Technology Integration Plan

            For this technology integration plan, I used a lesson plan I had previously made for High School Geometry class. This lesson plan focuses on using similarity and congruence properties, analyze information about sine and cosine in complementary angles, and apply previous knowledge to understand and apply the law of sine and cosines in non-right angle triangles. This lesson integrates effective learning through various uses of technology and different teaching strategies ranging from instruction, visual, and audio representations.

In the spreadsheet under access for the first row, the students will be first introduced to the material. The students will use what they know about similarity and congruence and explore how to find relationships in geometric figures. In order to begin, there is an introduction to the material through direct teaching, then a visual and oral presentation introducing the material in different learning methods. The smart board enables the students to be engaged to visual representations, which will introduce their online interactivity. The Elmo camera allows students to see what the teacher is holding or showing through a live camera connected to the projector to make sure all the students see and understanding the concepts from their online interactivity. This will help the students who are still confused about their hands on activity and concepts. The students are also required to be note taking throughout the direct teaching, computer interactivity experience, and hands on experience to combine what they have learned and their understanding through multiple views.

            Later in row two, students are required to analyze relationships of sine and cosine complementary angles. In order to do so the students are guided through direct teaching and the use of the smart board, also so every student can see. Students will be given different examples they will have to represent and compare, then through an online interactivity the students are going to analyze the relationship and use it to answer the online questionnaire that tells the students on the spot whether they are right or not and this will also be used as a formal assessment. Direct response is important, because some students will not attempt to find out if they are right or not and technology makes that possible. Students will also explain why they were wrong or right based on their online questionnaire.

            In order to evaluate and assess in the next row, the students will be asked review the formula for the area of a triangle by drawing. There will be a teacher demonstration through PowerPoint then the students will work in groups. In groups, the students will draw using geometer’s sketchpad for more accurate results. Then the students will come together in a group discussion to share their results. The students will also be allowed to use calculators and Math Input Panel, which is a software that converts written math expressions into text for a faster way of writing expressions on the computer.

            Students will prove the Law of Sines and Cosines using previous work in the class shown on the next row in order to communicate the concepts. Through a Khan video, they will compare their solutions. Through a class question and answer sessions students will analyze their proof and what they were missing or what they did right. Understanding the proof students will apply the laws in real life problem solving. The questions will be displayed through PowerPoint, so all the students could see and the answers will be shown after all the students participate and will be assessed by participation.

            Finally, in the final row, students will be able to understand the Law of Sines and Cosines and be able to apply it to any non-right triangle. The students must also be able to understand why this law only applies to non-right triangles through previous work. Students will work and be assessed in groups conducting an activity called triangles with stars. Students must find unknown lengths of earth to stars using information about triangle sides and angles. Students will then work individually and be assessed explaining their own work. It is important to know whether or not each student understands, so it is acceptable to work together to problem solve, but then each individual student should record and explain their results to ensure each student has understood the lesson. The students will be able to use OpenOffice Draw to explain their results visually if they are unable to by writing. Overall, the students must show they understand it does not matter how they represent their results.

URL: https://docs.google.com/spreadsheet/ccc?key=0Al-Ug3kw0QuYdG1XMWl0bllnNzdkTkk5Mms1bUFKZ3c&usp=sharing

Online Math Exams

        More and more schools are giving online exams for students, especially for entrance exams. Online tests may be difficult for students who are not familiar with the format, but it may be especially difficult for students taking math exams on the computer. There are pros and cons for students taking a math exam online some examples are the following.

        The pros to online math exams are a few. Students who take an online exam may receive their scores as soon as they are done taking the exam, unless there is a written part, but there most likely won’t for a math exam. Students can easily see what questions have been or have not been answered. Students may also have an easy accessible reference sheet. Also, sometimes students lose points on standardized tests for not filling in the bubble correctly, erasing poorly, and/or selecting more than one answer. Taking a math exam online won’t make these factors an issue.

        There are cons however. The students may have a hard time taking the online test because they are not use to the format. The students may have a hard time entering fractions, exponents, and negative numbers in the calculator.The students might also have a hard time figuring out how to access the formula sheet. Usually most people prefer to do their math work on a paper, and if the student is not given one they might have a harder time finishing the exam on time. For example, geometry problems should be drawn out for a clearer understanding. The students may also get anxious because as of now it is something new and not commonly used. I know that I do not like to use the computer to solve math questions, so the students might feel the same.

