jEnnifers Blog

“2009, It Was a Very Summative Year”

millejl — Thu, 17 Dec 2009 17:44:41 +0000

Find sums of consecutive integers that add up to 2009.

Can you find two consecutive integers with a sum of 2009?
Can you find three consecutive integers with a sum of 2009?
What other numbers of consecutive integers are possible?
How can you be sure you got them all?

What technology tools might be helpful? Keep track of the ways in which you use technology to explore this problem.

There are a variety of technology tools that could be helpful in finding a solution to these questions. The two tools that I found most helpful were Excel and the graphing calculator. I mainly just used the graphing calculator as a guess and check when working our this problem. Excel was the most useful resource I used with this problem because it allowed me to see a large amount of these numbers at once and I was able to make observations faster and more efficiently. Using Excel in column A I just listed all the numbers 1,2,3,4….2009. My column B consisted of 2009/column A. I was then able to observe that column A was equal to the number of consecutive integers that added up to equal 2009. I also observed that column B was equal to the number that is in the middle of these numbers. For example 2009/2=1004.5. This is because 1004+1005=2009, and 1004.5 is in the middle of these numbers. I also realized that column B gave me some numbers with many decimals but that I could use column B to help me decide what consecutive sums would be integers to help me work out this problem.

Presentation Questions Day 1

millejl — Thu, 17 Dec 2009 17:29:41 +0000

Paige: I noticed that you had a lot of information about the benefits of using a Smartboard. I found it very informative and I enjoyed reading about the different capabilities of the Smartboard. I was just wondering if you knew how much training a teacher would need on the Smartboard before actually using it in class. I was also wondering if a school did not have a Smartboard if you knew of how a teacher could make up the time and efficiency that the Smartboard would offer.

Kate: I really liked your activity “Walk the Plank”. It seems like it would be good interactive activity that students could really have fun playing with. I was wondering how and when you would plan on incorporating this activity into your lesson plan.

Presentation Questions Day 2

millejl — Thu, 17 Dec 2009 17:07:18 +0000

Claire: I think that Excel is a great and useful tool to incorporate into the mathematics classroom. I really wanted to use it in my presentation on linear functions. I was unable to find any interesting and educational activities involving Excel. I was wondering how you were able to find your activity and how effective do you think it would be.

Brittany: I always have trouble using GSP to perform translations, reflections, rotations, etc. I always seem to only reflect a piece of the object or I will have trouble rotating it a specific way. I was wondering if you could give me some tips to help me with transformations using GSP. I was also wondering how much time if any that you think that students would need to help them become more familiar with using GSP to perform transformations.

Workshop Experience

millejl — Thu, 17 Dec 2009 16:11:38 +0000

The workshop that I choose to explore was “Insights into Algebra 1: Teaching for Learning”. This workshop is for students in grades 6-12. I then decided to pick workshop 2 “Linear Equations and Inequalities”. I really enjoyed watching these videos and how the teachers were able to use real-life examples to help the students understand linear equations and inequalities. I think this was very encouraging for me to try and come up with real-life activities for my students to work through one day. In the first part of the workshop the teacher used a phone bill to help the students learn about linear equations. I really liked that he actually brought a real phone bill. Instead of just telling each student what to do he allowed them to analyze the data first and then come up with ideas about how they could best represent the data. The students were able to decide what calls they should and should not use in their data. The teacher even allowed the students to set the window and decided what the max and min should be. Throughout the whole lesson the teacher was encouraging and supportive. He continually proposed great questions to the class that promoted exploration and promoted conceptual understanding. One thing that I really liked that this teacher did was that he would ask a student a question about a problem, and then he would say alright take 30 seconds and come back to me with your answer. I really liked this because the students knew the time frame that they had and they knew that they had to get working on this problem right now because they only have 30 seconds to complete it. I think this is a great method of keeping students actively engaged in the lesson.

In the second part of the workshop the female teacher was able to create an activity that was not only related to a real-life situation but an activity that was related to the students themselves. The activity was about getting new football jerseys for their school by selling hotdogs. I really liked how before the students ever started working on the problem they were able to come up with questions of their own to see if this would even produce a profit for the team. The students came up with some really good questions and they then got to write the questions on the overhead. She made sure that she kept the students actively involved in the lesson. I thought it was also very influential to the students relational and conceptual understanding that the teacher showed them that they could find the solution algebraically, using the table, and using the graph. She also explained how even though it may seem for this specific problem that the algebraic method was most efficient, that there are other problems and situations where using the table of the graph would be the most efficient method. The teacher also allowed the students to make posters modeling what they have learned and the problem they were working with. The students were able to make a connection between equations and inequalities without the teacher actually telling them to do so. My experiences throughout this workshop were insightful and encouraging for what kinds of lessons I may be able to teach one day.

