Dividing Radical Expressions VIDEO

Dividing Radical Expressions

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Understanding Variables

In research, there are many terms that have the same underlying meaning which can be confusing for researchers as they try to complete a project. The problem is that people have different backgrounds and learn different terms during their studies and when they try to work with others there is often confusion  over what is what.

In this post, we will try to clarify as much as possible various terms that are used when referring to variables. We will look at the following during this discussion

  • Definition of a variable
  • Minimum knowledge of the characteristics of a variable in research
  • Various synonyms of variable

Definition

The word variable has the root of “vary” and the suffix “able”. This literally means that a variable is something that is able to change. Examples include such concepts as height, weigh, salary, etc. All of these concepts change as you gather data from different people. Statistics is primarily about trying to explain and or understand the variability of variables.

However, to make things more confusing there are times in research when a variable dies not change or remains constant. This will be explained in greater detail in a moment.

Minimum You Need to Know

Two broad concepts that you need to understand regardless of the specific variable terms you encounter are the following

  • Whether the variable(s) are independent or dependent
  • Whether the variable(s) are categorical or continuous

When we speak of independent and dependent variables we are looking at the relationship(s) between variables. Dependent variables are explained by independent variables. Therefore, one dimension of variables is understanding how they relate to each other and the most basic way to see this is independent vs dependent.

The second dimension to consider when thinking about variables is how they are measured which is captured with the terms categorical or continuous. A categorical variable has a finite number of values that can be used. Examples in clue gender, hair color, or cellphone brand. A person can only be male or female, have blue or brown eyes, and can only have one brand of cellphone.

Continuous variables are variables that can take on an infinite number of values. Salary, temperature, etc are all continuous in nature. It is possible to limit a continuous variable to categorical variable by creating intervals in which to place values. This is commonly done when creating bins for histograms. In sum, here are the four possible general variable types below

  1. Independent categorical
  2. Independent continuous
  3. Dependent categorical
  4. Dependent continuous

Natural, most models have one dependent categorical or continuous variable, however you can have any combination of continuous and categorical variables as independents. Remember that all variables have the above characteristics despite whatever terms is used for them.

Variable Synonyms

Below is a list of various names that variables go by in different disciplines. This is by no means an exhaustive list.

Experimental variable

A variable whose values are independent of any changes in the values of other variables. In other words, an experimental variable is just another term for independent variable.

Manipulated Variable

A variable that is independent in an experiment but whose value/behavior the researcher is able to control or manipulate. This is also another term for an independent variable.

Control Variable

A variable whose value does not change. Controlling a variable helps to explain the relationship between the independent and dependent variable in an experiment by making sure the control variable has not influenced in the model

Responding Variable

The dependent variable in an experiment. It responds to the experimental variable.

Intervening Variable

This is a hypothetical variable. It is used to explain the causal links between variables. Since they are hypothetical, they are observed in an actual experiment. For example, if you are looking at a strong relationship between income and life expectancy  and find a positive relationship. The intervening variable for this may be access to healthcare. People who make more money have more access to health care and this contributes to them often living longer.

Mediating Variable

This is the same thing as an intervening variable. The difference being often that the mediating variable is not always hypothetical in nature and is often measured it’s self.

Confounding Variable

A confounder is a variable that influences both the independent and dependent variable, causing a spurious or false association. Often a confounding variable is a causal idea and  cannot be described in terms of correlations or associations with other variables. In other words, it is often the same thing as an intervening variable.

Explanatory Variable

This variable is the same as an independent variable. The difference being that an independent variable is not influenced by any other variables. However, when independence is not for sure, than the variable is called an explanatory variable.

Predictor Variable

A predictor variable is an independent variable. This term is commonly used for regression analysis.

Outcome Variable

An outcome variable is a dependent variable in the context of regression analysis.

Observed Variable

This is a variable that is measured directly. An example would be gender or height. There is no psychology construct to infer the meaning of such variables.

