter like ‘a’ you will get an error message because Python is anticipating a number and not a string.

If Else Statements

The use of an else clause in an if statement allows for an alternative task to be executed if the first conditions in the if statement are not met. This allows the application to do something when the conditions are not met rather than leaving a blank screen. Below we modify our code in the previous example slightly so that something happens because of the else clause in the if statement.

if (number>0) and (number<10):
 print("Number is out of range")
Number is out of range

In this code above we did the following

  1. we set our number to 15
  2. We created an if statement that searches for a number greater than 0 and less than 10.
  3. If the conditions in step 2 are true we print the two statements
  4. If the conditions in step 2 are not met we print the statement after the else clause
  5. Our number was 15 so Python printed the statement after the else clause

It can get much more complicated and powerful than this but I think this is clear and enough for now.


This post provided an introduction to the if statement in Python. THe if statement will execute a command based on one or more conditions. You must be careful with the syntax. Lastly, you can also include an alternative task with the else clause if the conditions are not met.

Wolfgang Ratich

Wolfgang Ratich (1571 – 1635)was a practitioner of education during the 17th century. His work during his lifetime was mostly a failure but time was a better judge of his practical insights into education. In addition, Ratich was an early influence on Comenius who was one of the greatest educators of all time.

Ratich studied philosophy and theology at university with the goal of becoming a preacher. However, a speech impediment put an early end to his career in ministry. This led him to try teaching as his career.

Views on Education

Ratich quickly formed strong views on education. He believed that children should study their mother tongue first before learning about others, which is an idea that is still supported to this day.

Teaching should also be inductive in nature which means that the students learn from examples and experience first and use these experiences to form conclusions. This was radical at the time because most believe that learning involved making grand conclusions first and finding support for them which is called deductive thinking.

Ratich also despised rote learning as intellectual harmful to students. He preferred to allow a child to learn according to nature. This idea was further spelled out in the work of Piaget and Kohlberg who stressed development in young children.

Language Teaching MEthod

Ratich method for teaching English was methodical, to say the least. His method included about 6 steps.

  1. Teach the alphabet
  2. Form words and syllables
  3. Teacher reads a book out loud to the class with students following along
  4. Students take turns reading parts of a chapter from the book the teacher read
  5. Teacher teaches grammar
  6. Students identify grammatical examples of the English terms in the book

It’s rather amazing this system worked. However, it was ahead of its time. Unfortunately, the results were mixed but maybe not for the method but rather because of the teacher


After several years of trying Ratch was finally allowed to put his ideas into practice at a school. With his thoughts on education and detailed method results were assumed o be coming. However, the school was a failure. This is due primarily to the poor people skills of Ratich

Ratich alienated everyone with his personality and stubbornness. He was rude and considered arrogant. Even Ratich’s religion was a point of contention as Ratich was Lutheran and he was living and working among Calvinist. Eventually, Ratich irritated the prince and was thrown in prison for a while before leaving.


Ratich in many had the right ideas and wrong personality. His ideas were revolutionary and in many ways laid the foundation for ideas in TESOL such as inductive learning, the use of authentic reading etc. Ratich only problem was Ratich which may be one of the lessons a young Comenius learned when he visited Ratich’s school.

Making Functions in Python

Efficiency is important when writing code. Why would you type something a second time if you do not have to? One way coders save time, reduce error, and make their code easier to read is through the use of functions.

Functions are a way of storing code so that it can be reused without having to retype or code it again. By saving a piece of reusable code as a function you only have to call the function in order to use it again. This improves efficiency and reliability of your code. Functions simply take an input, rearrange the input however it is supposed to, and provide an output. In this post, we will look at how to make a function using Python.

Simple Function

A function requires the minimum information

  • A name
  • Determines if any requirements (arguments) are needed
  • The actual action the function is supposed to do to the input

We will now make a simple function as shown in the code below.

def example():
     print("My first function")

In the code above we have the three pieces of information.

  • The name of the function is “example” and you set the name using the “def” command.
  • There are no requirements or arguments in this function. This is why the parentheses are empty. This will make more sense later.
  • What this function does is use the “print” function to print the string “My first function”

We will now use the function by calling it in the example below.

My first function

As you can see, when we call the function it simply prints the string. This function is not that impressive but it shows you how functions work.

Functions with Arguments

Arguments are found with the parentheses of a function. They are placeholders for information that you must supply in order for the function to work. Below is an example.

def example(info):

Now our “example” function has a required argument called “info” we must always put something in place of this for the function to run. Below is an example of us calling the “example” function with a string in place of the argument  “info”.

example("My second function")
My second function

You can see that the function simply printed what we placed in the paratheses. If we had left the parentheses empty we would have gotten an error message. You can try that yourself.

