HOW TO SUCCEED AS AN ONLINE STUDENT, part 2: Learning from online lecture and text

HOW TO SUCCEED AS AN ONLINE STUDENT Part 2: HOW TO LEARN FROM LECTURE AND TEXT

Substituting online learning for the customary in-school lessons presents some unique challenges.   Materials presented online are less personal and lack the face-to-face connection that allows teachers to assess the comprehension level of class members and provides a student the immediate gratification of asking a question and getting an instantaneous response. 

 The new online role casts the student as an independent learner, requiring techniques that are rarely innate for a college student, much less those in middle school or high school.  But there are steps for navigating autonomous online learning which can be equally beneficial when school resumes and later in higher level education.  While compliance with every suggestion that follows is an unreasonable expectation, each action that is applied increases the probability of success for the elearning student.

STEP ONE:  As usual, the first step is to PREPARE, and that starts with an effective and efficient work area.  In addition to the suggestions given in Part 1 of this series, an efficient independent study space includes a few amenities not possible in the regular classroom.  An oral learner, for example, can have chewing gum or noshies at the desk, and every student should have water or similar fluid to help maintain hydration which is vital for productive brain function.

If the teacher provides a syllabus or similar course content index, a printed copy will serve as a ready reference throughout the semester and a casual reminder if posted at the work station on a white board or bulletin board.  Similarly, a calendar or assignment planner can formalize a study routine, and if the calendar is digital, notifications can ensure timely follow-through on assignments.  The purpose of each of these tips is to maintain assignments and due dates.  If the student is required to log on at specific times to engage in an in-person format, the calendar and notifications will ensure timely entrance in the video conference.

 

The study schedule should fit into the student’s daily routine.  Beginning the “school day” in the morning will make transition to the regular classroom easier whenever school resumes, but the flexibility of online learning offers options to accommodate the student’s preferred activity schedule.  While the timetable is more pliable than an in-school agenda, variability should be kept to a minimum in order to establish a true routine.  Envisioning an “ideal day” can form a template for arranging course work to include “every class/every day,” breaks, and other activities.  

To establish an appropriate environment for study, the student should get dressed as if going to school and establish an end to the study day to avoid becoming either obsessive or negligent.

IN-PERSON LECTURE VERSUS PRERECORDED FORMATS

PREPARATION: The classroom teacher may set up lectures either as in-person video conferences or as prerecorded presentations.  In either case, preparation beforehand should include review of the previous lesson.  This approach is common in Math classes where the instructor inspects homework and answers questions before moving on to the next issue.  For courses in social studies or English, it may be necessary for the student to independently survey previous discussions in order to establish context.

NOTE TAKING:  For in-person lectures, a strong procedure for contemporaneous note taking is required because of the one shot approach to information dissemination.  
    — Notes should be brief, highlighting the major concepts that can be expanded later in review.  Most people are unable to listen, retain, and write in full sentences simultaneously.  Key words and phrases are preferable for synchronous notes.  (Words highlighted in orange in this essay are examples of key items that would be the initial outline.)
    — The note taking template should leave a wide margin to the side so that additional notes to summarize or expand can be added during review.
    — If the instructor is mentioning categories first and then returning to fill in details, the outline should leave plenty of room in the body to add information as the lecture progresses.
    — The student should develop a coding system for frequently used terms. For example, a psi sign () could be used to represent psychology, psychologist, psychiatric, psychedelic, psychosomatic — depending on the course and context.

Since material presented in recorded lectures can be reviewed several times if necessary, note taking can be more loosely structured and altered as needed. Still, a consistent note taking format can improve the efficiency and effectiveness of study and should follow the same guidelines as recommended for in-person lectures.

PARTICIPATION:  A video conference lecturer might allow communication with other students or an opportunity to ask questions during a lecture.  
    — The student should understand how to join in the conversation without causing a disruption and be prepared to participate constructively.
    — Questions should NEVER be left dangling.  If participation is allowed, the question should be posed immediately.  As an alternative, the issue should be written down and either asked or researched as soon as possible.

