Capstone+Summary

My original capstone proposal is here:



I had deliberately left my initial proposal a bit vague at spots (in fact I seem to remember someone commenting in a discussion post that they were a bit jealous about that!). Below I hope to revisit parts of my proposal with a look at how the components turned out or how I expect them to turn out. In some cases if I didn't have anything to modify it may just be the same.

__ **Objectives** __ **I have included all program goals of the 21st Century Teaching and Learning Program; I have found their relevance to my trigonometry unit to be more or less as expected.**
 * 1) //Student-centered//: Trigonometry is a unit that is traditionally delivered using a large portion of didactic instruction. However, there are many opportunities for student exploration and discovery of new ideas. This unit will start with student-driven exploration and I will intervene with direct instruction throughout the unit to help students make connections and future discoveries. **Although I haven't had as many explorations with each sub-unit as I hoped, each day has typically included at least several minutes of group exploration, in addition to the original exploration that started the unit. We are going to move into some new territory soon that will lend itself well to continued exploration.**
 * 2) //Learning and Doing//: This program goal is easy to address as I have been steadily moving more to a model of allowing students to “do.” Instead of me showing, it will be students trying and sharing. Although direct transfer of information may be necessary at times, much time will be devoted for students to work through problems, both authentic and traditional in nature.
 * 3) //Using Information//: Students will be utilizing information they have already learned about basic features of triangles and circles in order to develop the fundamental tenets of trigonometry. These rules of trigonometry will then be used to solve real-life problems. **I have been impressed with how this group of students has taken minimal information and turned it in to new trigonometric rules. This has been in the theoretical sense so far, but will hopefully be evident in their final projects.**
 * 4) //Facilitator//: As mentioned above, students will tackle many of the problems that will be assigned in order to develop their own construct of trigonometry. I will serve in a coaching role as students work through these problems.
 * 5) //Flexible Grouping//: Students are already seated in groups of three to five in my classroom. These groups will change just prior to the start of the trigonometry unit. At that point, I will have some time to reflect on student work and will group the students heterogeneously according to their past and projected performance and abilities. These groups will sometimes be altered so that students can work with a variety of their peers for various student activities, such as jigsaw activities. However, the initial grouping will be used for collaboration throughout the unit. In addition, online activities will allow for grouping to go beyond the classroom walls and between the two classes that will be working on this unit. **Students are working with their groups on the final project. In addition, students took a quiz collaboratively with one other person. It was interesting to see how working with a partner seemed to reduce the scores slightly for some of the top students, while the general scores in the class rose significantly. One final note, when I shared my project with a colleague teaching the same course, she liked the idea of working together. So, the final project will actually be completed across three classes. Although my students won't be specifically grouped with hers, they will be communicating online.**
 * 6) //Multiple Instructional and Learning Modalities//: Content will be delivered using technology, in print, verbally, and with various activities in order to address the needs of the visual, auditory, and kinesthetic learners.
 * 7) //Higher order thinking skills//: Trigonometry is a mathematical unit that traditionally requires a significant amount of memorization of facts. While I don’t plan on significantly reducing these lower-order thinking skills, students will be challenged to the higher end of Bloom’s Taxonomy through application problems and challenging scenarios that will require students to make connections with the mathematical knowledge the hold. **I have given some extra attention in this area in quiz/test question development and in some of my instruction that reduces memorization and focuses instead on connections and analysis.**
 * 8) //Interdisciplinary//: Of the sixteen program goals, this goal may be the most indirectly addressed. Although direct interdisciplinary connections won’t be explicit, students will be working on problems with direct application to physics and other sciences. In addition, students will do a substantial amount of writing in a log that they will be keeping throughout the unit and the semester.
 * 9) //Collaboration//: Students will be specifically collaborating with their in-class groups on a daily basis. They will also be broken down into partners for some work. In addition, I hope to incorporate collaboration across classes using the Internet and other network resources. **I believe this has been addressed above and here already.**
 * 10) //Performance-based assessments:// I will be using traditional assessments to assess basic skills, but the impetus for learning the material will be driven by authentic problems and mini-projects throughout the unit. **This objective was where I specifically focused the thrust of my unit. The main performance-based assessment is a an authentic project where students must solve a problem using trigonometry and post their solution on a wikispace. Some of these problems are open-ended in nature. Other small assignments that are performance based in nature are included throughout the unit, including an upcoming graphing activity.**
 * 11) //Multiple sources of information, including technology//: Students will get information from me, textbooks, the Internet, and various software applications. My “dream resource” would be to contact a community member or someone else who uses trigonometry regularly in their work, but I will need to take time to explore that option. **Well, I didn't connect with my "dream resource." Admittedly, I did not dive into this aspect as much as I could have, although I did speak to some colleagues to fish around in this area. However, students have been getting information from me, textbooks through me, the Internet, and different software. We have utilized Geometer's Sketchpad, graphing calculators, Geogebra, and another graphing program. These applications will continue to be used throughout the rest of the unit.**
 * 12) //Technology fully integrated into the classroom//: Students will be using laptops, graphing calculators, graphing software, a course management system, and online discussion forums. Other technology will be implemented as I see fit at the appropriate time. **These technologies have all been used and will continue to be used.**
 * 13) //Teachers addressing the learning style of all learners//: The classes participating in this unit are tracked homogeneously; all of them have shown an advanced level of mathematical skill. However, these students still have a variety of learning styles. I hope to reach these students by employing multiple modes of instructional delivery, while focusing on peer interaction and peer instruction. **Now that I have had these students for quite some time I am much more able to address this objective. Just prior to the start of the unit I regrouped students to balance ability levels and maximize interaction. My focus is on differentiation through peer instruction and work. This balance I believe also led to the centralized scores on the recent collaborative quiz.**
 * 14) //Learning how to learn//: Students will be encouraged to reflect metacognitively through a double-entry journal and by reflecting on the ways in which information was presented and how they mastered it. **Although I have incorporated a journal / periodic log of questions, I have not incorporated the metacognitive aspect as pervasively as I originally envisioned. This will definitely be a part of the end of the unit, although the midpoint will provide another good place for this to occur.**
 * 15) //Using a variety of types of information to complete authentic projects//: As stated before, students will be working through a variety of authentic problems throughout this unit. They will often be synthesizing the various types of information while working with a partner or small group on these problems.
 * 16) //Students acting as professionals in the discipline//: At this point, I am not sure that this unit will culminate in a product that will be presented outside of the classroom. However, students will be performing the work of professional mathematicians on several problematic scenarios. **The final projects will be shared among two classes, but they will not be presented to an outside audience at this time. Some of the problems for the project do have students doing the mathematical work of a professional, while a few of the problems are a bit more contrived in nature.**

