Subsetting Data in R VIDEO

Subsetting data in R


Basics of LateX

In this post, we will explore more concepts about Latex the typesetting language.

Optional Commands

Optional commands appear in brackets [   ]  when you are using Latex. In the example below, we will set the font size to 20pt in the preamble of the document. The code is as follows.

\documentclass[4paper,12pt]{article} \begin{document} 
     Behold the power of \LaTeX

Here is what it looks like

Screenshot 2018-02-05 14:01:57.png

Inside the brackets, we set the paper size to A4 and the font size to 12pt. Many if not most commands have optional commands that can be used to customize the behavior of the document.


Like most coding languages Latex allows you to make comments. To do this you need to place a % sign in front of your comment. As shown below

\documentclass[4paper,12pt]{article} \begin{document} 
   Behold the power of \LaTeX
   %This will not print

Screenshot 2018-02-05 14:01:57

Everything after the % did not print. To stop this action simply press enter to move to the next line and you can continue with your document.

Fun with Fonts

There are many different ways to set the fonts. Generally, you can use the \text**{  } code. Where the asterisks are is where you can specify the behavior you want of the text. Below is a simple example of the use of several different formats to the font.

   You can \textit{italicized} 
   Text can be \textsl{slanted} 
   Off course, you can \textbf{bold} text 
   You can also make text in \textsc{small caps} 
   It is also possible to use several commands at the same \textit{\textbf{time}} 
   Behold the power of \LaTeX  

Screenshot 2018-02-05 14:01:57.png

Notice how you put the command in front of the word that you want to format. This might seem cumbersome. However, once you get comfortable with this it is much faster to format documents then the point and click style of Word.


If you want a certain effect to last for awhile you can use an environment. An environment is a space you declare in your document in which a center behavior takes place. Generally, environments are used to improve the readability of your code. Below is an example.

            Everything is bold here 
            Everything is bold here 
        Behold the power of \LaTeX  

Screenshot 2018-02-05 14:01:57

An environment always begins with the \begin command and ends with the \end command. In the curly braces, you type whatever is required for your formatting goals. There are scores of commands you can place inside the curly braces.


There is so much more to learn but this is just a beginning. One of the main benefits of learning Latex is the fixed nature of the formatting and the speed at which you can produce content once you are familiar with how to use this language.

Common Problems with Research for Students

I have worked with supporting undergrad and graduate students with research projects for several years. This post is what I consider to be the top reasons why students and even the occasional faculty member struggles to conduct research. The reasons are as follows

  1. They don’t read
  2. No clue what  a problem
  3. No questions
  4. No clue how to measure
  5. No clue how to analyze
  6. No clue how to report

Lack of Reading

The first obstacle to conducting research is that students frequently do not read enough to conceptualize how research is done. Reading not just anything bust specifically research allows a student to synthesize the vocabulary and format of research writing. You cannot do research unless you first read research. This axiom applies to all genres of writing.

A common complaint is the difficulty with understanding research articles. For whatever reason, the academic community has chosen to write research articles in an exceedingly dense and unclear manner. This is not going to change because one graduate student cannot understand what the experts are saying. Therefore, the only solution to understand research English is exposure to this form of communication.

Determining the Problem

If a student actually reads they often go to the extreme of trying to conduct Nobel Prize type research. In other words, their expectations are overinflated given what they know. What this means is that the problem they want to study is infeasible given the skillset they currently possess.

The opposite extreme is to find such a minute problem that nobody cares about it. Again, reading will help in avoiding this two pitfalls.

Another problem is not knowing exactly how to articulate a problem. A student will come to me with excellent examples of a problem but they never abstract or take a step away from the examples of the problem to develop a researchable problem. There can be no progress without a clearly defined research problem.

Lack the Ability to Ask Questions about the Problem

If a student actually has a problem they never think of questions that they want to answer about the problem. Another extreme is they ask questions they cannot answer. Without question, you can never better understand your problem. Bad questions or no questions means no answers.

Generally, there are three types of quantitative research questions while qualitative is more flexible. If a student does not know this they have no clue how to even begin to explore their problem.

Issues with Measurement

Let’s say a student does know what their questions are, the next mystery for many is measuring the variables if the study is quantitative. This is were applying statistical knowledge rather than simply taking quizzes and test comes to play. The typical student does not understand often how to operationalize their variables and determine what type of variables they will include in their study. If you don’t know how you will measure your variables you cannot answer any questions about your problem.

Lost at the Analysis Stage

The measurement affects the analysis. I cannot tell you how many times a student or even a colleague wanted me to analyze their data without telling me what the research questions were. How can you find answers without questions? The type of measurement affects the potential ways of analyzing data. How you summary categorical data is different from continuous data. Lacking this knowledge leads to inaction.

No Plan for the Write-Up

If a student makes it to this stage, firstly congratulations are in order, however, many students have no idea what to report or how. This is because students lose track of the purpose of their study which was to answer their research questions about the problem. Therefore, in the write-up, you present the answers systematically. First, you answer question 1, then 2, etc.

f necessary you include visuals of the answers. Again Visuals are determined by the type of variable as well as the type of question. A top reason for article rejection is an unclear write-up. Therefore, great care is needed in order for this process to be successful.


Whenever I deal with research students I often walk through these six concepts. Most students never make it past the second or third concept. Perhaps the results will differ for others.

Successful research writing requires the ability to see the big picture and connection the various section of a paper so that the present a cohesive whole. Too many students focus on the little details and forget the purpose of their study. Losing the main idea makes the details worthless.

If I left out any common problems with research please add them in the comments section.

Algebraic Mixture Problems

There are many examples in the world in which you want to know the quantity of several different items that make up a whole. When such a situation arise it is an example of mixture problem.

In this post, we will look at several examples of mixture problems. First, we need to look at the general equation for a mixture problem.

number * value = total value

The problems we will tackle will all involve some variation of the equation above. Below is our first example

Example 1

There are times when you want to figure out how many coins are needed to equal a certain dollar amount such as in the problem below

Tom has $6.04 of pennies and nickels. The number of nickels is 4 more and 6 times the number of pennies. How many nickels and pennies does Tom have?

To have success with this problem we need to convert the information into a table to see what we know. The table is below.

Type Number * Value = Total Value
Pennies x .01 .01x
Nickels 6x+4 .05 .05(6x+4)

total 6.04

We can now solve our equation.


We know that there are 18.83 pennies. To determine the number of nickels we put 18.83 into x and get the following.


Almost 117 nickels

You can check if this works for yourself.

Example 2 

For those of us who love to cook, mixture equations can be used for this as well below is an example.

Tom is mixing nuts and cranberries to make 20 pounds of trail mix. Nuts cost $8.00 per pound and cranberries cost $3.00 per pound. If Tom wants to his trail mix to cost $5.50 per pound how many pounds of raisins and cranberries should he use? 

Our information is in the table below. What is new is subtracting the number of pounds from x. Doing so will help us to determine the number of pounds of cranberries.

Type Number of Pounds* Price Per Pound = Total Value
nuts x 8 8x
Cranberries 20-x 3 3(20-x)
Trail Mix 20 5.5 20(5.50)

We can now solve our equation with the information in the table above.


Once you solve for x you simply place this value into the equation. When you do this you see that we need ten pounds of nuts and berries to reach our target cost.


This post provided to practical examples of using algebra realistically. It is important to realize that understanding these basics concepts can be useful beyond the classroom.

Intro to LaTex


LaTex is an open-sourced typesetting document developed about 30 years ago by Leslie Lamport and based on the Tex typesetting of Donald Knuth. It is commonly used in the domains of physics and math for producing mathematical equations and other technical documents. Below is a simple example of an equation developed using LaTex


LaTex is a document markup language, which means that you indicate the commands and then it is processed to produce the desired effect. This is in contrast to Microsoft Word which utilizes a WYSIWYG (What you see is what you get) approach.


Using LaTex provides several benefits. Cross-referencing is easily accomplish especially with the help of BibTex. It is also multi-lingual and able to make glossaries, indexes, and figures/tables with ease. In addition, LaTex is highly portable and opening a file on any computer is not a problem. Sometimes moving to another computer using Microsoft Word can cause issues with formatting.

Another benefit is psychology, using LaTex allows the author to focus on content and not appearance when writing. It is easy to get distracted when using Word to try and make something work through the point and click mechanism we are so used to when writing.


