Monthly Archives: June 2019

Factoring Trinomials VIDEO

Factoring trinomials

Pragmatic Teacher

In this post, we will take a look at pragmatism. This philosophy has played a critical role in shaping ideas about education for a long time. In particular, we will look at the characteristics of pragmatism, its philosophical implications, and how it may manifest it’s self in the classroom.

Background

Pragmatism is a uniquely American 19th century contribution to philosophy with some of the primary influences in this school being such people Charles Perce, William James, and John Dewey. The era in which pragmatism was developed was the industrial revolution and an era of great change. Science was gravitating towards the idea of evolution, which at the time was astounding and even the religious world was in turmoil with people speaking of the end of the world. This environment of rapid change was deeply influencing the thoughts of many people.

With all the chaos swirling throughout the world pragmatism came to the point that there were no ideals or principles to look for. Rather, the focus was on what works and benefits the most than on conforming to an external standard.  This position has had a profound impact on education through the work of the progressives as we shall see.

Philosophical Implications

There are no absolutes with a pragmatist. If there is some form of ultimate reality there is no way to know it here. In other words, while Plato bemoaned the cave and Socrates stated that the cave is all there is, a pragmatist may say that the world of forms is possible but since all we know for sure is the cave we should try to make it as nice as comfortable as possible.

One of the sources of argument that pragmatist make about the constant state of change implying a total lack of absolute truth is changes in science. Examples include, moving from a geocentric worldview to a heliocentric one, or moving from a creationist account of life to an evolutionary one. Since these ideas have changed there must not be any absolute truths to hold on to even though the realm of science is notorious for constant changed.

With all the chaos of the world, pragmatist has decided that truth is what works. Knowledge is based on experience. Through trial and error people learn how to deal with various problems. It is this active process of constructing knowledge through experience that knowledge is constructed. Knowledge is not external or outside the person, instead it is created through interaction with the world. This is a major shift in thinking from pass viewpoint and requires that the individual be an active rather than passive learner because they must interact with the world.

There is a separation in the mind of the pragmatist between knowledge and belief. Beliefs are private while knowledge is publicly available., which means it can be observed and verified by others. True knowledge or truth is relative because of the unstable and changing world that we live in.

Since truth is relative morals and values are relative as well. Local societies decide for themselves what is right and wrong and not an external standard. However, this does not mean anything goes. Stealing is disdained in most societies because it does not work as it tends to encourage crime and chaos. The same for murder. This does not mean to the pragmatist that there are universal moral laws, instead it is simply an indication that different groups of people have had similar experiences with stealing and murder and have made the same conclusion that this does not work.

Pragmatism and Education

A unique belief of pragmatism about students is that they need to be active learners. Students need to experience the world around them through learning activities. School is not preparation but is rather part of life it’s self. Therefore, life long learning is to be expected and not just a temporary period of life in which it is needed for studying.

The  teacher is an expert guide who helps the students. They  are a guide because the world changes too quickly to just dictate material to students. This means that the teacher is learning as well with the advantage of more experience living in a world of flux. Since truth is changing, there is no fix curriculum from yesteryear. Instead, the student’s interests are the center of how  the curriculum is built.

With the focus on the environment, the pragmatic teacher is focused heavily on having students impact the world. This means that an emphasis on social action is a part of the pragmatist classroom. In some classroom social change and attaining social goals (ie social justice warrior) is the entire purpose of education. Other philosophies were trying to maintain the status quo but pragmatism is trying to overturn it if it works.

Conclusion

Pragmatism, like most new movements of their time, is simply a reaction to what came before in response to the challenges of the current context. Pragmatist reject absolute truth except for the absolute truth that there is no absolute truth. The world was truly changing quickly when this school of thought was born. However, unlike Plato, who was also experiencing rapid change and decide to search for absolutes in order to find comfort, the pragmatist reject absolute truth for the comfort of constant change. Instead of trying to preserve knowledge it was better to go with the flow as long as it worked.

Existentialist Teacher

This post will examine the mysterious position of existentialism,  which is basic a school of thought that denies that it is a school of thought.  We will look at the origins of existentialism, the characteristics, and its role in education.

