Monthly Archives: February 2018

Teaching Math

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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.

Conclusion

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

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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

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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.

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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.

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

Parentheses
Exponents
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.

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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

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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.

Conclusion

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

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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.

Multiple

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

  • n
  • Counting number

The n  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 n = 2 and the counting numbers are 1,2,3,4,5. We get the following multiples of 2.

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You can see that the n 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

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

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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

 

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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.

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Conclusion

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

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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.

library(apaTables)
data("mtcars")

ANOVA

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

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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

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Correlation 

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

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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.

Regression

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

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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

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Conculsion 

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

Reading Comprehension Strategies

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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.

Conclusion

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

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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.

Conclusion

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

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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.

Conclusion

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

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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.

Definition

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.

Causes

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.

Conclusion

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

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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

Involvement

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.

Conclusion

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

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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.

History

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

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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.

Conclusion

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

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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.

Conclusion

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.