In addition to learning to use the technology, pedagogical issues associated with the instructional tools are emphasized.\u00a0 Specifically, the course focuses attention on how and when to use technology appropriately in mathematics classrooms.\u00a0 Misuses of technology are discussed and discouraged, such as using calculators as a way to avoid learning multiplication skills and using computers to practice procedural drills rather than to address conceptual understanding.\u00a0 Rather, preservice teachers discuss the uses and benefits of commercial software and handheld devices to explore different content topics that have become possible with technology and consider pedagogical issues.\u00a0 Some time is also spent previewing national curriculum projects that have a high involvement with technology (e.g., Key Curriculum Press, 2002).\u00a0 As a result, preservice teachers address and discuss issues of teaching prior to their clinical experience, which helps these students focus attention on these matters when participating in their practicum.<\/p>\n
Teacher candidates in the technology methods course apply their knowledge of technology and its uses in the teaching and learning of mathematics.\u00a0 These future mathematics teachers create several lesson plans using technology as an instructional tool.\u00a0 Lesson plans center around concepts and skills found in pre-algebra, algebra, geometry, precalculus and calculus that are enhanced using technology.\u00a0 Once a topic is selected for the lesson plan, preservice teachers determine an appropriate piece of technology that facilitates instruction.\u00a0 They develop and write instructional lessons using graphing calculators, an interactive mathematics computer environment, an interactive geometry application, computer spreadsheets, and the Internet.\u00a0 However, based on a selection of specific mathematics topics, each teacher candidate creates lessons using additional forms of technology examined in the course, including dynamic statistical software and a CAS.\u00a0 As a result, each teacher candidate has a unique experience of using technology to enhance mathematics instruction at the secondary school level.<\/p>\n
Depending on time constraints, preservice teachers teach at least one of their lessons with their peers as students.\u00a0 Our course ensures that these future mathematics teachers are able to write and deliver lesson plans that incorporate appropriate technology for mathematics courses at the level for which they are seeking licensure.<\/p>\n
It is important that teachers are able to develop well-conceived lesson plans that are structured and detailed, focusing on specific mathematics topics and using multiple representations, such as the examples in the appendices<\/a>.\u00a0 Open-ended exploration and inquiry-driven mathematics lessons using such software as interactive, dynamic geometry or algebra software are also developed after the teacher candidates are able to develop a detailed lesson that explores the topic with some depth.\u00a0 For students to experience a mathematics topic in depth, specific \u201cguided\u201d discovery lesson planning is required.\u00a0 Part of the objective is to counter a pervasive disposition of the mathematics curriculum in this country as being a mile wide and an inch deep.<\/p>\n Since the creation of the technology methods course, we believe that our program adequately addresses the needs of many preservice teachers to be competent at integrating these instructional tools for teaching and learning mathematics.\u00a0 The growth of future teachers\u2019 ability to use technology appropriately in the mathematics classroom during the course becomes evident in observations.\u00a0 The following illustrations provide detailed descriptions of the process in which preservice teachers engage as they learn, analyze, and apply a particular piece of technology in the course.<\/p>\n Interactive Computer Environment<\/p>\n One important feature of the course is to introduce future teachers to the world of possibilities open to instruction when computers are used effectively.\u00a0 The vast majority of our preservice teachers have had some experience using computers within and outside their high school mathematics courses, but few have had the opportunity to learn mathematics in an interactive computer environment.\u00a0 Providing this experience for our teacher candidates has created a template on which they can draw as future teachers.<\/p>\n For one activity, the preservice teachers use an interactive mathematics computer environment <\/i>as an electronic textbook.\u00a0 Embedded in the text is the derivation, using calculus, of the velocity of an object under the influence of earth\u2019s gravity as a function of time (i.e., v(t)<\/i> = gt<\/i> + v0<\/i>).\u00a0 Through this interactive environment preservice teachers manipulate parameters and see, in real time, the effects of those changes on the graphs and data tables of the function.