Monthly Archives: July 2020

Summation Notation VIDEO

Summation Notation

Intro to Agent-Based Modeling

Agent-Based Modeling (ABM) is a computational approach to modeling reality. ABM is not new having a history dating back to the 1960s. What is new is that the average computer often will possess the needed computational power to use ABM for modeling purposes. This has led to an explosion in interest in ABMs.

This post will introduce ABM and some terms associated with this field of research.

Terms

The term agent-based modeling (ABM) has a lot to it that we need to unpack first. The word “agent” in this context means a computational object that possesses specific actions and behaviors. An example of this might be a car in traffic or birds flying together. These examples will make more sense later.

A model is a description of a process, event, or system. Models are developed to explore a phenomenon because the model can be manipulated to extract understanding. Specifically, a computational model takes inputs (variables) and manipulates the inputs in an algorithm like way. This allows for the prior mentioned experimentation but also for the ability to communicate quantitative results differently than a traditional mathematical equation.

With our knowledge of agents and modeling, we can now say that ABM is a computational model of agents and their interaction with an environment created by the researcher.

More Terms

The rationale behind ABM is the idea of emergence. By emergence, it is meant that when agents interact patterns begin to “emerge.” For example, cars travel together leading to traffic jams and birds fly together in flocks. The pattern of a traffic jam and a flock is only possible when the agents (cars and birds) interact with each other in each system.

Emergence can be seen from two different perspectives. Integrative emergence is the observer knowing the behavior of individual agents but trying to determine patterns or see the “big picture” of the system. For example, you know how cars drive in traffic but you want to understand the patterns of a traffic jam.

Differential emergence is the opposite. It involves the observer knowing the general pattern or big picture but wanting to determine the behavior and actions of individual agents. For example, you know the pattern of a traffic jam but want to learn how individual cars drive in a traffic jam.

A common error people make when looking for emergence is something called deterministic-centralized mindset. This view holds there is no randomness in a pattern and that there is some form of a controller of the pattern. For example, someone is responsible for the traffic jam, or there is a leader among the birds flying in a flock. From these two examples, you can see that it is more common for people to err on the side integrative emergence in that they see individuals responsible for the patterns rather than the system.

Pros & Cons

ABM allows people to explore the complex phenomenon in a hypothetically way. It is possible to generate large amounts of data in a computationally cheap way. In addition, many people find the results of an ABM to be easier to understand because knowledge of calculus is not required. The removal of math seems convenient but equations offer a compact explanation that ABM is not able to duplicate making this a disadvantage.

Among supporters of ABM, there is a small tendency to over-promise the capabilities. There is an argument that the development of ABM is similar to the switch from Roman to Arabic numbers during the Middle Ages. This is unlikely to be a fair comparison because the switch in number systems had a tremendous practical influence in everyday life whereas ABMs might be useful for scholarly like people but not a more practical person such as a plumber or entrepreneur.

Conclusion

ABMs allow researchers to experiment with various scenarios in a highly cost-efficient way. Modeling system with agents provides an approximation of reality that was not possible before. All approaches to uncovering reality have their flaws. However, ABMs providing a unique contribution to research today.

Making Videos for Online Learning

Making online content is difficult. Without the interaction of the classroom, it’s easy for students to lose focus and struggle. However, with some basic help, teachers can make some small changes to their delivery approach to make videos that are more engaging for students.

Your Teaching Style

Before preparing your videos for your online class, you need to be honest with yourself about your teaching style. You need to ask your self how interesting you are as a teacher. The temptation is to think that you are an interesting and engaging teacher. However, personal experience has shown me that most teachers are terribly boring when they have to lecture in person and they are even more boring when they have to teach through a video online.

It is not a criticism if you are a boring teacher. Knowing this is important because it shapes how you approach the delivery of content when teaching online. An interesting teacher will be able to do things online that a boring teacher could never do.

If you cannot determine your style of teaching, you can consider the following options

  • Recording your face to face teaching and watch it
  • Examining course evaluations from prior teaching experiences.

