Design Project Report 2
ESE6939
Catherine Haight
Graphing Calculator Kick Start Program
Revisions since Report 1:
The revision since report one consist of deciding what calculator functions are most useful within the mathematical content of the course as well as the programs and applications that can assist student with all their school subjects. I have done a topic analysis to find that there are nine main branches of topics that would be appropriate for my students in this setting. In looking at the reading competency and attitudinal surveys; I know I have to model all the processes visually with support from text and graphics. The program will use hand-on practices to develop the comfort level and level they need to operate the device without frustration. The students need realistic ways to use the technology in their hands on a daily basis for them to feel it has a relevance to their learning. I plan on showing the connections to the math course they are currently in, as well as the uses for Science, standardize testing, organization, and studying for any topic through the use of a variety of examples and topics.
Goals Statement:
The goal of this program is to bring all students to a minimal level of competency in using graphing calculators. This will facilitate teaching using the technology for problem solving throughout the year. All students will be able to operate their graphing calculator for mathematical functions and be able to demonstrate the nine processes listed here.
1. Students will be able to adjust the basic settings on their calculator and know which are appropriate to change when using.
2. Students will be able to perform all Home screen operations for evaluating mathematical expressions
3. Students will demonstrate using the MATH menu for operations that are not on the keyboard.
4. Students will use the Graphing Menus and know how appropriately graph several types of functions.
5. Students will use the Matrix menu and perform operations with matrices on the Home screen.
6. Students will perform operations in DMS with Angle menu.
7. Students will use the STAT menu to find and graph several regressions for data
8. Students will demonstrate use the PGM menus to write, exec and transfer programs
9. Students will access and use several useful applications in the APPS menu and be able to associate them with school or real life uses.
Task Analysis tied to the Goals:
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The concept map above is a topic analysis of the material that is necessary in an Algebra 2 math course setting for graphing calculators. The topics in dark green are the nine essential goals I see for my students need to reach a minimal competency level with the technology device. I have revised the topics using what I know is taught in Algebra 2 above mathematics courses as well as common Science and organizational topics that can benefit them as students.
Each menu has several options and procedures to teach so below I will do the task analysis for my Matrix menu goal.
Task Analysis for Matrix Menu:
The flow chart below describes the basic procedures needed for Matrix mathematics in Algebra 2. There is an assumption that students have already been exposed to Matrices operations in the course so this module would occur during the chapter that addresses them.
Instructional Objectives:
Graphing Calculator Skills for Math
1. Basic Settings/Functions
o MODE: Students will set up the Mode menu on calculator to appropriate settings given a problem situation to solve without assistance with 100% accuracy. (cognitive synthesis)
o Memory: Students will manage the Memory menu of calculator to Reset, Clear Entries or Lists, and delete excess programs without assistance with 100% accuracy. (cognitive synthesis)
o Catalog: Student will describe in their own words the purpose and location of the Catalog feature on the calculator when prompted with 100% accuracy. (cognitive comprehension)
o ALPHA: Students will demonstrate the use of the Alpha key for inserting texting into the screen of their calculator when prompted or needed during operation of the device with 100% accuracy. (cognitive application)
2. Home Screen Operations
o 4 Functions: Students will solve problems with the calculator using the 4 basic functions of add, subtract, multiply and divide with 90% accuracy. (cognitive application)
o Fractions: Students will be able to enter and solve problems using fractions with the calculators and transform the answer into multiple representations including improper, proper, and decimal formats with 90% accuracy. (cognitive application)
o Exponents/Roots: Students will be able to enter and solve problems using exponents and roots on calculator with 90% accuracy (cognitive application)
o Pi/10^x/e^x: Students will be able to enter and solve problems that contain Pi, 10^x and e^x when appropriate on their calculator with 90% accuracy. (cognitive application)
o Trigonometry Functions: Students will be able to enter and solve problems that contain sin, cos, and tan on their calculators in both radians and degrees using their calculator with 90% accuracy. (cognitive application)
o STO> Button/RCL: Students will demonstrate the use of the store and recall functions of the calculator when needed to solve problems with 100% accuracy. (cognitive application)
3. MATH Menu
o MATH: Students will demonstrate the use of fraction to decimal conversions, entering cubes and cube roots, or any root from the MATH menu of the calculator given problems containing those operations with 90% accuracy (cognitive application).