Unobserved Variable

Unobserved variables are constructs that cannot be measured directly. In such situations, observe variables are used to try to determine the characteristic of the unobserved variable. For example, it is hard to measure addiction directly. Instead, other things will be measure to infer addiction such as health, drug use, performance, etc. The measures of this observed variables will indicate the level of the unobserved variable of addiction

Features

A feature is an independent variable in the context of machine learning and data science.

Target Variable

A target variable is the dependent variable in the context f machine learning and data science.

To conclude this, below is a summary of the different variables discussed and whether they are independent, dependent, or neither.

Independent Dependent Neither
Experimental Responding Control
Manipulated Target Explanatory
Predictor Outcome Intervening
Feature Mediating
Observed
Unobserved
Confounding

You can see how confusing this can be. Even though variables are mostly independent or dependent, there is a class of variables that do not fall into either category. However, for most purposes, the first to columns cover the majority of needs in simple research.

Conclusion

The confusion over variables is mainly due to an inconsistency in terms across variables. There is nothing right or wrong about the different terms. They all developed in different places to address the same common problem. However, for students or those new to research, this can be confusing and this post hopefully helps to clarify this.

T-SNE Visualization and R

It is common in research to want to visualize data in order to search for patterns. When the number of features increases, this can often become even more important. Common tools for visualizing numerous features include principal component analysis and linear discriminant analysis. Not only do these tools work for visualization they can also be beneficial in dimension reduction.

However, the available tools for us are not limited to these two options. Another option for achieving either of these goals is t-Distributed Stochastic Embedding. This relative young algorithm (2008) is the focus of the post. We will explain what it is and provide an example using a simple dataset from the Ecdat package in R.

t-sne Defined

t-sne is a nonlinear dimension reduction visualization tool. Essentially what it does is identify observed clusters. However, it is not a clustering algorithm because it reduces the dimensions (normally to 2) for visualizing. This means that the input features are not longer present in their original form and this limits the ability to make inference. Therefore, t-sne is often used for exploratory purposes.

T-sne non-linear characteristic is what makes it often appear to be superior to PCA, which is linear. Without getting too technical t-sne takes simultaneously a global and local approach to mapping points while PCA can only use a global approach.

The downside to t-sne approach is that it requires a large amount of calculations. The calculations are often pairwise comparisons which can grow exponential in large datasets.

Initial Packages

We will use the “Rtsne” package for the analysis, and we will use the “Fair” dataset from the “Ecdat” package. The “Fair” dataset is data collected from people who had cheated on their spouse. We want to see if we can find patterns among the unfaithful people based on their occupation. Below is some initial code.

library(Rtsne)
library(Ecdat)

Dataset Preparation

To prepare the data, we first remove in rows with missing data using the “na.omit” function. This is saved in a new object called “train”. Next, we change or outcome variable into a factor variable. The categories range from 1 to 9

  1. Farm laborer, day laborer,
  2. Unskilled worker, service worker,
  3. Machine operator, semiskilled worker,
  4. Skilled manual worker, craftsman, police,
  5. Clerical/sales, small farm owner,
  6. Technician, semiprofessional, supervisor,
  7. Small business owner, farm owner, teacher,
  8. Mid-level manager or professional,
  9. Senior manager or professional.

Below is the code.

train<-na.omit(Fair)
train$occupation<-as.factor(train$occupation)

Visualization Preparation

Before we do the analysis we need to set the colors for the different categories. This is done with the code below.

colors<-rainbow(length(unique(train$occupation)))
names(colors)<-unique(train$occupation)

We can now do are analysis. We will use the “Rtsne” function. When you input the dataset you must exclude the dependent variable as well as any other factor variables. You also set the dimensions and the perplexity. Perplexity determines how many neighbors are used to determine the location of the datapoint after the calculations. Verbose just provides information during the calculation. This is useful if you want to know what progress is being made. max_iter is the number of iterations to take to complete the analysis and check_duplicates checks for duplicates which could be a problem in the analysis. Below is the code.