If you choose to record yourself, ask yourself if you would really pay attention to what the teacher is saying if you were a student? If the answer is no, you need to determine what it is that is such a turnoff.

Guidelines

Once you know how engaging you are as a teacher, keep in mind the following to developing engaging online videos.

Keep it Short

Online videos should be between 10-15 minutes give or take. The reason being is that longer videos begin to put students to sleep and shorter videos become irritating because you always have to click for the next video. Another reason is that through watching television, people are already trained to pay attention for about 10-12 minutes at a time because that is how long a segment of a tv show lasts before a commercial break. If you talk for much longer than this you are not meeting the students’ preconceived expectation for how long they should receive content.

Whether you are closer to 10 minutes or 15 depends on how engaging you are as a teacher. A boring teacher should speak for 10 minutes or less while engaging teachers can go beyond 15 minutes because they know how to connect with their audience.

A general guideline to help you with timing and your PowerPoint slides comes from a Japanese presentation technique called PechaKucha. In this approach, you share 20 slides and talk for 20 seconds on each slide. This leads to a total presentation time of 6minutes and 40 seconds. This approach helps a presenter to talk less and show more which helps with engagement

7 minutes might be too short for your presentation. The point is not to adopt all the rules of PechaKucha but to use it as a guide to shape your presentations. Generally, you don’t want more than 30 slides in a presentation as things begin to bog down when teaching online.

More on Powerpoints

Powerpoints are a useful tool. However, the problem is that everybody uses them and this can be torture for students. If a student is taking 5 classes, he or she is probably experiencing 5 PowerPoint presentations every day. This is highly disengaging because of the ubiquity of PowerPoints.

An alternative to a PowerPoint is to use an on-screen whiteboard. This can be something like a simple paint app or an online tool such as Microsoft Whiteboard. By drawing are writing the concepts on the screen while recording can help to keep students much more engaged. This is due at least partly to the mental break students get while you are drawing/writing.

Of course, you can also have too much of a good thing. For example, if you are teaching math, it can be torture to have to wait for the math teacher to finish writing down the equation before solving it. In such situations, pre-written content can help to keep the video moving.

Naturally, I do not have to mention how you need to avoid reading your PowerPoint slides. Slides should be short and bulleted and should serve as a reminder of what you want to say rather than as a reading prompt.

Communications

There are also some tips for communications. You want to avoid highly formal language. This is because people tend to get lost when the language is dense. This means using 1st and 2nd person rather than third, which means speaking directly to the audience. When you talk directly to someone it forces them to pay attention at least a little bit.

A second suggestion is to avoid too many details. Experts love to share their expertise. However, most of our time is spent with non-experts. Therefore, every detail about every theory and concept is not always necessary. The amount of detail needs to match the expertise of your audience. College freshmen need fewer details than grad students. Generally, no matter what you are teaching, there is a good chance that the students will have another opportunity to learn it. This means it is not necessary to tell them everything if it causes them to fall asleep.

Whenever possible, try to wrap the content in a story. Storytelling is engaging and helps people to have a contextual frame in which to remember details. The stories don’t have to be that creative. It could be as simple as a story of when you first learned about the topic you are lecturing about. The point is to mix the theory with some form of reality that people can relate to.

Lastly, asking questions can also be beneficial. Of course, you will not be there to hear the response. However, when you speak directly to the audience and ask them what they think they have to pay attention to. If possible you may be able to make your videos interactive, which would allow you to post questions students can respond to during the video.

Beginning Middle and End

This is probably obvious but keep in mind that you need to introduce what you will talk about, present what you are talking about, and then summarize what you talked about. Many teachers can sometimes skip this. Doing so can lead to confusion for students at times.

Conclusion

Making videos online can be difficult. However, some basic tools can help a teacher to develop efficient and interesting content. It’s important to understand how you teach so you can maximize strengths and minimize weaknesses as you help students.