o NUM: Students will demonstrate and use the MATH NUM menu to calculate solutions to absolute value, least common multiple, greatest common divisor, and improper to proper fractions conversions using the calculator given problems that contain those operations with 90% accuracy (cognitive application).
o PRB: Students will employ the use of the MATH PRB menu to calculate problems that contain factorials, combinations or permutation situations with 90% accuracy. (cognitive application)
4. ANGLE Menu
o Students will access the Angle menu to find and enter the symbols of degrees, minutes, and seconds for solving problems with those measurement types with 100% accuracy.
o Students will convert DMS to Decimal form and back using the Angle menu of the calculator for problems requesting alternate representations of the answer with 100% accuracy. (cognitive application)
5. MATRIX Menu
o Students will be able to access and display stored matrices in their calculator from the Matrix Names menu when necessary to solve problems with 100% accuracy.(cognitive comprehension)
o Students will be able to calculate the determinate of a matrix using their calculator in the Matrix Math menu when needed to solve problems with 90% accuracy. (cognitive application)
o Edit: Students will be able to enter and edit any matrix needed for a math problem with 100% accuracy. (cognitive application)
o Students will be able to perform matrix operations of addition, subtraction, multiplication, and inverse using the HOME screen in conjunction with the Matrix menu to solve problems with 90% accuracy. (cognitive application)
6. Graphing Menus
o Y= : Students will demonstrate the graphing menu functions by turning on/off Plots, edition the screen to enter functions, and editing the display settings for various types of graphing problems with 80% accuracy. (cognitive application)
o WINDOW: Students will use the Window menu to set appropriate screen dimensions for the graphing of various functions on the calculator with 80% accuracy. (cognitive application)
o ZOOM: Students will employ the use of the Zoom menu features of the calculator to get a closer look at various functions critical behaviors with 80% accuracy.
o TRACE: Students will use the Trace menu and the cursor buttons to access data on the function that is graphed in the Graph screen of calculator when necessary with 90% accuracy.
o GRAPH: Student will demonstrate graphing various functions for math problems as well as formatting the screen, employing the Calc functions and looking at Tables related to that function with 80% accuracy.
7. Applications Menus
o AreaForm: Students will access and describe what AreaForm application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o Conics: Students will access and describe what Conics application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o CellSheet: Students will access and describe what CellSheet application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o Inequalz: Students will access and describe what Isequalz application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o Periodic: Students will access and describe what Periodic application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o Prob Sim: Students will access and describe what Prob SIm application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o PlySmlt2: Students will access and describe what PlySmlt2 application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o SciTools: Students will access and describe what SciTools application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
o StudyCards: Students will access and describe what AreaForm application’s purpose is from the APPS Menu with 100% accuracy. (cognitive comprehension)
8. PRGM Menu
o EXEC: Students will demonstrate the ability to execute programs in their calculator when necessary for solving problems with 100% accuracy. (cognitive application)
o EDIT: Students will demonstrate the editing of a program already stored in their calculator with assistance from instructor with 100% accuracy. (cognitive application)
o NEW: Student will demonstrate entering a new program into calculator given the commands and text to enter with 100% accuracy. (cognitive application)
o LINK: Students will demonstrate linking to other calculators and the computer to import and export programs with 100% accuracy. (cognitive application)
9. STAT Menu
o EDIT: Students will employ the use of the STAT Edit menu to enter data, sort data, clear lists and set up the editor when need for solving problems with 90% accuracy. (cognitive application)
o CALC: Students will access and identify the 1-variable and 2-variable statistics that are available on the calculator when needed for problem solving with 90% accuracy. (cognitive comprehension)
o Regressions: Students will demonstrate the use of several types of regressions using the STAT Calc menu to create functions for graphing when needed for problem solving with 90% accuracy. (cognitive application)
o STAT PLOT: Students will select the appropriate settings for the plotting of data on the graph screen when needed to solve data driven problems with 90% accuracy.