Background

Existentialism is all about the individual. In an interesting paradox, existentialism is so individualistic that they do not see themselves as a group with set of beliefs as other philosophies do. There is a rejection of any unified body of beliefs, thoughts, or system.

Early proponents of existentialism include Soren Kierkegaard and Friedrich Nietzsche. These two 19th century philosophers were reacting to the nature of Christianity during their time. Kierkegaard focused on emphasizing the responsibility of the individual believer and their choices within religion. Nietzsche went in a different direction and became convince that there was no God and that man was responsible for his actions alone. This conclusion  eventually drove Nietzsche crazy in a literal manner.

Between the extremes of Kierkegaard and  Nietzsche is where most beliefs of existentialism are. Primarily, existentialism is trying to regain the lost of the individual. This sense of lost may have come from more and more people living in cities to work for others along with the growth of the  government in providing services. The existentialist longed for the day when people were independent and could do what they wanted in returned for the responsibility for their actions.

Philosophical Implications

According to existentialism,  a person must define who they are. Defining who you are is not left to an Absolute Self or Natural Law but to the person who existence. Reality is found within the individual person. This is a major shift from idealism view that reality is beyond this world and realism’s belief that reality is in the physical world.

Truth is based on a person’s choice. People believe what they want because  they want to. This seems confusing but it is laying the foundation for post-modernism min the near future with its view of relative truth. Now, the individual is the source of authority and not any other code.

With a lack of external authority existentialism has to determine right and wrong with no source of authority. This source of freedom has been called a slavery to freedom by some. Slavery is bad but paradoxically too much freedom can be burdensome as well since there is no guidance in terms of how to act. Most people want some freedom but perhaps nobody wants complete freedom as this would be injurious to themselves and others if they could truly do whatever they wanted.

Existentialism and Education

A teacher with an existentialist perspective would be surprised at how students are taught. They would see it as oppressive and even with tendency towards being a form of propaganda. Students would need much more choice and responsibility for their own actions since the current form of teaching destroys individualism.

The existentialist teacher is not the center of the instruction but rather a facilitator. The goal is to help students better understand who they are as individuals. This also means that the student should have a choice in what they learn and that the curriculum needs to be somewhat flexible. The goal is the development of the individual and not the society as the society does not care for the ultimate development of the individual.

Conclusion

Existentialism is a system of thought that claims not to be a system because everyone within the system wants total freedom.  This is contradictory yet considered consistent among existentialist. The reaction they have towards the growing power of large society gives this philosophy a romantic longing for almost a wild pre-industrialization world. However, though many people may not agree with some of the tenets of this group many do wish that they could have at least a little more personal freedom and individuality.

Neo-scholastic Teacher

Scholasticism and Neo-Scholasticism is a philosophy that has had a stronger influence in Christian education rather than in secular circles. This post will explore the characteristics of these philosophies as well as their role in education.

Background

Neo-Scholasticism began as simply scholasticism and was simultaneously a movement and a philosophy that sprang up during the medieval time period in Europe somewhere between 1050 and 1350 originating in the early universities. This was primarily a movement within the Catholic church as they controlled higher education at this time in Europe. The scholars of this movement were not as concern about discovery new truth as it was with proving and establishing the validity of existing truth. In other words, Neo-Scholasticism was primarily reactionary in nature.

The reason for the reactionary nature of Neo-Scholasticism was the rediscovery of the writings of Aristotle. These writings had been lost for centuries but had been preserved in the Islamic nations. Through interactions with the Muslim world through trade and war Aristotle’s writings were translated from Arabic into Latin. Aristotle’s realistic views were a challenge to the Platonic/idealistic views of the Christian church.

Scholars, for whatever reason, were convinced that church teachings had to be harmonized with the writings of Aristotle. Why religious teachings and beliefs had to bow to the influence of one Greek philosopher is subject of debate but perhaps the status of Aristotle compelled the church to merge his ideas with their own in order to maintain intellectual leadership of Europe.