\u00a0 For example, after explaining that the value of the gravitational constant, g<\/i>, is 9.8 meters per second per second, teacher candidates integrate the gravitational constant with respect to time, t<\/i>, to obtain the velocity function:\u00a0 v(t)<\/i> = –gt<\/i> + v0. This function illustrates the physics principle that the velocity of an object is the integral of its acceleration.\u00a0 In Figure 1<\/a>, the result of changing the initial velocity from 49 meters per second to 4.9 meters per second is apparent by the graphs and tables.\u00a0 After completing this assignment, preservice teachers learn how to create an activity using the interactive computer environment.<\/p>\n The potential of such an instructional tool is readily apparent to teacher candidates.\u00a0 Instead of using a static textbook in which authors determine examples and illustrations, using an interactive computer environment in instruction allows the preservice teachers to choose their own examples and participate in dynamic illustrations.\u00a0 Additionally, the undergraduates can type and check spelling, as in any common word processor, respond to problems and questions embedded in the computer application, and print copies for classroom use or assessment purposes by the teacher.<\/p>\n Teacher candidates then develop lessons or activities using this technology that are appropriate for their future middle school or high school students.\u00a0 One possible activity applies the knowledge gained in the initial experience with the interactive computer environment.\u00a0 Appendix A<\/a> contains an example of one such activity used in our program as a guide for preservice teacher generated work that uses the height of an object acted upon only by the force of gravity as an application of quadratic equations.\u00a0 The scenario involves the launch of a model rocket into the air and requires high school students to model the height of the object as a function of time in tabular and graphical form.\u00a0 Such an activity demonstrates the multiple uses of important components of the interactive computer environment within an appropriate context of secondary mathematics.<\/p>\n Interactive Geometry Application<\/p>\n One way to introduce teacher candidates to a particular piece of technology is through classroom-ready, published materials.\u00a0 This is particularly useful when the software is well established and used regularly in classrooms, because teachers could adopt the activity for future classroom use. In one case, we use Bennett (2002) to introduce undergraduates to interactive geometry software on the computer.\u00a0 For example, the following problem could be posed at the beginning of a class session:\u00a0 How could you determine the height of a tree without measuring it directly?\u00a0 At the time they take the technology methods course, teacher candidates typically have an extensive cache of techniques to solve such a problem from prior geometry and trigonometry courses.\u00a0 Bennett (2002) utilizes interactive geometry software to find such indirect measures using lengths that are easy to measure and proportions in similar triangles.\u00a0 Specifically, the worksheet directs the learner to create line segments to represent the tree\u2019s height and the learner\u2019s height in the application; then learners construct parallel lines to simulate the rays of the sun.\u00a0 Finding the tree\u2019s height is a matter of calculating the unknown length (tree\u2019s height) in the proportion of ratios of object height to shadow length.\u00a0 Although preservice teachers often know this technique, constructing the solution in the interactive environment helps clarify concepts and procedures learned in prior courses.<\/p>\n After becoming familiar with the software from the activity, discussions take place on the appropriate uses of the technology.\u00a0 In the case of the interactive geometry software, teacher candidates should recognize several potential uses of the software in a high school geometry course.\u00a0 For example, appropriate use of the software can reinforce properties of similar triangles in students\u2019 minds.\u00a0 The preservice teachers should also recognize that the interactive component of the software allows their students to see that corresponding angle measures remain equal and that corresponding ratios of sides remain equal during actions that change the dimensions of the similar triangles. \u00a0Preservice teachers reflect on the ability of the software to have students discover these properties, rather than simply telling their students, thus creating a more student-centered classroom environment.\u00a0 These future teachers should also recognize the need to transfer the knowledge gained from the interactive domain to problem situations away from the technology, which leads to discussions of how this might be accomplished.<\/p>\n As a culminating experience with the technology, preservice teachers create lessons using the software that are applicable to a secondary mathematics course.