Instructional Sequencing:
This unit will is very content orientated and will be sequenced so that prerequisite skills are taught before they are needed for the next task. I also have to consider how the mathematical content of the program relates to the content the students currently know and or will be soon learning in the course. There are many things that can be modeled up front for the students and then recalled at a later date when the topic is more relevant to the course content. The goal of the kick start program is to show students how valuable the tool can be throughout the year as well as for their other courses. The sequencing I am employing is Learning-Related Sequencing teaching the skills that are needed for basic operations then progressing through to topics that build upon those.
Strategies for Teaching Objectives:
The instructional strategies that will be used include demonstration and modeling, providing examples and elaborating on why decisions were made at different steps in the procedure. Then the students will be provided with practice problems for each type of procedure. There will also be remedial support available online through their Moodle website in the form of video refreshers of each procedure on the calculator.
Ex: Students will watch as I demonstrate using the Ti-Smart view software I have for that matches the calculators they use. I will present a problem that can be done using the Matrix menu. I will then step them through the solution using a graphic organizer for the procedure and modeling the steps on the screen. After the students have recorded the example I will present several other practice problems for this type of procedure. They will be assessed on being able to enter the information without assistance and solve for the correct answer.
Details on Objectives:
Students will practice the skills that have been taught in class under my observation by doing similar examples and then through homework assignments for independent practice. They will receive informal formative assessment as we move through the different objectives and formally on tests and quizzes where they will use the graphing calculator as a problems solving tool.
Pre-instructional activities:
Students will begin the unit by watching 2 videos on one using Graphing Technology in mathematics and a second that is a music video about math and graphing calculators. These should help to peak interest in learning calculator skill during my kick-start program. I will also have to ensure that all students have access to a graphing calculator for instruction during class and I will encourage them to purchase or borrow one for the year while in this course. The Lesson essential questions will be for used to create a pre-test for each learning cognitive objective as we move through the curriculum as well as any key vocabulary terms that will be used. There will be a poster diagram in the classroom for reference of the graphing calculator for students to view as a visual cue. Students will develop flowchart/graphic organizers for each procedure as a guide for future application of the process which will be kept in a section of their notebooks.
Groupings and Media:
The student will work independently on their calculators by have the support of collaborative pairs to assist them when they are stuck. They will be able to view the Smartboard screen and their flow chart for text clues of the steps to perform in solving the problem. Students have practice workbooks that are associated with the course that will be used for practice and review. The videos of each procedure will also be available for view from their home computers if they need a refresher on a particular problem.
Sample Assessments:
Located below are samples of the pre-test and post test for the Matrix module of the instruction. Goal 5 is to help students understand how to enter, edit and perform basic operations in the Matrix menu before they address the content in the Algebra 2 course as a problem solving tool for systems of equations.
Goal 5: Students will use the Matrix menu and perform operations with matrices on the Home screen.
Objectives:
o Students will be able to access and display stored matrices in their calculator from the Matrix Names menu when necessary to solve problems with 100% accuracy.(cognitive comprehension)
o Students will be able to calculate the determinate of a matrix using their calculator in the Matrix Math menu when needed to solve problems with 90% accuracy. (cognitive application)
o Edit: Students will be able to enter and edit any matrix needed for a math problem with 100% accuracy. (cognitive application)
o Students will be able to perform matrix operations of addition, subtraction, multiplication, and inverse using the HOME screen in conjunction with the Matrix menu to solve problems with 90% accuracy. (cognitive application)
References:
Dewey, B., Singletary, T., & Kinzel, M. (2009). Graphing Calculator Use in Algebra Teaching. School Science and Mathematics, 109(7), 383-93. doi: 10.1111/j.1949-8594.2009.tb17869.x
Morrison,G., Ross,S., Kalman, H., & Kemp,J. (2011) Designing Effective Instruction, 6th Ed. John Wiley & Sons, Inc.
Bass, L., Bellman, A., & Johnson, A. (2010) Teaching with TI Technology, Pearson, Boston, MA.
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