LECTURE RESOURCES:  Some lectures will be a “talking head” while others may include PowerPoint or similar slides.  
    — Lecture notes offered by the instructor as printable worksheets should be saved, possibly in printed form, and used as reference for review.  The effort that goes into this resource is a direct indication of what is valued by the instructor and should inform the student for written projects and test review.

LEARNING FROM TEXT

PREPARATION:    As with learning from lecture, gaining information from the printed page involves review of previous material to set the stage for supplementing previous knowledge.  Effective learning creates several mental pathways to knowledge, connecting ideas through chronology as in history, through theme as in literature, through hypothesis in science, and through sequencing in math.  The goal of most learning is to add to existing intelligence, and efficient learning avoids recreating the wheel.

With printed text, preparation steps should include Survey of the new material.
    — An outline of key concepts begins with titles and headings.
    — Highlighted words offer a preview of important vocabulary.
    — Captions add detail and interest to key concepts.
    — Charts, graphs, and diagrams present vital statistics in visual form.

Establishing a purpose for reading revolves around the Question tactic.  When the social studies teacher assigns 8th graders a chapter to read and instructs them to answer the 3 questions at the end, most students will read the questions before delving into the written pages.  They are employing a Question tactic by identifying beforehand the information to search for.  Without this predetermined purpose, the student should formulate distinctive questions to motivate investigation of the text.

Actual Reading of the text is an active process.  The student should be prepared to highlight with pen or markers and also to jot notes either in margins or on separate paper.  Note taking techniques used when learning from lectures apply equally to documenting data points from text, but the latter can be less intense since it does not rely on a lecturer’s pace. 

FOLLOW UP

Once essential concepts have been gathered from either lecture or text, learning continues through the steps of Recite and Review.

The Recite maneuver can take several tracks, dependent on a student’s natural preferences and experience.
    — An inspection of notes can be a verbal recitation as if the student is giving a lecture on the topic, a recap of information through construction of a mind map, or revisions of notes through highlighting or addition of details.    
    — Attempts to answer the initial questions spotlight missing data points and establish an objective for the final step…

Review, during which the student returns to the printed material to augment notes with relevant information.

This process is dubbed SQRRR (Survey, Question, Read, Recite, Review) but could as easily be related to lectures as SQLRR (Survey, Question, Listen, Recite, Review).  It encourages the planning and thinking that orbits around actual reading or sitting through a lecture, which are, in reality, a small portion of the overall strategy.  It enhances the theory that “learning” is more than just listening to an expert or reading about an issue.  It requires moving information from working memory to short-term memory from which long-term memory is developed.  Classroom teachers can guide unsuspecting students through the method with periodic, subtle comments and review.  With elearning, it is up to the student to design and administer a study program to attain understanding, retrieve knowledge, and demonstrate comprehension through homework and exams.

Although our American style teaching is heavily dependent on students being in a group classroom environment, the online learning situation we find ourselves in today can provide the opportunity for our students to learn a system for higher level learning that could have impressive benefits after high school.  College, trade school, on-the-job training, or just pursuing a hobby or special interest all require  continuing education.  Unlike the fatalistic prognostication that elearning will put our kids behind, figuring out how to learn independently now can put them ahead of the game for a lifetime.

HOW TO SUCCEED AS AN ONLINE STUDENT Part 1: Preparing for online learning.

High school and college teachers experienced in distance learning have found that planning, consistency, and use of the vast array of outside resources increase the success rate of online students.   

While elearning is relatively new to high school curricula, colleges and some states have been exploring the distance model for decades and have gathered data on skills and practices needed for success.  A recent survey of online courses shows that the expected completion rate ranges around only 40%.  For our high school students, the requirement to complete every class suggests that as many as 60% will have difficulty just finishing a course, much less achieving the knowledge level desired.

