Technology Integration Plan

                Many students struggle to grasp the concepts and applications of rational numbers. Although every school covers these topics in their math curriculum, I find that students are immediately detoured from a math problem that they would be able to solve with integers because the rational numbers are ‘scary.’ This is why I choose to work with a lesson plan teaching students to solve expressions with rational numbers. The lesson should last about 5 days, depending on the comprehension of the students. The teacher may expand the lesson and provide more examples for any given part to ensure student understanding. Unfortunately, the lesson plan is not available online because I received it as a written page from my Inclusion professor last semester. It is imperative that students grasp the concepts of rational numbers because they will not only be found throughout the rest of the students mathematical education, but will also surround them in the real world. Throughout the post, I will be providing explanations for the technologies and strategies listed in my Technology Integration Plan Matrix.

          The lesson begins with the teacher giving a brief lecture and presentation providing students with the instruction and rules on applying operations to expressions with rational coefficients. During the lecture, the teacher will use the whiteboard to show students how to compute the calculations by hand. The students will follow along at their seats and provide their calculations’ in comparison with the teacher’s. Afterwards, they will break into small groups and discuss how they would solve a given set of problems and work through their calculations. The calculator will be provided at the end of the group work for students to evaluate their own calculations. This will provide them the opportunity to visually see that the numbers that they computed by hand are equal to their decimal equivalents.

          During the next topic, students will practice reorganizing problems to figure out what operation will be needed to solve. The teacher will post a different problem on the projector. The students will analyze the problems as a group and decide how they will rewrite the problem. They will write their response on the hand-held white board. The class will all hold up their answers and then have a group discussion answering why they chose to answer the problem this way and how it makes the solution more clear. The teacher may also shed light on how they could come to these decisions and why it will help them.

          The next part of the lesson, students will work together to solve multi-step problems involving rational numbers. Students will be completing a comprehensive worksheet that will allow them to organize rational numbers that are equivalent in different forms, and use them to solve problems. This worksheet will be collected by the teacher to provide a formative assessment of the student’s learning progress. Students will have calculators to help them see the equality of the different forms of the calculations and how they are equal. It will also provide a great opportunity for students to check their work.

          During the following activity, students will analyze real world problems and decide how they will create the equations used to solve them. They will decide how to solve the problems and will work together to discover the best answer. Students will use the graphing software to create graphs of these equations and show their solutions visually. They will then share their answers with the class and discuss what decisions they made and what problems arose while deciding how to answer this question. The teacher will chime in to provide guidance to ensure students find correct solutions.

          The final assessment to this lesson will be a homework assignment that will involve students answering a real world problem. They will work individually to solve a real world problem. While solving this problem, they will utilize all of the skills learned above to create a solution. They will then create a graph of the inequality using a computer graphing software. They will infuse this graph into a word document. In this word document, students will defend their answers and verbally explain how their answer is correct and what it means in relationship to the question asked. This assignment will serve as an assessment of learning for the lesson.

          Although the majority of the technologies in this lesson are not on the cutting edge of the technological advancements, they all provide an enriching purpose in the sake of the lesson. Students will be able to use these technologies in order to accurately visualize and conceptualize the topic at hand.

https://docs.google.com/spreadsheet/ccc?key=0AimhgsPBiWI6dFZfSFVyRmRubFB0RGgtZkI5X1BLOWc&usp=sharing

STEM Classes

     Some schools have created elective classes labeled STEM, which stands for Science Technology Engineering and Mathematics. In these classes, students work in an interactive classroom combining what they know about all of these subjects to create projects to be used in real life scenarios. 

     In one of my days substituting, I had the privilege of observing this class in action. They were working on a disaster relief project that would have real world uses. The class was set up with a few tables throughout the room with chairs all around. There were about 5 desktop computers as well as a cart of 10 laptop computers. The students were broken into groups of 4-5 and were all thoroughly engaged in their projects. 

     One group was working on an alarm to alert homeowners when their basement was starting to flood. This alarm was an alarm clock that had a water sensor attatched. Although the students have not had a formal class on building alarms, they were able to use videos and information tutorials online to create their device. 

     As technology contiues to grow, I hope to see more classrooms like this one. This class taught students to think outside the box and to access the plethora of information availible to them online to learn and create meaningful projects.

Smartboards in Mathematics

     All of the schools that I have substitute taught in have taken the money in their budget to put Smartboards or Smartboard knock offs in every classroom. Its wonderful that they have taken the initiative to try to integrate technology into their classrooms, but was this the best way? Although I can not speak for other subjects, I can say that I dont believe so for the Mathematic classrooms. 

     

     For math classes, the Smartboard does not have much more purpose than an overhead projector and a white board. There are not many purposes for math that a touch screen white board in math class. Teachers usually just use them as a white board and write on the notepad, they will show the rare math movie, or they will show pictures of graphs students may see. I do not believe that these are the best option to integrate technology into math class. 