Modeling

millejl — Thu, 17 Dec 2009 15:49:44 +0000

What should you take into account when modeling real-life data?

There are many things that you should consider when modeling real-life data. You must be selective when choosing real-life data and make sure that it is accurate and from a reliable source. You need to have a good understanding of what the data is so that you are able to choose the best way to model that data. You should also use many different way of modeling the data so that you can choose the best model that is appropriate for that specific data.

What are some of the issues that arose as groups presented their work in class? (Don’t mention specific names of presenters)

I know that we had an issue with our data. Our issue when presenting the data was not so much the data itself but it was our fault because we did not analyze and understand the data previously to modeling it. There were some abbreviations that we misunderstood and this caused us to have incorrect data. We also had trouble finding a relationship with our data because we did not correctly interpret our data in the first place.

How have you resolved any issues that you had in modeling your data?

I think that after we realized the mistake we had made involving misunderstanding the abbreviations we were able to have a better understanding of our data. We realized that our data represented a quadratic recursion. However, we were still unable to model our data as nicely as some of the other groups. I think we may have been more successful if we would have used additional methods of modeling our data.

Final Presentation: Linear Functions

millejl — Sat, 12 Dec 2009 05:19:13 +0000

This is a link to my powerpoint.

FINAL PROJECT PRESENTATION

Interesting Article

millejl — Wed, 11 Nov 2009 13:18:09 +0000

If I understand it correctly they are saying that teachers are not even allowed to send e-mails to their students from their cell phone. That seems a little bit ridiculous to me. I understand that they want to make sure that the teachers and students keep a professional relationship but there has to be some way for them to communicate. I also think that there are some students especially in middle and high school who look up to their teacher and need guidance. These students may not be able to seek the advise of their teachers due to the lack of communication. There may be issues students are having that they want to discuss with their teachers, but not in front of the whole class.

GSP PRO

millejl — Wed, 11 Nov 2009 12:43:11 +0000

Throughout this page of my blog I will be exploring the properties of a triangle with fixed perimeter. I will be using the software Geometer’s SketchPad to aid me in my construction as well as exploration of a triangle with a fixed perimeter of 16 cm. (For the duration of my investigation I will be referring to Geometer’s SketchPad as GSP.) I was given a hint to help me to construct this triangle. My hint was to subdivide a segment into three parts and use them as the sides of my triangle. I will then use GSP to measure the side lengths to find out what different side lengths are possible for this triangle. I will then use my findings to see if I can find an explanation for the possible side lengths of my triangle. Another area I will be exploring is the area of the triangle. I will use my construction to determine the largest and smallest ares of this triangle. I will then choose an extension to further my explorations of this investigation.

I started my investigation with the hint that I was given. So I knew that I needed to create a segment whose length was equal to the perimeter of the triangle. I first tried to just create a segment using the segment tool. I highlighted the segment and under the measure tab I clicked length. A box popped up that told me the length of the segment that I had just created. I tried to drag one endpoint of the segment till the length was 16 cm. I quickly realized that it was very difficult for me to get the length to be exactly 16 cm so I had to construct a segment of length 16 cm. I am sure that there are many other ways to do this but the way that worked best for me was to plot two points that are 16 cm away from each other and then construct a segment using these two points.

I started this by going to the graph tab and scrolling down to “Plot points…”. A box popped up asking me to enter in the values for x and y, I choose the point (0,0) and hit plot. For my next point I choose the point (16,0) and hit done. I used my segment tool to connect the two points I had just constructed and right clicked on the grid and scrolled down to hide grid. I also right clicked on both of my axis and scrolled down to hide axis. I repeated the same steps to hide my origin point and unit point. I then highlighted my new segment and under the measure tab I clicked on length to measure the length of the segment and a box popped up that showed me the length was in fact 16cm.