It takes extensive time to use LaTex. It looks similar to coding which is intimidating for many. However, once a certain mastery is achieved. Producing documents can be faster as everything is text-based and not point click based using a mouse.

Using LaTex

To use LaTex you need to install TexLive and TexWorks. TextLive is a LaTex distribution and TexWorks is one of many LaTex editors. The editor allows you to manipulate the LaTex code that you generate.

Once you have installed both programs you can type the following into TexWorks. Make sure the typeset is set to pdfLaTex. This allows the output to be a pdf file.

This is an example of what LaTex does


What happened is as follows

  1. We entered the command \documentclass{article}. All commands begin with a slash followed by the name. The curly braces are required arguments. In this case, we are using the article template which is one of many templates available in LaTex.
  2. The next command is \begin and this command indicates the beginning of the actual text of the document. Everything above the \begin command is part of what we call the preamble.
  3. Next is the actual text that we want to appear in the pdf.
  4. Lastly, we have the \end command which tells LaTex that the document is finished. Everything between \begin and \end command is part of the environment.


There is so much more that can be accomplished with this typesetting software. The possibilities will be explored in the near future.

Solving Equations with Fractions or Decimals

This post will provide an explanation of how to solve equations that include fractions or decimals. The processes are similar in that both involve determining the least common denominator.

Solving Equations with Fractions

The key step to solving equations with fractions is to make sure that the denominators of all the fractions are the same. This can be done by finding the least common denominator. The least common denominator (LCD) is the smallest multiple of the denominators. For example, if we look at the multiples of 4 and 6 we see the following.


You can see clearly that the number 12 is the first multiple that 4 and 6 have in common. You can find the LCD by making factor trees but that is beyond the scope of this post. The primary reason we would need the LCD is when we are adding fractions in an equation. If we are multiplying we could simply multiply straight across.

Below is an equation that has fractions. We will find the LCD


Here is an explanation of each step

  • A. This is the original problem. We first need to find the LCD
  • B. We then multiply each fraction by the LCD
  • C. This is the equation we solve for
  • D. We get the variable alone by subtracting 20 from each side
  • E. We have our new simplified equation
  • F. We further isolate the variable by dividing by 3 on both sides.
  • G. This is our answer

Solving Equations with Decimals

The process for solving equations with decimals is almost the same as for fractions. The LCD of all decimals is 100. Therefore, one common way to deal with decimals is to multiply all decimals by 100 and the continue to solve the equation.

The primary benefit of multiply by 100 is to remove the decimals because sometimes we make mistakes with where to place decimals. Below is an example of an equation with decimals.

1.pngHere is what we did

  • A. Initial equation
  • B. we distribute the 0.10
  • C. Revised equation
  • D. We multiply everything by 100.
  • E. Revised equation
  • F. Subtract 20 from both sides to isolate the variable
  • G. Revised equation
  • H. Divide both sides by 30 to isolate the variable
  • I. Final answer


Understand the process of solving equations with fractions or decimals is not to complicated. However, this information is much more valuable when dealing with more complex mathematical ideas.

Linear Equations

In this post, we will look at several types of equations that you would encounter when learning algebra. Algebra is a foundational subject to know when conducting most quantitative research.


An equation is a statement that balances two expressions. Often equations include a variable or an unknown value. By solving for the unknown value you are able to balance the equation.

There are many different types of equations such as

(1) Linear equation

(2) Quadratic equation

(3) Polynomial equation

See number 1 or 2. The rule for polynomial equation is that the exponent must be positive
(4) Trigonometric equation

(5) Radical equation

(6) Exponential equation

This post will focus on linear equations.

Linear Equation

A linear equation is an equation that if it is graph will render a straight line. It is common to have to solve for the variable in a linear equation by isolating as in the example below.


There are also several terms related to equations and the include the following

  • Conditional equation: An equation that is true for only one value of the variable. The example above is a conditional equation.
  • Identity: An equation that is true for any value of a variable. Below is an example

Any value of x will work with an identity equation.

  • A contradiction is an equation that is false for all values. Below is an example


No value of x will work with the equation above.


This post provided an overview of the types of equations commonly encountered in algebra.

Real Number Properties

In this post, we will examine several properties of math. The word property in this context means characteristic or trait. In other words, we are going to look at characteristics of math.

Communicative Property

The communicative property applies both to addition and multiplication. To express this simply the communicative property states that the order the of the numbers does not matter when we add or multiply. Examine the example below


Whether 8 =+ 9 or 9+ 8 it doesn’t matter as the answer is the same. However, this does not work for subtraction or division because the order of the numbers is critical. Consider the following


The point is order does not matter for addition and multiplication but the order does matter for subtraction and division.

Associative Property

The associative property has to do with the grouping of numbers. Often, numbers are grouped in equations with parentheses or brackets. When this is done for an addition and multiplication problem there is no change to the results. You can see this in the example below.


However, the associative property does not work with subtraction and division as the order of the numbers affects the final values as shown below.


Identity Property

The identity property of addition states that any number added to zero does not change. The identity property of multiplication states that any number multiplied by 1 does not change.

Inverse Property

There are also inverse properties for addition and nultiplication. The inverse property of addition states that adding the opposite value to a real number will result in zero. Or in other words


The inverse property of multiplication states any number multiplied by its reciprocal will equal 1. Or as shown below


Distributive Property

The distributive property is used to get rid of parentheses in order to simplify expressions. This is hard to explain but easy to figure out with an example as shown below.


In the example, you can see that we distributed the 6 by multiplying it with the values within the parentheses. By doing this we were able to remove the parentheses.


Understanding these properties are useful when it is necessary to do more complex calculations. When you know how the numbers should behave it is easier to identify when they do not behave appropriately.

Teaching Math

Probably one of the most dreaded subjects in school is math. Many students fear this subject and perhaps rightfully so. This post will provide some basic tips on how to help students to understand what is happening in math class.

Chunk the Material

Many math textbooks, especially at the college level, are huge. By huge we are talking over 1000 pages. That is a tremendous amount of content to cover in a single semester even if the majority of the pages are practice problems.

To overcome this, many have chapters that are broken down into 5 sub-sections such as 1.1, 1.2, etc. This means that in a given class period, students should be exposed to 2 or 3 new concepts. Depending on their background this might be too many for a student, especially if they are not a math major.

Therefore, a math teacher must provide new concepts only after previous concepts are mastered. This means that the syllabus needs to flexible and the focus is on the growth of students rather than covering all of the material.

Verbal Walk Through

When teaching math to a class, normally a teacher will provide an example of how to do a problem. The verbal walkthrough is when the teacher completes another example of the problem and the students tell the teacher what to do verbally. This helps to solidify the problem-solving process in the students’ minds.

A useful technique in relation to the verbal walkthrough is to intentional make mistakes when the students are coaching you. This requires the students to think about what is corrected and to be able to explain what was wrong with what the teacher did. The wisest approach is to make mistakes that have been experienced in the past as these are the ones that are likely to be repeated.

The verbal walkthrough works with all students of all ages. It can be more chaotic with younger children but this is a classic approach to teaching the step-by-step process of learning math calculations.

Practice Practice Practice

Daily practice is needed when learning mathematical concepts. Students should be learning new material while reviewing old material. The old material is reviewed until it becomes automatic.

This requires the teacher to determine the most appropriate mix of new and old. Normally, math has a cumulative effect in that new material builds on old. This means that students are usually required to use old skills to achieve new skills. The challenge is in making sure the old skills are at a certain minimum level that they can be used to acquire new skills.


Math is tough but if a student can learn it math can become a highly practical tool in everyday life. The job of the teacher is to develop a context in which math goes from mysterious to useful.

Algebraic Expressions and Equations

This post will focus mainly on expressions and their role in algebra. Expressions play a critical role in mathematics and we all have had to try and understand what they are as well as what they mean.

Expression Defined

To understand what an expression is you first need to know what operation symbols are. Operation symbols tell you to do something to numbers or variables. Examples include the plus, minus, multiply, divide, etc.

An expression is a number, variable, or a combination of numbers[s] and variable[s] that use operation symbols. Below is an example


Expressions consist of two terms and these are variables and constants. A variable is a letter that represents a number that can change. In our example above, the letter a is a variable.