     Students would benefit from using different technologies in their class than a Smartboard. A trip to the technology lab could give students a much better experience. There are many websites that show great graphs that are easily manipulated for students to experiment with. They would benefit significantly more by allowing them to explore graphs and computations on a computer than they benefit from having a Smartboard in the classroom. 

The Khan Academy

     Online websites are enabling students to find deeper understanding of math topics at home. Students are able to relearn lessons taught in class that they have questions on or catch up on concepts that they have been absent for at the Khan Academy website, http://www.khanacademy.org. This website, although credible, will in no way be able to replace the value of a teacher, but is a supportive tool to aide students in understanding the topics at hand.

     There is no replacement for a teacher. Every student needs the individualized care and instruction that can only come from a teacher. The student needs the interaction with and support from their mentor in order to learn the best that they can. Therefore the Khan Academy website should not be used to teach concepts, but should be used instead as a tool for students to used when they need more help understanding a topic.

     The Khan Academy website has lessons on almost all topics covered in high school and middle school math and science classes. These lessons have clear and concise explanations for how to complete the problem given and sometimes have explanations for what the problems are used for. This kind of assistance is great for when students are at home doing homework and need extra help. 

     Overall, the Khan Academy is a great resource availible for math students. It should not be used as the main method to teach students math, but instead as a tool to re-teach materials to students who need a different approach or explaination for a math lesson.

Calculators in Math Class

Calculators have become an integral part in the teaching of mathematics. In many classrooms that I have substitute taught in, the students need to use a calculator to complete addition and subtraction computations. From this the question arises, do these students understand the fundamental concepts behind the calculations that the calculators are performing for them or have they just formed a dependency on this tool? With the growing accessibility to calculators in today’s society, it is imperative that students not only learn how to complete the operations with the calculator, but also to understand the operations behind the calculator.

            With technology today, it is almost impossible to find yourself without access to a calculator. We have them installed on our phones, computers and tablets, and we can always find more complex versions on the internet. Therefore, we are transitioning to a time when memorizing multiplication tables are no longer necessary. With consistent access to calculators, how will we now teach addition, subtraction, multiplication, and addition? How will we be able to assess that students understand these concepts? To what degree is it acceptable for a student to depend on calculators for their computations? These questions, among many more, must be well thought out in educating students.

Unit Plan Canvas

On the PLAYground website, I have set up a canvas for the unit plan of graphing polynomials. This process was unique perspective of the beginning stages of planning a unit plan. It enabled me to think critically about what topics would be covered, as well as how they would be presented to the students. Becoming familiar with the website was the first obstacle I encountered. Although I, as many of my peers are as well, am very familiar with designing profiles on social networking sites, such as MySpace, Twitter, and Facebook, this network utilizes different applications to create a page. After a short period of playing around with the website, it became easy to edit and customize the canvas to my lesson plan.

My unit of graphing polynomials is based in exploratory lessons, such as the lesson, All in the Family, mentioned in my previous post. The video linked to the page, serves as an introductory attention grabber. I hope that it will help students to think out of the box about what the graphs of functions are and to think about how the functions we will be learning now are actually the foundations of functions they will learn to graph as their math education expands. The links I have provided will provide students with links to known interactive websites where they are welcome to further explore the topic or search for a clearer understanding of the topic. The pictures that I have included are not the best pictures for the unit; however, I have not found the perfect fit of pictures to capture the students’ interest in the topic. 

PLAYground Canvas

Technology & Pedagogy

The lesson plan, "All in the Family," is a great lesson that combines prior knowledge of geometric terms and definitions to represent algebraic functions. Through using an online website as a companion to the lesson, the students are enabled to discover the relationships of a square and explore the uses of algebraic equations when they represent something that they can physically see.

The curriculum focused on identifying different kinds of functions and comparing how the relationships of these functions are different between the different families of functions. The strategies used are a self discovery group work project, and a teacher centered Q & A. I believe that the lesson also teaches students about the coordinates that make up the function. It allows them to understand how the numbers fall into the x and y axes and what those numbers represent.

This lesson requires that students use a computer to access the website that this lesson uses. This lesson is easily adaptable depending on class size and the amount of computers available. I believe that students should also be given a graphing calculator. Using this tool, they will be able to manipulate the graphs that they are deriving from the points and further understand the lesson. These technologies are both crucial to achieving the curriculum goals of this lesson. Without the computer or graphing calculator, the students would be unable to truly “discover” these equations and relationships the same way. The students would have to work with graphs printed on paper or graph the points of each relationship on a graph and discover what it would look like. Neither of these options give the same effect as the lesson involving technology. 

"All in the Family" lesson plan ananysis