tsne<-Rtsne(train[,-c(1,4,7)],dims=2,perplexity=30,verbose=T,max_iter=1500,check_duplicates=F)
## Performing PCA
## Read the 601 x 6 data matrix successfully!
## OpenMP is working. 1 threads.
## Using no_dims = 2, perplexity = 30.000000, and theta = 0.500000
## Computing input similarities...
## Building tree...
## Done in 0.05 seconds (sparsity = 0.190597)!
## Learning embedding...
## Iteration 1450: error is 0.280471 (50 iterations in 0.07 seconds)
## Iteration 1500: error is 0.279962 (50 iterations in 0.07 seconds)
## Fitting performed in 2.21 seconds.

Below is the code for making the visual.

plot(tsne$Y,t='n',main='tsne',xlim=c(-30,30),ylim=c(-30,30))
text(tsne$Y,labels=train$occupation,col = colors[train$occupation])
legend(25,5,legend=unique(train$occupation),col = colors,,pch=c(1))

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You can see that there are clusters however, the clusters are all mixed with the different occupations. What this indicates is that the features we used to make the two dimensions do not discriminant between the different occupations.

Conclusion

T-SNE is an improved way to visualize data. This is not to say that there is no place for PCA anymore. Rather, this newer approach provides a different way of quickly visualizing complex data without the limitations of PCA.

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Force-Directed Graph with D3.js

Network visualizations involve displaying interconnected nodes commonly associated with social networks. D3.js has powerful capabilities to create these visualizations. In this post, we will learn how to make a simple force-directed graph.

A force directed graph uses an algorithm that spaces the nodes in the graph away from each other based on a value you set. There are several different ways to determine how the force influences the distance of the nodes from each other that will be explored somewhat in this post.

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The Data

To make the visualization it is necessary to have data. We will use a simple json file that has nodes and edges. Below is the code

{

"nodes": [

{ "name": "Tom" },

{ "name": "Sue" },

{ "name": "Jina" },

{ "name": "Soli" },

{ "name": "Lala" }

],

"edges": [

{ "source": 0, "target": 1 },

{ "source": 0, "target": 4 },

{ "source": 0, "target": 3 },

{ "source": 0, "target": 4 },

{ "source": 0, "target": 2 },

{ "source": 1, "target": 2 }

]

}

The nodes in this situation will represent the circles that we will make. In this case, the nodes have names. However, we will not print the names in the visualization for the sake of simplicity. The edges represent the lines that will connect the circles/nodes. The source number is the origin of the line and the target number is where the line ends at. For example, “source: 0” represents Tom and “Target”: 1 means draw a line from Tom to Sue.

Setup

To begin the visualization we have to create the svg element inside our html doc. Lines 6-17 do this as shown below.

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Next, we need to create the layout of the graph. The .node() and the .link() functions affect the location of the nodes and links. The .size() affects the gravitational center and initial position of the visualization. There is also some code that is commented out in below that will be discussed later. Below are lines 18-25 of our code.

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Now we can write the code that will render or draw our object. We need to append the edges and nodes, indicate color for both, as well as the radius of the circles of the nodes. All of this is captured in lines 26-44

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The final step is to handle the ticks. To put it simply, the ticks handles recalculating the position of the nodes. Below is the code for this.

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We can finally see are visual as shown below

You can clearly see that the nodes are on top of each other. This is because we need to adjust the use of the force in the force-directed graph. There are many ways to adjust this, but we will look at two functions. These are .linkDistance() and .charge().

The .linkDistance() function indicates how far nodes are from each other at the end of the simulation. To add this to our code you need to remove the comments on line22 as shown below.

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Below is an update of what our visualization  looks like.