Today, students who are required to or choose to continue with digital learning need specialized skills if they are to excel in their studies. The potential for our students’ success as they earnestly enter the realm of online learning can be accelerated by following the suggestions of experienced elearning practitioners.


CHARACTERISTICS OF SUCCESSFUL VIRTUAL LEARNING STUDENTS

Years of experience have revealed specific characteristics of highly successful virtual learning students.  They are skilled in managing their time and can communicate effectively in both speech and writing.  They are self motivated, academically ready for the next level of study, and have a strong background in the use of technology.

While most 13 to 18 year olds are not in this elite category of exceptional students, there are practices that can level the playing field and contribute to success in this rookie year of virtual education.

    1. Establish a work space environment.
    2. Maintain a calendar to keep up with homework.
    3. Log on to “school” every day, checking in with each class.
    4. Engage a variety of resources.



PREPARATIONS FOR SUCCESSFUL VIRTUAL LEARNING

WORK SPACE ENVIRONMENT: Controlling routine tasks and deadlines requires a robust organization system, starting with the work space.  As parents have heard since the kids were in kindergarten, students should have a dedicated study space in the house.  But today, for distance learners, this requirement is even more crucial.  A corner of the kitchen table between meals is insufficient when the student is working on course material for 5 or more hours a day. 

Even if the appointed desk is a series of TV trays, the surface area should be adequate to accommodate auxiliary computer components like multiple screens and other equipment that is ergonomically functional for the student.  The location should be away from household traffic and devoted to only one thing: school. Think of this as the student’s “home office.”   Students should avoid the temptation to “study in bed” or on the sofa.  Seating should be in a comfortable, structured chair.

The space should include the requisite physical tools: large screen computer, pens and pencils, calculator, paper, reference materials, and miscellaneous supplies of the student’s preference.  Access to a printer is advisable, but it does not have to be in the study space.

Digital tools to acquire might include a cell phone as an auxiliary source of internet research, an online calculator or cell phone app, and online resources such as the Quizlet app.  Newer computers might support HDMI for displaying the screen on an appropriate television.

MATERIALS:  The useful materials for any class go beyond a textbook and #2 pencil.  For the distance learner, a computer and access to internet are obviously requisite.  Suggestions from experienced on-line teachers include using the largest screen available and exploiting a wide variety of internet resources.  Opening multiple screens during lectures and presentations could provide greater flexibility by using one for accepting input and another for notetaking or additional research.  Students should eschew using a cell phone for coursework because of the potential to lose details on a small screen, reserving this device for quick tasks like basic arithmetic.

Teachers should be publishing a course syllabus that lists expectations, due dates, and grading criteria.  The most helpful outline will also include the order in which topics will be assigned on the calendar.  If an inventory of topics is not announced, the school’s course catalog can provide a list of subjects that will be covered.

A printout of worksheets and added research materials, as well as notes recorded on the computer screen, can be a permanent resource, easily organized, and a way to record and update notes for review before tests and quizzes.

Online schooling is not anonymous education, but distance learning removes the student’s voice from the educational environment.  Teachers cannot see the confused look on a student’s face or the raised hand of inquiry.  The successful online learner will develop a cadre of resources with which to participate in the learning process and interject immediately when a question arises.  The syllabus should include how to contact the course instructor: internet consultation, email, phone, or text.  Having a study group of other students provides an opportunity to compare notes, exchange homework, and share ideas.  Engaging a private tutor who can explain complex ideas in ways that match the student’s learning style and unique foundational knowledge can offer a personal connection to the virtual material.


TIME MANAGEMENT: Once the work space is organized, the student should consider how to keep up with the daily, weekly, and periodic expectations.  An assignment planner should be used regularly.  Since the student will not be in the classroom where the teacher can remind everyone that the test is on Friday, a structured calendar will help to stay up-to-date.  Suitable examples include a white board, cell phone reminder app , Google calendar, or Apple watch.  The planner should include a notification signal to remind the student of upcoming due dates several days beforehand.