You can assign a default value to your argument. This is useful if people do not provide their own value. Below we create the same function but with a default value for the argument.

def example(info="You forgot to give a value"):

We will now call it but we will not include the argument

You forgot to give a value

return and print

When creating functions, it is common to have to decide when to use the “return” or “print” function. Below are some guidelines

  • Print is for people. If a person only needs to see the output without any other execution the print is a good choice.
  • Return is appropriate when sending the data back to the caller for additional execution. For example, using one function before using a second function

If you take any of the examples and use “return” instead of “print” they will still work so the difference between “return” and “print” depends on the ultimate purpose of the application.


Functions play a critical role in making useful applications. This is due to their ability to save time for coders. THere are several concepts to keep in mind when developing functions. Understanding these ideas is important for future success.

Melancthon Life & Educatioal Views

This post will take a brief look at the life and educational views of Philip Melancthon (1497-1560) a highly influential protestant reformer in Germany.

Life of Melacthon

Melanchthon was considered by many to be a highly gifted prodigy. In addition to his mother tongue of German, Melanchthon was a master of Greek and Latin to a level that astonished his teachers.

In 1512, at the age of 15, Melanchthon did not start college, rather he would finish college. This means that he probably started university studies at 11-12 years of age. He was also supposed to receive his master degree but the university may him wait because of his age.

In 1518, Melancthon begins teaching and of course, was a phenomenal teacher. His primary field was theology and Greek but he was formidable in other areas as well. It was at this point in his life that Melancthon would become friends with Martin Luther, the reformer.

Melancthon was also a prodigious writer of books. He wrote on various subjects including Greek, Latin, ethics, logic, rhetoric, physics, and theology. Some of the textbooks he wrote were so good that they were used for almost 100 years. A feat that is impossible to with the speed at which new knowledge now develops.

Views on Education

Melancthon believed in leading by example and that attitude was contagious. Target students to study teacher needed to have energy and enthusiasm for the subject. Melancthon was a voracious student and at times this infected his students as well.

Melancthon also developed what is now known as the “Saxony Plan.”  This plan was a brief philosophy of education with three tenets.

  1. Teachers should not teach children several languages at the same time. This is overwhelming for the child. Instruction in Germany should first be focused on Latin.
  2. Teachers should not teach too many subjects. This also is damaging to the student.
  3. Development of different levels or classes should be used. Melancthon, in particular, believed that there should be three grades or classes for young students.
    • LEvel 1-Teaches reading, writing, arithmetic and basic concepts from the Bible
    • Level 2-Adds Latin  grammar and continues bible instruction
    • Level 3-More Latin along with rhetoric, logic, and classes were now taught in Latin

Looking back, these ideas do not seem revolutionary, however, at the time these were ground-breaking concepts. Melancthon was reacting to common teaching habits of the time. In other words, it was common to teach children several languages at once, to focus on too many subjects, and to not have the students organized into groups based on ability.


Melancthon provides us with a look at a reformer of education during the protestant reformation. His work as a teacher and scholar is second to none. In addition, his ideas on education help to rectify many problems in German education at the time.

Educational Views of Michel Montaigne

By the 16th century, the Renaissance was in full swing, the Protestant Reformation had already been around for over a generation and people had serious doubts about the intellectual and spiritual grip the Church had on society. Since the Church also controlled education people began to question these methods. As this wave of humanism swept Europe.

It was during this time of doubt and skepticism that Michel Montaigne (1533-1592) arrived on the scene. Montaigne was not so much an educator as he was a person who had a strong opinion of how education should be. He also knew how to write witty insightful essays on the subject of education along with other subjects of his interest. This post will take a brief look at his life and educational philosophy

Montaigne’s Life

Montaigne was born into a well to do family in France in 1533. He was natural brilliant and was able to speak Latin, in addition to his mother tongue of French by the age of six. Yes, Montaigne was brilliant but he also had a German tutor who did not know French and used Latin to communicate with the child.

By 13, Montaigne had finished college. He turned his attention to politics and was a member of parliament by the age of 20. Soon after, he became mayor of his 20. Despite what looked to be a brilliant political future Montaigne left politics after becoming Mayor to live a life of quietness. Since he was already well off he did not need to endure the rigors of financial gain and power to maintain his livelihood.

It was in this semi-retirement that Montaigne began writing his famous humanistic “Essays” on various subjects. In fact, Montaigne was one of the first people to popularize the idea of an essay, which is now standard practice in school today. Our attention will be on his views on education.

Views on Education

Montaigne views on education were almost a reaction against Church views on education. Montaigne believed in a wholistic education of the man and not to divide him into pieces. He also criticized the study of Latin and Greek because he supported the development of the mother tongue first. This debate over mother tongue use is a recurring theme in early language education.

Montaigne also criticized the study of the classics as it did not prepare students for practical life but rather bade them conceited. Another target of criticism was the teaching methods of the day, which were often lecture-style. Montaigne views this pouring knowledge into the mind and not useful for the student.

Montaigne supported a more interactional approach to teaching in which the students and teacher take turns talking and listening. THrough action came understanding in his opinion.