A constant is a number whose value remains the same. In our example above, the numbers 2 and 4 are constants.

Expression vs Equation

An equation is when two expressions connected by an equal sign as shown below.


In the example above we have to expressions. To the left of the equal sign is 2a * 4 and to the right of the equal sign is 16. Remember that an expression can be numbers and or variables so 16 is an expression because it is a number.

Simplify an Expression

Simplifying an expression involves completing as much math as possible to reduce the complexity of an expression. Below is an example.


In order to complete this expression  above you need to know the order of operations which is explained below

Multiplication Division
Adition Subtraction

In the example above, we begin with multiplication of 8 and 4 before we do the addition of adding 2. It’s important to remember that for multiplication/division or addition/subtraction that you move from left to right when dealing with these operation symbols in an expression. It is also important to know that subtraction and division are not associative (or commutative) that is: (1 – 2) – 3 != 1 – (2 – 3).

Evaluating an Expression

Evaluating an expression is finding the value of an expression when the variable is replaced with a specific number.


Combining Like Terms

A common skill in algebra is the ability to combine like terms. A term is a constant or constant with one or more variables. Terms can include a constant such as 7 or a number and variable product such as 7a. The constant that multiplies the variable is called a coefficient. For example, 7a, 7 is the constant and the coefficient while a is the variable.

Combining like terms involves combining constant are variables that have the same characteristics for example

  • 3 and 2 are like terms because they are both constants
  • 2x and 3x are like terms because they are both constants with the same variable

Below is an example of combining like terms


In this example, we first placed like terms next to each other. This makes it easier to add them together. The rest is basic math.


Hopefully, the concept of expressions makes more sense. This is a foundational concept in mathematics that if you do not understand. It is difficult to go forward in the study of math.

Basic Algebraic Concepts

This post will provide insights into some basic algebraic concepts. Such information is actually useful for people who are doing research but may not have the foundational mathematical experience.


A multiple is a product of  and a counting number of n. In the preceding sentence, we actually have two unknown values which are.

  • n
  • Counting number

The can be any value, while the counting number usually starts at 1 and continues by increasing by 1 each time until you want it to stop. This is how this would look if we used the term n,  counting number, and multiple of n. 

n * counting number = multiple of n

For example, if we say that = 2 and the counting numbers are 1,2,3,4,5. We get the following multiples of 2.


You can see that the never changes and remains constant as the value 2. The counting number starts at 1 and increases each time. Lastly, the multiple is the product of n and the counting number.

Let’s take one example from above

2 * 3 = 6

Here are some conclusions we can make from this simple equation

  • 6 is a multiple of 2. In other words, if I multiply 2 by a certain counting number I can get the whole number of 6.
  • 6 is divisible by 2. This means that if I divide 2 into six I will get a whole number counting number which in this case is 3.

Divisibility Rules

There are also several divisibility rules in math. They can be used as shortcuts to determine if a number is divisible by another without having to do any calculation.

A number is divisible by

  • 2 when the last digit of the number 0, 2, 4, 6, 8
    • Example 14, 20, 26,
  • 3 when the sum of the digits is divisible by 3
    • Example 27 is divisible by 3 because 2 + 7 = 9 and 9 is divisible by 3
  • 5 when the number’s last digit is 0 or 5
    • Example 10, 20, 25
  • 6 when the number is divisible by 2 and 3
    • Example 24 is divisible by 6 because it is divisible by 2 because the last digit is for and it is divisible by 3 because 2 + 4 = 6 and six is divisible by 3
  • 10 when the number ends with 0
    • Example 20, 30 , 40, 100


Factors are two or more numbers that when multiplied produce a number. For example


The numbers 7 and 6 are factors of 42. In other words, 7 and 6 are divisible by 42. A number that has only itself and one as factors is known as a prime number. Examples include 2, 3, 5, 7, 11, 13. A number that has many factors is called a composite number and includes such examples as 4, 8, 10, 12, 14.

An important concept in basic algebra is understanding how to find the prime numbers of a composite number. This is known as prime factorization and is done through the development of a factor tree. A factor tree breaks down a composite number into the various factors of it. These factors are further broken down into their factors until you reach the bottom of a tree that only contains prime numbers. Below is an example



You can see in the tree above that the prime factors of 12 are 2 and 3. If we take all of the prime factors and multiply them together we will get the answer 12.



Understanding these basic terms can only help someone who maybe jumped straight into statistics in grad school without have the prior thorough experience in basic algebra.

APA Tables in R

Anybody who has ever had to do any writing for academic purposes or in industry has had to deal with APA formatting. The rules and expectations seem to be endless and always changing. If you are able to maneuver the endless list of rules you still have to determine what to report and how when writing an article.

There is a package in R that can at least take away the mystery of how to report ANOVA, correlation, and regression tables. This package is called “apaTables”. In this post, we will look at how to use this package for making tables that are formatted according to APA.

We are going to create examples of ANOVA, correlation, and regression tables using the ‘mtcars’ dataset. Below is the initial code that we need to begin.



We will begin with the results of ANOVA. In order for this to be successful, you have to use the “lm” function to create the model. If you are familiar with ANOVA and regression this should not be surprising as they both find the same answer using different approaches. After the “lm” function you must use the “filename” argument and give the output a name in quotations. This file will be saved in your R working directory. You can also provide other information such as the table number and confidence level if you desire.

There will be two outputs in our code. The output to the console is in R. A second output will be in a word doc. Below is the code.

apa.aov.table(lm(mpg~cyl,mtcars),filename = "Example1.doc",table.number = 1)
## Table 1 
## ANOVA results using mpg as the dependent variable
##    Predictor      SS df      MS      F    p partial_eta2
##  (Intercept) 3429.84  1 3429.84 333.71 .000             
##          cyl  817.71  1  817.71  79.56 .000          .73
##        Error  308.33 30   10.28                         
##  CI_90_partial_eta2
##          [.56, .80]
## Note: Values in square brackets indicate the bounds of the 90% confidence interval for partial eta-squared

Here is the word doc output


Perhaps you are beginning to see the beauty of using this package and its functions. The “apa.aov.table”” function provides a nice table that requires no formatting by the researcher.

You can even make a table of the means and standard deviations of ANOVA. This is similar to what you would get if you used the “aggregate” function. Below is the code.

apa.1way.table(cyl, mpg,mtcars,filename = "Example2.doc",table.number = 2)
## Table 2 
## Descriptive statistics for mpg as a function of cyl.  
##  cyl     M   SD
##    4 26.66 4.51
##    6 19.74 1.45
##    8 15.10 2.56
## Note. M and SD represent mean and standard deviation, respectively.

Here is what it looks like in word



We will now look at an example of a correlation table. The function for this is “apa.cor.table”. This function works best with only a few variables. Otherwise, the table becomes bigger than a single sheet of paper. In addition, you probably will want to suppress the confidence intervals to save space. There are other arguments that you can explore on your own. Below is the code

apa.cor.table(mtcars,filename = "Example3.doc",table.number = 3,show.conf.interval = F)
## Table 3 
## Means, standard deviations, and correlations
##   Variable M      SD     1      2      3      4      5      6      7     
##   1. mpg   20.09  6.03                                                   
##   2. cyl   6.19   1.79   -.85**                                          
##   3. disp  230.72 123.94 -.85** .90**                                    
##   4. hp    146.69 68.56  -.78** .83**  .79**                             
##   5. drat  3.60   0.53   .68**  -.70** -.71** -.45**                     
##   6. wt    3.22   0.98   -.87** .78**  .89**  .66**  -.71**              
##   7. qsec  17.85  1.79   .42*   -.59** -.43*  -.71** .09    -.17         
##   8. vs    0.44   0.50   .66**  -.81** -.71** -.72** .44*   -.55** .74** 
##   9. am    0.41   0.50   .60**  -.52** -.59** -.24   .71**  -.69** -.23  
##   10. gear 3.69   0.74   .48**  -.49** -.56** -.13   .70**  -.58** -.21  
##   11. carb 2.81   1.62   -.55** .53**  .39*   .75**  -.09   .43*   -.66**
##   8      9     10 
##   .17             
##   .21    .79**    
##   -.57** .06   .27
## Note. * indicates p < .05; ** indicates p < .01.
## M and SD are used to represent mean and standard deviation, respectively.

