Cynthia's+Page

Go Back Home OR Continue to Dina's Page =Cynthia's Math Lab 3=

**Reflective Paper** Observation Strategies
Since I am observing in two different rooms, I will write on both observations because they were so different. My first observation was in the Algebra Readiness class where two-thirds of the students are English language learners. The teacher even informed me that the class I was observing was her lowest achieving class of all her classes. Although the teacher is using high tech tools to teach her lesson, she in a sense is teaching her students in the traditional way, just giving out information as the students copy what is being presented. Brahier defines this way of teaching as deductive teaching, “where a teacher states a rule or definition and then expects the students to apply it” (Teaching Secondary and Middle School Mathematics, 2009, p. 63). While going over the new material, many of the students said they did not understand, yet she continued with her lesson. There were two students who understood the lesson and answered every one of the closed questions she asked. After the lesson was taught she told her students to begin their homework, with no talking. Several students had questions concerning their homework, but the teacher did not want to go over them then, she asked the students to come in at lunch or after school. The learning strategies I observed in this class were limited and probably more old school techniques than anything. The second teacher began her lesson with a couple of problems which reviewed the material from the night before. These problems were carefully selected, because she used them as scaffolding for her upcoming lecture. She led into her new lesson on identifying functions with four problems on the overhead. These problems showed the different ways ordered pairs could be displayed: tables, mapping, ordered pairs, and graphing. As she taught her lesson she would draw names of her students from popsicle sticks in a container and ask her students individual questions. After the lesson was taught she cued her students to “now show me what you know”, as she stated this, all students picked up a white board next to their desk and sat quietly ready to work. The teacher showed four more problems on the overhead and the students began to solve the problems. The teacher then informed the students they had five minutes to work on the problems, after the allotted time she glanced over all the white boards to make sure all students had the correct answers. The students then were instructed to begin their homework. The dialogue and questions were specific to find out if the students knew the material. The ideas and applications helped the students connect to the material (Brahier, 2009). Most importantly the students, unlike the first class, were involved and participated throughout the period. =__Part 2:__= =**Reflective**= I place a high value on knowing and understanding mathematics, because knowing and understanding mathematics will open many doors of opportunities. As a high school student, I was limited to career choices because I was a girl. This restricted me to what classes I could take in high school. My options were nursing, teaching, and clerical. I gave clerical a try and failed, because I did not know how to spell. I had no interests in teaching (one would have to spell!) or nursing (one would have to know math!). The only math I took in high school was basic math. Several years later, I found I had an interest in the technical things and started taking engineering courses at the local junior college. Needless to say, I had to start with basic classes, classes I should have had in high school but did not. Working full time and going to college, it took me ten years to earn my AA in mechanical engineering. This was a long and tiring process and if I am able, I like to encourage young people to consider their tomorrows. When I was teaching at the private high school I brought in college catalogs for the students to look through. I shared with them the many options and classes that will open up to them when they start college and I also showed them the prerequisites needed to take the majority of classes. Most often than not, English and math were the requirements needed in order to take classes. Plus, both are needed to graduate. I also like to share my life experience with students because although I struggled in most of my classes, I enjoyed math because I had a goal to obtain. Through hard work and time, I was able to learn and achieve in a subject most people try to avoid. So, in my teaching and assessment, I want my students to know math is a very important subject. I want to make sure they are not only getting the problems right, but have an understanding of why the problem is right. If the concepts are understood students will be able to use their knowledge as a foundation for further knowledge. In my assessment of the Line Design, I want the students to understand the concept in more than one way, to be able to work from a line to an equation and from the equation to the line. Although this sounds like an easy concept to learn, this was one that caused me much difficulty in my schooling, and I know it is a struggle for many other students. ** Line Design ** Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Interpret the equation //y// = //mx// + //b// as defining a linear function, whose graph is a straight line. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
 * Standards ** :

A student will understand the concept 1) if given 2 points on a line an equation can be found by using the point-slope formula and can be rewritten in standard form. 2) An equation in standard form can be rewritten in slope-y-intercept form to draw a line 3) function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range.
 * Goals: **


 * Lesson Plan ** : (students will work in pairs)