The leader of this merger of faith and reason was Thomas Aquinas. He proposed that people should learn as much as they can through human reason and have faith in matters that cannot be reasoned about. Therefore, at the heart of scholasticism was human reason which in many ways had displaced faith.

Neo-Scholasticism is the modern equivalent of Scholasticism.  The primary difference is that Neo-Scholasticism has religious and secular branch whereas Scholasticism had only one main branch or school of thought.

Philosophical Implications

Scholasticism focus was on accommodating the philosophy of Aristotle with christian thought. Therefore, many of Aristotle’s beliefs are reinterpreted as much as possible to be consistent with Christianity. For example, Aristotle spoke of the Unmoved Mover, which he stated was the first cause of all other causes in the universe. Aquinas equated the Unmoved Mover with God.

Reality had a dualistic nature to it for the scholastic. The natural world was understood through reasoning while the supernatural world was available through revelation and intuition. Truth could be self-evident such as “2+2 = 4” or it can depend on observed experience such as “The average life expectancy is 72 years.” The greatest truth are the unchanging self-evident such as those found in mathematics rather than observed experiential truth.

Morality is governed by reason. There is an assumption that people are rational at their core. The more rational the higher moral quality a person should have.

Neo-Scholasticism and Education

The teacher’s role from a Neo-Scholastic perspective is to help rational students develop their reasoning, will power, and memory. The teacher is the center of the education process and works with students to transfer information. The subject matter takes precedent over the students’ interest.

With  its religious roots, Neo-Scholasticism see the teacher as a spiritual leader. This involves discipleship and even discipline at times. Only through this process can the student acquiring understanding of the unalterable truths of the world.

The curriculum of Neo-Scholasticism would include the humanities, math, and foreign languages (primarily Greek and Latin). The humanities allow students to understand the logic and thinking of great minds, math demonstrates unchanging truths, and foreign languages provides rigors training for the mind. The mind is a muscle that must be strengthened through examining the works of other men.

Conclusion

Neo-Scholasticism has not had the impact on education that idealism or realism has. The emphasis on teacher-centered instruction and memorizing is a major departure from modern forms of teaching. A good memory is not the same as a critical thinker. As with all schools of thought, Neo-Scholasticism suffers from a lack of balance. What is really needed is a flexible position that varies depending on the context.

Path Generators in D3.js

D3.js has the ability to draw rather complex shapes using techniques called path generators. This will allow you to many things that would otherwise be difficult when working with visualizations.

In this post, we will look at three different examples of path generation involving d3.js. The three examples are as follows

  • Making a triangle
  • Duplicating the triangle
  • Make an area chart

Making a Triangle

To make a triangle we start by appending a svg to the body element of our document (lines 7-12). Then when create an array that has three coordinates. We need three coordinates because that is how many coordinates a triangle needs (lines 13-17). After this, we create a variable called generate and use the .svg.line() method to draw the actual lines that we want (lines 18-20).

After this, we append the data and other characteristics to the svg variable. This allows us to set the fill color and the line color (lines 21-28). Below is the code followed by the output.

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A simple triangle was created with only a few lines of code.

Create a Triangle and Duplicate

This example is an extension of the previous one. Here, we create the same triangle, but then we duplicate it using the translate method. This is a powerful technique if you need to make the same shape more than once.

The new code is found in lines 29-36

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You can see that the new triangle was moved to a different position based on the arguments we gave it.

Area Chart

Area charts are often used to make line plots but with the area under the line being filled with a certain color. To achieve this we do the following.

  • Add our svg element to the body element (lines 7-10)
  • Create some random data using the .range() method and several functions (lines 12-18)
    • we generate 1000 random numbers (line 12) between 0 and 100 (line 14)
    •   We set the Y values as random values of X in increments of 10 (line16-17)
  • We create a variable called generate to create the path using the .area() method (line 20-23)
    • y0 has to do with the height or depth of the area the other two attributes are the X and Y values
  • We then append all this to the svg variable we created (lines 25-31)

Below is the code followed by the visual.

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Much more can be done with this but I think this makes the point for now.

Conclusion

This post was just  an introduction to making paths with D3.js.