Here is the word doc results


If you run this code at home and open the word doc in Word you will not see variables 9 and 10 because the table is too big by itself for a single page. I hade to resize it manually. One way to get around this is to delate the M and SD column and place those as rows below the table.


Our final example will be a regression table. The code is as follows

apa.reg.table(lm(mpg~disp,mtcars),filename = "Example4",table.number = 4)
## Table 4 
## Regression results using mpg as the criterion
##    Predictor       b       b_95%_CI  beta    beta_95%_CI sr2 sr2_95%_CI
##  (Intercept) 29.60** [27.09, 32.11]                                    
##         disp -0.04** [-0.05, -0.03] -0.85 [-1.05, -0.65] .72 [.51, .81]
##       r             Fit
##  -.85**                
##             R2 = .718**
##         95% CI[.51,.81]
## Note. * indicates p < .05; ** indicates p < .01.
## A significant b-weight indicates the beta-weight and semi-partial correlation are also significant.
## b represents unstandardized regression weights; beta indicates the standardized regression weights; 
## sr2 represents the semi-partial correlation squared; r represents the zero-order correlation.
## Square brackets are used to enclose the lower and upper limits of a confidence interval.

Here are the results in word


You can also make regression tables that have multiple blocks or models. Below is an example

apa.reg.table(lm(mpg~disp,mtcars),lm(mpg~disp+hp,mtcars),filename = "Example5",table.number = 5)
## Table 5 
## Regression results using mpg as the criterion
##    Predictor       b       b_95%_CI  beta    beta_95%_CI sr2  sr2_95%_CI
##  (Intercept) 29.60** [27.09, 32.11]                                     
##         disp -0.04** [-0.05, -0.03] -0.85 [-1.05, -0.65] .72  [.51, .81]
##  (Intercept) 30.74** [28.01, 33.46]                                     
##         disp -0.03** [-0.05, -0.02] -0.62 [-0.94, -0.31] .15  [.00, .29]
##           hp   -0.02  [-0.05, 0.00] -0.28  [-0.59, 0.03] .03 [-.03, .09]
##       r             Fit        Difference
##  -.85**                                  
##             R2 = .718**                  
##         95% CI[.51,.81]                  
##  -.85**                                  
##  -.78**                                  
##             R2 = .748**    Delta R2 = .03
##         95% CI[.54,.83] 95% CI[-.03, .09]
## Note. * indicates p < .05; ** indicates p < .01.
## A significant b-weight indicates the beta-weight and semi-partial correlation are also significant.
## b represents unstandardized regression weights; beta indicates the standardized regression weights; 
## sr2 represents the semi-partial correlation squared; r represents the zero-order correlation.
## Square brackets are used to enclose the lower and upper limits of a confidence interval.

Here is the word doc version



This is a real time saver for those of us who need to write and share statistical information.

Reading Comprehension Strategies

Students frequently struggle with understanding what they read. There can be many reasons for this such as vocabulary issues, to struggles with just sounding out the text. Another common problem, frequently seen among native speakers of a language, is the students just read without taking a moment to think about what they read. This lack of reflection and intellectual wrestling with the text can make so that the student knows they read something but knows nothing about what they read.

In this post, we will look at several common strategies to support reading comprehension. These strategies include the following…

Walking a Student Through the Text

As students get older, there is a tendency for many teachers to ignore the need to guide students through a reading before the students read it. One way to improve reading comprehension is to go through the assigned reading and give an idea to the students of what to expect from the text.

Doing this provides a framework within the student’s mind in which they can add the details to as they do the reading. When walking through a text with students the teacher can provide insights into important ideas, explain complex words, explain visuals, and give general ideas as to what is important.

Ask Questions

Asking question either before or after a reading is another great way to support students understanding. Prior questions give an idea of what the students should be expected to know after reading. On the other hand, questions after the reading should aim to help students to coalesce the ideals they were exposed to in the reading.

The type of questions is endless. The questions can be based on Bloom’s taxonomy in order to stimulate various thinking skills. Another skill is probing and soliciting responses from students through encouraging and asking reasonable follow-up questions.

Develop Relevance

Connecting what a student knows what they do not know is known as relevance.If a teacher can stretch a student from what they know and use it to understand what is new it will dramatically improve comprehension.

This is trickier than it sounds. It requires the teacher to have a firm grasp of the subject as well as the habits and knowledge of the students. Therefore, patience is required.


Reading is a skill that can improve a great deal through practice. However, mastery will require the knowledge and application of strategies. Without this next level of training, a student will often become more and more frustrated with reading challenging text.

Criticism of Grades

Grading has recently been under attack with people bringing strong criticism against the practice. Some schools have even stopped using grades altogether. In this post, we will look at problems with grading as well as alternatives.

It Depends on the Subject

The weakness of grading is often seen much more clearly in subjects that have more of a subjective nature to them from the Social sciences and humanities such as English, History, or Music. Subjects from the hard sciences such as biology, math, and engineering are more objective in nature. If a student states that 2 + 2 = 5 there is little left to persuasion or critical thinking to influence the grade.

However, when it comes to judging thinking or musical performance it is much more difficult to assess this without bringing the subjectivity of opinion. This is not bad as a teacher should be an expert in their domain but it still brings an arbitrary unpredictability to the system of grading that is difficult to avoid.

Returning to the math problem, if a student stats 2 +2 =  4 this answer is always right whether the teacher likes the student or not. However, an excellent historical essay on slavery can be graded poorly if the history teacher has issues with the thesis of the student. To assess the essay requires subjective though into the quality of the student’s writing and subjectivity means that the assessment cannot be objective.

Obsession of Students

Many students become obsess and almost worship the grades they receive. This often means that the focus becomes more about getting an ‘A’ than on actually learning. This means that the students take no-risk in their learning and conform strictly to the directions of the teacher. Mindless conformity is not a sign of future success.

There are many comments on the internet about the differences between ‘A’ and ‘C’ students. How ‘A’ students are conformist and ‘C’ students are innovators. The point is that the better the academic performance of a student the better they are at obeying orders and not necessarily on thinking independently.

Alternatives to Grades

There are several alternatives to grading. One of the most common is Pass/fail. Either the student passes the course or they do not. This is common at the tertiary level especially in highly subjective courses such as writing a thesis or dissertation. In such cases, the student meets the “mysterious” standard or they do not.

Another alternative is has been the explosion in the use of gamification. As the student acquires the badges, hit points, etc. it is evidence of learning. Of course, this idea is applied primarily at the K-12 level but it the concept of gamification seems to be used in almost all of the game apps available on cellphones as well as many websites.

Lastly, observation is another alternative. In this approach, the teacher makes weekly observations of each student. These observations are then used to provide feedback for the students. Although time-consuming this is a way to support students without grades.


As long as there is education there must be some sort of way to determine if students are meeting expectations. Grades are the current standard. As with any system, grades have their strengths and weaknesses. With this in mind, it is the responsibility of teachers to always search for ways to improve how students are assessed.

Passive vs Active Learning

Passive and active learning are two extremes in the world of teaching. Traditionally, learning has been mostly passive in nature. However, in the last 2-3 decades, there has been a push, particularly in the United States to encourage active learning in the classroom.

This post will define passive and active learning and provide examples of each.

Passive Learning

Passive learning is defined from the perspective of the student and means learning in which the students do little to nothing to acquire the knowledge. The most common form of passive learning is direct instruction aka lecture-style teaching.

With passive learning, the student is viewed as an empty receptacle of knowledge that the teacher must fill with his knowledge. Freire called this banking education as the student serves as an account in which the teacher or banker places the knowledge or money.

There is a heavy emphasis on memorizing and recalling information. The objective is the preservation of knowledge and the students should take notes and be ready to repeat or at least paraphrase what the teacher said. The teacher is the all-wise sage on the stage.

Even though it sounds as though passive learning is always bad there are times when it is beneficial. When people have no prior knowledge of a subject passive learning can provide a foundation for future active learning activities. In addition, if it is necessary to provide a large amount of information direct instruction can help in achieving this.

Active Learning

Active learning is learning in which the students must do something in order to learn. Common examples of this include project-based learning, flipped classroom, and any form of discussion in the classroom.

Active learning is derived from the philosophy of constructivism. Constructivism is the belief that students used their current knowledge to build new understanding. For example, with project-based learning students must take what they know in order to complete the unknown of the project.

