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Right Triangle Trigonometry Portfolio

Kyle Linford

Eastern Michigan University

EDMT 330

Dr. Michael McVey

Winter 2015

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Table of Contents

Education Technology and Me ................................................................................................................. 3

ISTE Standards ........................................................................................................................................... 5

Components of an Effective PowerPoint .................................................................................................. 9

Technology Integration ........................................................................................................................... 11

Reflection on Web Development ............................................................................................................ 12

Plagiarism ................................................................................................................................................ 13

Reaching Out with Digital Age Media ..................................................................................................... 16

Online Teaching ...................................................................................................................................... 18

Moodle Organization .............................................................................................................................. 19

Visualization in the Classroom ................................................................................................................ 21

Moodle Reflection................................................................................................................................... 24

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Education Technology and Me

Educational technology can be described as any technological tool that aids in the

explanation and understanding of information. A major benefit to these tools is that teachers

can use them to better present information to their class in many ways that they could not

before. Whether it is to help explain a complex topic or just add another dimension to the

lesson, technological tools can help teachers present the information to students visually,

audibly, kinesthetically, or in many other ways that help them to better understand the lessons.

In a high school algebra or geometry course, a teacher can utilize the software Geometer’s

Sketchpad to help the students visualize concepts they are learning. With software like this,

students would be able to create figures and interact with them in a way that helps them to

better understand topics like transformations, congruency, area, ratios, tangency, and many

more. Rather than spend time drawing images by hand or working out simple computations,

classes can use technology to quicken their work so that they are able to focus more on main

concepts they are learning. While technology can be very beneficial to a classroom, it is up to

the instructor to judge the appropriateness of the piece of technology for the class. Not all

technology will be helpful to a course and those that are will not be used every day. It is up to

the teacher to assess the value of the different technological tools at their disposal and

determine when they are appropriate for use. They must see that the tools will in fact help the

students’ understanding and be worth the time to use.

My personal experience with educational technology is minimal but developing. Having

taken the course Math 305, I have gained both a better understanding for the importance of

technology in the classroom, as well as some situations it can be used. However, I am still

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actively seeking to improve my understanding of the many ways it can be used and their

appropriateness. During my time in Math 305, the class had a discussion about the appropriate

use of calculators in the classroom. While many people found calculators to be a crutch for

students, the teacher questioned this view by having the class think about what they consider

important for students to be able to do. She asked if always being able to remember what

certain products of numbers are should be the main focus of a math class. The situation she

gave suggested that if we had a student who had difficulty remembering multiplication, should

we really worry since there are many pieces of technology that can do the computation for

them, or should we focus more on making sure they understand the concept of multiplication

and its application? This questioning of the traditional view of education caused me to examine

the importance of technology in a new way and the ways it can be implemented in a class.

Though I am still learning when it is appropriate, I can value the use of educational technology

in a class and begin to supplement technology that I find is helpful and beneficial to future

classes.

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ISTE Standards

1. Facilitate and Inspire Student Learning and Creativity—Teachers use their knowledge

of subject matter, teaching and learning, and technology to facilitate experiences that

advance student learning, creativity, and innovation in both face-to-face and virtual

environments.

Summaries of Standard Meeting Technology

a. Core Math Tools: Core Math Tools is an online office suite that provides users

with a collection of free mathematical programs. These programs include a

computer algebra system, a dynamic geometry environment, a simulation

runner, and many other features that are beneficial for a math class. These

programs provide users with a collection of abilities that replace other, more

expensive programs like Microsoft Excel, Geometers Sketchpad, or the TI-Nspire

CAS. Because of these free capabilities, this program is one that would be

beneficial to incorporate into any classroom. While a math classroom will

receive the full benefits of this suite, classes in other subjects who are unable to

use expensive programs designated for the math classes can download Core

Math Tools for free and utilize its many features. Whether it is exploring

geometry with the interactive whiteboard, running advanced simulations, or

working through the calculation functions, Core Math Tools is a suite that

provides helpful and necessary math features to any possible classroom.