\u00a0 Often, ideas for these activities are generated by recognizing alternative solution methods for problems already considered.\u00a0 After exploring the interactive geometry software while solving the tree problem, teacher candidates are encouraged to develop alternative solution methods for solving indirect heights.\u00a0 Appendix B<\/a> presents a follow-up activity for finding indirectly unknown heights of objects.\u00a0 The problem involves finding the height of a flagpole when a mirror is placed on the ground between an observer and the flagpole.\u00a0 The activity leads learners to find an indirect height using similar triangles formed by the reflection in the mirror because the angle of incidence equals the angle of reflection for light.\u00a0 Additionally, the solution plan requiring learners to reflect a ray across a line demonstrates the principles involved, as well as a more sophisticated feature of the interactive geometry environment.<\/p>\n Handheld Data Analysis<\/p>\n One of the easiest technologies for preservice teachers to learn, and yet one of the most adaptable for classroom instruction, is graphing calculator technology.\u00a0 Still, too few secondary school mathematics teachers are comfortable using graphing calculators or know how to use them effectively for classroom instruction.\u00a0 A primary goal of the technology methods course is to provide instruction and experience with handheld technology.\u00a0 Utilizing graphing calculators in a statistical application is one way to meet this goal.<\/p>\n Recording, graphing, and analyzing data are important skills in mathematics, as well as in everyday life.\u00a0 The notion that data exist everywhere in the world is important for students to realize.\u00a0 Additionally, the ability to organize data provides a person with quick numerical and visual representations of the data and the power to predict, to within a predetermined degree of accuracy, future related events based on the data.\u00a0 An introductory lesson for managing data using handheld technology is to enter and graph party affiliations of the presidents of the United States.\u00a0 Two common representations of the data are bar graphs and circle graphs (see Figure 2).<\/p>\n <\/p>\n Figure 2<\/strong>.\u00a0 Circle graph and bar graph of presidential party affiliations in TRACE mode.<\/p>\n One of the issues that should be raised by preservice teachers involves the best visual representation of the political parties of the presidents.\u00a0 They should discuss the advantages and disadvantages of their bar graphs and circle graphs, as well as other common graphical representations.\u00a0 Although the graphs can be obtained from computer spreadsheet technology, students must recognize the importance of being familiar with handheld technology as well.\u00a0 We want our teacher candidates to be capable and experienced with various technological tools so that they are comfortable using the technology available to them in the schools in which they will be teaching.<\/p>\n One required activity of the course is to develop a problem involving the collection, graphing, and analysis of data for middle school or high school mathematics students to complete.\u00a0 Appendix C<\/a> contains an authors\u2019 example of one such activity used in the technology methods course but applicable for a high school class.\u00a0 This activity uses presidential data, similar to the introductory activity, but involves the ages of the presidents at the time of inauguration.\u00a0 The activity extends the relatively simple task of representing data using handheld technology and includes more statistically rigorous analysis of the presidential ages.\u00a0 The activity highlights the mathematical power available to most students to make sense of the world around them using statistical analysis.<\/p>\n Conclusion<\/p>\n Teachers will use technology appropriately and effectively in their mathematics classrooms if they are familiar and comfortable with the technology and, especially, if they have had successful experiences with the technology in an instructional environment.\u00a0 Additionally, teachers who are able to use today\u2019s technology in the classroom will be prepared to learn and utilize tomorrow\u2019s technology.\u00a0 This core course for the secondary teacher education program provides that experience.\u00a0 After this course, the teacher candidates integrate the technology in their field experiences conducted in one of the university\u2019s partner schools.\u00a0 In one instance, preservice teachers use technology during their first clinical teaching experience.\u00a0 At another time, during their semester-long student-teaching experience, host teachers and university faculty members evaluate student teachers on their ability to integrate technology in the classroom.\u00a0 Upon graduation, these future teachers should not only be knowledgeable as to which mathematics concepts are best learned through technology, but also will have had many successful experiences in developing and carrying out lesson plans that involve a variety of different technologies.