For the flipped classroom, students review the lecture style information before class. During class, the students participate in activities in which the use what they learned outside of class. This in turn “flips” the learning experience. Out of class is the passive part while in class is the active part.

There is a reduction or total absence of lecturing in an active learning classroom. Rather students interact with each and the teacher to develop their understanding of the content. This transactional nature of learning is another characteristic of active learning.

There are some challenges with active learning. Since it is constructivist in nature it can be difficult to assess what the students learned. This is due in part to the subjective nature of constructivism. If everybody constructs their own understanding everybody understands differently which makes it difficult to have one objective assessment.

Furthermore, active learning is time-consuming in terms of preparation and the learning experience. Developing activities and leading a discussion forces the class to move slower. If the demands of the course require large amounts of content this can be challenging for many teachers.


There is room in the world of education for passive and active learning strategies. The main goal should be to find a balance between these two extremes as over reliance on either one will probably be a disadvantage to students.

Teacher Burnout

Teacher burnout is a common problem within education. The statistics vary but you can safely say about 1/3 of teachers suffer from some form of burnout at one point or another during their career. This post will define burnout, explain some of the causes, the stages of burnout, as well as ways to deal with burnout.


Essentially, teacher burnout is an experience of a person who is overwhelmed by the stress of teaching. The most common victims of this are young teachers as well as female teachers.

Young teachers are often at higher risk because they have not developed coping mechanisms for the rigors of teaching. Women are also more often to fall victim to teacher burnout because of the added burning of maintaining the home as well as difficulties with distancing themselves emotionally from their profession as a teacher.


Teacher burnout is generally caused by stress. Below are several forms of stress that can plague the teaching profession.

  • Workload-This is especially true for those who can never say “no.” Committees, field trips, student activities, grading, lesson plans, accreditation. All of these important tasks can overwhelm a person
  • Student behavioral problems-Classroom management is always a challenge as families continue to collapse.
  • Issues with leadership
  • Boredom-This stressor is more common with experienced teachers who have taught the same content for years. There are only so many ways to teach content that are appealing to the teacher before there is some repetition. Boredom can also be especially challenging for a teacher who values learning more than personal relationships with students.

Stages of Burnout

The stages of teacher burnout follow the same progression as burnout in other social work like professions. Below are four stages as developed by McMullen

  1. Closed off- The burnout victim stops socializing and is rigid against feedback. Signs include self-neglect.
  2. Irritable-The victim temper shortens. In addition, he begins to complain about everything. Problems are observed everywhere whether they are legitimate or not.
  3. Paranoia-The teacher is worried about everything. Depression is common at this point as well as a loss of motivation.
  4. Exhaustion-THe teacher is emotionally drained. They no longer “care” as they see no way to improve the situation. Compassion fatigue sets in which means that there is no more emotional support to give to students.

Dealing with Burnout

Perhaps the most important step coping with burnout is to prioritize. It is necessary for a sake of sanity to say no to various request at times. Personal time away from any job is critical to being able to return refreshed. Therefore, teaching cannot be the sole driving force of the typical person’s life but should be balanced with other activities and even downtime.

It may also be necessary to consider changing professions. If you are not able to give your best in the classroom perhaps there are other opportunities available. It is impractical to think that someone who becomes a teacher must stay a teacher their entire life as though there is no other way to use the skills developed in the classroom in other professions.


Burnout is a problem but it is not unique to education. What really matters is that people take control and responsibility of their time and not chase every problem that comes into their life. Doing so will help in coping with the rigors of the teaching profession.

Motivating Students

It can be frustrating for a teacher to spend hours in preparation and planning activities only to have to students who have no desire to learn or enjoy the learning experience. There are ways to help students to be more motivated and engaged in their learning. This post will provide some basic ideas.

Types of Motivation

In simple terms, there are two types of motivation. These two types of motivation are intrinsic and extrinsic motivation. Intrinsic motivation is an inner drive to do something or in other words to be self-motivated.

Extrinsic motivation is when the push to do something comes from outside of the person. Due to uncontrollable circumstances, the person is pushed to do something.

Each teacher needs to decide which form of motivation to focus on or whether to try and address both in their classroom. A teacher with more of a cognitivist view of teaching will probably lean towards developing intrinsic motivation. On the other hand, a teacher who has more of a behavioral view of teaching may focus more on influencing extrinsic motivation.

Ways to Motivate


Nothing motivates like having to help those around you. Getting students involved in their learning and in the management of the class often affects motivation. When students are called to help they realize that they have a role and that others are depending on them. This brings a naturally social pressure to fulfill their role.

Make it Relevant

Teachers often fall into the trap of knowing what’s best for students and sticking to teaching this. However, the student does not always agrees with what is best for them and thus are not motivated to learn.

To alleviate this problem, a teacher must provide immediate applications of knowledge. If the student can see how they can use the information now rather than several years from now they will probably be more motivated to learn it.

One way to develop relevancy is discovery learning. Instead of teaching everything in advance let the students work until they can go no further. When they realize they need to learn something they will be ready to listen.

Acknowledge Excellence

When students are doing good work, it is important to let them know. This will help them to understand what is acceptable learning behavior. People like positive reinforcement and this needs to come from a person of authority like a teacher.

A slightly different way to acknowledge excellence is simply to expect it. When the standard is set high often students naturally want to reach for it because they often want the approval of the teacher.


We have all faced situation when we were not interested or motivated to learn and study. It is important to remember this when dealing with students. They have the same challenge with motivation as we all do.

The Fall of Cursive Handwriting

Writing in a cursive style has been around for centuries. However,  there has been a steep decline in the use of cursive writing in America for the past several decades. This post will trace the history of cursive writing as well as what is replacing this traditional form of writing.


Cursive in one form or another dates back until at least the 11th century with examples of it being found in documents related to the Norman Conquest of England. Cursive was originally developed to prevent having to raise the quill from the page when writing. Apparently, quills are extremely fragile and constantly reapplying them to the paper increase the likelihood they would break.

Cursive was also developed in order to fight more words on a page. This became especially important with the development of the printing press, With people hated the condense font of the printing press that they revolted and developed a cursive writing style.

In America, people’s writing style and penmanship could be used to identify social rank. However, this changed with the development of the Spencerian method, developed by PLats Spencer. This writing style standardized cursive thus democratizing it.

After Spencer, there were several writing systems that all had their moment in the sun. Examples include the cursive styles developed by Palmer, Thurber, and Zaner. Each had its own unique approach that all influenced children during the 20th and early 21st century.

The Decline

The initial decline of cursive writing began with the advent of the typewriter. With typing, a person could write much faster than by hand. Writing by hand often has a top speed of 20 wpm while even a child who has no trying in typing can achieve 20wpm and a trained typist can reach 40 wpm with pros reach 75 wpm.

Typing also removes the confusion of sloppy handwriting. We’ve all have been guilty of poor penmanship or have had to suffer through trying to decipher what someone wrote. Typing removes even if it allows the dread typos.

With computers arriving in the 1970’s schools began to abandon the teaching of cursive by the 1980’s and 90’s. Today cursive writing is so unusual that some young people cannot even read it.

Going Forward

Typing has become so ubiquitous that schools do not even teach it as they assume that students came to school with this skill. As such, many students are using the hunt and peck approach which is slow and bogs down the thought process needed for writing. The irony is that cursive has been forgotten and typing has been assumed which means that it was never learned by many.

To further complicate things, the use of touch screens has further negated the learning of typing. Fast typing often relies on touch. With screens, there is nothing to feel or press when tyoing. This problem makes it difficult to type automatically which takes cognitive power from writing as now the student has to focus on remembering where the letter p is on the keyboard rather than shaping their opinion.

Critical Thinking Strategies

Developing critical thinking is a primary goal in many classrooms. However, it is difficult to actually achieve this goal as critical thinking is an elusive concept to understand. This post will provide practical ways to help students develop critical thinking skills.

Critical Thinking Defined

Critical thinking is the ability to develop support for one’s position on a subject as well as the ability to question the reasons and opinions of another person on a given subject. The ability to support one’s one position is exceedingly difficult as many people are convinced that their feelings can be substituted as evidence for their position.