The student should log on to “school” every day and survey each course.  Assignments should be entered into the Planner and grades checked and recorded.

Organizing the class schedule could take a fixed or flexible track.  Some students find it helpful to schedule individual “class” time, just like the in-school schedule, with order and time allotments predetermined.  Or the student may establish the order in which classes will be opened, but let the duration of attention remain flexible to accommodate assignment difficulty.  The most flexible approach might alter, even on a daily basis, the order in which classes are approached, but then must include a follow-up system to ensure “every subject, every day.”  The most important point is to have a consistent plan to cover all classes. The workable scheme will depend on how the teacher organizes lectures and other resources, whether there are specific hours for student participation and homework submission.  The schedule is intended to set a cadence that encourages continuous momentum and closely follows the routines which will be reestablished once students return to the school building. 

A word of caution from experienced online teachers warns that students should avoid the temptation to work on a different subject each day, e.g. Math on Monday, English on Tuesday, etc.  While an emersion tactic can be seductive for some learning styles, it diminishes long term learning and, when the school is requiring daily work in each class, presents the possibility of missing assignment dates and participation points.  Students should strive to maintain the rhythm expected of the regular school term when in-class instruction returns.

If the student is easily distracted, teachers recommend installing apps like OFFTIME for Apple or Android that block non-school interference.

Although many in-school subjects are set in a 45-minute scaffold, on-line students have more freedom and may want to experiment with a Pomodoro-style format: 20 to 25 minutes of study, followed by 10 minutes of “relaxation” before another 25 minutes of study, and so forth.  This approach supports consistent productivity while the frequent breaks keep motivation and creativity at their peek.


ADDITIONAL RESOURCES:  Many questions remain regarding the framework of lectures, assignments, consultations, and other strategic procedures of online learning as schools, students, and teachers are thrust into digital education.  Plans differ among local districts and individual classes and teachers.  The syllabus provided for each class should include methods for contacting the teacher which should be the first and immediate step to follow whenever questions arise.  The student should be aware, however, that there may be a delay in response, so additional sources should be developed.

The absence of a controlled classroom also means the absence of an assembly of like-minded classmates.  If the online teacher does not establish work groups, students should assume the responsibility to form associations with other students taking the same class, not necessarily with the same teacher.  These informal groups can serve both an academic and social purpose.  On the academic front, input from other students adds depth to the virtual learning environment and can provide direction when the online teacher is not available.

There are also many online resources to find alternative explanations of complex issues, develop deeper foundational knowledge, or learn background information to enhance understanding.  A few worth exploring include www.grammarly.com for free online writing help, www.sparknotes.com for summaries of novels, and www.cliffsnotes.com for novel summaries and general academic topics.  In addition, an internet search can be initiated by entering either a general topic (e.g. complete the square) or a specific question (like a word problem from the math text).  A few searches will pinpoint specific sites that the student finds useful.

To skirt the complication that might arise from the need for skills and knowledge which differ from those in a more traditional classroom setting, the State of Michigan’s elearning program (established in 2014) assigns a tutor to each student for the purpose of ensuring homework completion and adequate knowledge development.  Tutors provide critical support to online learners by developing a face-to-face connection, keeping students on schedule, and providing support which make online courses less overwhelming and more manageable for students.  This tutoring system is shown to increase student success by as much as 25%.


The path to successful online learning can be encapsulated into four steps:
    1. Establish a work space environment.
    2. Maintain a calendar to keep up with homework.
    3. Log on to “school” every day, checking in with each class.
    4. Engage a variety of resources.

It is often said that today’s teens are the most technologically literate group in history.  The time is right to apply that sophistication to the educational arena.

Dr. Ferguson leads a group of tutors who meet with individual students through Facetime, Skype, and Zoom for face-to-face distance learning.