<\/p>\n Since the creation of our technology-based methods course, its need is apparent.\u00a0 Although technology in typical secondary schools is sparse, several of our partnership schools are dedicated to utilizing technology in mathematics education.\u00a0 From interactive chalkboards to data-sharing hubs for handheld devices, our preservice teachers are beginning to experience these instructional tools during their field experiences.\u00a0 Consequently, we think it is important to prepare them for these eventualities.\u00a0 Our preservice teachers\u2019 experience with technology in our program makes them attractive to secondary school selection committees.<\/p>\n The quality of our preservice teachers since our program emphasized technology in the mathematics classroom is apparent.\u00a0 As university supervisors, we often hear from the host teachers that our graduates are highly knowledgeable in dealing with technological instructional tools.\u00a0 Many host teachers admit to learning valuable teaching strategies using technology from individuals in our program.\u00a0 Although most of our preservice teachers receive favorable technology evaluations, we think we can do better.\u00a0 Our preservice teachers continue to think pedagogically in ways that they were taught rather than to think of the potential learning gains using technology.\u00a0 This course does lay the foundation for these teachers as they become more comfortable with their teaching practices and different ways to educate their students.<\/p>\n Today\u2019s middle school and high school students were born into a world with technology.\u00a0 Using technology during mathematics instruction is natural for them, and to exclude these devices is to separate their classroom experiences from their life experiences.\u00a0 One objective in preparing teachers for the future is to ensure that their classrooms will include the technology that will be commonplace for a future generation of mathematics learners, thus ensuring that the mathematicians, mathematics educators, and citizens of tomorrow experience harmony between their world of mathematics and the world in which they live.<\/p>\n References<\/p>\n Bennett, D. (2002). Exploring geometry with Geometer\u2019s Sketchpad.<\/i> Emeryville, CA: Key Curriculum Press.<\/p>\n Burke, M, Erickson, D., Lott, J. W., & Obert, M. (2001). Navigating through algebra in grades 9 \u2013 12.<\/i> Reston, VA: National Council of Teachers of Mathematics.<\/p>\n Kaput, J. J. (1992). Technology and mathematics education. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning<\/i>, (pp. 515\u2013556). New York: MacMillan Publishing Company.<\/p>\n Key Curriculum Press. (2002). IMP sample activities<\/i>. Retrieved November 15, 2004, from http:\/\/www.mathimp.org\/curriculum\/samples.html<\/a><\/p>\n Mathematical Sciences Education Board. (1990). Reshaping school mathematics: A philosophy and framework for curriculum.<\/i> Washington, DC: National Academy Press.<\/p>\n National Center for Education Statistics. (1999). Digest of education statistics 1998.<\/i> Washington, DC: U.S. Department of Education.<\/p>\n National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics<\/i>. Reston, VA: Author.<\/p>\n National Council of Teachers of Mathematics. (2004). Illuminations<\/i>. Retrieved November 8, 2005, from http:\/\/illuminations.nctm.org\/<\/a><\/p>\n Waits, B. K., & Demana F. (2000). Calculators in mathematics teaching and learning: Past, present, and future. In M. J. Burke & F. R. Curcio (Eds.), Learning mathematics for a new century<\/i> (pp. 51\u201366). Reston, VA: National Council of Teachers of Mathematics.<\/p>\n Author Note:<\/p>\n Robert Powers William Blubaugh <\/a><\/p>\n Figure 1<\/strong>. Changing the value of v0<\/em> in the function v<\/em>(t<\/em>) is apparent in the graphs and tables.<\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/p>\n <\/a>Appendix A<\/p>\n Computer Algebra System: Rocket\u2019s Flight<\/p>\n Rocket\u2019s Flight<\/p>\n Statement of the Mathematical Situation<\/i><\/p>\n A model rocket blasts off from a position 2.5 meters above the ground.\u00a0 Its starting velocity is 49 meters per second.\u00a0 Assume that it travels straight up and the only force acting on it is the downward pull of gravity.\u00a0 Describe the rocket\u2019s flight path and any key aspect that may be significant or important to the problem.\u00a0 Also, note that the acceleration due to gravity is 9.8 m\/sec2.<\/p>\n Directions for Students<\/i><\/p>\n Analyze the above situation and describe it using tabular, graphical, and symbolic representations.\u00a0 After you have completely analyzed the situation in two different ways, describe in your own words the biggest challenge you had in analyzing and completing the task.\u00a0 You may choose (but are not required) to follow the steps below.<\/p>\n Step 1:\u00a0\u00a0 What is the value of h(0)?\u00a0 <\/i>\u00a0<\/b>What is the real-world meaning of h(0)<\/i>?