It is also difficult to question the reasons and opinions of others as it requires the ability to identify weaknesses in the person’s positions while having to think on one’s feet. Again this is why many people stick to their emotions as it requires no thinking and emotions can be felt much faster than thoughts can be processed. Thinking critically involves assessing the strength of another’s thought process through pushing them with challenging questions or counter-arguments.

Developing Critical Thinking Skills

Debates-Debates provide an opportunity for people to both prepare arguments as well as defend in an extemporaneous manner. The experience of preparation as well as on the feet thinking help to develop critical thinking in many ways. In addition, the time limits of debates really force the participants to be highly engaged.

Reciprocal Teaching-Reciprocal teaching involves students taking turns to teach each other. As such, the must take a much closer look at the content when they are aware that they will have to teach it. In addition, Reciprocal teaching encourages discussion and the answering of questions which further supports critical thinking skills development.

Discussion-Discussion through the use of open-ended question is another classic way to develop critical thinking skills. The key is in the open-ended nature of the question. This means that there is no single answer to the question. Instead, the quality of answers are judged on the support the students provide and their reasoning skills.

Open-ended assignments-Often as teachers, we want to give specific detailed instructions on how to complete an assignment. This reduces confusion and gives each student a similar context in which learning takes place.

However, open-ended assignments provide a general end goal but allow the students to determine how they will complete it. This open-ended nature really forces the students to think about what they will do. In addition, this is similar to work in the real world where often the boss wants something done and doesn’t really care how the workers get it done. The lack of direction can cause less critical workers problems as they do not know what to do but those who are trained to deal with ambiguity will be prepared for this.


Critical thinking requires a context in which free thought is allowed but is supported. It is difficult to develop the skills of thinking with activities that stimulate this skill. The activities mentioned here are just some of the choices available to a teacher.

Teaching Reflective Thinking

Reflective thinking is the ability to look at the past and develop understanding and insights about what happened and using this information to develop a deeper understanding or to choose a course of action.  Many may believe that reflective thinking is a natural part of learning.

However, I have always been surprised at how little reflective thinking my students do. They seem to just do things without ever trying to understand how well they did outside of passing the assignment. Without reflective thinking, it is difficult to learn from past mistakes as no thought was made to avoid them.

This post will examine opportunities and aways of reflective thinking.

Opportunities for Reflective Thinking

Generally, reflective thinking can happen when

  1. When you learn something
  2. When you do something

These are similar but different concepts. Learning can happen without doing anything such as listening to a lecture or discussion. You hear a lot of great stuff but you never implement it.

Doing something means the application of knowledge in a particular setting. An example would be teaching or working at a company. With the application of knowledge comes consequences the indicate how well you did. For example, teaching kids and then seeing either look of understanding or confusion on their face

Strategies for Reflective THinking

For situations in which the student learns something without a lot of action a common model for encouraging reflective thinking is the  Connect, Extend, Challenge model. The model is explained below

  • Connect: Link what you have learned to something you already know
  • Extend: Determine how this new knowledge extends your learning
  • Challenge: Decide what you still do not understanding

Connecting is what makes learning relevant for many students and is also derived from constructivism. Extending is a way for a student to see the benefits of the new knowledge. It goes beyond learning because you were told to learn. Lastly, challenging helps the student to determine what they do not know which is another metacognitive strategy.

When a student does something the reflection process is slightly different below is an extremely common model.

  • what went well
  • what went wrong
  • how to fix what went wrong

In this model, the student identifies what they did right, which requires reflective thinking. The student also identifies the things they did wrong during the experience. Lastly, the student must problem solve and develop strategies to overcome the mistakes they made. Often the solutions in this final part are implemented during the next action sequence to see how well they worked out.


Thinking about the past is one of the strongest ways to prepare for the future. Therefore, teachers must provide their students with opportunities to think reflectively. The strategies included here provide a framework for guiding students in this critical process.

Classrooom Management at the University Level

Classroom management is different at the university level when compared to K-12. Often the problem is not behavioral in nature (with the exception of cell phones). Rather a lot of the classroom management problems at a university are academically related. In the classroom, the problem is often inattentiveness or idleness. In general, the challenge is completing assignments and being prepared for assessments.

Clear Syllabus

Making sure the syllabus is clear is critical for better performance of students. The syllabus includes the calendar, assignment requirements, rules, etc. When these are laid out in advance expectations are set the students strives to reach.

If the syllabus is unclear it normally means the expectations are unclear and even that the teaching is unclear. Most universities have a standard format for their syllabuses but it is still the teacher responsibility to explain clearly the expectations

Stick to the Syllabus

When the course has begun the commitments and expectations stipulated in the syllabus should be fully committed to. It is better to think of the syllabus as a binding contract between two parties. Once it is distributed and discuss there is nothing left to negotiate.

Related to this is the need to actually enforce rules. If there is a late policy it must be enforced otherwise students will think that you are not serious and the students will push for more concession. This can quickly snowball into chaos. If you actually have a rule against cellphones than it needs to be supported or you will develop students who have a disdain for people who don’t enforce their rules.

Provide Feedback

Perhaps one of the biggest problems in academia is a lack of feedback. Many professors may only have three assignments in a course per year. Given that there is almost always a mid-term and final in many courses and these are primarily summative assessment and not really for learn only. Many students have one assignment that extends beyond multiple choice.

This means that students need constant feedback. This allows for students to learn from their mistakes as well as provide them with motivation to complete their students. It is not always practical to mark every assignment. A shortcut would be to look at a sample of assignments and explain common errors to the class.

Mix Teaching Styles 

The last useful strategy will help to reduce daydreaming and listlessness. The most common teaching approach is usually lecture or direct-instruction. The problem is that if everyone does this it becomes really boring for any students. Therefore, lecturing is only bad if this is the only instructional model being used.

To maintain engagement means to used different teaching methodologies. While the syllabus should be structured and unchanging good teaching often has a flair and a slight degree of unpredictability that makes the classroom interesting


Teaching at any level is hard. However, classroom management at the university level can be challenging as this is not the most widely discussed topic. For, success a professor needs to commit to the syllabus while being flexible in their delivery of content.

Classroom Management Ideas

One of the greatest challenges in teaching is classroom management. Students are always looking for ways and opportunities to test the limits of acceptable behavior. For teachers, these constant experimentation with the boundaries of how to act are extremely tiresome.

However, there are several strategies that teachers can use to limit poor behavior. Some of these ideas include the following.

  • Setting routines
  • Rehearsing transitions
  • Anticipating behavior
  • Non-Verbal cues

Set Routines

Establishing clear routines will help to regulate the behavior of students tremendously. When everybody knows their role and what to do there is usually less curiosity for a student to see what they can get away with.

Routine need to be explained, demonstrated, and practice in order for students to master them. Once a routine is established most students enjoy the predictability of having set actions that they need to perform and certain times of the day. While instruction should be varied and exciting routines provide a sense of stability and security to brilliant teaching.

Rehearse Transitions

A specific form of routine are transitions. Transitions are those moments in class when you have to move from one activity to another. An example would be going out to recess or coming in from recess, etc.

It is at moments like these that everyone is active. With so many moving parts and actions taking place, this is when the most breakdowns in behavior can often take place. Therefore the teacher needs to be extra diligent during the moments and make sure the routines are thoroughly drilled to avoid near absolute chaos.


Anticipating has to do with seeing what might happen before it actually happens. An analogy would be to an athlete who sees an opportunity to make a great play because of the actions of his opponent. A teacher must be able to read the class and be one-step ahead of the students.

A term related to this is called withitness which means to have a constant awareness of what is happening in the classroom. Or in other words to have eyes in the back of your head. As a teacher gets to know their students it becomes easier to predict their actions and to make adjustments beforehand. This can greatly reduce behavioral problems.

Non-Verbal Cues

Talk is cheap, especially with students. Non-verbal cues save the voice while getting students to do things. Every teacher should have several non-verbal commands that they use in their classroom. Examples may include ways to get the classes attention, to grant permission to go to the bathroom, to give permission get out of one’s seat, etc.

Most classes have a rule for students to raise their hand. However, non-verbal cues should not stop there. The more non-verbal cues the less talking. In addition, non-verbal cues reduce arguing because there were no words exchanged.


Behavior is a challenge but there are ways to overcome at least some of it. Teachers need to consider and employ ways to anticipate and deal with behavioral problems preferably before they become big problems.