b. Fakebook: Fakebook is a website that allows users to create parody Facebook

pages of historical figures and well known celebrities. While it can be seen as a

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comedic endeavor, Fakebook can be used by classrooms to promote thinking

that is of high cognitive complexity values. Instructors can use this feature to

engage students understanding of a specific topic to analyze, interpret, and

create a Fakebook page. For example, an English instructor can assign students

to create a Fakebook for some literary character. Students will need to truly

understand the literature they are studying to create the persona of their

character online. Similarly, a history class can utilize their understanding of

historical events to create an account for a historical figure.

c. TI Nspire: As a mathematical tool, the TI Nspire provides users with the benefits

of both a graphing calculator as well as a computer algebra system. For a class,

students would be able to perform all of their calculations on the Nspire, while

also working through the benefits of the CAS. They will be able to create and

save files for their work, explore dynamic geometry environments, and many

other interactive features. Some of these features are available online for

download from the Texas Instrument website. These features include

preprogrammed features for instructors to use for their students. As a teacher,

one can have students work through these preprogramed downloads and

interact with the different visual features they provide. The benefits of this tool

become incredibly beneficial to helping to better achieving the desired learning

goals.

2. Design and Develop Digital-Age Learning Experiences and Assessments—Teachers

design, develop, and evaluate authentic learning experiences and assessments

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incorporating contemporary tools and resources to maximize content learning in

context and to develop the knowledge, skills, and attitudes identified in the NETS•S

Summaries of Standard Meeting Technology

a. Movenote: Presentations and lectures are important to lessons. Especially with

online learning experiences, they provide students with necessary information in

an abbreviated and organized way. However, posting them online for students

to read can become confusing and uninformative without a narrative. By

utilizing Movenote, instructors can provide narrative commentary for their

presentations to provide students with both a visual breakdown of the lecture,

as well as an auditory explanation. This interactive program can allow

instructors to record their auditory lecture over different slides and interact with

the slides through the use of a laser tool. When having to incorporate a lesson

into an online environment, this tool will be extremely helpful to ensure the

necessary information is presented to the students in way that fits the desired

learning goals. Rather than link students to external videos or simply post slides

to a lecture, the instructor can provide an explanation that fits their class’s

needs.

b. Skitch: Skitch is a tool from Evernote that allows users to interact and mark up

images. Similar to the benefits of Movenote, Skitch provides instructors with a

way to interact with images that are important to helping students understand

the desired learning outcomes. From this interaction, teachers can highlight key

information for students and provide commentary along with it. Students in a

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math class might find this particularly helpful when their instructor can interact

with and explain the components of a mathematical concept being visually

represented.

3. Model Digital-Age Work and Learning—Teachers exhibit knowledge, skills, and work

processes representative of an innovative professional in a global and digital society.

4. Promote and Model Digital Citizenship and Responsibility—Teachers understand local

and global societal issues and responsibilities in an evolving digital culture and exhibit

legal and ethical behavior in their professional practices.

5. Engage in Professional Growth and Leadership—Teachers continuously improve their

professional practice, model lifelong learning, and exhibit leadership in their school and

professional community by promoting and demonstrating the effective use of digital

tools and resources.

a. Organizations like Edutopia and ISTE help teachers meet this standard by

providing them with resources and information to better improve their ability to

understand and integrate technology into the classroom.

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Components of an Effective PowerPoint

There is a reason that PowerPoint causes people to cringe. Many individuals have had

horrible experiences either making or being forced to watch poorly made slideshows. These

presentations are often lackluster, hard to follow, and mind numbing. However, if they were to

be adjusted by following several techniques for PowerPoints, these slideshows would become

far more powerful for an audience.