Finally, Montaigne was a critic of corporal punishment. He viewed almost as if one was training an animal rather than a person. Again most of these criticisms were of common practices in education at that time period and the education was mostly controlled by the church.


Montaigne was a theoretician on education but not much of a practitioner. His experience as a student led him to write strong reactionary criticisms against education. In spite of his lack of practical experience Montaigne’s thoughts are highly insightful and somewhat applicable to this day.

Common Data Types in Python

All programming languages have a way of storing certain types of information in variables. Certain data types or needed for one situation and different data types for another. It is important to know the differences in the data types otherwise serious problems could arise when developing an application. In this post, we will look at some of the more commonly used data types in Python.

Making Variables

It is first important to understand how to make a variable in Python. It is not that complicated. The format is the following

variable name =  data inside the variable

You simply type a name, use the equal sign, and then include the data to be saved in the variable. Below is an example where I save the number 3 inside a variable called “example”


The “print” function was used to display the contents of the “example” variable.

Numeric Types

There are two commonly used numeric data types in Python and they are integers and floating point values.


Integers are simply whole positive or negative numbers. To specifically save a number as an integer you place the number inside the “int” before saving as a variable as in the example below.



You can check the data type by using the “type” function on your variable. This is shown below.

Out[17]: int

The results are “int” which stands for integer.

Floating-Point Types

Floating-point numbers are numbers with decimals. If your number includes a decimal it will automatically be stored as a floating type. If your number is a whole number and you want to save it as a floating type you need to use the “float” function when storing the data. Below are examples of both

#This is an example of a float number



#This is an example of converting a whole number to a floating point



Floating points can store exponent numbers using scientific notation. Floating point numbers are used because decimals are part of the real world. The downside is they use a lot of memory compared to integers.

Other Types

We will look at two additional data types and they are boolean and string.


A boolean variable only has two possible values which are True or False. This seems useless but it is powerful when it is time to have your application do things based on conditions. You are not really limited to True or False you can also type in mathematical expressions that Python evaluates. Below are some examples.

#Variable set to True



#Variable set to True after evaluting an expression




A string is a variable that contains text. The text is always enclosed in quotations and can be numbers, text, or a combination of both.

example="ERT is an awesome blog"

ERT is an awesome blog


Programming is essentially about rearranging data for various purposes. Therefore, it only makes sense that there would be different ways to store data. This post provides some common forms in which data can manifest itself while using Python.

Luther and Educational Reform

Martin Luther (1483-1546) is best known for his religious work as one of the main catalysts for the Protestant Reformation. However, Luther was also a powerful influence on education during his lifetime. This post will take a look at Luther’s early life and his contributions to education

Early Life

Luther was born during the late 15th century. His father was a tough miner with a severe disciplinarian streak. You would think that this would be a disaster but rather the harsh discipline gave Luther a toughness that would come in handy when standing alone for his beliefs.

Upon reaching adulthood Luther studied law as his father diseased for him to become a lawyer. However, Luther decided instead to become a monk much to the consternation of his father.

As a monk, Luther was a diligent student and studied for several additional degrees. Eventually, he was given an opportunity to visit Rome which was the headquarters of his church. However, Luther saw things there that troubled him and in many laid the foundation for his doubt in the direction of his church.

Eventually, Luther had a serious issue with several church doctrines. This motivated him to nail his 95 theses onto the door of a church in 1517. This act was a challenge to defend the statements in the theses and was actually a common behavior among the scholarly community at the time.

For the next several years it was a back forth intellectual battle with the church. A common pattern was the church would use some sort of psychological torture such as the eternal damnation of his soul and Luther would ask for biblical evidence which was normally not given. Finally, in 1521 at the Diet of Worms, Luther was forced to flee for his life and the Protestant Reformation had in many was begun.

Views on Education

Luther’s views on education would not be considered radical or innovative today but they were during his lifetime. For our purposes, we will look at three tenets of Luther’s position on education

  • People should be educated so they can read the scriptures
  • Men and women should receive an education
  • Education  should benefit the church and state

People Should be Educated so they Can Read the Scriptures

The thought that everyone should be educated was rather radical. By education, we mean developing literacy skills and not some form of vocational training. Education was primarily for those who needed it which was normally the clergy, merchants, and some of the nobility.

If everyone was able to read it would significantly weaken the churches position to control spiritual ideas and the state’s ability to maintain secular control, which is one reason why widespread literacy was uncommon. Luther’s call for universal education would not truly be repeated until Horace Mann and the common school. movement.

The idea of universal literacy also held with it a sense of personal responsibility. No one could rely on another to understand scripture. Everyone needs to know how to read and interpret scripture for themselves.

Men and Women Should be Educated

The second point is related to the first. Luther said that everyone should be educated he truly meant everyone. This means men and women should learn literacy. The women could not hide behind the man for her spiritual development but needed to read for herself.