Things are better but the nodes are still on top of each other. The real differences is that the edges are longer. To fix this, we need to use the .charge() function. The .charge() function indicates how much nodes are attracted to each other or repel each other. To use this function you need to remove the comments on line 23 as shown below.

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The negative charge will cause the nodes to push away from each other. Below is what this looks like.

You can see that as the nodes were moved around the stayed far from each other. This is because of the negative charge. Off course, there are other ways to modify this visualization but this is enough for now.

Conclusion

Force-directed graphs are a  powerful tool for conveying what could be a large amount of information. This post provided some simple ways that this visualization can be developed and utilized for practical purposes.

Essentialist Teacher

Essentialism was an educational philosophy that was reacting to the superficiality of instruction that was associated with progressivism and the aristocratic air that was linked with perennialism. Essentialism was a call to teach the basics. This position of providing a no frill basic education for employment is the primary position of most educational positions in the world.

1Background

Starting in the 1930’s, essentialism is based on the philosophies of idealism and realism. Essentialism supporters have stressed the need to return to a more subject centered approach vs child centered position. Transmission of knowledge is more important than transforming society.

There were two major moments in American history that propelled essentialism to the forefront of education. The first, happened in 1957 when the Russians launch the Sputnik satellite. Critics of progressivism stated that all this child-centered teaching had crippled an entire generation who lacked basic skills in math and science to compete with the Russians. This was a major blow to progressivism as schools refocused on teaching math and science and having a subject centered curriculum.

In essentialism was not already triumphant it certainly was by the 1980’s when the article “A Nation at Risk” was published. This article stated that American education was mediocre and lead to schools needing to focus on the five basics. By the 1990’s such ideas as “core knowledge” or “common core” was being pushed. Such ideas demonstrate how there are basic truths and ideas that supposedly all students need to have.

Philosophy

School is a place where students master basic skills in preparation for working in society. This includes the three R’s (reading, writing, arithmetic) and some of the humanities. The subject matter cannot always be interesting or even immediately relevant for students.

The mind needs to be trained and some memorization is required. However, there is  less of a focus on raw intellectualism such as is found in perennialism. The center of learning is the teacher and the students are there to follow the teacher.

Essentialism has similarities to perennialism. However, there are differences such as the idea that Essentialism does not have a problem with adapting ideas from progressivism for their on own purposes.   There is also a general indifference to time honor classics  in the humanities for the training of the mind.

In Education

An essentialist teacher is going to focus on developing skills and competency rather the learning knowledge for the sake of knowledge. There will be a focus on the basics of education and the classroom will be subject centered. There will not be much tolerance for meeting needs or understanding differences among students.

Focus on job skills and training towards employment would also be stressed. The focus of the education is in training people to be equipped for the workplace and not for personal fulfillment. If students enjoy what they learn this is an added bonus but not necessarily critical for the learning experience.

Conclusion

Essentialism was in many ways a working-class version of perennialism. Stripped of the humanities and focused on developing job skills, essentialism is the engine of education in many parts of American education. As long as the economy and employment are most important to people we will continue to see a continued support for essentialism.

Perennialist Teacher

Perennialism was a strong educational movement in the early part of the 20th century. It pushed a call to return to older ways of learning and instruction in order to strengthen the man in preparation for life. In this post, we will look briefly at the history, philosophy, and how a teacher with a perennialist perspective may approach their classroom.
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Background

Perennialism came about as a strong reaction against progressivism. The emotional focus of the child-centered approach of progressivism was seen as anti-intellectual by perennialists. In place of child- center focus was a call for return to long establish truth and time honored classics.

Supporters of perennialism wanted a liberal education, which implies an education rich with the classical works of man. The purpose of education was the development of the mind rather than the learning of a specific job skill. This position has often been seen as elitist and has clashed with what the working class need for the education of  their children to be in a more practical manner.