__ **Strategy** __
 * While this was originally a broad stroke in my original proposal at what was to occur, here you will find a day-by-day time line of what did occur, what will occur, or even what could occur.**


 * Day 1: An exploratory lesson about special right triangles and similar triangles; generally this is review of material they learned in geometry. Students will work in their groups on the activity.**


 * Day 2: An introduction to the basics of trigonometry using a collaborative partner exploration activity on Geometer's Sketchpad.**


 * Day 3: Finish the Geometer's Sketchpad activity.**


 * Day 4: An acquisition lesson on the right triangle definitions of the six trigonometric functions. This lesson begins with a debriefing and discussion of the Geometer's Sketchpad activity.**


 * Day 5: Collaboratively work on real-world problems that require right triangle trigonometric definitions to solve.**


 * Day 6: An acquisition lesson with some exploration on converting between degrees/decimal and degrees/minutes/seconds.**


 * Day 7: Students will travel around the school in their groups with a clinometer and find the height of various objects using the tangent function. The remaining time will be spent reviewing what was learned so far.**


 * Day 8: Project presentation and initial rubric development. (In the future I would plan on presenting the project even earlier, preferably Day 1. In addition, presenting the project and developing the rubric were a lot to accomplish in one period; the latter may be better reserved for a second day.)**


 * Day 9: An individual quiz on the basics of the six trigonometric functions.**


 * Day 10: An acquisition lesson on angles of rotation and triangles on the coordinate plane, again with short exploration.**


 * Day 11: Development of the Unit Circle.**


 * Day 12: Finish the Unit Circle and have students develop some basic trigonometric identities from an expansion of the Unit Circle.**


 * Day 13: Students will take a quiz on the Unit Circle and angles of rotation collaboratively with one other member of their group.**


 * Day 14: An acquisition lesson on radian measure for an angle, beginning with a unit conversion log entry and a short exploration. Radians are added to the Unit Circle.**


 * Day 15: Finish up radians on the Unit Circle and work on application problems relating angular speed and linear speed.**


 * Day 16: A day of collaborative review.**


 * Day 17: An individual unit test of what was covered so far: Triangles, Basic Trigonometry, the Unit Circle, and Radians.**