Again the idea of women education was controversial at the time. The Greeks believed that educating women was embarrassing although this view was not shared by all in any manner.

WOmen were not only educated for spiritual reasons but also so they could manage the household as well. Therefore, there was a spiritual and a practical purpose to the education of women for Luther

Education Benefits the Church and the State

Although it was mentioned that education had been neglected to maintain the power of the church and state. For Luther, educated citizens would be of a greater benefit to the church and state.

The rationale is that the church would receive ministers, teachers, pastors, etc. and the state would receive future civil servants. Therefore, education would not tear down society but would rather build it up.


Luther was primarily a reformer but also was a powerful force in education. His plea for the development of education in Germany led to the construction of schools all over the Protestant controlled parts of Germany. His work was of such importance that he has been viewed as one of the leading educational reformers of the 16th century.

Logarithmic Models

A logarithm is the inverse of exponentiation. Depending on the situation one form is better than the other. This post will explore logarithms in greater detail.

Converting Between Exponential and Logarithmic Form

There are times when it is necessary to convert an expression from exponential to logarithmic and vice versa. Below is an example of who the expression is rearranged form logarithm to exponential.


The simplest way to explain I think is as follows

  • for the logarithm, the exponent (y) and the base (a) are on opposite sides of the equal sign
  • For the exponent form, the exponent (y) and base (a) are on the same side of the equal sign.

Here is an example using actual numbers1.png

As you can see the exponent 3 and the base 2 are on opposite sides of the equal sign for the logarithmic form but er together for the exponential form.

When the base is e (Euler’s Number) it is known as a natural logarithmic function. e is the base rate growth of a continual process. The application of this is limitless. When the base is ten it is called a common logarithmic function.

Logarithmic Model Example

Below is an example of the application of logarithmic models

Exposure to noise above 120 dB can cause immediate pain and damage long-term exposure can lead to hearing loss. What aris the decimal level of a tv with an intensity of 10^1 watts per square inch. 

First, we need the equation for calculating the decibel level.


Now we plug in the information into the word problem for I and solve


Our tv is dangerously loud and should include a warning message.  We dropped the negative sign because you cannot have negative decibel level.


Logarithms are another way to express exponential information and vice versa. It is the situation that determines which to use and the process of concert an expression from one to another is rather simple. In terms of solving actual problems, it is a matter of plugging numbers into an equation and allowing the calculator to work that allows you to find the answer.

Education During the Reformation

By the 16th century, Europe was facing some major challenges to the established order of doing things. Some of the causes of the upheaval are less obvious than others.

For example, the invention of gunpowder made knights useless. This was significant because now any common soldier could be more efficient and useful in battle than a knight that took over ten years to train. This weakened the prestige of the nobility at least temporarily while adjustments were made within the second estate and led to a growth in the prestige of the third estate who were adept at using guns.

The church was also facing majors issues. After holding power for almost 1000 years people began to chaff at the religious power of Europe. There was a revival in learning that what aggressively attacked by monks, who attacked the study of biblical languages accusing this as the source of all heresies.

The scholars of the day mock religion as a superstition. Furthermore, the church was accused of corruption and for abusing power. The scholars or humanists called for a return to the Greek and Romans classics, which was the prevailing worldview before the ascension of Catholicism.

Out of the chaos sprang the protestant reformation which rejects the teachings of the medieval church. The Protestants did not only have a different view on religion but also on how to educate as we shall see.

Protestant Views of Education

A major tenet of Protestantism that influenced their view on education was the idea of personal responsibility. What this meant was that people needed to study for themselves and not just listen to the teacher. In a spiritual sense that meant reading the Bible for one’s self. In an educational sense, it meant confirming authority with personal observation and study.

Out of this first principal springs two other principles which are education that matches an individual’s interest and the study of nature. Protestants believed that education should support the natural interest and ablities of a person rather than the interest of the church.

This was and still is a radical idea. Most education today is about the student adjusting themselves to various standards and benchmarks developed by the government. Protestants challenged this view and said education should match the talents of the child. If a child shows interest in woodworking teach this to him. If he shows interest in agriculture teach that to him.

To be fair, attempts have been made in education to “meet the needs” of the child and to differentiate instruction. However, these goals are made in order to take a previously determined curriculum and make it palpable to the student rather than designing something specifically for the individual student. The point is that a child is more than a cog in a machine to be trained as a screwdriver or hammer but rather an individual whose value is priceless.

Protestants also support the study of nature. Be actually observing nature it reduced a great deal of the superstition of the time. At one point, the religious power of Europe forbade the study of human anatomy through the performing autopsies. In addition, Galileo was in serious trouble for denying the geocentric model of the solar system. Such restrictions stalled science for years and were removed through Protestantism.


The destabilization that marks the reformation marks a major break in history. With the decline of the church came the rise of the common man to a position of independent thought and action. These ideas of personal responsibility came from the growing influence of Protestants in the world.