 * 1) Students will make a line design on a coordinate plane. The design must have at least 7 lines with a minimum of one horizontal lines and one vertical line.
 * 2) Students will identify and label the intersection of the lines with ordered pair in the form of ( x, y ).
 * 3) Using a pair of ordered pairs from the same line; students will find the equation for that line using the point-slope formula. The equation will then be placed in standard form.
 * 4) Domain and ranges will be found for each equation and will be written in the form of an inequality.
 * 5) To check-the students will exchange equations and then rewrite the equations that are in standard form into slope-intercept form. Using this equation the students will graph their equation on a coordinate plane. They will then check their lines with their partner’s original drawing.
 * 6) Domains and ranges will be checked using the inequality and plugging in a lease 3 //x// values, one minimum, one greater, and one within range to see if this matches the given segment.
 * 7) The student will then trace their segment drawing using a light board (or window) and then creatively detail their drawing anyway they want.
 * 8) All papers will be turned in as a packet in the following order: Final drawing is neat and efficient with all papers neatly presented in the following order: Original line design, segment drawing, point-slope equations, domain/ranges, equations in slope-intercept form, and the equations drawn on graph paper
 * 9) Following questions will be answered and included in project:
 * 10) What part of the assignment came easy for me?
 * 11) What part of this assignment was difficult for me?
 * 12) What new concepts did I learn?
 * 13) If I were to do this project again, what would I do differently?
 * 14) Give a real-life situation can relate your project to?
 * 15) How would you grade your effort on this project 1-10, 10 being the highest score.

=__Part 3:__ = =Assessment 1 Analytic Rubric = = =

** Rubric Assessment: ** Students are to prepare their Line Design project according to the rubric. Total weight 100%.
(which could be a line) || The student efficiently and accurately identified all line intersections with an ordered pair in the form of ( x, y ) || Students will create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Equations of all line segments have been correctly identified using the point-slope formula and are in standard form || Students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. The domain and ranges of all equations are accurate and in precise format || To check equations students will Interpret the equation //y// = //mx// + //b// as defining a linear function, whose graph is a straight line. All equations have been accurately checked by rewriting them in slope-intercept format, graphed on a coordinate plane, and compared to original drawing || Final drawing is neat and efficient with all papers neatly presented in the following order: Final drawing, Original line design, segment drawing, point-slope equations, domain/ranges, equations in slope-intercept form, and the equations drawn on graph paper. Required questions are answered correctly using academic language. ||
 * Weight ||  Line Design   10%  ||  Segments   10%  ||  Equation   20%  ||  Domain & Ranges   10%  ||  Equation Check   20%  ||  Final Package   30%  ||
 * 3 || The student carefully produced a creative and neat line design on a coordinate plane following the precise directions of having a minimum of 7 lines, with at least one being vertical line and one being a horizontal line. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve
 * 2 || The student made a line design following the defined instructions of having a minimum of 7 lines, with at least one being vertical line and one being a horizontal line. || The student labeled some of the line intersections with an ordered pair in the form of ( x, y ) || Equations of all line segments have been found using the point-slope formula, but are not in standard form || All domain and ranges have been identified but are not in format || At least 5 of the equations have been rewritten in slope-intercept form and checked with the original drawing || Final drawing is neat and efficient with papers not presented in the accurate order. Questions answered but no using academic language. ||
 * 1 || The student drew a line design with a minimum of 7 lines || The student did not label any of the line intersections || Equations have not been correctly formulated nor placed in standard form || Domain and ranges are not correctly identified nor in the accurate format || Less than 5 of the equations have been re-written in slope-intercept form and checked with the original drawing || Care has not been taken in the production of the final drawing nor the package complete. Questions have not been addressed. ||
 * Total ||   ||   ||   ||   ||   ||   ||

=__Part 4: __= =Assessment 2 =

**Portfolio Assessment**** : ** Students are to prepare their Line Design project according to the listed instructions. Project is to be presented in a folder. Total point value 100 pts.
= = 1) Using graph paper make a line design using a minimum of 6 lines – more may be used ( at least one horizontal and one vertical line must be used ). Number each line. ||  10  ||   || 1) Using a sheet of notebook paper neatly write out an equation for each line from the line drawing (match numbering with its line) 2) Using point-slope formula to find the equation of the line. 3) Place equation in standard form. || 20  ||   || = =
 * Section ||  Possible Score  ||  Score  ||
 * Line Drawing
 * Segment drawing
 * 1) Label were lines intersect with a set of ordered pair ( x, y ), defining your drawing ||  15  ||   ||
 * Line equations
 * Domain and Ranges of all lines
 * 1) Find the domain and ranges of all lines set as an inequality. ||  15  ||   ||
 * Check equations and Domain/Ranges
 * 1) Rewrite all equations in slope-y intercept form and graph on another sheet of graphing paper.
 * 2) Check against original line design. If there is a discrepancy, correct either line or equation.
 * 3) Plug in 3 values for //x// to test domain and range inequality. A min/max/ and one within range, compare findings to segment drawing for correctness. ||  10  ||   ||
 * Color design
 * 1) Using plain paper trace segment design and color, detailing final picture ||  15  ||   ||
 * Portfolio
 * 1) All papers neatly in order with a title page, project papers, and index
 * 2) Answer questions regarding project.
 * 3) Place project in a folder. ||  15  ||   ||

