Standard III:  Teaching, Learning, and the Curriculum
Teachers implement curriculum plans, that include methods and strategies for applying technology to maximize student learning.

    The objectives of this project were to integrated technology as a means of enhancing the content and to design lessons that would engage students and incorporate different learning styles.  I wanted all students to benefit from applying technology; therefore, activities were not limited to a certain unit of material, but spanned the curriculum of that subject matter. Technology was implemented where suitable with the topic of instruction for each course:  Algebra One, Geometry, and Advanced Placement Calculus.  I often incorporated activities into current lessons and used the technology in place of past practices.  As a result, each class had technology-based lessons included as part of their course work.

• Rigid Transformations:
  
• Lesson:The students will use Geometer Sketchpad to create rigid transformations including translations, rotations, and reflections, and identify the properties of transformations.
• Purpose:  To understand definitions of Rigid Transformations while examining and employing properties.
  
• Commentary:  I used the lesson as a reinforcement instead of doing worksheets. The students were provided with an instruction sheet that they had to follow.  Because it was their second time with Geometer Sketchpad, we did not work together.  It seems to help the students to work at their own pace on the computer.  Although some did not finish the assignment, the students showed a better understanding to the properties. The program is interactive and the students can move an object and note the results as other dependent objects moved.  The students were able to visualize results as transformation were made.  Questions posed as the students moved along the lesson encouraged critical thinking and mathematical communication.  Each student had his or her own computer to work with, therefore management issues were limited to students who could not log on for some reason.  Those students were paired with others. 
  
• Mathematics Standards: II.1.2, II.1.3, II.2.3
• NETS:  8, 9, 10
• Standards Category:  1, 3, 6
• COATT Indicator:  A, B, C, D
• Student Artifacts:  1, 2, 3, 4, 5
  


• Conditional Statements & Properties
  
• Lesson:  Inspiration was used to create webs of the material that will be assigned for the Chapter test.  This will be used as a study and review guide when completed 
  
• Purpose:  To assist the students in organizing and clarifying their understanding of chapter concepts and demonstrate to students a type of study aid. 
  
• Commentary:  The students were assigned topics from the chapter that must be used in a graphic organizer. I have done graphic organizers in the past, but traditionally as a paper/pencil project.  I often had a number of students who didn't do the project.  I placed the students in groups of two because there were no enough computers for each to have their own. The difference in doing it with Inspiration was exciting.  They loved using the program and being able to personalize their web with graphics and colors.  Most importantly the students worked great together.  They were discussing ideas and examples, (required), they were checking notes and debating definitions.  This was a teachers dream!  I stood there and saw them learning .  I was so pleased with this activity that I repeated it again second semester with a new group of students.  The  results were just as exciting. 
  
• Michigan Mathematics Standards:  II.1.1 - II.1.4, VI.2.2
• NETS:  1, 8, 10
• Standards Category:  1, 3, 6
• COATT Indicator:  A, B, C, D
• Student Artifacts:  1, 2, 3, 4

• Power point Presentations
• Lesson:  Students were assigned to groups and created Power point presentations for a section of the chapter to be utilized as a test review. 
  
• Purpose:  To encourage the students to contribute to review activities and provide them with another avenue for test review and study skills. 
  
• Commentary:  Each group of four students was assigned a section of the chapter and asked to create a Power Point presentation as a review for that section. The students were provided with the criteria for creating their presentation and given two class hours to create the slide show.  One day was set aside for presentations.  As with the Graphic Organizers lesson the students were able to benefit from working with groups.  They were able to discuss ideas and the meaning of content with others in their group.  The students really enjoyed their presentation and did an excellent job. Copies of the slide shows were provided as review sheets for the chapter test. 
  
• Michigan Mathematics Standards: II.1.1-II.1.4, II.2.2, II.3.1, II.3.2
• NETS:  2, 3, 4, 10
• Standards Category:  1, 3, 5
  
• COATT Indicator:  A, B, C, D
• Student Artifacts: 1, 2, 3, 4, 5
  

• Communicating Mathematically
• Lesson:  The students used Microsoft Word and a set of writing standards to answer a variety of questions provided by the instructor that pertain to a range of lessons given throughout the semester.
  