Secular Education During the Middle Ages

The Middle Ages (500-1500 CE) is often viewed as a low point in the world of education. This was a time a strong superstition among people and a lack of scientific progress.

The European world was divided into three classes or estates which were the Priest, Nobility, and lastly, everyone else. These were the three estates. The Priestly estate held significant power over the other two estates. The priests would use the psychological terror of removal from having access to the sacraments of the church to maintain power.

When an individual was denied the sacraments it was called excommunication, when a region loss access to the sacraments it was called an interdict, final if an entire province or kingdom was denied the sacraments war was then declared and this was called a crusade.

There were two common forms of education below the university and these were the Knightly schools and the Burgher schools.

Knightly Schools

Knightly schools trained boys to become knights. The training was divided into 3 segments of seven years each. The first segment was from 0-7 years of age under the care of the mother. From ages 7-14, the boy would live with another knight perhaps as a page. The third stage from 14-21 had the boy serving as a squire. At the age of 21, a young man was declared a knight.

The subjects taught in the KNightly practicum focused on the physical, artistic, and strategic. Music, chess, manners, poetry, and military training were all part of the curriculum. There was almost no intellectual training but an obsession with practical learning.

Burgher Schools

Burgher Schools were for tradesmen and artisans and provided a basic education. The subject taught included reading, writing, and arithmetic as well as geography, history, natural science, and Latin.

THere was a constant power struggle between commoners and the priest for control of these schools. Locals wanted to control these schools themselves. However, technically only the church had permission to teach. This resulted in alternating back and forth in terms of control.

Teachers in these schools were paid almost nothing and traveled from school to school as vagrants. Teaching was not seen as a noble profession at this time thus having a powerful effect on the quantity and quality of education.


Education in the Middle Ages was designed to meet the needs of the three estates. People would often attend school corresponding to their rank in society. This system had an air of stability until rapid social changes brought about the decline of this system.

Expontial Models

There are times when we want to understand growth that is not constant. An example of this would be the growth of a virus. As time goes by the virus growth rate increases more and more. Another example would be in the world of finance when we are dealing with interest.

In situations like the ones mentioned above, it is critical to understand the use and application of exponential models. This post will go through examples of the use of exponential models.

Finance Example

One common exponential model in finance is for compounded interest. The equation is as follows…


Below is a simple word problem that calls for this equation

You invest $10,000 in a mutual fund to prepare for retirement. The interest rate is 5% compounded monthly, how much will be in the account when you plan to retire in 25 years. 

Below is what we now

  • balance = ?
  • principal = $10,000
  • rate = 0.05
  • years=  25
  • times in year = 12 * 25 = 300

Now, we simply plug this information into the equatiom to get the answer.


The answer is shown above. The initial investment would grow to almost $35,000 dollars over 25 years.

Continuous Growth

In some fields, such as the life sciences, you want to now the growth of a virus or bacteria. Unlike in finance where the balance grows several times a year,  a bacteria is growing continuously. This leads to a slightly different exponential model as shown below.


e is an irrational number that serves as the base. With this information, we can address the problem below

A student starts their experiment with 10 bacteria. He knows the bacteria grow 100% every hour. He will come back and check in 12 hours. How many bacteria will he find?

Here is what we know

  • final size =?
  • initial size = 10
  • rate = 1/hour
  • time = 12

We plug this into the equation to get the answer


As you can see, the growth of the bacteria is almost incomprehensible in such a short time. This is the power of exponential growth.


Exponential models provide another way to find answers to questions people have. Whether the growth is over a certain number of times or continuously the model can be adjusted to deal with either of this situations.

Monastic Schools

During the early Middle Ages (500-1000 CE) monastic schools began to take shape and heavily influence education. Their influence was felt for over a millennia providing education directly or indirectly to a countless number of people.


The monastic schools grew out of the philosophy of Asceticism. Asceticism is the belief in a life of severe self-denial from the viewpoint that the body was evil. Practitioners of asceticism would forego marriage, financial gain, and most earthly pursuits, in order to focus on spiritual development usually in isolation. This a strong reaction to the non-Christian world’s focus on eating a drinking

There were two common ways to follow Asceticism. Hermits would often live in nearly complete isolation to pursue spiritual development. Monks, on the other hand, practice asceticism as well but would stay near communities of people in order to provide spiritual care for others. In addition, monks would live together in monasteries to support and encourage each other. Of course, at least in the past, monks were only men. Women could become nuns if they desired to live in similar conditions among women.

The largest order of monks was the Bendectin Order. The monasteries served as an asylum for the oppressed, as a missionary station, and most importantly as a preserver of knowledge.


The curriculum of the monastic schools consisted of the 7 liberal arts. These seven subjects can be broken into two categories, which are the trivium and the quadrivium.