The first tip labeled is one that, in my experience, has been the biggest problem with

presentations: “Simplify and limit the number of words on each screen.” If someone is

unprepared for or unsure about their presentation, they will cram an excessive amount of

information onto a slide. This provides the viewer with too much information to read and pulls

their attention away from the presenter. During one of my education courses at Washtenaw

Community College, my instructor would constantly load the screen with paragraphs of text. As

viewers, we were unable to focus on what she was saying as we tried to read and copy the key

information from the slide. These slides were so wordy that she was unable to do anything but

read right off the screen. This inability to talk directly to the audience presents another issue

people have with PowerPoint.

People often set PowerPoints up as if the screen is their notecard. They read from the

slide and speak to it. These two issues are listed specifically as “Do not read from your slides,”

and “Do not speak to your slides.” This causes the audience to become unfocused on what the

message is because the speaker is not speaking to them. During a group presentation, a

partner I had been working with spoke in this way. Their actions reflected to the audience

someone who was unprepared and disinterested in what they were saying. Soon the audience

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lost interest in us and were unfocused on the turned around speaker. No matter how well the

slides are prepared, the speaker loses the audience by their inability to properly communicate

what they intend.

To further explore the things that can cause an audience to lose focus on a presentation,

the disorienting and distracting effects of flashy transitions is discouraged. The tip suggests for

presenters to “avoid the use of flashy transitions.” In my experience with good presentations,

the speaker always kept their transitions and animations consistent and minimal. This kept the

focus on the speaker and the message they are conveying. By utilizing this and other

techniques, a person can better develop a presentation that resonates with the listeners and

conveys the message needed to be understood.

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Technology Integration

My Definition:

Technology integration is the incorporation of technological tools into classrooms for student

learning.

Edutopia Video:

In the video Technology Empowers Student Fieldwork, the use of technology was integrated

into the classroom as a tool to help further student understanding with a class project. For this

project, students and local farmers worked together to track horny toad lizards with the

NatureMapping program, as well as GPS trackers. This equipment allowed the students to be

able to better track where the animals were located and how they can monitor them and the

environment. The director of the task mentioned how she finds that the project-based task is

able to bring science, math, technology, and even art to the students in a way that provides

them with real world applications. From using these sophisticated technologies, students

appeared to be more engaged in the information they were learning, the differentiated tasks

allowed them to work in a variety of ways, and their ideas can be exchanged with other schools

across the country.

Level of Integration:

Based on the information from the videos, the classroom appears to be at the appropriation

level of integration. Here, the students are working collaboratively with their classmates and

local farmers to better understand and track the horny toad lizard. They are sharing their

research on the Internet and working together to achieve a goal.

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Reflection on Web Development

The ability to develop original web content is a skill that teachers can benefit from as

professionals and educators.

As a professional seeking employment, the ability to develop a personal website is very

important. It signifies that one is knowledgeable about technology, and it presents their

professional resume to potential employers. Now, administrators are able to not only access a

person’s resume and see their skill sets, but also, they can have direct links to projects and work

the person has created. This technological skill set helps to further show one’s ability to create

original web content for students.

By creating an original WebQuest, I was personally able to use my technological skills to

develop an engaging online experience for students to practice both their conceptual

knowledge of trigonometry and online research. The task for the students is one that forces

them to use their knowledge of trigonometric identities to create a rainwater irrigation system.

By using math to solve a real world application problem, students are able to have a better

understanding of the trigonometric identities they are using and how they can be implemented

to solve problems. However, by asking students to question their responsibility and

involvement with their local communities, they are able to further build on their

understandings of larger concepts, like community and the environment. From creating simple

projects like a WebQuest or a person webpage, teachers are more able to better demonstrate

their abilities as a professional and educator.

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Plagiarism

There is more to writing a paper than cutting and pasting information. Plagiarism is a

serious ethical issue that educators are facing. Often, students will submit an assignment as

their own even though it is someone else’s work. However, a student’s desire to cheat is not

always to blame for a situation like this. Sometimes, an individual’s ignorance about plagiarism

can cause the incident to occur. To help lessen the occurrence of this issue, strong, clear

information about plagiarism should be discussed openly with students in a classroom.