• Purpose:  To improve the student ability to communicate effectively in mathematics and assess understanding of current lessons.
• Commentary:  I find it a valuable teaching and learning tool for the students to answer journal questions.  Through their writing I can effectively assess knowledge and misconceptions.  Often misconceptions become apparent in a journal question that don't always show up in a traditional testing situation.  However, the students' ability to communicate mathematically is often extremely poor.  I have a difficult time with reading work to correct it. Therefore, I incorporated into my class journal questions to be completed on Microsoft Word instead of paper/pencil. With the technology, the students could focus on the mathematics, not be concerned about neatness and spelling.  Special Education and 504 Plan students were not self conscious of writing abilities allowing them to concentrate on the content.  The students were also more likely to discuss their thoughts with others while at the computers allowing them to communicate their ideas verbally was well as written.  As an assessment I utilized the schools Language Arts Writing Rubric and tracked improvement of the students.  See Graph. 
  
• Michigan Mathematics Standards:  To communicate mathematically is part of the Mathematics Vision Statement and applies to all curriculum standards.
• NETS:  1, 2, 3, 4, 10
• Standards Category:  1, 3, 4
  
• COATT Indicator:  A, B, C, D
• Student Artifacts:  1, 2, 3
  


• Matrices and Excel
• Lesson:  The students will be provided with Cost and Revenue Tables and will enter the data into a spreadsheet, calculate profit, and reconstruct the table in matrix form.
• Purpose:  To provide students with a realistic matrix application and to learn the applications of spreadsheets in mathematics. 
  
• Commentary:  This lessons was used to provide the students with a situation where a matrix would be useful to use in business.  It also gave the students a review of MS Excel and showed a connection between mathematics, technology and business.  This lesson took one hour and the students were interested in the Excel program as well as the math.  Worksheets were provided with data tables and instructions for creating table in Excel.  The students work  included creating the tables and formulas.  The lesson is valuable in that it allows the students to relate the matrices to business.   The students saw the value in using the matrix for manipulating the mathematics, or using the excel table for with column headings for presentation.  Some students who were intersected in business and marketing found this especially useful.  The journal question assigned with the assignments incorporated H.O.T. skills and communication skills.
  
• Michigan Mathematics Standards:  I.1.2, V.1.2
• NETS:  3, 8, 9, 10
• Standards Category: 1, 3, 6
  
• COATT Indicator:  A, B, C, D


• Drawing and Interpreting Scatter Plots
• Lesson:  The students will use a Fathom computer program to create a scatter plot of data gathered through a class activity, ans will create and examine trend lines for the data as well as make predictions based on those trend lines. 
  
• Purpose:  To help students interpret scatter plots and analyze trends of data.
  
• Commentary:  This lesson followed two days of instruction where the students gathered data through an experiment and then created a scatter plot with paper/pencil.  I did not want to give up the none technology portion of this lesson.  There is value in having the students create their own plots where they have to choose values for the axises and plot the points.  With the students plots created we used Fathom to recreate the plots [worksheet] and compare the results.  Fathom was also used to develop the concept of trend lines and their usefulness.  Using the program the students were able to move around the trend line and see how the equation changes and how it affects the results of the prediction using the line.  Many students did not understand the usefulness of the trend line and the program really got the point across.  Suddenly they saw why and how it effected their answers.  Again we used a communication/journal piece to add to HOT skills. 
  
• Michigan Mathematics Standards:  II.2.1,  III.1.2, III.1.3, III.2.2, III.3.4
• NETS:  3, 8 ,9, 10
• Standards Category:  1, 3, 6
  
• COATT Indicator:  A, B, C, D
• Student Artifacts and Photos: 1, 2, 3, 4, 5
  

• Families of Functions
• Lesson:  Geometer Sketchpad will be used with a Discovery Lesson where the students will identify characteristics of function families.  Students will answer questions based on their discoveries. 
  
• Purpose:  The students will be able to categorize functions based on function characteristics and graphs. 
  
• Commentary:  This lesson worked wonderfully.  I the past this material was delivered through lecture.  This time I provided the students with a  list of equations to graph  and a chart to fill in acording to the type of graph produced.[document]  After the chart was completed the students were required to analyze and make judgments as to what was the factor of the equations causing the common type of graph.  As a closing activity they answered a journal question on MS Word, (see Algebra Communications Lesson).  The students did great with this.  They learned quickly which what the equations would look like, making the connection between the power and the type of graph.  They were interested and making predictions about how the graph would look.  They later remembered the material more completely. 
  
• Michigan Mathematics Standards:  I.1.2,  I.1.4, I.2.2, I.2.5
• NETS:  5, 8
• Standards Category:  1, 6
  
• COATT Indicator:  A, B, C, D
• Student Photos: 1, 2, 3

• Probability Internet Activity
• Lesson:  The students will use Internet web sites to define basic probability terms such as outcomes, equally likely, events, and learn how to calculate the probability of a given event. 
  
• Purpose:  To help the students discover and explore basic probability properties, terminology, and formulas. 
  