Homeschooling Multiple Children

Homeschooling one child is challenging enough. Now imagine trying to teach more than one or even several. There are things that become more complex but also more efficient with the addition of each new member to the homeschooling context.

It Gets Easier Each Time

When you begin to teach the second child it is surprisingly easier. You have learned from the mistakes made teaching the first child and are familiar with the curriculum. The content is probably fresh in your mind and you’re no longer trying to remember how to do all of these basic skills that are now automatic for you such as reading and counting. You also have learned shortcuts and other tricks that make your teaching more efficient.

The second child has also probably watched you teach the first one. When this happens they learn a lot of the content almost through osmosis. I have seen three years playing with how to write when the older sibling could barely write at five years of age. Just watching the older sibling sped up the development of the younger one.

The second child is also more likely to be eager to learn from watching the older child be in school as well since there is a culture of learning in the house now. They can’t wait for their turn to learn and this also makes things easier. Combine this with an experience parent and adding an additional student is not as burdensome as it seems.

Working Together

To be efficient and not stressed out many families teach non-core subjects (history, science, art, PE, etc.) to all children at the same time. The reason for this is that often in non-core subject the order the content is learned is not as important or linear. For example, in science, if a second grader learns about the weather before learning about plants it probably will not cause too much damage in their development if any at all.

Core-subject (reading, math) are taught separately because the difference in skill in the subjects can be extensive and there is a clear linear development in these subjects. The exception to this would be to have the older sibling serve as a teacher or tutor for the younger one. This really helps everyone involve in developing a better understanding and reduces the stress on the parent.

Independence of the Senior Student

With the addition of the second child to the homeschool, this calls on the oldest to become more independent. There is less one-on-one time to support them with the time that is no given to other children. Therefore, the older child will have to sometimes figure things out on their own. The benefit of this is the development of autonomy which is a hard to find skill in this world.

Instead of watching everything they do the parent is now more of a monitor who drops by to check progress rather than watch every academic move. This places some of the burden of learning on the child which is good for developing a sense of responsibility.


With a combination of experience, efficiency, and the help of older children, homeschooling multiple children is highly doable. The key is to get everyone working together to achieve the educational goals of the family.

Supporting ESL Student’s Writing

ESL students usually need to learn to write in the second language. This is especially true for those who have academic goals. Learning to write is difficult even in one’s mother tongue let alone in a second language.

In this post, we will look at several practical ways to help students to learn to write in their L2. Below are some useful strategies

  • Build on what they know
  • Encourage coherency in writing
  • Encourage collaboration
  • Support Consistency

Build on Prior Knowledge

It is easier for most students to write about what they know rather than what they do not know.  As such, as a teacher, it is better to have students write about a familiar topic. This reduces the cognitive load on the students allows them to focus more on their language issues.

In addition, building on prior knowledge is consistent with constructivism. Therefore, students are deepening their learning through using writing to express ideas and opinions.

Support Coherency 

Coherency has to do with whether the paragraph makes sense or not. In order to support this, the teacher needs to guide the students in developing main ideas and supporting details and illustrate how these concepts work together at the paragraph level. For more complex writing this involves how various paragraphs work together to support a thesis or purpose statement.

Students struggle tremendously with these big-picture ideas. This in part due to the average student’s obsession with grammar. Grammar is critical after the student has ideas to share clearer and never before that.

Encourage Collaboration

Students should work together to improve their writing. This can involve peer editing and or brainstorming activities. These forms of collaboration give students different perspectives on their writing beyond just depending on the teacher.

Collaboration is also consistent with cooperative learning. In today’s marketplace, few people are granted the privilege of working exclusively alone on anything.  In addition, working together can help the students to develop their English speaking communication skills.


Writing needs to be scheduled and happen frequently in order to see progress at the ESL level. This is different from a native speaking context in which the students may have several large papers that they work on alone. In the ESL classroom, the students should write smaller and more frequent papers to provide more feedback and scaffolding.

Small incremental growth should be the primary goal for ESL students. This should be combined with support from the teacher through a consistent commitment to writing.


Writing is a major component of academic life. Many ESL students learning a second language to pursue academic goals. Therefore, it is important that teachers have ideas on how they can support ESL student to achieve the fluency they desire in their writing for further academic success.

Videoconferencing in Online Course

Videoconferencing is a standard aspect of the professional world. Most large companies have some sort of video conferencing happening in terms of meetings and training. In terms of personal life, video conferencing is common as well. We probably have all used skype or google hangout at one time or another to talk with friends. However, video conferencing is not as common in education.

Video Conferencing Before Video Conferencing

Before video conferencing became common, many educators would upload videos to their online course or post them on youtube. This allowed the student to see the teacher and have more of a traditional classroom experience but real-time interaction was impossible. Instead, the interaction was asynchronous meaning not at the same time. As such communication was jilted at the least because of the lag time between interactions.

Things to Consider Before Video Conferencing

In order to have success with video conferencing you will need some sort of application that allows this. There are many different applications to choose from such as skype, google hangouts, and even Facebook. However, you want some sort of software that allows you to show your screen as well as control the flow of the conversation.

One app that allows this is called Zoom. This software allows you to schedule meetings. In addition, students do not need to download anything. Instead, the students are sent a web link that takes them to the online meeting. You can share your screen as well as monitor the discussion with the added benefit of being able to record the meeting for future use.

Pros and Cons of Video Conferencing

For whatever reason, video conferencing is engaging for students. The same discussion in class would lull them to sleep but through webcams, everyone is awake and stimulated. I am not sure what the difference is but this has been my experience

The biggest enemy to video conferencing is scheduling. This is particularly true if students are spread out all over the world. The challenges of time zones and other commitments make this hard.

This is one reason that recording a video conference is so important. It allows students who are not available to at least have an asynchronous learning experience. It also serves as a resource for students who need to see something again. Keep in mind you have to post the video either on your LMS or on youtube so that students have access to it.


Video conferencing provides a familiar learning experience in a different setting. It is able to give students who are not physically present an opportunity to interact with the instructor in meaningful ways. As such, the instructor must be aware of possibilities in how to use this tool in their online teaching.

Maintaining Student Focus During E-Learniing

Self-motivation is perhaps one of the biggest problems in e-learning. Students who are left to themselves to complete learning experience often just do not successfully finish the learning experiences prepared by the teacher. For whatever reason, often the internal drive to finish something such as an online class is missing for many people.

There are several strategies that an online teacher can use in order to help students who may struggle with self-motivation in an online context. These ideas include…

  • Brief Lessons
  • Frequency Assessment
  • Collaboration

Brief Lessons

Nothing is more discouraging to many students than having to read several pages of text or even several hours of video to complete a single lesson or module in an online course. Therefore, the teacher needs to make sure lessons are short. Completing many small lessons is much more motivating for many students than completing a handful of really large lessons. This is because frequent completion of small lessons is rewarding and indicates progress which the brain rewards.

How long a lesson should depend on many factors such as the age and expertise of the students. Therefore, it is difficult to give a single magic number to aim for. You want to avoid the extreme of lessons too short and lessons to long.

IN my own experience most people make their lessons too long so the majority of us probably need to reduce the content in an individual lesson and spread it over many lessons. All the content can be there it is just chunked differently so that students experience progress.

Frequency Assessment

Along with brief lessons should be frequent assessment. Nothing motivates like knowing something is going to be on the quiz or there is some sort of immediate application. Students need to do something with what they are learning in order to stay engaged. Therefore, constant assessment is not only for grades but also for learning. Besides the stress of a small quiz provides an emotional stimulus that many students need

The assessment also allows for feedback which helps the student to monitor their learning. In addition, the feedback provides more evidence of progress being made in a course which is itself motivating for many.


Nothing motivates the same as working together. Many people love to work in groups and get energy from this. In addition, it’s harder to quit and give a course when you have group members waiting for your contribution. In addition, interacting with students deepens understanding of the course material.

Communicating with other students online to complete assignments is one way of establishing community in an online class. It is similar to traditional classroom where everyone has to discuss and work together to have success.


Motivated students are successful students. IN order for this to happen in an elearning class studnets need to be engaged through brief lessons that inckude frequent assessment tjat includes social interaction.

Tips for Online Studying

Today it is common for students to study online. This has both pros and cons to it. Although e-learning allows students to study anytime and anywhere it also can lead to a sense of disconnection and frustration. This post will provide some suggestions for how to study online successfully.