A major influencer of perennialism is neo-scholasticism, which is also a supporter of classical studies and was based  on idealism. Perennialism was originally focused higher education and high school but by the 1980’s its influence had spread to elementary education. Prominent supporters of this style include Motimer Adler and Maynard Hutchins.

Philosophical Position

Perennialism believes that people are rational rather than primarily emotional beings. This is the opposite of progressivism which is always worried about feelings. Furthermore, human nature is steady and predictable which allows for everyone to have the same education. Thus, the individual is lost in a strong perennial classroom.

The focus of the classroom is not on the student but rather on the subject matter. The classroom is preparation for life and not design for real-life situations as in progressivism. The mind needs to be developed properly before taking action. Through the study of the greats it is assumed this will help the student become great.

Perennialism and Education

A perennialist teacher would have a classroom in which all the students are treated the same way. Material is taught and delivered to the students whether they like it or not. This is because material is taught that is good for them rather than what they like.

This material would include ancient time tested ideas because that is where truth is and exposure to this great minds would make  great mind. The learning experiences would be mostly theoretical in nature because training in this manner allows for intellectual development.

The classroom might actually be a little cold by the progressivist’standard that focuses on group work and interaction. This is because of the rational focus of perennialism. When the assumption is everyone  is rational and only needed exposure to the content with or without an emotional experience.

Conclusion

Reacting is not always the best way to push for change. Yet this is exactly what brought perennialism into existence. Seeing the lost of absolute truth and long held traditions, perennialism strove to protect these pillars of education. There are some problems. For example, their emphasis on the rational nature of man seems strange as the average person is lacking in the ability to reason and control their emotions. In  addition, the one-size fits all when it comes to education is obviously not true as we need people who have a classic education but also people who can build a house or fix a car. In other words, we need vocational training as well in order to have a balanced society.

Another problem is the fallacy of the appeal to tradition. Just because something is a classic does not make it truth or worthy of study. This simply allow the traditions of the past to rule the present. If all people do is look at the past how will they develop relevant ideas for the present or future?

The main benefit of these different schools of thought is that through these conflicts of opinion a balanced approach to learning can take place for students.

Pie Charts with D3.js

Pie charts are one of many visualizations that you can create using D3.js. We are going to learn how to do the following in this post.

  • Make a circle
  • Make a donut
  • Make a pie wedge
  • Make a segment
  • Make a pie chart

Most of these examples require just a minor adjustment in a standard piece of code. This  will make more sense in a minute.

Make a Circle

Making a circle involves using the .arc() method. In this method there are four parameters that you manipulate to get different shapes. They are explained below

  • .innerRadius() This parameter makes a whole in your circle to give the appearance of a donut
  • .outerRadius() Determines the size of your circle
  • .startAngle() is used in combination with .endAngle() to make a pie wedge

Therefore, to make several different shapes we manipulate these different parameters. In the code below, we create the svg element first (lines 7-10)  then our circle (lines 11-15). Lastly, we append the path to the svg element (lines 16-21). Below is the code and picture.

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The rest of the examples primarily deal with manipulating the existing code.

Donut

To make the donut, you need to change the value inside the .innerRadius() parameter. The larger the value the bigger the hole in the middle of the circle will become. In order to generate the donut below you need to change the value found in line 12 of  the code to 100.

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Pie Wedge

To make a wedge you need to replace lines 14-15 of the code with the following

.startAngle(0*Math.PI * 2/360)

.endAngle(90*Math.PI * 2/360);

This is telling d3.js to start the angle at 0 degrees and stop at 90 degrees. This is another way of saying making a wedge of 1/4 of the circle. Doing this will create the following.

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Segment

In order to make the segment you keep the code the same as above for the pie wedge but at a change to the .innerRadius() parameter. AS shown below,

.innerRadius(100)

.outerRadius(170)

.startAngle(0*Math.PI * 2/360)

.endAngle(90*Math.PI * 2/360);

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Pie Chart

A pie chart is just a more complex version of what we have already done. You still need to set up your svg element. This is don in lines 7-14. Notice that we also had to add a g element and a transform attribute.