GRAPHING RATIONAL FUNCTIONS

QUICK TIPS FOR 

GRAPHING RATIONAL EQUATIONS
(A topic for the 2020 School Closing Series)

 

The ‘artist’ in me loves graphing.  I could watch my TI-84 (or any grapher) draw pictures all day.  I even like homework assignments that force me to graph by hand.  What I DON’T like are instructions that expect me to “calculate” 50 points before “sketching” a graph.  When I just need to imagine what the graph looks like, where it is positive or negative, what direction the end points face, etc, I’m in favor of estimating.  I believe it’s a good practice even when a more specific graph is eventually called for, because I can quickly find silly errors.

Here’s a quick and dirty review on finding a few specific points when graphing rational expressions.


1.  FIND VERTICAL ASYMPTOTES by setting the denominator to 0.

 

 

2.  FIND THE X-INTERCEPT by setting the numerator to 0.

 

Notice that both of these tell you something about the X-axis and run left and right in the original equation, like the X-axis does on the graph. 

 

3.  FIND THE HORIZONTAL ASYMPTOTE by reducing the leading variable. 

 

 

 4. FIND THE Y-INTERCEPT by reducing the constants.

       

 

5.  FILL IN THE GRAPH.

     Done. Sketched. 

 

 

 

Other conditions tell even more about the graph.

-- Suppose in step 3, the exponent on the denominator’s variable is larger than the one on the numerator.  Think of ‘end behavior,’ what happens way out there at infinity.  If the leading coefficient of the demominator is LARGER than the one in the numerator, the fraction gets very, very small at infinity -- almost nothing.  So the horizontal asymptote is 0.

-- Suppose reducing the leading coefficients leaves a variable in the numerator, like y = x  or  y = x/3.  This indicates a SLANT (or SKEW) ASYMPTOTE, which is not considered “horizontal” even though it goes through the y-axis.  Notice that it also goes through the x-axis. 

-- Suppose there is no constant in the numerator.  Fill in a place holder, 0.  Then the fraction is zero divided by something and equals zero.

-- Suppose there is no constant in the denominator.  Again, fill in a place holder, 0.  The fraction becomes division by zero, which is undefined and the graph never crosses the y-axis.

-- Look at a bunch of rational graphs.  Notice that asymptotes are like the poles of a magnet.  They repel the graph.  The segments separated by the asymptotes act in a similar way.  In MOST (but not all) cases, if the graph is heading up on one side of the asymptote, the other side will NOT follow the same pattern.  Simple rational expressions generally occupy only 2 quadrants formed by the vertical and horizontal asymptotes: I and III, or II and IV. 

 

 

FINDING THE BLACK HOLES OF A RATIONAL EQUATION 

As problems become more complicated, factoring and reducing become necessary.

  This reduced form gives a vertical asymptote at x = -1, but x can not equal +3 either because it was part of the original equation.  Although there is no vertical barrier at x = 3, the graph will skip over that point and create a hole.

 

 

 

WHAT DOES THE GRAPH LOOK LIKE WHEN THERE ARE 2 VERTICAL ASYMPTOTES?

 
The principle of repulsion....

 

 

 

 

And some equations present wierdnesses like part of the graph crossing the horizontal asymptote, looping around, and finally adopting the behavior we expected.  

WITNESS:

Notice the x and y intersections and the repulsion principle.  For this one, a couple of calculated -x values could be useful in verifying that they fall BELOW the horizontal asymptote.

 

--- And another rule breaker....

How does it get that squiggle?  No vertical asymptote because it's an imaginary number, but a horizontal asymptote at 0.  For X between -sqrt 2 and (roughly) 2.4, the y value is increasing; for all other values it is ever decreasing.   While the numerator can turn negative, the denominator will always be positive.   

--- Here's a cute one that defies the repelling principle.
Will this graph ever enter negative territory?  Nope.  The fraction will always be positive. 

With just a few morsels of data, the general shape of most rational equation graphs can provide valuable information to check more intricate drawings, as well as inform Calculus questions later in math study.  So let's get graphing!