Make a Schedule

In a traditional classroom, there is a fixed time to come to class. This regulated discipline helps many students to reach a minimum standard of knowledge even if they never study on their own. In e-learning, the student can study whenever they want. Sadly, many choose to never study which leads to academic failure.

Success in online studying requires a disciplined schedule in which the student determines when they will study as well as what they will do during the study time. As such, you will need to set-up some sort of a calendar and to do list that guides you through the learning experience.

It is also important to pace your studying. With flexible courses sometimes the assignments are due at the end of the course. This temptation leads to students who will do all their studying at the last minute. This robs the student of in-depth learning as well as the ability to complete assignment thoroughly. Learning happens best over time and not at the last minute,


In a traditional class, there are often opportunities to participate in class discussions or question and answer sessions. Such opportunities provide students with a chance to develop a deeper understanding of the ideas and content of the course. Students who actually participate in such two-way dialog usually understand the material of the course better than students who do not.

For the online student participation is also important and can render the same benefits. Participating in forums and chats will deepen understanding. However, I must admit that with the text-heavy nature of online forums reading the comments of peers can in many ways boost understanding without participation. This is because you can read other’s ideas at your own speed which helps with comprehension. This is not possible during an in-class discussion when people may move faster than you can handle.

Communicate with the Instructor

When a student is confused they need to speak up. For some reason, students are often shy to contact the instructor in an online course. However, the teacher is there to help you and expects questions and feedback. As such, reach to them.

Communicating with the instructor also helps to establish a sense of community which is important in online learning. It helps the instructor to establish presence and demonstrates that they are here to help you to succeed.


E-learning is a major component of the future of learning. Therefore, students need to be familiar with what they need to do in order to be successful in their online studies.

Tips for Teaching Online

Teaching online is a unique experience due in part to the platform of instruction. Often, there is no face to face interaction and all communication is in some sort of digital format. Although this can be a rewarding experience there are still several things to consider when teaching in this format. Some tips for successful online teaching include the following.

  • Planning in advance
  • Having a presence
  • Knowing your technology
  • Being consistent

Plan in Advance

All teaching involves advance planning. However, there are those teaching moments in a regular classroom where a teacher can change midstream to hit a particular interest in the class. In addition, more experienced teachers tend to plan less as they are so comfortable with the content and have an intuitive sense of how to support students.

In online teaching, the entire course should be planned and laid out accordingly before the course starts. It is a nightmare to try and develop course material while trying to teach online. This is partially due to the fact that there are so many reminders and due dates sprinkled throughout the course that are inflexible. This means a teacher must know the end from the beginning in terms of what the curriculum covers and what assignments are coming. Changing midstream is really tough.

In addition, the asynchronous nature of online teaching means that instructional material must be thoroughly clear or students will be lost. This again places an emphasis on strong preparation. Online teaching isn’t really for the person who likes to live in the moment but rather for the person who plans ahead.

Have Presence

Having presence means making clear that you are monitoring progress and communicating with students frequently. When students complete assignments they should receive feedback. There should be announcements made in terms of assignments due, general feedback about activities, as well as Q&A with students.

Many people think that teaching online takes less time and can have larger classes. This is far from the case. Online teaching is as time intensive as regular teaching because you must provide feedback and communication or the students will often feel abandon.

Know Your Technology

An online teacher must be familiar and a proponent of technology. This does not mean that you know everything but rather you know how to get stuff done. You don’t need a master in web design but knowing the basics of HTML can really help when communicating with the IT people.

Whatever learning management system you use should actually be familiar with it and not just a consumer. Too many people just upload text for students to read and provide several forums and call that online learning. In many ways, that’s online boredom, especially for younger students.


Consistency is about the user experience. The different modules in the course should have the same format with different activities. This way, students focus on learning and not trying to figure out what you want them to do. This applies across classes as well. There needs to be some sense of stability in terms of how content is delivered. There is no single best way but it needs to similar within and across courses for the sake of learning.


These are just some of many ideas to consider when teaching an online course. The main point is the need for preparation and dedication when teaching online.

Blended Learning Defined

E-Learning is commonly used tool at most educational institutions. Often, the e-learning platform is fully online or a traditional model of face-to-face instruction is used. Blended learning is something that is available but not as clear in terms of what to do.

In this post, we will look at what  blended learning is and  what it is not

What Blended Learning is

Blended learning is an instructional environment in which online learning and traditional face-to-face instruction coexist and are employed in a course. There are at least six common models of blended learning.

  • Face-to-face driver – Traditional instruction is supported by online materials
  • Online driver –The entire course is completed online with teacher support made available
  • Rotation – A course in which students cycle back and forth between online and traditional instruction
  • Labs – Content is delivered online but in a specific location such as a computer lab on-campus
  • Flex – Most of the curriculum is delivered is online and the teacher is available for face-to-face consultation.
  • Self-blend – Students choose to augment their traditional learning experience with online coursework.

These models mentioned above can be used in combination with each other and are not mutually exclusive.

For a course to be blended, it is probably necessary for at least some sort of learning to happen online. The challenge is in defining learning. For example, the Moodle platform places an emphasis on constructivism. As such, there are a lot of opportunities for collaboration in the use of the modules available in Moodle. Through discussion and interaction with other students through forums, commenting on videos, etc., students are able to demonstrate learning.

For a more individualistic experience, if the course is blended the students need to do something online. For example, completing a quiz, add material to a wiki or database, etc. are all ways to show that learning is taking place without as much collaboration. However, a teacher chooses to incorporate blended learning the students need to do something online for it to truly be blended.

What Blended Learning is not

Many teachers will post there powerpoints online and have students submit assignments online and call this blended learning. While it is commendable that online tools are being used this is not really blended learning because there is no learning taking place anytime online. Rather this is an excellent example of using cloud sources to upload and download materials.

The powerpoints were seen in class and are available for review.  Uploading assignments are trickier to classify as online learning or not but if it required the students to complete a traditional assignment and simply upload it then there was no real online learning experience. The students neither collaborated nor completed anything online in order to complete this learning experience.


The definition here is not exhaustive. The purpose was to provide a flexible framework in which blended learning is possible. To make it as simple as possible, blended learning is the students actively learning online and actively learning in a traditional format. How much of each component depends on the approach of the teacher.

Benefits of Writing

There are many reasons that a person or student should learn to master the craft of writing in some form or genre. Of course, the average person knows how to write if they have a k-12 education but here it is meant excelling at writing beyond introductory basics. As such, in this post, we will look at the following benefits of learning to write

  • Makes you a better reader and listener
  • Enhances communication skills
  • Develops thinking skills

Improved Reading and Listening Skills

There seems to be an interesting feedback loop between reading and writing. Avid readers are often good writers and avid writers are often good readers. Reading allows you to observe how others write and communicate. This, in turn, can inspire your own writing. It’s similar to how children copy the behavior of the people around them. When you write it is natural to bring with you the styles you have experienced through reading.

Writing also improves listening skills, however, this happens through the process of listening to others through reading. By reading we have to assess and evaluate the arguments of the author. This can only happen through listening to the author through reading his work.

Communication Skills

Writing, regardless of genre, involves finding an audience and sharing your own ideas in a way that is clear to them. As such, writing natural enhances communication skills This is because of the need to identify the purpose or reason you are writing as well as how you will share your message.

When writing is unclear it is often because the writer has targeted the wrong audience or has an unclear purpose for writing. A common reason research articles are rejected is that the editor is convinced that the article is not appropriate for the journal’s audience. Therefore, it is critical that an author knows there audience.

Thinking Skills 

In relation to communication skills is thinking skills. Writing involves taking information in one medium, the thoughts in your head, and placing them in another medium, words on paper. Whenever content moves from one medium to another there is a loss in meaning. This is why for many people, there writing makes sense to them but to no one else.

Therefore, a great deal of thought must be placed into writing with clarity. You have to structure the thesis/purpose statement, main ideas, and supporting details. Not to mention that you will often need references and need to adhere to some form of formatting. All this must be juggled while delivering content that critically stimulating.


Writing is a vehicle of communication that is not used as much as it used to be. There are so many other forms of communication and interaction that something writing is obsolete. However, though the communication may change, the benefits of writing are still available.