Next I wanted to label my points, so I right clicked on the point that was furthest to the left and choose label point. I entered in A as the label for the point. I repeated the same steps for my next three points B,C, and D. So that my points were labeled A,B,C,D from left to right. Next I wanted to measure the lengths between my points but I realized to do so I must construct segments between these points first. To do this I clicked on point A and B then under the construct tab I clicked on segment. I then repeated the same steps for points B and C as well as C and D. So that I have now divided my line into three segments. To measure the lengths of my three new segments I just clicked on the line between the two points A and B and under the measure tab I scrolled down to length. I did the same to measure my other two segments

Next I wanted to create a visual that showed that the sum of the three segments is equal to the segment AD. You can do this by going to the measure tab and scrolling down to calculate. Then on the screen click the text box that shows the length of the segment AB. Then in the calculation box hit the plus sign and continue this step so that you add all three of your segments together. Your final calculation should look like mAB+mBC+mCD, then click on the “ok” button. A box will appear on your worksheet showing the sum of the three segments is 16cm.

If you right-click on the point B and drag it right or left you will notice that the lengths of AB and BC are changing but the length of AD stays the same. And when you drag point C the lengths of BC and CD change but the length of AD stays the same.

The next thing I wanted to do was give a visual of these values so I click on the text boxes labeled mAB, m BC, mCD and the box labeled mAB+mBC+mCD=16cm. With all of these boxes highlighted I went to the graph tab and scrolled down to tabulate. A box appeared with all of these measurements labeled. If you grab point B or C and drag it you can see the measures of the segments change but the length of AD remains the same. if you double-click in the box the values at that time will recorded and there will be a new box that will appear below that shows the values as you continue to move points B and C. Below is a picture so you can see what the tabulate box looks like.

Now that we have constructed our segment 16cm in length and subdivided it into three segments, we need to form a triangle whose side lengths are equal to these three segments, and who perimeter is equal to 16cm, the length of segment AD. We will do this by creating circles whose radius is equal to the lengths of the segments.

Click on segment CD and the point C and then under the construct tab scroll down to “center + radius”. There will not be a circle whose center lies on point C and whose radius is equal to the length of segment CD. Do the same with segment AB and the point B. The center of this circle will be located on point B and it will have a radius equal to the length of segment AB. Using your point tool, place a point on the intersection of the two circle(you can place this point at either of the two intersections of these circles by for the purpose of this investigation place the point on the intersection above the circle) label that point E. Using your segment to create a segment connecting point B and E and another segment connecting points C and E. I then measured the lengths of my two new segments. Below is a picture of this construction.

As you can see from the picture above the lengths of segment BE and AB are equal and the lengths of segments CE and CD are equal.

Now that I have constructed a triangle with fixed perimeter I want to see what happens to the area of the triangle as the side lengths change. To find the area I first have to find the height of the triangle. I do this by clicking on points C, then, E, then B (in this order, the order you click the points is important). Then under the construct tab scroll down to angle bisector. The angle bisector will appear and then construct a segment from point E to the point where the angle bisector intersects the base BC. Now you can measure the length of this segment and use it as your height. In the picture below you can see the area that I computed using the calculate option. There is also another box that I created using tabulate, but this time I added in the area of the triangle too. You can also notice in the picture below that the triangle is isosceles.

Below is another picture of my GSP worksheet. In the picture below I started moving around points B and C to see what its possible side lengths where and how the area changed as the side lengths change. I wanted to see what were the smallest and largest areas of this triangle. I also right clicked on my triangle to hide them so that I could get a better visual of the rectangle.

Knowledge gain from investigation:

This investigation was very educational for me. Throughout this investigation I have really had a chance to explore everything that GSP has to offer. I have used GSP before and had some basic understanding of constructing shapes, measuring lengths, calculate, tabulate, etc. But not until I did this project that I understood how educational of a resource GSP is. I was able to have all of the information about my triangle listed neatly and accurately so that I could draw conclusions from it. I was able to see how the perimeter stayed the same even though the area changed. I was able to see the different possible side lengths of this particular triangle. What I have concluded from this investigation is that the largest possible area is 12.32cm^2. I noticed that the area was the largest when the triangle was isosceles. The smallest area I was able to calculate was 0.57cm^2. There are a large amount of possible side lengths. But the sum of the three side lengths must be equal to 16.