Line 16 contains the data for making the pie chat. This is hard coded but we can also use other forms of data. Line 17 uses the .pie() method with the data to set the stage for our pie chart.

Lines 19-27 are for generating the arc. This code is mostly the same except for the functions that are used for the .startAngle() and .end Angle() methods. Line 29 sets the color and Lines 30-42 draw the paths for creating the image. The code with the // will be explained in a moment. Below is the code and the pie chart.

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Pie Chart Variation

Below is the same pie chart but with some different features.

  • It now has a donut (line 20 change .innerRadius(0) to .innerRadius(50))
  • There are now separations between the different segments to give the appearance that it is pulling apart. Remove the // in lines 36-37 to activate this.

Below is the pie chart

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You can perhaps now see that the possibilities are endless with this.

Conclusion

Pie charts and their related visualizations are another option for communicating insights of data

Progressive Teacher

Progressivsim is an educational philosophy that in many ways is the foundation of educational theory in the United States. In this post, we will look at the background of progressivism as well as the beliefs and how it may be practiced by a teacher.
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Background

Progressivsim is yet another reaction to traditional teacher. The era in which this philosophy was developed was the late 19th to early 20th century. This was a time of rapid change and the development of the philosophy called pragmatism, which had a strong influence on progressivism.

Pragmatism had such beliefs as that there was no fixed truth and that whatever works is true. Progressivism adapted and expended on this idea in the context of education. Another major source of influence on progressivism was the work of Freud who encourage self-expression in his writings.

The primary movers in propagating progressivism includes William Kilpatrick, George Counts, John Dewey, and others. This movement dominated educational theory in America from the 1920’s to the 1950’s until the launching of the Sputnik satellite by Russian moved Americans away from child centered self expressive education to an education focused on the essentials in order to compete in a global competition.

Philosophical Position

In the classroom progressivism does not support a teacher-centered approach, nor a heavy focus on textbooks or memorization. there is even concerns with the classroom environment in that the use of fear or physical punishment is discouraged.

The child is the centered of learning rather than the subject. This means that the interest of the child should be taken into consideration when developing learning experiences. Of course, there is a limit to the child’s input as the teacher has a certain responsibility for the learning. However, to even consider the child’s opinion on learning was somewhat revolutionary at the time.

Students need to be active rather than passive. This  means that lectures are unusually because the student not active when listening. Learning by doing is a primary assumption of progressivism. The teacher and the student interact and learn from action rather than from listening.

In order to establish active learning, problem solving is one of the primary tools for teaching. Problem-solving leads to a whole lot of thinking in a systematic manner in ways that are tied to reality rather than to theory.

Lastly, progressivism supports the idea of a democratic classroom. This means that everyone is a learner, including the teacher, and the learning environment encourages discussion and debate. The motive behind this is preparing students to participate in a democratic world.

Progressivism in the Classroom

There is little here to add that was not already mentioned. A progressive teacher is going to support a warm and engaging classroom. The teacher will see themselves as a facilitator of knowledge rather than as a dictator of it. Students will work in groups or alone depending on interest and the content learned  will have input from them. There will be few lectures and more hands on learning activities with a focus on the thought process rather than the product of the  learning.

Conclusion

Progressivism is yet another philosophical system that claimed to have the answer for learning only to eventually lead t people’s disappointment. It was hard to assess learning during the progressives era due to the open nature of problem solving. In addition, when the Russians beat the Americans into space. Focusing on the child simply became impractical due to the perceived threat of Russia. In many ways, progressivism was successful because when it was no longer practical it was abandon and this is something that progressivism teaches.

Dendrogram with D3.js

Dendrogram is a type of hierarchical visualization commonly used in data science with hierarchical clustering. In d3.js, the dendrogram looks slightly different in that the root is in the center and the nodes branch out from there. This idea continues for every parent child relationship in the data.