The Trivium consisted of three subjects which were Latin, logic, and rhetoric. Latin was the lingua Franca of the Chuch at the time so its grammar was taught extensively. Logic was derived from the ideas of Aristotle and included deductive and inductive reasoning. Rhetoric is another term for public speaking and this was studied for the purpose of developing communication skills.

The quadrivium consisted of four subjects which were arithmetic, geometry, astronomy, and music. Many of the subjects are not studied as they are today. Arithematic study the mysterious or gnostic properties of numbers. Geometry was studied superficial and of little use. Astronomy was treated almost the same as astrology.

However, music was studied for the purpose of worship. The chants that the monks sang came to be called Gregorian chants named after Pope Gregory who had the chants codified. This is some of the earliest written version of western music. The notational system was different from modern notation using four lines instead of five and use squares instead of ovals to indicate notes.

The significance of Gregorian chants cannot be overestimated as they laid the foundation for modern music. Chants in the halls of monasteries provided the beginnings of most music found today.


Radical views in terms of the body led to the idea of asceticism. From this focus on self-denial comes the idea of living among like-minded people in monasteries. While in monasteries the monks would pursue education for personal development. This led to the liberal arts curriculum that is still used in part to this day.


Education in the Early Church

The early church provides a unique look at the development of a system of religious education fairly recently in history. With the death of the apostles, believers who were still alive had to face the reality of two major problems.

  1. What do we do with our children in terms of their education?
  2. How do we educate people who want to join the church?

The answers to these two questions intersect in many ways. This post will examine education in the early church.

Education of Children

The education of children was a problem for the early church. Children needed an education but state-run schools were not really an option. The reason has to do with the difference in philosophy of Christian education and state education.

Christian education is focused on character development and being prepared for eternity. In contrast, state education is focused on skill development and the here and now as eternity is often not a concern. As a result of this, Christians did not consider state-controlled schools as an option for their children.

In addition, it was common for state-led schools to mix Roman worship with education and for the Christians this was unacceptable. It is also important to realize that Christians were frequently persecuted as atheists during this time so it was impossible to go to school when one’s life was in danger.

The solution to this was the one that the Jews used, which was homeschooling. The focus of the child’s training was to develop a trust in the Christian God. By keeping the child at home he or she was protected from the influence of the world for a time. This led to a simplicity of taste that non-Christians found bewildering.

The Bible was the sole book for most children. The stories within it served as nursery tales. Scripture was memorized and the Bible was even used for learning to read.

With the focus on character development and a sense of morals, Christian education was vastly different from the education of other societies. Even without the focus on the classics and even technical training Christians were a spectacle to the world at this time. In terms of the results of this education among women one heathen author exclaimed “What wives these Christians have” indicating his awe in how these people conducted themselves.

Catechetical Schools

As the church grew, it became difficult to address the needs of new members. In particular, there were concerns over how to prepare prospective members for church membership. One answer to this problem was the development of Catechetical schools which were a place for prospective and current members to receive training in Christian beliefs.

For people considering baptism, the training could last anywhere from a few months to as long as three years. The curriculum consisted of learning the Ten Commandments, Lord’ Prayer, other parts of scripture, and as well as a confession of faith.

For people who were already Christian, they could receive advanced training that would prepare them for ministerial work as a teacher or leader. Some of the subjects covered for believers included philology, rhetoric, math, and philosophy.

The most prominent of these schools was found in Alexandria, Egypt. For several centuries after this,  Alexandria has a powerful influence on the Christian church.


The purpose of education is to meet the needs of the people in the context in which it is needed. The Early Christian Church had the dilemma of having to be separate from the world while still developing skills needed to survive in it. This led to the development of the homeschool for children and the Catechetical School for new converts.

Intro to Python

Python is a highly popular programming language. It is so popular that it is now the most commonly used programming language for machine learning/data science purposes having surpassed R.

However, Python is not limited to just statistical tools. Python is also used by many companies for a host of reasons including Yahoo, Dropbox,  Google, NASA, IBM, and Mozilla.

One secret to Pythons popular is its flexibility. When using Python it is possible to employ several different coding styles. Below is just some of them.

  • Procedural: This is the simplest form of coding and involves executing each line of code sequential.
  • Functional: Functions are used to transform data as found in mathematics.
  • Imperative: Employs statements to achieve a goal
  • Object-oriented: The use of objects (aka data structures) to model the real world. Not fully implemented in Python.

You can mix these styles together to make powerful applications.

Using Python

You can download Python by searching for “Anaconda Python” in Google. The Anaconda version of Python downloads several additional features to besides Python including the Spyder IDE which is what we will use here.

Once you download and install Anaconda, on your computer you need to search for the program called “SPyder”. When you open it you will see the following.


Here is what each pane represents.