=__Part 5: __= =Assessment 3 = = =
 * Presentation:** Students to create a line design according to the listed requirements and then present their project to the following requirements.
 * **Category** ||  **Scoring**  ||
 * **Introduction**: Project is clearly introduced with: procedure, standards meet, and by showing illustrations || (20 pts) ||
 * **Content:** Each section is presented describing the necessary steps to complete the required project. Academic language is used to define and direct presentation. || (20 pts) ||
 * **Presentation**: Clear and precise. Timing within range, voice projected. || (20 pts) ||
 * **Responses**: Answered and responded to questions quickly and efficiently || (20 pts) ||
 * **Member of the audience**: Gave peers respect, listening quietly during presentation and participating politely to peers projects. || (20 pts) ||
 * || Total points ||

=__Part 6: __= =Excel chart/graph = = = = =
 * Algebra 1 Line Design Project ||
 * Name || Line Design || Segment Dwg || Equation || Domain/Ranges || Equation Check || Final Pkg ||
 * Score || 10 || 10 || 20 || 10 || 20 || 30 ||
 * Ben || 10 || 10 || 17 || 9 || 18 || 28 ||
 * Matt || 9 || 9 || 16 || 9 || 18 || 27 ||
 * Katie || 10 || 10 || 20 || 10 || 20 || 30 ||
 * Sam || 10 || 10 || 19 || 9 || 19 || 30 ||
 * Becca || 8 || 8 || 14 || 8 || 17 || 27 ||
 * Caleb || 7 || 7 || 14 || 8 || 17 || 26 ||
 * Danny || 8 || 8 || 18 || 9 || 17 || 28 ||
 * Sheri || 10 || 10 || 18 || 10 || 20 || 30 ||
 * Lexi || 9 || 9 || 17 || 9 || 18 || 28 ||
 * Logan || 10 || 10 || 20 || 10 || 20 || 30 ||
 * Matti || 9 || 9 || 16 || 9 || 18 || 28 ||
 * Traci || 10 || 10 || 19 || 10 || 19 || 30 ||
 * Total || 120 || 120 || 228 || 120 || 241 || 372 ||
 * Category ||  || Student Total || Score of 100 ||   ||   ||   ||
 * Line Design ||  || 120 || 170 ||   ||   ||   ||
 * Segment Drawing || 120 || 170 ||  ||   ||   ||
 * Equation ||  || 232 || 240 ||   ||   ||   ||
 * Domain/Ranges || 120 || 170 ||  ||   ||   ||
 * Equation Check || 241 || 340 ||  ||   ||   ||
 * Final Pkg ||  || 372 || 360 ||   ||   ||   ||
 * Equation Check || 241 || 340 ||  ||   ||   ||
 * Final Pkg ||  || 372 || 360 ||   ||   ||   ||



= = =__Part 7:__= =**NCTM 6** **Assessment Standards**= Since I believe my rubric is the best way to assess my project, I am going to use it to evaluate the NCTM standards. It is difficult for some students to understand the concept  of finding an equation from 2 points on a line using  the point-slope formula and then rewriting it in standard form, to rewrite an equation in standard form into slope-y-intercept form to draw a line, or to learn know that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. This project and its assessment will assure that the students are able to make the connection between the concepts. These are critical math concepts that will be used as scaffolding for future math instruction and be revisited in future test materials for class placement, college entrance exams and job employments. The assessment restates the goal of the lesson and the math standard to be learned. By using the rubric, students will be able to evaluate and assess their work before it is turned in for a grade. Students will also be able to apply what they have learned by applying it to a real world situation when they answer the guiding questions. Students are allowed to work in groups; working together will assure that both students understand the math concepts involved and how their work will be assessed. Students are given the opportunity to do their best work by following the rubric’s structure and to know the minimum amount of work required for a passing grade. By following the rubric parents will be able to help their children work on all elements of the assigned project. The rubric also gives all students the ability to work in their different strengths by offering a variety of assessment strategies in the rubric. For this rubric students and parents were not invited to participate in its creation. In the future, it would be beneficial for all to have them help in the designing of the rubric. This will assure that all involved understand what is required in the project. <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The evidence provided from the assessment is broken up into six segments of the total package. Under each section criteria is listed as to what is required for each of the three divisions of scores. This will assure there is no bias involved in the grading system. <span style="font-family: 'Arial','sans-serif';">The assessment uses the state standard and states the goal of the lesson. Students will know by following the rubric to create their project they are fulfilling the required state standards.
 * <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">The Mathematics Standard **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The Learning Standard **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The Equity Standard **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The Openness Standard **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">The Inferences Standard **
 * <span style="font-family: 'Arial','sans-serif';">The Coherence Standard **