Metaphysics & Education

Metaphysics is the study of reality and the nature or character of it. This branch  of philosophy deals primarily with what is real. This may seem like an obvious question with an obvious answer. However, different people answer this question in different ways based on what they believe about the nature of reality and how we come to know it.

There are at least four sub-branches of metaphysics  that attempt to address the question of the nature of reality. These four branches are…

  • Cosmology
  • Ontology
  • Anthropology
  • Theology

We will look at each of these and then try to examine how metaphysics manifest itself in education.

Cosmology

Cosmology deals with the origins of the universe. The main views of the origins of the universe can be seen as a continuum from the universe was created or design by God or the other extreme that everything about the universe has happened by accident as is commonly viewed by evolution.  A middle ground along this continuum would be theistic evolution, which states that a divine being used evolution to create the world.

The beliefs an  individual has about cosmology affects other aspects of their life, education, and how they interpret what they experience. For example, an atheist scientist see nature and is awed by the random movement of natural selection to create such beauty. However, a theist would see the same evidence in nature and be led to the conclusion that God has created a beautiful climate. When these two sides meet they cannot agree because they have different assumptions or beliefs about origins and interpret what they see based on these beliefs.

Ontology

Ontology is the study of existence. This is probably one of the harder positions to understand. However, ontology deals with such ideas as whether reality is physical or spiritual, or a combination of the two. In addition, Ontology addresses whether reality is orderly and stable.

People’s beliefs about being can impact how the approach life. If there is nothing there is no reason to care or do anything. However, if there is something beyond this life and life was created with purpose this will alter a person’s behavior as they consider how they may be held accountable for their actions.

Anthropology

Anthropology is the study of man. Some questions that anthropology focuses on in particular is the relationship between the mind and the body. Is it the mind or the body the primary agent of behavior. Other questions include examining whether people or good or evil or morally neutral. Lastly, anthropology addresses the question of the freedom people have. Do people have choice or is their behavior determined by their environment?

The nature vs nurture argument is an old argument about the condition of man. The ultimate question is who is responsible for the actions that people take. The answer to this question evolves around views of the will.

Theology

Theology is the study of the nature of God and plays a profound role at least indirectly in all philosophy. Atheist strongly believe there is no God. As such, the support primarily science as a way of understanding reality. Theists believe there is a God or gods and this natural affects how they view realty.

Even among theists there is disagreement over how many gods there are. Polytheists believe in many gods while monotheists believe in one God. Pantheists believe god(s) is in everything and that they are gods. The position a person has on God can change how they view the world. Monotheists often believe in having a relationship with  one God in order to prepare for the reality of death in this life and the promise of living forever. Polytheists tend to have a contractual quid pro quo relationship with many different gods in order to do better in this world now and smooth the transition to living another life via some form of reincarnation.

Metaphysics and Education

Metaphysics manifest itself in many ways in education. In terms of cosmology and theology, most schools support the idea that the world came about by chance and that life evolved from almost nothing billions of years ago. This is related to theology in that most schools doubt the existence of God being openly atheistic in nature or may at most be agnostic in nature.   In a non-Western context, gods or polytheism is acknowledged and accepted in everyday life but traditional science and atheistic origins of the universe are generally taught in school. This can lead to a dual world view at times.

In terms of ontology and anthropology, the views on ontology vary by culture in education. In the West, the spiritual aspect of man is not acknowledged in education due in part to the focus on science. However, this is beginning to change with the emphasis on mindfulness and meditation in public education. In the East, there is a more open view towards the spiritual nature of man.

In terms of education, students are generally taught that man is inherently good but  may be corrupted by his environment and culture. In the East, education teaches that man is good by nature but may make mistakes. Culture is rarely criticized in eastern education.

Conclusion

Metaphysics is a difficult concept to try to address and understand. The important thing to remember is that metaphysics deals with the question of what is reality and that different people answer this question i different ways. How people answer these questions depends in part on their beliefs about cosmology, ontology, anthropology, and theology.