Implications:

GSP is an excellent resources that allows students to now just draw but actually construct geometric shapes. It is a very fun and interactive educational software. Instead of just routinely learning the properties of geometric shapes they are able to construct these shapes, analyze them, and draw conclusions themselves. This amazing technological resource allows students to learn from who knows them best, themselves. With students engaged in this interactive software the teacher is able to walk around and have one-on-one time with students who may be struggling. The Principles and Standards for School Mathematics implies that, “The use of dynamic software enables students to examine many cases, thus extending their ability to formulate and explore conjectures.” (NCTM 309)

Student Benefits:

With the use of GSP to complete this investigation students would have a better visual representation of the problem. They would also be able to see many different measures (angle, side lengths, perimeter, area, etc..) simultaneously so that they are able to easily and efficiently find information. The easy access to this information will help students to accurately draw conclusions of this problem. Students will also gain a better understanding of the relationship between the side lengths of a triangle and its angles. Students will literally be able to see that even thought the perimeter stays the same the area changes as the side lengths change

Objectives:

According to the Principles and Standards for School Mathematics students at the indicated levels should be capable of doing the following:

High School Level:

analyze properties and determine attributes of two- and three-dimensional objects (NCTM 308)
draw and construct representations of two- and three- dimensional geometric objects using a variety of tools(NCTM 308)

Middle School Level:

understand, select, and use units of appropriate size and type to measures angles, perimeter, area, surface area, and volume (NCTM240)
selects and apply techniques and tools to accurately find length, area, volume, and angle maeasures to appropriate levels of precision (NCTM 240)

Sources:

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Assignment #3: Identification of Technology Activities

millejl — Mon, 09 Nov 2009 13:12:12 +0000

Assignment #3: Identification of technology activities

Lesson plans for 12th grade Algebra II class.

Background information: Since the beginning of our observations the class has been exploring the different properties of quadratic equations. They have been using graphing calculators and algebraic methods to find the vertex, max, min, axis of symmetry, and zeros to help them visualize and create a solid understanding of the graph of a quadratic equation. The class has also covered linear inequalities prior to our observations.

Description of unit: The unit we will be teaching is on quadratic inequalities. We will be giving the class their first introduction to quadratic inequalities. This unit focuses on understanding the graph of a quadratic inequality and how it differs from the graph of a quadratic equation. This unit also focuses on solving these inequalities and understanding why the solution set of the inequalities differs from the quadratic equations that have recently been learning about. Students will use the graphing calculator, pen and paper, and algebraic methods in their exploration of quadratic inequalities.

Activity 1: Graphing Calculator Investigation: Quadratic Inequalities and the Test Menu

-Solving quadratic inequalities using graphing calculator
-Use the intersection option to help find solution
-Graph each side of inequality
- Expressing the solution of an equation, inequality, or applied problem as a graph on a number line, or by using set or interval notation (ALCOS 7a)
-Solve equations and inequalities (TEAM-Math A1, e)

Description

In this activity the students will be using their calculators to help them to solve quadratic inequalities. In both of the examples the quadratic inequality is given to them and it is their objective to graph it and find its solution. This activity gives the students two separate methods to solve quadratic inequalities using their calculator. In the first method the students use the trace option of their calculator to find the solution. And in the second they use their calculator to graph both sides of the inequality. Then they use the intersection option to find their solution. At the end of the activity the students are given addition examples to practice solving quadratic inequalities.

This is a link to the activiety. http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=4110

Use

This activity will be used as an investigation for the students. It allows the students to explore quadratic inequalities as well as explore the capabilities of their calculator. This activity introduces the students to quadratic inequalities with only one variable. It also offers different ways to look at and solve quadratic inequalities. The extensive use of the graphing calculator in this activity allows the students to learn about quadratic inequalities in a hand on approach.

Source: Texas Instruments Incorporated. (2009). Retrieved from. http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=4110

Activity 2: Quadratic Inequalities

-Solving quadratic inequalities by exploring their tables and graphs
-Using the graphing calculator to solve quadratic inequalities
-Using algebra to solve quadratic inequalities
- Identify the characteristics of quadratic functions from their roots, graphs, or equations. (ALCOS)
-Graphing a function when given its equation (ALCOS 5b)
- Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains (ALCOS 3a, TEAM-Math A1c)

Description

This activity is an investigation like the last but it promotes a higher level of exploration and a more in-depth look at quadratic inequalities. In this activity the students are given quadratic inequalities and they are to use their calculator to find the solution. The students get to use their table to explore the various values of x. They also get a chance to change the table setup to explore how this will affect the information they are given in their table about their inequality. In this activity the students get to explore, graph and compare quadratic inequalities.