  • To the left is the text editor, you can type code that you want to save here.
  • In the top right is the variable explorer. Here you can find a list of the objects you have made.
  • In the bottom right is the Interactive Python console or “IPython” console for short. Here you can type code quickly without the need of storing it for long-term use. In addition, the results of any code execution is normally displayed here as well

When writing code remember that you can save it long term in the text editor or just execute it quickly in  the console,

First Line of Code

We will now run our first line of code. Followed by the output in the IPython Console. Below is what we typed into the Console

print("Hello to Python")

Here is what it looks like in the console


Here is what we did.

  1. We typed “print(“Hello to Python”)” into the console. This is an example of the use of a function.
  2. The output provides several pieces of information.
    • The blue shows what line this is in the console. In other words, this is the third line of code I had typed in the console. You may have a different number.
    • The purple is the function being used which for us is the “print” function which simply displays the input
    • The green is the argument that the function is changing. Our argument is a string of text that is put in quotes deliberately
    • The text in black is the actual output

Of course, there is much more to Python then this. However, this serves as an introduction for a future post.


Python is a popular programming language used in a variety of application. The source of its popularity has to do with it general-purpose philosophy. There’s a little bit of something for everybody in this language which encourages its use. Using the Spyder IDE will allow you to experience Python for the purpose of acquiring new skills.

Education in Ancient Rome

The Roman Empire was around in one form or another for over 1,000 years. To attempt to try and cover the educational approach of an empire over such a long period is not practical in a blog post. Instead, certain key ideas will be highlighted to provide a brief picture.


The Romans had a war-like spirit due in part to the context in which they found themselves. They were surrounded by enemies on all sides and had no choice but to fight for their survival. This war context influence education in that the Romans were focused on a practical utilitarian education for their children. This is in stark contrast to the aesthetic education of the Greeks who loved beauty for beauty sake.

Another unique characteristic of Roman society was the status given to women. Women in Roman culture were often viewed as Queens of the Household and wielded tremendous power behind their husbands.

What they Taught

The Romans taught the same basic subjects of many other ancient cultures. Some of the subjects included reading, writing, math. grammar, poetry. However, due to their practical nature, the early Roman empire did not have a strong aesthetic culture. This came later as Rome began to absorb and imitate Greek life.

How Learning was Organized

Education was divided into three main stages of life. The first stage lasted from birth until about the age of 7 and was under the mother. Basic life skills were taught and not too much in terms of academics. Later, the mothers would reject this responsibility and leave their children in the care of a pedagogue but this did not happen until Rome began to decline.

From ages 7-12 a child went to elementary school and studied under a literature. Being a literator was often viewed negatively as someone who had failed in life. Therefore, primary education was full of washed up men. Corporal punishment was common as well and stern discipline was instilled.

From age 12-16 a boy would receive advanced training under a literatus. Unlike the primary teacher, the literator, the literatus was highly respected and could earn a great deal of money from his occupation.

At the age of 16, a boy was considered an adult and would pursue his life work which could be anything such as agriculture, law, politics, military, etc. were some of the many options available.


Roman education was focused on what was necessary to improve the practical life of the people. There quest for conquered lands help them to spread their influence over the entire planet.  Therefore, Rome is remembered for their sense of independence that is still remembered until this day.

Completing the Square

One method for solving quadratic equations is called completing the square. This approach is a little confusing but we will try to work through it together in this post.

What is Completing a Square

Completing the square is used when your quadratic equation is not a perfect square. Below is an example of a perfect square quartic formula =. The first is in the standard quadratic form and the second is after it has been simplified.


However, not all equations are this easy, consider the example below.


There is no quick way to factor this as there is no perfect square. We have to use something called the binomial square pattern.


This is where it gets confusing but essential what the binomial square pattern is saying is that if you want to find the third term (b squared) you must take the second term and multiple it by1/2. We multiplied by 1/2 because this is the reciprocal of multiplying by 2 as shown in the equation. Lastly, we square this value. Below is the application of what we just learned from our problem equation.


By taking the second term, multiplying by 1/2 and squaring it we were able to create the trinomial we needed to create the perfect square. By doing this we also solved for x if this was a full equation.


When using the completing the square approach with a quadratic formula there are some additional steps. We will work through an example below


We are missing the third term and we need to find this first. Our second term is 8 so we will plug this in to find the third term


We take this number 16 and add it to both sides which is a rule whenever manipulating an equation. Therefore, we get the following.


We can now factor the left side as shown below.


To remove the square we need to square root both sides. In other words, we are employing the use of the square root property.


This leads to our two answers as shown below


There are variations of this but they all involve just moving some numbers around before the steps shown here. As such, there is not much need to discuss them.


Completing the square provides a strategy for dealing with quadratic formulas that do not have a perfect square. Success with this technique requires identifying the terms you know and do not know and taking the appropriate steps to calculate the third term for the trinomial.

The Quadratic Formula

The quadratic formula is used for solving quadratic equations. The actual creation of this formula is somewhat complex. Creating it requires the use of completing the square as well as square root property. Below is what the equation looks like.