        Overall, this is a work in progress and students should be able to practice in the same format they are being tested if they are going to be tested online.

Online Textbooks

         Online textbooks seem to be used more and more now throughout schools. My first encounter with a math online textbook was freshman year of college. Now more and more high schools are getting online textbooks as opposed to hard copies, sooner or later there will be no more textbooks in a classroom or to take home. There are some pros and cons to this.

         The benefits of online textbooks is that the students will not have to carry heavy textbooks back in forth. Students could have all of their textbooks on their laptop, iPad, or any other tablet. Additionally, textbook companies can include online resources and manipulatives along the text, so students could explore on their own. Students can easily look up unknown words or extra help right away if their textbook is digital.
          However, there are also cons to having an online textbook. The access to the textbook may not be fair to some students. Some students could possibly only have one computer in a household and might have to wait to use it. Some students may also have difficulties using it if not taught properly. Additionally, will the student be able to use their online textbook in class? If the student is allowed to, who is to say the student is not looking at other things during class. If the student is not allowed to, will this help the student if the student is struggling? Some students might also just prefer to have a textbook, since they are use to it.

          Overall, students should be given a choice to their preference and access to the textbook. Each student should be given an opportunity to choose which method will best help specifically to their needs. Each student is different and some might benefit from having an online textbook, while other might not, so instead of changing all the textbooks to being only accessible online the students should choose.

Catchup Math

Catch up math is an online curriculum support for math. Some schools use this website for middle school students who are not at the math level they are supposed to be and need better math foundations. This website allows the students to have an account where they can work at their own pace through lessons, questions, and quizzes. The teacher also has an account to track where the students are and how they are doing.

The students are first shown lessons, which may include videos. The students are given questions to answer about the lessons, where they have to apply what they have learned. If the student needs help with a question, they could ask for a hint or several hints. For each hint they use it takes off points off the student’s final grade. Depending on the type of questions the student gets wrong or asks for hints the website generates questions with what the student needs help with. Although two students may be working on the same lesson, the questions might be different depending on the student’s individualized needs.

This website also tracks improvement and overall work of a student, and is accessible to both the student and teacher. This way both the student and teacher know the individualized strengths and weaknesses of the students and could individualize instruction for each need. This website also only allows students to access calculators only for the problems it is required. This is helpful because this way the student will not feel the need to use the calculator for everything. Using the calculator for everything in classrooms in my opinion is a big problem we are faced with today. Students who become too dependable on calculators do not know how to apply some skills required for further content.

Overall, this website is very helpful for students and teachers. The students are able to do the work at their pace to ensure better understanding of each concept and the teacher is able to focus on the needs of each student, since the website identifies what they need help with and where they are.

PowerPoint for Teaching

            PowerPoint is a great presentation program for teaching Mathematics and any other content area. With PowerPoint, teachers could outline their lesson plan with text and media. Standing in front of a classroom and teaching is difficult because there are many things to cover and it is easy to forget something, but having a PowerPoint presentation makes it easy to follow a clear organized format. Additionally, having an outline of the lesson could be helpful to send students who were absent that day, or to post up. Taking notes is important to refer back to when solving problems for homework or studying for a test, but it is also time consuming in class from focusing on what has to be learned and practice. To make time more efficient students could use the class time to review the PowerPoint, take notes on what is not on the PowerPoint that they feel is important, then spend the rest of the class learning, practicing, and asking questions.

            There are also many great tools for learning that could be used to teach and engage students in learning. PowerPoint allows teachers to add slides with text, pictures, videos, sound, and animations. Having the option to make the power point not only educational, but also interactive engages students to want to learn more. PowerPoint is much more of an attention grabber than just writing on the board. This would be similar to creating a canvas, like for the unit plan, but more detailed and focused on a particular topic. Another great feature for the PowerPoint is creating shapes, this would be perfect for a lesson on geometry. There is also an option that the students may print out the PowerPoint slides as handouts, which the students could use to study, because they would be like index cards. The students could also print out the slides with lines on the sides to have the PowerPoint slides in their notes and take additional notes to each slide that they feel needs further explaining or is unclear. 