<\/p>\n Step 2<\/i>:\u00a0 What is the initial value of the velocity, given by v<\/i>(0)?<\/p>\n Step 3<\/i>:\u00a0\u00a0 What is the acceleration due to gravity, or g<\/i>?\u00a0 How\u00a0 would any equation describing the rocket\u2019s flight show that this force is downward?<\/p>\n Step 4<\/i>:\u00a0 Write the unique quadratic function that represents the height, h(t),<\/i> of the rocket identified in the problem statement t<\/i> seconds after liftoff.\u00a0 Hint below.<\/p>\n Remember that Step 5<\/i>:\u00a0 In the space below:\u00a0 (a) Graph your function h(t)<\/i> using the best viewing window that shows all important parts of the parabola.\u00a0 (b) Make a table of heights above the ground, for the first 10 seconds of flight, increment by 1 second.<\/p>\n Step 6<\/i>:\u00a0 How high does the rocket fly before falling back to Earth?\u00a0 When does it reach this highest point?<\/p>\n Step 7<\/i>:\u00a0 How much time passes while the rocket is in flight?<\/p>\n Step 8<\/i>:\u00a0 Write the equation you must solve to find when h<\/i>(t) = 50.<\/p>\n Step 9<\/i>:\u00a0 When is the rocket 50 meters above the ground?\u00a0 Approximate your answer to the nearest tenth of a second.<\/p>\n Step 10<\/i>:\u00a0 Describe in words and show graphically your answer to Step 9.<\/p>\n Related Online Resource:<\/strong><\/p>\n Online Graphics Calculators:\u00a0 <\/p>\n <\/p>\n <\/a>Appendix B<\/p>\n Geometry Application: Flagpole Problem<\/p>\n Flagpole Problem<\/p>\n To find the height of a flagpole, a student placed a mirror on the ground and stood so that she could look in the mirror and see the reflection of the top of the flagpole.\u00a0 See figure on the right.<\/p>\n Sketch and Investigation<\/i><\/p>\n 1.\u00a0\u00a0\u00a0\u00a0\u00a0 2.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct the line j perpendicular to segment 3.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct point C on line j to represent the location of the observer.<\/p>\n 4.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct line l perpendicular to line j at point C.<\/p>\n 5.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct point D on line l to represent the eye level of the observer.<\/p>\n 6.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct point E between points C and B on line j to represent the location of the mirror.<\/p>\n 7.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct ray 8.\u00a0\u00a0\u00a0\u00a0\u00a0 Construct the line m perpendicular to line j through E.<\/p>\n 9.\u00a0\u00a0\u00a0\u00a0\u00a0 Mark line m as a mirror.<\/p>\n 10.\u00a0 Reflect ray 11.\u00a0 Construct the intersection of the reflected ray and the line l.\u00a0 Label it point F.<\/p>\n 12.\u00a0 Hide line m.<\/p>\n 13.\u00a0 Measure the lengths of 14.\u00a0 Measure angles Questions:<\/i><\/p>\n 1.\u00a0\u00a0 Drag point E between C and B.\u00a0 What do you notice about angles 2.\u00a0\u00a0 Drag point E until point D and F coincide.\u00a0 What are the measures of 3.\u00a0\u00a0 Using the relation between triangles 4.\u00a0\u00a0 The student measured the distance from herself to the mirror to be 1.19 meters, from the mirror to the base of the flagpole to be 6.65 meters, and her eye level height to be 1.70 meters.\u00a0 How tall is the flagpole? Dynamic Geometry for the Internet: http:\/\/www.keypress.com\/sketchpad\/javasketchpad\/about.php<\/a><\/p>\n <\/p>\n <\/a>Appendix C<\/p>\n Data Analysis: The Presidency of the United States<\/p>\n The Presidency of the United States<\/p>\n 1st<\/b>:\u00a0 Using the Internet, school library, or a history book obtain the ages, at inauguration, of the presidents of the US.<\/p>\n Question<\/i>:\u00a0 What do you initially observe about the ages of our presidents?<\/p>\n 2nd<\/b>:\u00a0 Using the statistical lists of your graphics calculators, enter the presidential order (1st, 2nd, 3rd, etc.) and the inauguration age for each president in “Order” and “Age” lists.<\/p>\n Question<\/i>:\u00a0 To enter the data in the “Order” list, do you remember the quick way of entering an arithmetic sequence using the seq( <\/i>\u00a0\u00a0command?<\/p>\n 3rd<\/b>:\u00a0 Construct and display a histogram of ages at inauguration on the screen of your calculator.<\/p>\n Question<\/i>:\u00a0 From this graph, what do you notice about the inauguration ages of the presidents?<\/p>\n 4th:<\/b>\u00a0 Construct a box-and-whiskers plot of their ages at inauguration on the screen of your calculator.<\/p>\n Questions<\/i>:<\/p>\n (1) What five-number summary is obtained from the box plot?<\/p>\n (2) What does the box plot reveal regarding the spread of the data?<\/p>\n (3) By looking at its shape and length, what else does the box plot reveal?<\/p>\n 5th:<\/b>\u00a0 Display your histogram and a box-and-whiskers plot of the above ages as two different plots, and display them on the same screen.<\/p>\n Questions<\/i>:<\/p>\n (1) By looking at two different graphical representations at the same time, what additional information or reinforcing comments can you make?