Though there are cases were the act of plagiarism was knowingly committed by a

student, some situations reflect more of the student’s ignorance about the issue. According to

a survey by the ATL, they suggest that most students “don’t know the difference between

plagiarism and legitimate research” (rpt. in Clay). Teachers need to understand that students

caught plagiarizing may be unaware why their actions are considered wrong and unethical.

Self-reflection will be needed in this situation to properly judge whether the topic of plagiarism

was properly covered in the class and if the student is responsible for their actions. According

to Chris Harrick of Turnitin.com,

“The big challenge that educators have is to make sure that they teach their

students the proper way to find material on the web, how to document it,

what’s acceptable and what’s not, and then use tools to make sure that those

protocols are followed” (qtd. in Zwang 9).

Working at the Washtenaw Community College writing center, I have had to help many

students understand the concept of proper citations. It appears that about half of the students

I work with are unaware of how to properly cite information in MLA or APA format and are

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unsure about what information they can consider original. Teachers need to discuss this ethical

issue in their classroom to help ensure that students understand both the technical and ethical

aspects of the matter. In this way, students will be able to better find research and understand

when to cite it in their work.

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Works Cited

Clay, James. “‘Internet Plagiarism is a Serious Problem’ Says 58% of Teachers.” Online video

clip. YouTube. YouTube, 18 Jan. 2008. Web. 27 Jan. 2015.

Zwang, Jenna. “Social Websites are Latest Sources for Plagiarized Material.” eSchool News.

eSchool News, 1 Sept. 2011. Web. 27 Jan. 2015.

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Reaching Out with Digital Age Media

By using media like newsletters and blogs to reach out to parents, teachers are better

able to fulfill the ISTE standard that requires the effective communication of relevant

information and ideas to students, parents, and peers through the use of digital age media and

formats. This communication allows teachers to present this information in a professional and

organized way that all parents are able to access. Teachers can first think about what they

want to convey to the parents and organize it in a way that is easier to comprehend. Parents

are then able to learn important information from their child’s instructor in a clear and concise

way.

Further, this information can become easily accessible. By creating a blog or emailing a

newsletter, teachers can be in quick communication with all parents. Anyone with computer

access can read the teacher’s messages and respond appropriately. However, teachers will still

need to take the technological divide into consideration and make appropriate

accommodations.

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Online Teaching

With the ever growing development of technology and forms of communication,

education has new ways to differentiate and progress.

Because of modern technological advancements, education can reach past the

classroom walls. Technological tools, like Moodle, Weebly, live chats, videos, and blogs, allow

teachers to present their lessons to students at any time and location; they are not confined to

just the hour long sessions in their classrooms. This online teaching creates individual

opportunities for students to learn at a speed that suits them. Students are able to work

individually and focus on the material in an environment that suits their preference. However,

though the students can work individually on the activities and lessons, they do not have to

work from this on their own.

A main aspect of the technological advancement is the progress in communication.

Teachers and students have access to different ways of communicating outside of the

classroom. Students are now able to live chat with their instructors, make Skype calls, and

interact with their teacher and the academic lesson more often. Other than just the individual

student and teacher communication, whole classes can interact online to discuss the lesson and

information they are working from in the class. Both individual and cooperative learning can be

branched out from the classroom lesson.

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Moodle Organization

Title:

Right Triangle Trigonometry

Introduction:

To introduce the students to the online lesson, I will begin by introducing myself as their

instructor. Included are my name, contact information, and a link to my professional website.

Additionally, students will find a list of standards that will be used in the lesson and several

external links to extra information about trigonometry.

Anticipatory Set:

This lesson will proceed with the assumption that students are unaware of the trigonometric

relationships involved with right triangles. To help introduce them to these relationships, or

review them for those who already are knowledgeable, a short video will be used that explains

these relationships in depth. In the video, I will explore what a right triangle and its

components are; angle measures, including degrees and radians; the trigonometric identities of

sine, cosine, tangent, cosecant, secant, and cotangent; the inverse relationships; and some

application problems.