Drag, Pan, & Zoom Elements with D3.js

Mouse events can be combined in order to create some  rather complex interactions using d3.js. Some examples of these complex actions includes dragging,  panning, and zooming. These events are handle with tools called behaviors. The behaviors deal with dragging, panning, and zooming.

In this post, we will look at these three behaviors in two examples.

  • Dragging
  • Panning and zooming

Dragging

Dragging allows the user to move an element around on the screen. What we are going to do is make three circles that are different colors that we can move around as we desire within the element. We start by setting the width, height of the svg element as well as the radius of the circles we will make (line 7). Next, we create our svg by appending it to the body element. We also set a black line around the element so that the user knows where the borders are (lines 8-14).

The next part involves setting the colors for the circles and then creating the circles and setting all of their attributes (lines 21 – 30). Setting the drag behavior comes later, and we use the .drag() and the .on() methods t create this behavior and the .call() method connects the information in this section to our circles variable.

The last part is the use of the onDrag function. This function retrieves the position of the moving element and transform the element within the svg element (lines 36-46). This involves using an if statement as well as setting attributes. If this sounds confusing, below is the code followed by a visual of what the code does.

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If you look carefully you will notice I can never move the circles beyond the border. This is because the border represents the edge of the element. This is important because you can limit how far an element can travel by determining the size of the elements space.

Panning and Zooming

Panning allows you to move all visuals around at once inside an element. Zooming allows you to expand or contract what you see. Most of this code is a extension  of the what we did in the previous example. The new additions are explained below.

  1. A variable called zoomAction sets the zoom behavior by determining the scale of the zoom and setting the .on() method (Lines 9-11)
  2. We add the .call() method to the svg variable as well as the .append(‘g’) so that this behavior can be used (Lines 20-21).
  3. The dragAction variable is created to allow us to pan or move the entire element around. This same variable is placed inside a .call() method for the circles variable that was created earlier (Lines 40-46).
  4. Lines 48-60 update the position of the element by making two functions. The onDrag function deals with panning and the onZzoom function deal with zooming.

Below is the code and a visual of what it does.

You can clearly see that we can move the circles individually or as a group. In addition, you also were able to see how we could zoom in and out. Unlike the first example this example allows you to leave the border. This is probably due to the zoom capability.

Conclusion

The behaviors shared here provide additional tools that you can use as you design visuals using D3.js. There are other more practical ways to use these tools as we shall see.

Realistic Teacher

Realism is another philosophy that has had a tremendous impact on education and the world in general. The modern world seems to be almost exclusively realist in terms of its worldview thanks in part to the scientific position that most individuals take on matters.

In this post, we will look briefly at the characteristics of realism. In addition, we will also examine how a teacher who believes in realism may approach teaching and realism’s impact on the broader educational process.

Background

Just as Plato was reacting to the change that was surrounding him when he developed his views on idealism, his pupil Aristotle react to idealism by proposing realism. Realism states that objects we perceive with our senses are independent of our mind. In other words, what see exist independently of us and our mind.

However, realism is not a rejection of idealism but in many ways an extension of it. Aristotle thought that everything was made of a combination of form and matter. Form was similar to the ideals of Plato’s idealism and matter was the new contribution that Aristotle was making which is a focus on the material aspect of an object. Form or ideas can exist without matter, such as the ideal or form democracy. Yet matter cannot exist with a form, such as a physical chair with the idea or form of a chair.

Aristotle further proposed that studying the world or matter would lead to a better understanding of universal ideas. This concept has had a strong impact on research in the development of inductive methodology also known as the scientific method.

Philosophical Implications

Reality as seen through idealism is the physical world. The world is similar to a giant machine in which humans are both passively acted upon and actively influencing as well. There are also natural laws that govern the physical world that can be discovered through observation.

Knowledge is gained only through the senses. Something is true because  it was observed. The natural law is within the reality of the natural world and the realist is looking for this through specific examples. This inductive process helps the realist to understand the world around him. In many ways, the Natural Law of the realist is the Absolute Self of the idealist. The difference is in how each is discovered. The idealist thinks about the Absolute Self and knows through intuition that there is an external standard. The realist observes the Natural Law with is senses which confirms the Natural Law’s reality.

