Limits of Functions with the Help of Microsoft Excel

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Limits of Functions with the Help of Microsoft
Excel

• -16-18 years old
• -12th Grade Calculus
• -Daniel Masi
• -September 25, 2008
• EDU 357

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• Given that the students have had the proper
  preparation in Pre-calculus the students will be
  able to understand the limit of a function. In
  addition the students will also learn the
  definition of the limit. As well as be familiar
  with the different techniques required to
  find these limits and prove that they can use
  these proper techniques.

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• To help with this chapter of Calculus (Chapter
  2), the students will be introduced to Microsoft
  Excel which could help benefit the students, and
  give them a better understanding of the material.
  In order to properly educate the students it will
  take up to a minimum of a week, where it will
  then be expected that the students will have a
  general knowledge of the chapter.

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• To begin this week long chapter, I will start by
  handing out all the vocabulary terms needed to
  learn the material. Having done so I will then go
  over them as a class, where at that moment it
  will be appropriate to hand out all of the notes
  for the chapter.

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• By giving the students the notes ahead of time
  there will be more time in the classroom rather
  than copying them from the chalkboard. Also in
  doing so it will leave the students in a better
  learning environment.

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• They will be more concentrated on the lesson
  being discussed, opposed to their attention on
  their notes. At the beginning of the first
  lecture I will bring their attention to what is
  expected of them and by doing so will let them
  know what is to be learned.

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• Motivating students for Calculus can sometimes be
  an impossible task. However, as this week lesson
  includes finding the limit of a function it is
  desired to know the graphs of these functions.

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• Having said this, I feel that a great motivator
  for these students will be to introduce them to
  Microsoft Excel. Showing the students such a tool
  will only cause greater interest in the material,
  as well as illustrate to them the functions being
  learned.

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• To provide information on the desired material to
  be taught I will hand out the notes and
  vocabulary preferred for the chapter. (Since
  Monday will be the day of lecture). Though
  lecture can be a great tool for certain students
  to grasp the material, not all are able to hold
  on to the matter in such a way.

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• Alongside my lecture to the class we will always
  review certain examples of the chapter being
  discussed. True lecturing puts the information
  into your brain, but examples will keep it there.
  In addition to the lecture and practice examples,
  I will end the class by first introducing them to
  Microsoft Excel by using a computer and a
  projector.

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• In doing so I will give them a brief preview on
  how they can see the actual limits to certain
  functions when using this tool. As Microsoft
  Excel is great in illustrating the graphs of
  given functions.

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The second day of class (Tuesday) will
strictly be for giving the students practice
problems on chapter two. In addition to the
example problems in class the students will be
given mandatory homework due the next day.
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• This will provide practice for the students
  outside of class and will show myself if the
  material that has been gone over is indeed being
  learned. Everyday the students will be given a
  manageable homework amount, although Tuesday will
  be the only mandatory day where it will be
  collected.

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• These homework assignments will be similar to the
  examples given in class as the homework will be a
  repetition of what was taught in class.

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• To give the students the proper practice to learn
  the task at hand aside from class and homework,
  will be an opportunity for the students to
  explore Microsoft Excel. To do so we will spend
  at least half of the class in the computer lab,
  where everyone will get an individual chance to
  explore through certain problems.

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• In doing so the students will get a chance to
  learn a new useful tool as well as illustrate to
  them the limits of the functions previously
  explored through Excel.

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• Wednesday or the third day of the lesson, will be
  the day for feedback on their individual
  progress. The students will hand in their
  completed homework assigned from the previous
  night. After collection of this they will then be
  given a vocabulary quiz on the chapters terms.

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• While they are taking the quiz I will then go
  over the collected homework and give them written
  feedback. I will grade each of them like a future
  test so that each student will understand my
  grading policies. My feedback will show them what
  they are doing right, and what they need to work
  on.

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• Though this feedback on there homework is
  important, each individual should also have the
  right to express their concerns to me verbally.
  So after the vocabulary quiz the students will
  each be given a couple of minutes to describe
  their feelings and concerns about the material.

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• If they wish to have more one-on-one time to go
  over the material they will be given the chance
  to stay after school that day where we can review
  their desired problems in a more personal setting.

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• To review the material we will briefly go back
  through what has been taught to keep the overall
  grasp of learning the limit fresh in their head.
  In addition to this, Thursday will be a day
  strictly for review with the class as a whole. If
  need be the class will be spent repeating the
  lesson previously taught.

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• For review I will go over the vocabulary on the
  quiz Wednesday which I will return graded. As
  well as review the different techniques used to
  determine a functions limit. By doing so this
  should give the students a general understanding
  of the lesson.

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• I will give the class sample test questions with
  the answers for the students a study guide to go
  over to better prepare for Fridays test. This
  study guide will not only direct the class to
  focus on certain key points of the lesson, but
  will give them a sense of what the test will be
  like prior to it.

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• This should keep them more relaxed during the
  test so they will not panic and achieve the best
  they can. At the end of class I will ask the
  class if they have any questions or concerns they
  have for the test.

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• To asses whether or not the students have learned
  the chapter they will be tested on their ability
  to find the limit of a function, and show that
  they are able to use the different techniques
  appropriately to find these limits. The Test will
  be given on the last day of the lesson.

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• It will be a test on the basics of chapter two,
  with questions which require different techniques
  and formulas to answer them. The test will
  integrate the class and homework examples, along
  with their knowledge of the definitions.

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• True, the test will have a big impact on the
  students grasp of the material, they will also
  be judged on their participation throughout the
  week.

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• Based on the effort each student has showcased
  during class work, computer lab time, and their
  individual attempt on the homework the student
  will be rewarded a bonus onto the test.