YouTube for Teaching and Learning Math

            YouTube is a great website for educational purposes. YouTube is great because there are tons of videos for tutoring purposes, teaching, or fun learning videos. There are many videos uploaded by many users that could help a student learn any math topic and how to apply it for problem solving. The great thing about this is that not every student learns the same, so if the student does not understand the way one user is explaining it the student may simply look up another video.

Teachers today could make up their own videos for students. There will always be those days when a student is out for health reasons that may take up to one or more days. It is difficult for a student to come back and catch up especially if something new was taught and the teacher cannot simply reteach the lesson when the student returns. Even if the teacher does a short 5-10 minute video on the lesson, it is much better than the student having nothing to refer to for help. The other great thing about doing this is the video could also help students that do not take great notes to refer to as well and the video could stay up and help other students from other schools.
There are also fun learning videos that may help students learn in different ways. There are videos that have songs and short stories on different topics for math, such as the Pythagorean Theorem, the distance formula, and many more. There are unlimited amounts of videos that may help students learn and remember through creative videos. Students could also be asked to make their own video as a project to apply what they have learned. I believe a great way to ensure students are learning is to have the students explain or apply what they have learned through numerous ways and making a video allows students to apply this skill. Overall, whether to teacher uses the videos to teach or the students use the videos to refer to for help it is a great technology for teaching, learning, and applying math.

Collaboration Canvas

At first selecting a canvas to remix was difficult, because there are so many options and math could go hand and hand with many other content areas. I decided to choose a physics unit plan on Newton’s Laws because students need to have a basic understanding of algebraic expressions and functions in order to apply these laws. I added many things to this unit plan. The first thing I included was the different ways of expressing functions. I then added the mathematical representations of Newton’s Laws, for example for each law I included the expression and graphical representation of each law underneath. I then added two videos that were both about Newton’s Laws and the math in his laws, for example one of the videos included sports scenarios with some examples that expressed his laws and were solved through plugging in these values into the variables. I did not want to remove anything from the original canvas, because everything was also related to math. Math and physics collaborate very well together in general, so both canvas fit very well together. I believe that these lessons go very well together and support each other perfectly.

URL: http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2589&mode=view#network6

FluidMath

            FluidMath by Fluidity Software, Inc is an extrodinary software for both teachers and students in grades 6-12. This software is a handwritten based mathematics app that helps students learn and teachers instruct on an interactive app without having to go through the hassle to look for math symbols. The software recognizes the handwritten math and automatically converts it into computer text underneath. This is both helpful for mathematical reasons and if the student wants to refer to what they did, it is much easier to look at the computer-generated text, since it is more organized and easier on the eyes.
            FluidMath is like a notebook calculator for students. This software recognizes mathematical expressions when handwritten and allows the students to graph not just one but multiple expressions on the same graph or on different graphs side by side. It also tells the students how many variables are in the expression and allows the student to solve for the variables with just a click of a button, and everything is labeled. Students can also graph inequalities, with different colored representations on the graph and with a table value alongside the graph. Students could also see graph relationships and change the variables as many times as they want, which will also change the graph. It even allows students to simplify and approximate fractions and radicals. Not allow does it allow students to do so, but also shows the students systematically how to. Lastly, if a student uses this program to solve a problem and messes up on a step, after fixing the step the program will edit and fix the answers to all the following steps, so that the student does not have to redo the problem. Overall, this is a great software for students to practice math and catch their mistakes. 

Unit Plan Canvas

            Creating a PLAYground canvas was not as hard as I initially thought it would be. Like anything, the website was confusing when I started creating my canvas, but then I found it to be easy. It was easy because when I placed my mouse over the widgets everything was labeled, which made it simpler. I liked how each widget had its own purpose; it made the canvas easier to set up. After completing my canvas, I saw the purpose in using this website as an introduction to a unit plan.
            My canvas focuses on a unit plan on probability for 7^th grade. This unit will teach students what probability is, how to solve for probability of a given event, and probability of compound events. In addition, students will learn how to use visual representations to represent and relate probability to the real world. The first image gallery shows mathematical and visual representations of theoretical and experimental probabilities that students will learn and apply throughout the unit. The second image gallery shows real life applications that probability could be applied for to predict the chances of an event occurring. The videos represent what probability is and how different probabilities are applied to different events. Finally, the students are given the opportunity to explore additional resources that contain probability in the news, further explanations of the content learned, interactive websites to explore, and a further explanation on why probability is important.