Ancient Egyptian & Jewish Education

In this post, we will look at ancient Egyptian and Jewish education. Through many stories, such as those found in the Christian Bible, Egyptian and Jewish civilizations are connected.

Egypt

The Egyptians employed a caste system. This system consisted primarily of three levels but this varies based on interpretation. These three levels are the priest, military, and unprivileged. The priests made up the highest caste. This caste did not only consist of religious functions but also included surveyors, engineers, teachers, etc. In many ways, the equivalent today would be highly skilled white-collar jobs.

It was the priestly caste that educated the others. They were generally the only ones who were literate. Also, the priests owned 1/3 of the land and were not required to pay taxes. As such, priests were generally wealthy due to these economic concessions.

The military was the second caste. These were the soldiers who defended the country and also found ways to expand it. `The pharaoh was a part of this caste be he was also often put in a caste by himself at the top of the system. It was also possible for people to move between the priestly and military classes. For example, a soldier could have a brother who was a priest and vice versa.

The lowest class was called the unprivileged. This included everyone who was not in the other two classes mentioned already. This group was further subdivided into craftsmen, farmers, merchants, and slaves.

The education of youth was practical. A boy was expected to follow the trade of his father. However, there was flexibility in this depending on the interest and skill of the child. The education was physically demanding but also include many of the subjects expected in a school (reading, writing, math, etc.)

Jews

Jewish education was highly unique when compared to other forms of education. There was no caste system among the Israelites as found in other civilizations. Also, there was no government-controlled education until the Assyrian and Babylonian captivity period. This implies that Jewish youth were primarily homeschooled, which was almost unheard of in any advanced civilization during ancient times.

Even though Jewish education was primarily controlled by the family for several thousand years there were exceptions to this. One example is the School of the Prophets during the monarchy period of the Jews. At this school, students studied philosophy, medicine, poetry, history, law, etc. These schools were erected to provide spiritual leaders for Israel.

Another school founded mostly after the captivity was the School od the Rabbis. There were several of these and they were run independently by famous rabbinical teachers. They were similar to the School of the Prophets in terms of curriculum and students studied such subjects as theology, politics, law, history, math, etc.

By the first century AD, and after the Babylonian captivity, Rabbis began to require that every community have a school and that attendance to such a school was mandatory. This eliminated to a large degree the tradition of homeschooling among Jews.

The teachers at these schools had to be married men with experience. What is implied here is that people who had reached full maturity through being married and perhaps with children were considered ready to deal with children.

Conclusion

How people choose to prepare children for the world will always be different. Egypt was focused on raising people to support a caste system. Israel was focused on the development of the individual and not only the state. The superiority of one system over the other depends on the individual. However. both of these systems have a rich history that is still impactful to this day.

Assessing Students Online

Assessing students online is a major concern for many teachers. Generally, traditional tools may not work because of the ease in which students can cheat. However, there is a place for traditional assessment if they are used for feedback rather than for points. In this post, we will look at assessing students online

Before the assessment

When planning the assessment you want the students to do you need to first consider the objectives of the course/unit. In addition, you need to think about what kind of assessment are you trying to conduct. Is this going to be a formative or summative assessment? Will this be a product or process type of assessment? Finally, you also need to think about whether this will be a traditional or project-based assessment. Keep in mind that traditional assessment is often for formative purposes and projects are generally for summative purposes in an online context. What we have discussed so far deals primarily with curriculum questions that do not have much to do with technology yet.

Speaking of technology, you also need to consider what tools are available for you to use in the online setting to achieve your objectives. With enough creativity, almost anything can be done in any learning management system. For example, I once had my students do presentations online. Rather than watch them live (which is generally boring) I had the students record their presentations, upload them to YouTube, and past the link inside a forum on Moodle. By doing this, students did not have to watch every presentation but just the ones I assigned them. In addition, because the presentation was inside the forum I could assign a score and even provide feedback in the forum. This saved me a lot of time.