<>Commentary:  With this activity the students utilized Internet web sites to obtain definitions and examples of basic probability concepts.  Additionally, the students used a number of Java Applet sites to simulate different probability situations and answer questions regarding the activity. (See Exhibits for worksheets) Each activity and site helped the students to understand and apply the concepts of Experimental and Theoretical Probability.  Although most sites were provided to the students through links on my teacher web page, the students also had to search the web to obtain definitions that were not on listed sites.  Using the Applets for simulating probability really brought to life the lesson.  The students could immediately see the results of an experiment and how the probability is affected.  It also allowed me to incorporate the idea of the law of large numbers, without having to do it as a separate lesson, because simulations could be done quickly.  

• A consideration in managing this lesson was making sure the students were able to get to the necessary web sites quickly.  To help the students access the web sites quickly I created links to the necessary sites on my teacher web page.  However, they were still required to use a search engine for some parts of the lesson.   Another consideration was to make sure the web sites were not blocked by  the schools filtering system.  Do do that I needed to test sites in advance and ask to have a site unblocked if needed. 
  
• Michigan Mathematics Standards:  III.1.1-III.1.5, VI.1.1-VI.1.5
• NETS:  2, 7, 8
• Standards Category: 1, 3, 4, 5, 8
  
• COATT Indicator:  A, B, C, D
• Student Artifact: 1, 2, 3, 4, 5
  

• Related Rates
  
• Lesson:  The students used the Internet and a Virtual Learning Tool Question Board to pose related rates problems, answer problems and critique other students' answers.
• Purpose:  To deepen the students understanding of related rates problems and to consider the ramifications of posting information to a question or discussion board.
  
• Commentary:  Using the question board for this lesson gave me the flexibility to have the students create problems of their own and post to the board.  Creating a problem requires a better understanding of the components of the problem.  With the Question Board the students were able to look at other problems for ideas, but also had to solve some else problem.  Students were able to reply to each other about missing information, or the realism of the question.  Units became a consideration, which has never happened before.  The students started to evaluate other students problem mathematically.  The social issues involved came to light with  students who put possibly inappropriate questions up.  We discussed the appropriateness of information on the web and  stereo typing individuals and groups. 
  
• Michigan Mathematics Standards:  I.1.3 - I.1.5, I.2.2-I.2.6, III.2.1, IV.1.3, IV.1.4, IV.2.2, IV.2.3, IV.2.5, V.1.2, V.2.4
• NETS:  1, 2, 4, 5
• Standards Category:  2, 4
  
• COATT Indicator:  A, B, C, D
• Student Artifacts: Sample of Question Board


• Sketching Derivatives:
• Lesson:  This is a discovery lesson with the objective of helping the students to graphically identify the derivative of a function. 
• Purpose:  To aid the students in developing ways to identify the graphs of derivative and their functions. 
  
• Commentary:   The students have had a great deal of practice algebraically finding the derivative of different types of function.  They next have to be able to identify the derivative of a function graphically.  The students have a difficult time visualizing the function and its derivative graphically, therefore I tried having them graph function and their derivatives on Geometer Sketchpad.  They were provided with a worksheet and we discussed characteristics to focus on.  The activity went well.  For the first time the students really seemed to understand that the functions they did algebraically related to a graph.  They had to look for patterns in the results of graphing each of the function and their derivatives then identify characteristics of the two.  Discovering the information and discussing  with others helps the students retain the information better and longer. 
  
• Michigan Mathematics Standards:  I.1.4
  
• NETS:  8, 10
  
• Standards Category:  1, 6
  
• COATT Indicator:  A, B, C, D
• Student Photos:  1, 2, 3, 4, 5
  

Joanna Secco
Experienced Teacher

Roosevelt High School
Wyandotte, Michigan
Secondary Mathematics

seccoj@wy.k12.mi.us

• Algebra One
• Communicating Mathematically
• Matrix Applications
• Scatter Plots and Trend Lines
  
• Families of Functions
• Probability
  
• Geometry
• Conditional Statements & Prosperities
  
• Rigid Transformations
• Power Point Review
  

• Calculus
• Related Rates
• Sketching Derivatives
  

III. Teaching, Learning, and the Curriculum.
Teachers implement curriculum plans, that include methods and strategies for applying technology to maximize student learning.

Teachers:

1. Facilitate technology-enhanced experiences that address content standards and student technology standards.
   
2. Use technology to support learner-centered strategies that address the diverse needs of students.
   
3. Apply technology to develop students' higher order skills and creativity.
   
4. Manage student learning activities in a technology-enhanced environment.