Guided Practice:

As the students begin to understand the large concepts of right triangle trigonometry, they will

begin to practice their knowledge through a series of problems in a Microsoft Word document

to help in their understanding of the topic. These problems will walk students through the

necessary steps and build in complexity. As they work, students will be able to contact me and

schedule quick discussions to help answer any questions they might have about a problem.

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Independent Practice:

Having gained a sufficient knowledge about the topic of right triangle trigonometry, the

students will be challenged to demonstrate their understanding by completing the inquiry-

based application WebQuest I created. In this activity, students will put their understanding of

right triangles to use in creating a rainwater irrigation system for their school’s community

garden. By working from this web formative assessment, students will be exposed to a better

understanding of both the applications and concepts of right triangles as they strengthen their

computation skills. This WebQuest will be linked to the Moodle page along with a description

of what students are expected to do for the activity.

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Visualization in the Classroom

Visualization is an important factor for the improvement of one’s education. It allows

students to better interpret and understand concepts and topics being discussed. Visualization

in the classroom can be implemented through the use of software like Inspiration or the

webpage creator, Weebly. The Inspiration software allows for users to organize creations in a

way that help themselves and others to visualize the different aspects being covered. Teachers

can use this for their own explanations of concepts to a class. As an instructor attempting to

breakdown the topics for a particular lesson, one can utilize the Inspiration capabilities to

create a visual organizer for the students to better understand the content. Similarly,

instructors can also use the webpage creator Weebly to further help organize and develop their

lessons in a larger way. Rather than focusing of the breakdown of a specific topic, Weebly

pages allow for users to create sites that can be broken down into different sections and

presented in a way that engages the students. Additionally, students can work through

creating these diagrams to explore their own understanding. For example, students beginning

to write essays can create organized outlines and clusters from this software in a way that

provides more options than just writing it out traditionally. From these connections, the

visualization and organizational aspects of programs like Inspiration and Weebly can be seen to

better improve the understanding of students.

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Moodle Reflection

The Moodle page I created is the page Right Triangle Trigonometry. The main focus for

this lesson was to explore the trigonometric identities through the components of a right

triangle, as well as solving for these specific components with given information. While

students work through these specific topics, they will gain a better understanding of the specific

concepts being explored by seeing how mathematics can be applied to the development of

their communities. To accomplish these learning outcomes, the Moodle features a collection of

materials, including quizzes, embedded videos, downloadable files, and a WebQuest activity.

From these different features on the Moodle pages, students will be better able to explore the

topics being discussed in an organized and engaging way. The students will begin with an

introductory, diagnostic assessment that gauges their entry understanding of topics that will be

taught. They will then watch a series of videos that provided detailed information about the

identities being learned and their applications. These videos were found to provide very helpful

explanations of not only what the identities are, but the reasoning behind their development as

well. By exploring these detailed explanations of these videos, students will find themselves

more confident in their understanding of the topic and its applications to community. The

students can then practice this understanding through the downloadable homework and

demonstrate their potential mastery of the topic on the final quiz and WebQuest activity. The

WebQuest was created as an inquiry based project that required the students to demonstrate

their full understanding of the topic and apply it to their exploration of a community problem.

In this way, students can follow an ecojustice education framework to explore the subject’s

connections to community and individual responsibility, as well as their own ability to use the

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high level complexity of creating on Bloom’s taxonomy. However, though the unit helps to

ensure students achieve the desired learning outcomes, future changes can be made to the

layout and the materials used.

There are some changes that can be implemented into current layout of the Moodle

page. In particular, the page could include a dropbox for the downloaded assignments for the

students. Though this would require the assumption that every student has the ability to scan

their homework solutions, the addition of this resource may prove helpful in the

implementation of this unit. Additionally, providing personally filmed videos that explore the

concepts being taught would allow the instructor to be in more control of the information

being presented to the students. With these few changes, the Moodle page can be better

improved for the benefit of the student’s learning.