In a different situation, I had students do peer reviews of their papers through Moodle Every student was made a “student-teacher” in the assignment activity. Two or three students would then upload their paper to the “student-teacher” assignment activity and the “student-teacher” would provide feedback. I was able to see the feedback and could grade the teacher for their participation in providing feedback.

These are just two non-traditional ways of using your learning management tools. It really boils down to creativity and a desire to determine a way to get something done. Moodle in particular was built for all of these workarounds to support students.

During the assessment

Once the assessment is determined it is time to implement. At this point, clear communication is critical for student success. All directions and expectations must be written down and communicate for student success. If anything is left unspoken students may become confused and this could be a major problem.

There are at least two additional ways to alleviate anxiety students may face. One is to make sure you respond quickly to questions. The second is to provide some sort of an example of a finished product. Providing examples is especially important for project type assessment as students can you use this as a springboard for their own. This assumes that you have prepared a rubric for a project-based assessment.

Technology has a bad habit of failing. This means that you need a plan for the random disaster of internet access. If students are taking a quiz and the server crashes what will you do is a question you need to consider. If the students need to submit a project, how hard will the deadline be? For projects, my approach is to have a recommended deadline and a hard deadline. The recommended deadline might be 24 hours before the hard deadline. This means that students who have technology problems have 24 hours to find a connection to upload their projects. If students miss the hard deadline this is when the negotiating begins

After the Assessment

Now is the time to determine if the students have achieved the objectives of the course/unit. This is based on their actual performance of the assessment. For example, if students did well with a quiz, it indicates that it is time to move on. If they struggled then reteaching may be necessary. The reteaching can be done by sharing a message explaining the common mistakes that students made and or responding to individual quizzes when marking them. Quizzes should be mainly for formative purposes because it is hard to tell if the student was honest during the assessment

For a project-based assessment, the same principle applies. You can respond to mistakes individually and or share common misconceptions through the development of a message for the entire class. The message can be written or a short video. Off course, since projects have rubrics, you will be sure to make the completed rubric available to the students as well

Conclusion

Planning, communication, and execution are the main steps to keep in mind when assessing students online. Whatever creative or boring idea you have can be accomplished if you share your expectations with the students and provide tools for them to do it.

Arithmetic Sequences: Finding the nth Term of an Explicit Formula VIDEO

Arithmetic Sequences and Finding the nth Term of an Explicit Formula

Prussian Education in the 19th Century

In this post, we will look at the Prussian education system during the 19th century. This system has been praised by many and influenced the development of the American educational system. In particular, we will look at the schools and the requirements for becoming a teacher in this historical system.

The Schools

Prussian education begins for many with the Common Schools. These schools were designed for the masses and cover what we would consider to be K-8 today. These schools lasted six days a week for 42 weeks a year. Generally, students would be in class anywhere from 16-28 hours per week. Teachers of course work 28 hours a week.

Attendance was compulsory for children age 6-14. Parents could face disciplinary action if they did not send their children to schools. Generally, there were few problems or resistance to compliance

Completion of Common School studies did not automatically lead to going to high schools. Often, if a student wanted to continue to study he would study at continuation schools. These schools were offered on Sundays and during the evenings. For most lower-class individuals this was the only way to continue studying.

Secondary school had three types of schools these are the gymnasium, reallgymnasium, and the oberrealschule. All three of these schools prepared for university. The difference between these three types of schools is the amount of focus each school had on classical studies. The gymnasium was the most heavily focused on the classics, followed by the realgymnasium, and the oberealschule was the most practical.

If a student from the common schools had a goal of attending university, he had to enroll at a secondary school before he was 10 years old. This indicates that it was difficult for late bloomers to have academic success at university.

For those who go to university, those who choose to become teachers typically do not teach at the common schools. Generally, they teach at secondary school, private school, or work as tutors. Usually, only former common school students would teach at common schools. Whether this is right or wrong is open to debate but this was the reality of the time.

Teacher Preparation

Becoming a teacher required that a student’s teacher and the local administrator notice academic talent in a child. If the administrator believes the child can be a teacher, he will next contact the parents and see if they agree to have the child become a teacher. If the parents agreed the child is then sent to a preparatory school for about 3 years (age 14 – 17).