Natural Law also extends into the realm of ethics. It is through observing nature and the world that what is right and wrong, beautiful and ugly can be determined according realism. In the Declaration of Independence, Thomas Jefferson  alludes to realism when he speaks of “inalienable rights.” In other words, Jefferson was proposing that some of the rights of man are obvious if one examines the world in which they live.

Realism and Education

A realistic teacher stresses that students learn through their senses. This involves teaching methodologies that have students doing and experiencing things rather than just listening. This can include such activities as field trips, group work, projects etc.

On a darker side, a realist teacher may believe that students are a product of their environment. This has been interpreted as meaning that students do not truly have choice as they are simple responding to the stimuli in their environment. This has lead to a push in education for a focus on behaviorism and even classical conditioning. Furthermore, most learning objectives are behaviorist in nature because a teacher can “see” a behavior which is evidence that the student can do something.  Off course, this has clash with cognitivism (idealism in the 20th century) which focuses on the mind rather than the behavior.

The teacher’s role is to provide sound information about the reality of the physical world and the Natural Law. This is further supported by a focus on math and science, which today is viewed as a focus on STEM majors. One thing all STEM majors have in common is a focus on what can be seen and a disinterest in the realm of ideas and the highly theoretical. Critical thinking is focus almost exclusively on  problem solving and never for the development of an opinion. What really matters are facts and not so much what people think about them.

With the focus on the senses, one thing the teacher and the students will notice is that the world is in a constant state of change. This has led to a rejection of a permanent Natural Law due to the ephemeral quality of reality.

Conclusion

Realism is the primary worldview of education  today. Seeing is believing as the saying goes. Almost nothing is taken seriously unless there is clear observable evidence to support it. Of course, many people believe that feelings and personal experience counts as evidence. This is because feelings and personal experience have actual occurred in the individual person’s life.

Intro to Interactivity with D3.js

The D3.js provides many ways in which the user can interact with visual data. Interaction with a visual can help the user to better understand the nature and characteristics of the data, which can lead to insights. In this post, we will look at three basic examples of interactivity involving mouse events.

Mouse events are actions taken by the browser in response to some action by the mouse. The handler for mouse events is primarily the .on() method. The three examples of mouse events in this post are listed below.

  • Tracking the mouse’s position
  • Highlighting an element based on mouse position
  • Communicating to the user when they have clicked on an element

Tracking the Mouses’s Position

The code for tracking the mouse’s position is rather simple. What is new is Is that we need to create a variable that appends a text element to the svg element. When we do this we need to indicate the position and size of the text as well.

Next, we need to use the .on() method on the svg variable we created. Inside this method is the type of behavior to monitor which in this case is the movement of the mouse. We then create a simple way for the browser to display the x, y coordinates.  Below is the code followed by the actual visual.

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You can see that as the mouse moves the x,y coordinates move as well. The browser is watching the movement of the mouse and communicating this through the changes in the coordinates in the clip above.

Highlighting an Element Based on Mouse Position

This example allows an element to change color when the mouse comes in contact with it. To do this we need to create some data that will contain the radius of four circles with their x,y position (line 13).

Next we use the .selectAll() method to select all circles, load the data, enter the data, append the circles, set the color of the circles to green, and create a function that sets the position of the circles (lines 15-26).

Lastly, we will use the .on() function twice. Once will be for when the mouse touches the circle and the second time for when the mouse leaves the circle. When the mouse touches a circle the circle will turn black. When the mouse leaves a circle the circle will return to the original color of green (lines 27-32). Below is the code followed by the visual.

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Indicating when a User Clicks on an Element

This example is an extension of the previous one. All the code is the same except you add the following at the bottom of the code right before the close of the script element.

.on('click', function (d, i) {

alert(d + ' ' + i);

});

This .on() method has an alert inside the function. When this is used it will tell the user when they have clicked on an element and will also tell the user the radius of the circle as well what position in the array the data comes from. Below is the visual of this code.

Conclusion

You can perhaps see the fun that is possible with interaction when using D3.js. There is much more that can be done in ways that are much more practical than what was shown here.