In this post, we will make a simple dendrogram with d3.js using   a simple json file shown below.

{

  "name": "President",

          "children": [

        { "name": "VP of Academics",

        "children":[

          {"name":"Dean of Psych"},

          {"name":"Dean of Ed"}

        ] },

       { "name": "VP of Finance" },

        { "name": "VP of Students" }

      ]

    }

You will need to save the code above as a json file if you want to make this example. In the code, this json example is called “university.json”

Making the Dendrogram

We will begin by setting up the basic svg limit as found in lines 1-19 below.
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In lines 20-26, the radius of the nodes is set and added to the svg element. The clusters are set with the creation of the cluster variable. Below is the code.

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In lines 27-37, we set the position of the nodes and links as well as diagonals for the path.

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Lines 49-80, have three main blocks of code.

The first block creates a variable called nodesGroups. This code provides a place to hold the nodes and the text that we are going to create.

The second block of code is adding circles to the nodeGroups with  additional settings for the color and radius size. Lastly, the third block of code adds texts to the nodesGroups.

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When all the steps have been taken, you will see the following when you run the code.

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You can see how things worked. The center is the president with the vp of academics of to the right. The president has three people under him (all VPs) while the VP of academics has two people under him (deans). The colors for the path and the circle are all set in the last block of code that was discussed.

Conclusion

Dendrograms allow you to communicate insights about data in a distinctly creative way. This example was simplistic but serves the purpose of exposing you to another way  of using d3.js

Postmodern Teacher

During the last half of the 20th century the philosophical school of post-modernism arose. Just as with existentialism, post-modernism is a school of thought that is anti-definition and anti-organized. As such, it is hard to pinned down exactly what post-modernist believe and stand for in a way that this could be done for older philosophies. In many, ways, as we get closer to the present era the ideas and tenets of the current philosophies become almost invisible  perhaps because we are living directly under their effect rather than looking at their influence in the past.
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Background

Post-modernism, like almost all philosophies it seems, is a reaction  to modernism.  Modernism primary tenet was to understand the world through the use of reason. Modernist believed that the world had fixed laws that could be observed and understood. Science was the way to understand reality and attain truth. There was also this sense of continuous progress, which is something that is still repeated in the media today.

However, modernism did not solve all problems and lead to a Utopian existence. Instead, throughout the late 19th and 20th century there were consequences of scientific and social progress from pollution, to atomic destruction, wars, famine, disease, etc. It seemed as if every time science solved one problem it eventually led to more problems that were not anticipated.

The foundation for post-modernism was laid by Friedrich Nietzsche who claimed that truth and God are dead. This shifted knowledge from something that was absolute to something that was human generated.

Pragmatism and existentialism further laid the groundwork for post-modernism with pragmatism’s position that knowledge was provisional and constantly changing. Existentialism simply reinforces Nietzsche’s position that knowledge is constructed rather than discovered.

Perhaps one of the strongest influences on post-modernism is Marxism. Karl Marx was focused on class struggles from an economic perspective. Within Postmodernism this was extended to other aspects of society including feminism, racism, sexism, LGBT,  weightism, or generally any minority group who is crying out against the perceived “privilege” of the majority.

Philosophical Implications

Postmodernists essential question everything and it almost seems as if they tear down everything with no real replace for what they are tearing down. It is permissible to have opinions about anything but there is no truth except for the truth that there is no truth because they say so.

An example of questioning reality itself  is in the work of Jacques Derrida and his work on deconstructionism. According to Derrida, language has blocked us from understanding reality because we are using words to describe this reality. This means that whenever we read or examine text we have to unpack or deconstruct the assumptions that the author of the text had in terms of their word choices and context. This is critical because the dominant group writes in a way that excludes the minorities and those without power. Of course, you would need to support Derrida’s words even though they may not be representative of reality either

Other postmodern philosophers suggest that reality is socially constructed by those who have power. Those in power shape reality to benefit themselves. There are examples of this in history, as people in power normally portray the powerless negatively. This has even happened in the world of science where views on bloodletting and even the consumption of cocaine.