Upon completing preparatory school, the student goes to a normal school (teacher college). This training lasted for 3 years. Two of the years are book work and the last year is what we would call a student internship today. After completing normal school, the student goes back to their childhood school and begin their first teaching position.

Once they get their first job, the student is now a probationary teacher for 3 years. When the 3 years are over, the student then has to pass a final examination that covers questions about pedagogy. Only after passing this exam does the student become a tenured teacher, which essentially means having a job for life. Not bad considering many would be less than 25 years old.

Conclusion

The Prussian system was a major component of the development and growth of Germany during the 19th century. There was criticism of how it perpetuated the class structure through the differences found in the common vs secondary schools. However, all systems have their inherent strengths and weaknesses and there is no exception in the case of the Prussian educational approach.

Johann Basedow: German Educator

Johann Basedow (1723-1790) was an influential German educator of the 18th century. In this post, we will look at the life and work of this influential educator.

Life

He was born in Hamburg, Germany. As a child he was temporarily a runaway do to a strained relationship with his father. However, with time, he was reconciled with his father and return home

As a young man, Basedow studied theology at university. However, he was found to be too difficult in terms of personality to be fit for ministry. In fact, Basedow’s personality was a frequent cause of his failures. He was unorthodox by nature but what really cause him problems was poor people skills, a penchant for criticizing others, and being somewhat capricious in his decision making.

With his hopes of ministry being thwarted, Basedow turned to being a tutor. He developed a somewhat unorthodox approach to teaching Latin. In his approach, Basedow would point to different objects that he encountered with his students and tell them the name of the object in Latin. Through this focus on practical vocabulary the students quickly learned the language. At the time, this was a revolutionary way to teach language.

After working as a tutor for a time, Basedow next appointment was to work as a Professor of Morals at a university in Denmark. Given his raucous past, it is ironic that the rebellious runaway was now a guardian of morality. Unfortunately, Basedow’s unorthodox style and strong independence streak led to conflict with the university.

Basedow was heavily influenced by Rousseau and especially by Rousseau’s book “Emile”, which was a book on Rousseau’s views of education. This book which advocated avoiding educating a child for the first 12 years or so of life, providing minimum moral training, and the avoidance of discipline is seen by many to be a bizarre approach to education. However,, for Basedow, it led him to the next step in his life, which was the founding of his own school.

Philanthropin

Prince Leopold, fascinated by Basedow, decided to finance Basedow in the developing of a school were Basedow could implement Rousseau and his own educational theories. The name of this school was the Philanthropin.

Basedow’s school was popular in that everybody heard of it. Yet, few parents wanted to actual send their children to such an experimental school. In fact, when several school leaders came to the school they only found 13 students there. To make matters worst, two of the thirteen were Basedow’s own children.

The lack of success of the school can be based on several reasons. For starters, Basedow’s personality cause problems. He lacked the charisma needed for a leadership position along with the tact needed to maneuver difficult situations. Basedow was also a frequent critic of other educators and this did not win him friends and or support. In addition, Basedow, was unpredictable in decision making and suspicious of his subordinates.

Another problem was the strict secular nature of the school. Based on Rousseau’s “Emile” there was no religious instruction in the school as Rousseau believed it was too early in a child’s life to have religious training. This is considered normal today, however, during this time, the idea of separating church and state was still unheard of. This was a few years before the United States was born and it was still expected that schools provide religious education. Basedow’s decision to ignore this was revolutionary.

Eventually, Basedow resigned from his leadership position and the school would close several years after his death. With the closure of the school the teachers dispersed and took with them the ideas that they learned from Basedow.

Conclusion

Basedow’s failure are his primary gift to future educators. Some people show the next generation what works while others show the next generation what does not work. Basedow’s innovations were primarily unsuccessful but if he had never attempted to dream big and implement them the world would have never known. Even worst, Basedow himself would have never known.