URL:  http://www.play.annenberginnovationlab.org/play2.0/challenge.php?idChallenge=2272&mode=view#network6

Geometer’s Sketchpad

Geometer’s Sketchpad is an educational software for students of most grade levels ranging from 3^rd grade to college. This software allows students to visualize math in a new way that engages students and allows students to have a deeper understanding of mathematical concepts. This program not only helps students solve problems, but also allows them to prove why things work such as theorems, by using pre-built construction in the software and dragging around shapes, graphs and more.

Geometer’s Sketchpad allows students to prove geometric definitions. Each shape has properties whether they are regular or irregular. Using this software, students can visualize why certain shapes have these properties. An example would be, to prove the angle sum of any type of triangle is 180 degrees students can create a triangle. With the triangle, created students could measure each of the angles and side lengths using the program and have it displayed. While the angles are displayed, students can also use the program to add up the angles. After the angles are added, the student can drag the corners of the triangles changing the angle measurements and side lengths. While doing so the students can observe that although the angles and side lengths of the triangles change, the triangle angle sum remains at 180 degrees. This will allow students to visually see and understand that the angle sum of any triangle is 180 degrees.

With the use of Geometer’s Sketchpad, students can manipulate models, number lines, geometric patterns, explore ratio, proportion, explore numerical functions, and relationships using graphical representation.  The measure option in this software also allows students to measure any model, shape, side length, perimeter, area, and ratio accurately. With all these tools, students have the ultimate “interactive whiteboard” in their hands where they can explore, interact, and learn. With these tools present, teachers as well as students do not have the hassle of wasting time trying to create these shapes, graphs, models and more on paper. In addition, the measuring tool also saves time and allows both students and teachers to be accurate, because there is always an uncertainty measuring on paper. Overall, Geometer’s Sketchpad provides a quick efficient way for teachers to prove, supplement, or just simply make their lesson more engaging. Similarly for students Geometer’s Sketchpad provides students with the tool to better understand mathematical concepts, proofs, and use manipulatives to support their thinking. 

Technology & Pedagogy

I chose this lesson plan because probability is a difficult topic in math, so I wanted to explore lesson plans that teachers have made that would help students and me in the future.

 For the most part the curriculum goals, teaching strategies, and technologies used were aligned, with a few exceptions. One of the curriculum goals was missing, which is an important factor in learning probability. Students not only need to learn how to find the probability of a given event, but also should be able to visually represent it. The missing curriculum goal covered the visual representation of probability events of one or more event occurring. The strategies were also mostly aligned, except for two, the one that was missing and the last one. A strategy that would be good is working with hands on manipulatives and discussing in groups. The technology was not aligned very well, the teacher provided a couple of opportunities for the use of technology, but did not go through with them and just made it an option for the students.

The technology listed is essential to support the instructional strategies because it proves what the teacher tells the students. The video Probability and odds provides another viewpoint for students understanding, which allows the students to see in more than one way. The students were also provided to access on the computer, which did not really support the lesson, but allowed them to look up any additional information they needed to know. Other technologies that would better support the strategies for the goals would be the smart board/power point for visual representation, calculators, online manipulatives, and Microsoft excel. Each of these technologies would allow students to see what they are trying to find and support their answers.

URL: https://docs.google.com/spreadsheet/ccc?key=0Al-Ug3kw0QuYdHQ3TzdEbDZBZ1ZPYjRJVUloR18wR2c&usp=drive_web#gid=0

Math Can be Fun too

            Students who sit in a lecture listening to a teacher talk have a harder time concentrating and learning. There are so many fun, engaging learning math games for every subject. Sheppard Software is a website that has games for most content areas that goes up until some high school level. These games are interactive activities for students to play to be supplementary to lesson plans. In addition, these games are completely free and students can access it from their homes as well.

There are many fun interactive materials for almost any lesson plan, and this website is one of the many out there. There are also available questions that students could try that will tell the student within a second whether they are right and why. The website also encourages students to beat high scores of previous players that have played that game and has a scoreboard with names of students. These high scores not only serve as a positive reinforcement, but also encourage the students to learn the material even more by making them play more to get a higher spot. When students get a high score, they will most likely have a more positive attitude about the material and want to keep learning.