This is the link to this activity. http://education.ti.com/educationportal/activityexchange/Activity.do?aId=6413&cid=US

Use

This activity highly promotes exploration by asking a multitude of questions throughout the investigation. Students get the opportunity to use a wide range of options their calculator has to offer. The students get to see how they can use the table setup option to increase the amount of values in their table. They also get to see how they can use the window option to provide a better visual of their graph. In this activity the students also get to use algebra to find the solutions for the quadratic inequality. This would be a great activity to use for teaching a lesson to a diverse group of learners because it offers different ways of viewing and solving quadratic inequalities.

Source: Texas Instruments Incorporated. (2009). Retrieved from http://education.ti.com/educationportal/activityexchange/Activity.do?aId=6413&cid=US

Activity 3: Solving Quadratic Inequalities

-Solving quadratic inequalities using intersection
-Using the table to see when the inequality is true
- Expressing the solution of an equation, inequality, or applied problem as a graph on a number line, or by using set or interval notation (ALCOS 7a)
- Identify the characteristics of quadratic functions from their roots, graphs, or equations (ALCOS 5)

Description

In this activity you are given the equation of the quadratic inequality and you are asked to use your graphing calculator to find the solution. This activity asks that you graph the inequality by entering in one side of the inequality in Y1, set Y2 equal to zero then set Y3 equal to Y1>Y3. The graph will give you an idea of the solution but the activity notes that you should use intersection to find the exact solution. This activity also shows the students that they can look at the table to determine where the inequality is true and where it is false.

This is the link to this activity. http://mathbits.com/MathBits/TISection/Algebra2/quadraticinequalities.htm

Use

This activity would be great to use in small groups or even pairs. The students could go through the investigation together and discuss their issues or solutions. This activity also refers back to linear inequalities which I feel will help the students realize that they have worked with inequalities before so they may feel more comfortable when working through this investigation. Students will learn about the different aspects of their calculators that they can use to solve quadratic inequalities.

Source: MathBits.com. (2000-2009). “Solving Quadratic Inequalities”. Retrieved from http://mathbits.com/MathBits/TISection/Algebra2/quadraticinequalities.htm

Activity 4: Inequalities, They Are Not Just Linear Anymore

-Graphing equations with and without a graphing calculator
-Comparing quadratic equations to quadratic inequalities
-Graphing quadratic systems of inequalities
-Giving examples of real life situations associated with quadratic equations
- Solve systems of linear equations or inequalities in two or three variables using algebraic techniques, including those involving matrices. (ALCOS
- Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains (ALCOS 3a)
- Identifying real-world situations corresponding to families of functions (ALCOS 3b)
- Identify the characteristics of quadratic functions from their roots, graphs, or equations. (ALCOS 5)
-Generating an equation when given its roots or graph (ALCOS 5a)
-Graphing a function when given its equation (ALCOS 5b)

Description

This activity is by far my favorite activity that we were able to find. At the very beginning of this activity, in the introduction, it gives you a list of real life objects that are related to quadratic equations. Then before you ever start working with quadratic inequalities you are asked to graph the quadratic equation y=x^2. This activity asks you to plug in coordinates that we know are on the parabola of y=x^2 into the inequality y>x^2. This is to help students realize the difference between the solution sets of the two. As you can see from the link below that this is a very long activity. Due to the length of this activity we have decided to only hand out the first three pages, problems 1-9, to the students. If time permits we were going to hand out the 7th page of the activity labeled “Student Worksheet” problems 1-4. If there is not enough time then the students would do this final worksheet for homework practice.

This is the link to the activity. http://education.ti.com/educationportal/activityexchange/Activity.do?aId=4286&cid=US

Use

This is a very useful activity for teaching quadratic inequalities. It allows students to relate quadratic inequalities to real life situations. This is a great activity to use in a small group class setting. It asks many detailed questions and does not lead the student to any certain conclusion but insists that they explore their knowledge of quadratic equations to make their own assumptions about quadratic inequalities. This activity ensures that the students will have a good understanding of the solution set and how the inequality symbols work before actually being expected to graph it. Students can use this activity to help them solve these inequalities both algebraically and then by the use of their graphing calculator.