For our purposes, we will go through an example that solves a quadratic equation using the quadratic formula. In addition, we will also explore the idea of the discriminant as it relates to quadratic formulas.


The mechanics of solving a quadratic formula using this approach is similar to most other methods. You simply plug in the substitutes in the equation to get your actual answer. Below is an example,


We will now plug in the values and determine x.




The discriminant of a quadratic equation is used to determine the type if the answer you would get if you solve the equation. THere are three types of answers that you can get when solving a quadratic equation.

  • Two real solutions-This happens when the discriminant results are positive.
  • One real solution-Happens when the discriminant results are zero
  • Two complex-Happens when the discriminant is negative

A complex solution involves the use of an imaginary number. This happens when the square root number is negative, which is technically impossible. To deal with this in math the letter i is used instead of the negative sign below is an example.


The actual formula for calculating the discriminant is already in the quadratic formula. You simply calculate only the information under the square root. This is shown below.


IN our first example, we got two real solutions. We will now confirm this by calculating the discriminant.


Are answer is positive, which means that we can expect to calculate to real solutions for this particular problem.


The quadratic formula provides another way to solve a quadratic equation. This is probably the easiest method to learn as it is simply a matter of plugging numbers into the formula. This may explain why the quadratic formula is frequently the first method algebra students learn for solving quadratic equations.

The discriminant is a shortcut calculation that allows you to determine the quality of the solutions you would get if you solve the equation.

Education in Ancient Athens

In many ways, Athens is the home of Western thinking. Countless philosophers were either from Athens or at least spent time there. In this post, we will take a look at education in Ancient Athens.


Athens is located in Central Greece and during antiquity had a population of about 500,000 with about 80% of this population being slaves. This huge disparity between freemen and slaves makes it more amazing that a population of only 100,000 could contribute so much to history.

Generally, slaves and women were not educated. It was considered embarrassing for women to obtain an education. It was the father’s responsibility to educate his son for usefulness.  Failure to do so meant the father forfeited whatever support his son would give him in old age.

The government was shaped largely by Solon. As a democracy, Greece was revolutionary for its time. Solon also established other laws such as outlawing the selling of children and requiring fathers to train their children.

What they Taught

The Athenian education was focused on aesthetics. The idea of beauty influenced everything that was taught.  Subjects taught in Ancient Athens included reading, writing, rhetoric, math, philosophy, music, and poetry. Music and poetry often worked together as poems were set to music. Music was viewed positively as a hobby but professional musicians were looked down on as common laborers.

Physical education was also rigorously taught as beauty was so important. Subjects include swimming, wrestling, running, jumping. One field of study that was often neglected was moral training. The Greek gods were not the best role models.

In place of morals, Greek boys were taught to be patriotic, respect religious rights, and generally to always strive to maintain a good appearance in public.

The teaching methods involved primarily transmission approaches. The teacher would read or say something and the student wrote it down. This was how most subjects were taught.

How they Organized Education

There were essential four levels of education in Ancient Greece. From 0-6 years of age, a boy was under domestic training under his mother or a nanny. Nannys were for the rich.

From 7-14 years of age, the boy was placed under a guardian called a pedagogue and sent to school. There he studied with private teachers the basics of education.

From 14-18 there was a split, the rich continue their education while the poor would branch off and focus on learning a trade from their fathers. For the rich, they would study more complex subjects such as philosophy or higher match. At 18 years of age, a boy would enter military service.


The education found in Ancient Athens was unique in its focus on aesthetics. However, there was at times an indifference to substance and there was almost no interest in moral development. However, educational systems have their flaws and even Ancient Athens is without exception in this regard.

Quadratic Equations and the Square Root Property

A quadratic equation is an equation that includes a variable raised to the second power. Below is a common format for a quadratic equation.


This characteristic makes it difficult to rely on linear equation tricks of addition, subtraction, and multiplying to isolate the variable. One trick that we often have to use now is factoring as shown below.


An alternative way to solve quadratic functions is through having knowledge of the square root property which is shown below.


Below is the same example as our first example but this time we use the square root property.


This trick works for numbers that cannot be factored.


This leads us to the point that the square root property is used for speed or when factoring is not an option.

With this knowledge, all the other possible ways to solve a linear equation can be used to solve a quadratic equation


In the example below is a quadratic formula in which you have to divide to isolate the variable. From there you solve like always1.pngFraction

To remove a fraction you must multiply both sides by the reciprocal as shown below.


When we got the square root of 18 we had to further simplify the radical by finding the factors of 18. In the second to last line if you multiply these numbers together you will get 18 because  9 * 2 = 18. Furthermore, if you square root 9 you get 3 but you cannot square root 2 and get a whole number. This is why the final answer is 3 * the square root of 2.



Quadratic formulas are common in algebra and as such there are many different ways to solve them. In this post, we looked at an alternative to factoring called the square root property. Understanding this approach is valuable as you can often solve quadratic equations faster and or they can be used when factoring is not possible.