 * Day 18: Finish student design of project rubric. An acquisition lesson on periodic graphs.**


 * Day 19: Students will work in their groups to develop hand drawn graphs of the six trigonometric functions. Graphs will then be analyzed and compared for various features and technology will be utilized to construct the graphs and analyze domain and range.**


 * Day 20: An exploration of period, amplitude, and shift of trigonometric graphs using graphing software.**


 * Day 21: Finish up graphing activity and close with summary.**


 * Day 22: Use graphing calculators and Internet resources to develop trigonometric regression equations for data sets.**


 * Day 23: An acquisition lesson on the graphs of inverse trigonometric functions. Students will develop graphs based on prior knowledge of inverse functions.**


 * Day 24: Collaborative review of trigonometric graphs.**


 * Day 25: A quiz of trigonometric graphs.**


 * Day 26: An acquisition lesson on inverse functions and solving real-world right triangle problems using inverse trigonometric functions.**


 * Day 27: An exploratory/acquisition lesson on the Law of Sines and its use in real-world problems.**


 * Day 28: An exploratory/acquisition lesson on the Law of Cosines and its use in real-world problems.**


 * Day 29: An acquisition lesson on solving trigonometric equations utilizing graphing calculators.**


 * Day 30: A day of collaborative review on inverse trigonometric functions and solving trigonometric equations.**


 * Day 31: A quiz on inverse trigonometric functions and solving trigonometric equations.**


 * Day 32: A lesson on basic trigonometric identities and simplifying trigonometric expressions.**


 * Day 33: An acquisition lesson on sum and difference trigonometric identities.**


 * Day 34: An acquisition lesson on double- and half-angle trigonometric identities.**


 * Day 35: An exploratory/collaborative lesson on proving trigonometric identities.**


 * Day 36: Finish proving trigonometric identities.**


 * Day 37: Collaborative review.**


 * Day 38: Continued collaborative review.**


 * Day 39: A unit test on the second half of the unit: trigonometric graphs, solving trigonometric equations, and trigonometric identities.**


 * Day 40: Discussion and review of projects.**


 * Day 41: An online view and collaborative quiz / journal write-up on projects of peers.**


 * It is not included in the above list, but a couple of days would be interspersed for working on the final project. That would bring the entire unit up to around 45 days, or approximately one quarter of the year.**

__ **Resources** __ For this learning unit and project I will need student laptops, Internet access, graphing calculators, Graph software, Geogebra software, Geometer’s Sketchpad software, an interactive white board, and of course non-technology resources such as a textbook and other print documents. Thankfully, all of these resources are currently readily available in my school and my classroom, so access is not a concern. As I implied previously, I would like to make a connection to an outside person or organization that uses trigonometry regularly. This connection is not currently addressed in my general strategy, but I am hopeful that such a resource would become available and I would be able to implement it into my unit. **I have had all of the above resources available and have utilized them, although this year has brought some of the worst network problems we have ever had. Thankfully the network interruptions have not impeded the continuity of the unit. I am hopeful that next year I could take this unit beyond the classroom walls with the inclusion of some experts that use trigonometry in their career.**

__ **Desired Outcomes** __ In some ways, I have already expressed my desired outcomes within my rationale section of this proposal. I want students to be engaged in learning trigonometry, to appreciate the usefulness of trigonometry in authentic problems, and to develop a mastery of trigonometry. I will evaluate the success of this project in a variety of ways. First and foremost, I will collect anecdotal evidence during each day’s lesson. I feel that I am in tune with my students enough to realize if forward progress is being made. In addition, I will evaluate success by analyzing student assessment scores on traditional assessments, performance assessments, and projects. Some of these scores I will be able to compare with prior classes and some with a colleague teaching the same course, while others will be observed independently. Finally, I will use [|www.surveymonkey.com] to construct a survey for students to complete in order to give me feedback from their perspective. I highly value the student experience in my classroom and carefully consider it in future planning. Overall, I am looking to implement an authentic unit where I don’t just resort to teaching trigonometry the same way I have in the past. As illustrated above, I already have many ideas implementing 21st-century teaching and learning principles and I plan on developing more as the unit begins. **I have been able to collect a good bit of anecdotal evidence and also scores from several activities. In my opinion the unit has been a success so far. I feel that my students have been very engaged and are doing quite well understanding the concepts and making the connections. I am looking forward to expressing the same sentiment at the end of the entire unit when final projects are completed and all of the work is in the books.**