<\/p>\n (2) Which of the two graphs provide the more important information and why?<\/p>\n (3) Support your conclusions from Question 2 above by calculating 1-Var Stats <\/i>of the Presidents\u2019 ages.<\/p>\n 6th:<\/b>\u00a0 Now graph the ages at inauguration by the order of their presidency.<\/p>\n Questions<\/i>:<\/p>\n (1) Describe any patterns that you see in the points.<\/p>\n (2) If we divide the presidency into three parts, say the first 14, the middle 15, and the last 14 presidents, how do the 3 parts compare with each other?<\/p>\n (3)\u00a0 Verify your observations, using the statistics available in your calculator.<\/p>\n (4)\u00a0 Based on the ages of the last 14 presidents, what “predictions” can you make regarding the next president?<\/p>\n 7th<\/b>:\u00a0 Knowing the inauguration ages and political party affiliation of each of our presidents, what questions were not asked that you would like answered?<\/p>\n Extension:\u00a0 <\/b>If time permits, perform the additional analysis involving confidence intervals and tests of significance.<\/p>\n 8th<\/b>:\u00a0 Determine the Confidence Interval, at the 95% level for the mean, for the age at inauguration of our next president.<\/p>\n Questions<\/i>:<\/p>\n (1) What does a 95% Confidence Interval mean?<\/p>\n (2)\u00a0 Would the 95% Confidence Interval be the same for the mean and the median of the ages?\u00a0 Elaborate.<\/p>\n (3)\u00a0 Based on the ages of all U.S. presidents at inauguration, what is the interval that will likely contain the age of the next president at the 95% confidence level?<\/p>\n (4)\u00a0 Using only the ages of the last 14 presidents, what is the 95% confidence interval that will likely contain the age of the next president?<\/p>\n (5) What is the difference between 3 and 4 above, and why?<\/p>\n 9th<\/b>:\u00a0 Suppose we were to randomly select the age of one of our past presidents to help determine the likely age of the next president.<\/p>\n Question<\/i>:\u00a0 What is the probability that the next president would be between 40 and 46 years old (a) using the ages of all 43 presidents, and (b) using the ages of the last 14 presidents?<\/p>\n 10th<\/b>:\u00a0 Use a t<\/em>-test of independent sample means available on your calculator to determine if the ages of the first 14 presidents at inauguration are significantly different from the ages of the last 14 presidents at inauguration.<\/p>\n Questions<\/i>:<\/p>\n (1) What is the meaning of this calculator result?<\/p>\n (2)\u00a0 Why was this test used?<\/p>\n <\/p>\n Related Online Resources:<\/strong><\/p>\n Political Party Data:\u00a0 http:\/\/www.presidentsusa.net\/partyofpresidents.html<\/a> <\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_1a.jpg\")
<\/a> ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_1b.jpg\")
<\/a> Figure 1.<\/strong> Changing the value of v0 in the function v(t) is apparent in the graphs and tables. <\/em>(Click anywhere on figure to view the enlarged image.)<\/p>\n\n
![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_7.jpg\")
\u00a0\u00a0\u00a0\u00a0\u00a0 ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_8.jpg\")
<\/p>\n<\/blockquote>\n\u00a0<\/b><\/h3>\n
\nUniversity of Northern Colorado
\nrobert.powers@unco.edu<\/a><\/p>\n
\nUniversity of Northern Colorado
\nbill.blubaugh@unco.edu<\/a><\/p>\n\n
<\/p>\n<\/p><\/blockquote>\n<\/blockquote>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_5.gif\")
<\/p>\n
\nhttp:\/\/www.scugog-net.com\/room108\/calculator99\/<\/a> and
\nhttp:\/\/matti.usu.edu\/nlvm\/nav\/frames_asid_109_g_4_t_1.html?open=activities<\/a>.<\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_3.jpg\")
In this activity, you will solve the flagpole problem using an interactive geometry application.<\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_4.jpg\")
Construct line segment ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_8.gif\")
\u00a0to represent the flagpole.<\/p>\n\u00a0at point B to represent the ground.<\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_9.gif\")
.<\/p>\n\u00a0about line m.<\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_10.gif\")
, ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_11.gif\")
, and ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_12.gif\")
.<\/p>\n![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_13.gif\")
\u00a0and ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_14.gif\")
.<\/p>\n\u00a0and ?\u00a0 What does this imply about triangles ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_15.gif\")
\u00a0and ![](\"https:\/\/citejournal.org\/wp-content\/uploads\/2016\/04\/v5i3math\/5474_16.gif\")
?<\/p>\n, , and ?\u00a0 Describe these measures in the context of the flagpole problem.<\/p>\n\u00a0and , determine a formula for calculating segment .\u00a0 What is the measure of ?<\/p>\n
\nRelated Online Resources:<\/strong><\/p>\n
\nAges at Inauguration:\u00a0 http:\/\/www.campvishus.org\/PresAgeDadLeft.htm<\/a>
\nData Plots\/Graphs: http:\/\/matti.usu.edu\/nlvm\/nav\/category_g_4_t_5.html<\/a><\/p>\n