These games include math skills and math literacy. This website includes games ranging from solving problems to becoming familiar with math vocabulary. Some math skill games include counting, decimals, divisions, fractions, factors, measuring, and much more. Some math literacy games include identifying math operations, naming geometric shapes ranging from polygons, non-polygons, distinguishing the difference between similar and congruent, different types of triangles, different types of quadrilaterals, identifying basic and 3-D shapes. Both math skills and math literacy are equally important, so it is even better that there are games to help students with both.

Overall, not all students learn the same; some need more help than others need. Often times students who struggle find a harder time catching up, but this website holds a range of games from k-10^th grade and there are many other websites like this. Even if a student is falling behind, having a hard time understanding, or even just wants to refresh their memories these games allow students to learn and practice to make sure that they will succeed. These games provide a fun interactivity for student whether or not they need the help, it could also just be for fun.

Boards Can be Smart too

            The smart board has revolutionized how students learn curriculum. From blackboards to whiteboards, education takes a giant leap with smart boards. A smart board is able to do anything a whiteboard can do and more. It allows the material taught to be displayed and interactive through many of its functions. A great tool to use for math teachers while using a smart board would be the SMART Notebook Math Tools software, which combines math tools and interactive practices at a teacher and students’ hands.

            A smart board alone has many features for a teacher. With a smart board, teachers and students could display notes and are not limited to the space because the page can be expanded; the notes could later be saved to be shared or printed for notes. This is beneficial to students who missed the day. There are also many fun education games to play as a class, by touching the smart board. Along with the educational games, there are also interactive worksheets and interactive websites that can supplement to learning about a topic. There is also a click and drag feature, which can be used for moving around measuring tools if learning about angles or different types of measurements.

            Although any of these features could be used for math features, the SMART Notebook Math Tools software focuses mainly on math topics. The software includes a geometry tools where students can create any shapes even personalized shapes, measure from side lengths to arcs, select angles or personalize angles based on the degree. There is even a tool that allows shapes to be divided into equal parts for learning fractions. There is even a function for students to learn and create irregular polygons, curved lines, semi-circles, and even all the different types of triangles there are. There are also features that include displaying functions as graphs and charts. This allows any function to be visually displayed for a better understanding. Another feature is a resizable ruler, so students could have an easier time measuring small or big side lengths with just one ruler. The software also has built in problems that will take students through a systematic procedure to learn how to solve the problem, while interacting with the board. Overall, the smart board has many great features for any classroom. The SMART Notebook Math Tools software however focuses greatly on math and allows students participate in it.

History of Technology in Mathematics

Slateboard: imprinting math and erasing mistakes since the 19^th century.

Calculating Calculators

            Technology has improved tremendously over the years from personal use to educational use. As a future teacher, I do not believe in the traditional ways of teaching a classroom through lectures and memorization. Teaching and learning are supposed to be interactive, hands on, visual, and authentic. Now a days technology could play a great role in supporting lesson plans, to meet the needs of students.

            Over the years, teachers and students have been using calculators in math classes, and no matter the math class one is usually needed. I know that I have needed a calculator for every math class I have taken from a young age to now in college, but what does a calculator really do? There are many types, but here are some of the most popular used today. There are standard calculators, which are to add, subtract, multiply and divide. There are fraction calculators that allow the conversion of decimals to fractions and vice versa. There are scientific calculators, which are used to solve problems in science, engineering in math. Scientific calculators usually include scientific notation, logarithmic functions, exponential functions, constants, conversion of units, variables, calculus notations, equation solving, probability, statistics, complex numbers, and fractions. There are graphing calculators used to graph functions for visual representation of a trend. There are area calculators that make solving for the area of any shape easier. Then there are other calculators that help students prepare for the adult life, such as mortgage calculator, loan calculator, lease calculator, and currency calculator, which are self-explanatory. Then there are calculators for fun like love calculators, which predict the likeness that two people will be together. Each of these calculators plays a role in the student’s understanding of math.