=<span style="color: black; font-family: 'Times New Roman','serif';">__Part 8:__ = =<span style="color: black; font-family: 'Times New Roman','serif';">UbD Assessment Matrix = The students will produce a project displaying the concepts they learned. This includes a line design with equations. Also included is the checker’s revised equations and graphed solutions. Answers to the guided questions will also show understanding of project. Students can create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Students can interpret the equation //y// = //mx// + //b// as defining a linear function, whose graph is a Students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain with exactly one element of the range. || **Explanation** Students will be able to analyze and explain the relationship between a line and an equation, ordered pair and a line. They will also be able to justify the domain and range of a given line segment and how to predict if an equation matches a given line || **Valid** The rubric for this assignment measures what the standard states as important and valid information. The evidence is the proof the goal was reached in using this assessment. || **Accomplishments** A student will understand the concept 1) if given 2 points on a line an equation can be found by using the point-slope formula and can be rewritten in standard form. 2) An equation in standard form can be rewritten in slope-y-intercept form to draw a line 3) function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. || The students produced a project displaying the concepts they learned. This includes a line design with equations. Also included is the checker’s revised equations and graphed solutions. Answers to the guided questions of the project. Students made a graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Students used equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Students used the equation //y// = //mx// + //b// as defining a linear function, whose graph is a Students understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain with exactly one element of the range. || **Application** Students show their knowledge and skill in following the given instructions as outlined. || **Sufficient -** The portfolio assessment is sufficient to produce the minimum of what is required in the desired standard, but does not guarantee adequate assessment to be reproduce the required results over time or for understanding of the concepts used. || **Accomplishments** If the students followed the given directions they will have created an eye appealing project where they used the formulas: Slope-intercept, point-slope formula, and the inequality for domain and range. || Students presented their line design project in a clear and concise manner. Students displayed project for peers to analyze. Students paid attention to their presentations of their peers and asked questions pertaining to the project. || **Interpretation** Students show their ability to interpret the assignment with the given instructions. Translating their project into a display for a presentation for their peers. || **None** The presentation does not offer valid, sufficient, nor reliable assessment which is demanded to meet the given standard. || **Accomplishments** Students will share their line design project by presenting it to the class and answering the guided questions at the end of the instructions. ||
 * **Key Questions:**
 * **What is the evidence of the desired result?**
 * **In particular; what is appropriate evidence of the desired understanding?** || **Design Considerations?**
 * **Six Facets of understanding** || **Filters (Design Criteria)**
 * **Valid**
 * **Reliable**
 * **Sufficient** || **What the final Design Accomplishes**
 * **Lesson (unit) anchored in credible and useful evidence of the desired results** ||
 * **Rubric**
 * **Portfolio**
 * **Presentation**

=__<span style="color: black; font-family: 'Times New Roman','serif';">Part 9: __= =<span style="color: black; font-family: 'Times New Roman','serif';">Gap Analysis = = = <span style="color: black; font-family: 'Times New Roman','serif'; font-size: 16px;">There is a gap of understanding when comparing the student work samples with the listed assessments for this project. By following the modeling of the teacher’s examples on how to work on the problems and construct the line design, the work samples and scores demonstrate how well the students followed directions. The concept of understanding was never assessed. Because the instructions an assessment much like the one above there is no way of knowing if the lesson was taken to the level of understanding. = =

= = =__<span style="color: black; font-family: 'Times New Roman','serif';">Part 10: __= =<span style="color: black; font-family: 'Times New Roman','serif';">Gradebook Example =

=
RenWeb [] When I was teaching the school used RenWeb. It was very efficient and easy to use. Each year the teachers created their grade books and weighted them according to their grading system. RenWeb offered many options many I did not even use for my grading. I will list a few to give an idea of what was available: one was an area where a teacher could input a test, quiz, or assignment for the student to take at home after they logged on to the system. Another was a seating chart where attendance could be taken, or a table where students were listed in alphabetical order. The students profile was included with phone numbers to parents and other essential information. In the grade book there was a comment area where the teacher could reply to an assignment, often times the parents knew grades or comments before the students made it home from school.=====