After identifying these injustices, the postmodernist is not content to identify problems but to push change. The marginal groups need to rise up from the shackles of their oppressors. Pragmatism push change slightly but postmodernism can almost be revolutionary in its language for transformation. Everything is viewed with an eye towards suspicions that begets change except for the idea of viewing everything with skepticism that leads to change.

When everything is viewed as oppression eventually everything is overturned. Whoever gains power will then be viewed as oppressive until they too are overthrown. Eventually, there is nothing left. The problem with postmodernism is not that it identifies problems but that they have no solution beyond tearing everything down over and over again.

In Education

A postmodern teacher is going to be skeptical of absolute truth. They will stress the idea of doubting the text and trying to identify the inconsistencies in an author’s argument. There will be a focus on minority groups and how they are oppressed by those who are privileged.

With deconstructionism, students are trained to be sensitive to language and its use. This is perhaps one reason why such terms as politically correct are used today. People have been trained to be sensitive to language that does not fit the narrative and to identify hurtful language as almost dangerous.

All opinions are expected to be embraced and appreciated no matter how much they lack in validity and credibility unless they are defined as insensitive. Students will never be called upon to store and share the knowledge of the past. Rather, students are change agents who are called to overthrow the social injustice of the planet. This is not revolution as Marx saw it but rather reconstruction of what was deconstructed.

The curriculum is a process and not based on content. The teacher is also a social justice warrior. What is needed is people who challenge the status quo rather than work within it. Therefore, postmodernist thought is much more people in the softer sciences rather than in STEM fields. STEM requires stability in order to expand technology and make discoveries and money. Unfortunately, social stability is not required as much for a sociology or liberal arts major.  The idealistic nature of postmodernism denies the reality that life has never been fair ever in the entire history of humanity.

Tree Diagram with D3.js

Tree diagrams are used for showing hierarchical relationships in data. This post will explain how to make a tree diagram using d3.js.

The Data

We are going to use a simple json file. Below is the code inside the json file.

{

"name": "President",

"children": [

{ "name": "VP of Academics",

"children":[

{"name":"Dean of Psych"},

{"name":"Dean of Ed"}

] },

{ "name": "VP of Finance" },

{ "name": "VP of Students" }

]

}

The code above is json file that models relationships among different positions you would find at a university. The root node is “president”. Under president, there are three children which are “VP of academics”, “VP of Finance”, and “VP of students”.

VP of academics also has two children which are “Dean of Psych” and “Dean of Ed.” You need to save this code on your computer somewhere as a json file for use in the d3.js code.

Below is a picture of what the final visual looks like.

1

The code is too long to post in its entirety here. Rather, you can download the code at the link here.

The code is explained below.

Code Description

Lines 1-26 setup the general documents, loads the data, adds an svg element to the body, and a g element to the svg element. Below is the code.

1.png

Lines 27-34 creates the actual tree and creates variables for the nodes and links that will be used later.

1.png

Lines 36-50 creates the diagonals and the nodes for the diagram. The diagonal is created using the .projection() method. Attributes are set for the diagonal as well under the .selectAll() method and includes the stroke color, width of the stroke, and the fill. The code is below.

1.png

Lines 52-66 create the circles for each node. This involves appending information in the element as well as setting colors for the circles.

1.png

Finally, lines 68-85 involve the text from the json file. The first method calls the text, the second method deals with position, and the last method also addresses position somewhat.

1

A lot of work but can be valuable in certain situations.

Conclusion

Making tree diagrams is another visualization available using d3.js. If the nature of the data is hierarchical this may be a useful approach to consider when make visualizations.

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.