Source: Texas Instruments Incorporated. (2009). Retrieved from http://education.ti.com/educationportal/activityexchange/Activity.do?aId=4286&cid=US

Survey of Technology Resources

millejl — Wed, 04 Nov 2009 16:09:53 +0000

The extensive availability of technological resources in this classroom as well as the school was quite surprising for me. There is a wide variety of technological tools that are accessible for both teachers and students. The teachers are also equipped with up-to-date software to aid them in their teachings such as TI-Smart View, Fathom, and Geometer’s Sketchpad. Some of the most prominent tools I have seen here are calculators, computer labs, and the Smart Board. I have observed how accessible these tools are to teachers and how extensively the teachers use these tools.

Graphing calculators are a very present tool in this school, especially in the Algebra II class I have been observing. Each student is loaned their own personal TI-84 graphing calculator for the year. In the classroom there are two desktop computers and a laptop. One of the computers is at the teacher’s desk and the other desktop is mainly used by the special education teacher. The other computer is a laptop which the teacher uses to control the Smart Board. It is a very intriguing laptop because the teacher is able to actually rotate the screen around, flip it over (so that the laptop is closed) and then write on the screen which is miraculously projected onto the Smart Board. The school also has many computer labs; two are right across the hall from the teacher’s room. These computer labs have software such as GSP and Fathom.

Since each Algebra II student has their own TI-84 graphing calculator the graphing calculator is an extremely accessible resource for teachers, and it is extensively used on a daily basis. The extent to which this resource is used can be seen through the student’s knowledge and understanding of this tool. The students in this class are much more advanced in their use of the graphing calculator than I was at the beginning of the semester, or maybe even more than I am now. Instead of just teaching a lesson step-by-step the teacher is able to allow his or her students to investigate the problem using their graphing calculators. The students know how to enter a function in, graph it, view the table, zoom, use trace, and find the zeros, just to name a few. The discussion and exploration associated with the use of this technology enhances the students desire to really be engaged in the lesson. The accessibility of this resource as an educational tool for mathematics teachers is furthered by a combination of the Smart Board and software.

The smart board is the most versatile and visually pleasing technological tool that I have encountered. Since there is a Smart Board in the teacher’s room it is very accessible. This technological tool is also used on a daily basis. My teacher uses the smart board to go over the homework, review the notes, or perform both of these tasks simultaneously. The Smart Board is capable of projecting internet documents, software such as GSP and Fathom, and pages from the textbook, just to name a few. The Smart Board at its best is when you combined it with software for mathematics.

The teacher has software called the TI-Smart View (84). With this software the teacher can project a huge calculator on the screen of the Smart Board. This software allows you to actually press the buttons of the calculator on the screen just as the students will be pressing the buttons on their calculator. There is also a screen to the right of the calculator that keeps a record of every button the teacher has pressed so if a student gets behind they can refer back to the screen to see what they have missed. There is also an option to minimize this record and pull up another document, possibly notes, so the students can visualize the problem and the calculator simultaneously. If the teacher was graphing a function she could pull up another software call Windows Journal which would provide graphing paper. So on the left of the Smart Board would be a huge graphing calculator and to the right of it would be graphing paper so that you can graph a function on the calculator and on paper at the same time. The use of technology is not limited to just this one classroom but it can be seen throughout the school which has many computer labs.

There are two computer labs that are directly across the hall from my teacher’s room. These two computer labs are technically the math computer labs but anyone can use them. But it is not an issue if these two computer labs are occupied because every computer lab in the school comes equipped with software such as GSP and Fathom. Even though a teacher’s use of the computer labs has to be scheduled the labs remain a fairly accessible resource for teaching. I have observed the use of the wide use of computer labs while using GSP to teach the student’s to construct a parallelogram, rectangle, and rhombus. Even though I have not seen the teacher utilize the Fathom software I am aware that the statistics teacher extensively utilizes this resource. The computer lab is not used on a regular basis for teaching Algebra II but it is often used for teaching Geometry. My teacher uses the computer lab at least one time a week but often two or three times a week. The computer labs are a great resource that provides student with hands-on lessons and an interactive environment.

There is such a wide variety of technological tools and software that mathematics teachers can incorporate into their teachings. Technology allows the teachers to better relate the concepts to the students. Mathematics teachers can use technology to give their students multiple different ways of viewing a lesson. Students are introduced to a wide range of technology which will help them to be more prepared for the technological society that we are living in. Technology also saves a lot of valuable class time which gives teachers the ability to enhance their students’ educational opportunities.