            There are endless possibilities with what can be done with a calculator and teach. A calculator is beneficial for a student to see a problem better, look at a problem from a different approach, or to understand the problem. In math, there are always various representations, such as a function, a graph, a chart, and more. Not every student learns the same, so each representation can help a student more than another. Doing each of these three representations could sometimes be time consuming, even if a student already knows how to do each. However, with a TI-84, a TI-Inspire, or any other advanced calculator, a student can do each of these in a matter of seconds, compare the three different representations, observe what is going on and make a judgment about which is the best to represent the given data. There are even talking calculators for students who are visually impaired.

            It is just as important for a student to know how to apply their math skills on paper, as how to apply them on a calculator. Once a student has a full understanding on the material, it is important to teach them how to do it on the calculator as well for a few reasons. The first reason being certain things in math could be time consuming like graphing, while using a calculator takes a few seconds for results. This reason allows students to get answers for various problems, while comparing and contrasting the solutions for understanding as to why the results are different. An example would be graphing different scenarios and comparing the data trend for each scenario to make predictions and understand why the trends are different. This would be a lot faster on the calculator than by hand. The second reason is that although math skills are great to have, jobs do not require employees to do the work by hand, but to get the work done fast and effectively using technology/equipment to complete projects, like Statisticians. The final reason is calculators allow students to check their work, to see if they did it correctly. It is only natural to have human error and to make silly mistakes, calculators allow student to check their work and find their mistakes, so they will learn not to do it again. Overall, calculators are enlightening and are supplementary for students learning math today. Calculators are also portable, some are pocket sized, most are inexpensive for its functions, and some are even solar powered.

Technology Autobiography

Nowadays it is strange to meet a person who does not depend on technology. Technology is all around us from cellphones to the doors from local supermarkets. It has affected our world for the better and even for the worse. The most important technology that I use is my cellphone, and I find myself never leaving my home without it. My cellphone is my handheld information; from it, I receive news, social, and media updates. With just a few clicks away, any question that puzzles me can be accessed anywhere I am on the go. As a student this resource is beneficial whenever I am doing work. However, there is always a “but” to every good thing. Although cellphones could be very resourceful, not everything on the internet is true and I find myself having the terrible habit like many others of using improper English while using my phone. It is difficult sometimes to distinguish what is true or not on the internet, but it is the most practical technology with access to the internet. Whether it is to Google something or to simply respond to a text words are often shortened, sentences are usually run-ons, and no capitalization is used for faster replies. This downfall, also mentioned in the video may influence many students as it affects me sometimes. Just because this type of English is acceptable on cellphones does not make it acceptable in real life scenarios such as schools or jobs, so I always have to proof read my work to make sure I do not use any of these.

My laptop is the second technology that has influenced me the most; I am even using it right now. Like my cellphone, I use my laptop to look up information.  I use it for research papers, schoolwork that I have difficulties with, and for video tutorials when I want to watch how to do something. However as stated before these things are great, but sometimes it is hard to tell what is true and what is not on the internet. Aside from that being on my laptop can be very distracting. I find myself procrastinating while doing my work because there are so many things to do like social media, games, or even chatting with people.

            The third technology that I use the most is my television. Although I cannot control when and where I access the information for my television, it enables me to learn things, which I did not know or even think of. Whenever I watch television, it allows me to learn about the most recent news events, some, which I knew, and others, which I had no, idea had occurred. The news covers many things all around which I would not even think about looking up. Additionally, there are specific channels that I could learn different types of information, such as news channel, weather channel, sports channel, cooking channels and entertainment channel. Each one of these channels allows me to learn different types of information. Overall, having access to this information has been beneficial and has to be true, if on these channels. Although I have access to these channels I only watch then occasionally and use television mostly for my personal use, to watch my shows, which are not educational.

There are several similarities and differences between the way the students in the video and I use technology. More than one student has mentioned laptop and cellphones, which are my top two technologies. Like two of the students mentioned my phone is always with me at all times where ever I am an it is used mainly as a way of communication through texting. In addition, one of the students mentioned how she dislikes when people abbreviate words when texting, which are not actual English words. Almost everyone I know does this. Like these students, I also use my laptop for social media and looking up things when I need assistance. Although two out of three of the items I mentioned the students also did, they did not mention the television, but rather mentioned some gaming systems. I am not sure whether it is because the students seem to be younger than I am in the video, but video games having been as influential to me as they are to the students in the video. The times I have played video games were just to pass time or to have some fun. Overall, there are not many differences except the one mentioned.