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Math Lab 5 Lesson Plan : )



Math Lab 3


 * Reflective Paper **

 At Foshay Learning Center, Mrs. Christman has a daily routine for the three different courses she teaches. Through her routine she incorporates different learning theories in her instruction.

 At the beginning of the period, she will have two to three problems based off her students’ homework from the previous night. The students work on these problems individually while she walks around and checks their homework. She stamps their homework calendar if the problems from their homework have been attempted and completed, with the necessary work shown. After she finishes, she collects the homework and assigns students problems from the work to be completed on the board. The students who are assigned those problems also have to present how they solved the problems to the class. During these presentations, my teacher will provide positive feedback with comments such as “good job” and “very nice work” or if there is an error, ask the student or the class if they can find the error and has them correct it. Once classroom presentations are over, she will have the students take notes on the new material. Her lecture will last about 20 minutes and is strictly teacher based. There are no questions presented to the students to engage them through the learning of the new material. After Christman has completed a few practice problems herself, she will ask the students to try a couple on their own. During this time, she might have the students work with their neighbor if they have difficult or she will circle the room to address individual questions. She will ask for student volunteers to tell how they solved the problems as she writes them on the board. The period is close to being over at this time, so to end she will either do a variety of things. She will either asks the students to write on their notes a response to a question relating to the new material or old material, provide last minute comments about a previous or future assignment, or she will encourage them to make sure they stay on top of their work and complete their assignments.

 Through observation, Christman incorporates several theories into her teaching practices. On a daily basis, Christman is encouraging her students to do the assigned work and put the effort into their work. She communicates high expectations but also gives her students adequate scaffolding when it comes to learning new material. Through these teaching implications she is using Constructivism. Christman also uses Developmental theory through modeling prosocial behavior by showing her students how to complete problems based on new material (Ormrod, 2011). She also asks her students to explain their answers during class presentations. She also incorporates Social Cognitive Theory during class presentations because she shows successful peer models when they present their assigned problem. She will say ‘does everyone see what [this student] did?” so promote either a common error made by all the students or a good point in a student’s work. She allows her students to work with each other during class work problems. This process incorporates Sociocultural theory because she will give them tasks that fall within their zone of proximal development and gives them the opportunity to use surrounding students to help each other in solving the problems.

 Through her daily routines, she is able to keep the students focused on a method of doing mathematics. She does not stray from the usual because of the possibility of concepts being lost in instruction or lack of focus from her students. The strategies that she is currently using have been effective according to Mrs. Christman in getting the information across to her students and them being able to show understanding of the material (personal communication, October 20, 2011).

//Standard 1.0 - Solving equations and inequalities involving absolute value//

**References **

Christman, J. (2011, October 20). Interview at //Foshay Learning Center//.

Ormrod, J. E. (2011). //Educational Psychology: Developing Learners// (7th edition). Boston, MA: Pearson.


 * Reflective-narrative Paper **

What I value in teaching is that my students are learning the material, not just memorizing it. I feel that if students can communicate effectively with one another about a particular topic then they have understood the material. If they can show that communication on paper through completing problems then they have learned the material. I feel that those values are demonstrated in the assessment tools I have chosen. I feel that if students can communicate their thought process into words then they logically understand what they are doing. If they can communicate with each other when working in pairs or in groups then they are learning. For example, if one student can explain or teach to another student how to apply a concept and then that student can answer a question based off of what the other said then they have understood the material. From the sample work I have gathered I feel that my values are represented in how I chose to create the different assessments presented in the following Math Lab. I feel that through journals and observations the students’ understanding can be assessed by a teacher. Of course you have the standard written exams which only determine if they get the problem right of wrong; through these other methods of assessment one can see if they indeed understand what they are learning. The written test can then be a supplement to the other assessments (which might just represent that a student understands the process and possibly made a small error in their work). For a student to be able to leave the classroom having learned something and not just memorizing it shows a great deal on their part and also the teacher.

**__Homework Review Rubric __** Total Grade: __/9
 * Assessment #1 **
 * || <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">Understanding || <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">Accuracy ||
 * <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">Scale || <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">80% || <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">20% ||
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">3 points __ || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Student shows sophisticated understanding of how to solve equations with absolute value. || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Supportive work shown with no errors present. ||
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">2 points __ || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Student shows solid understanding of how to solve equations with absolute value. || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Show a great deal of supporting work along with answers with minor mistakes present ||
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">1 point __ || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Student shows little understanding of how to solve equations with absolute value. || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Show minimal supporting work with major mistakes present or no supporting work shown. ||
 * __<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">0 points __ || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Student does not attempt the problem. || <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Student does not attempt to solve problem. ||
 * <span style="display: block; font-family: 'Times New Roman','serif'; font-size: 16px; text-align: center;">Comments ||  ||   ||
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assessment #2: Journal Entry **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">In the past when I have taught math classes I have had my students keep a journal. These journals were called “POD” notebooks. P.O.D. stood for “Problem of the Day” so this is where they did they daily warm ups as well as reflections. For my second assessment instead of given them a homework review, I would have them respond to one or all of the following prompts:

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Write in words and complete sentences the process of solving an equation with an absolute value symbol.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Write an equation that has only one solution.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Write an equation that has any solution.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Write an equation ONLY that has no solution. Do not solve.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Write why you have to check your solutions.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Through the first prompt, students are explaining in words how to solve an equation with absolute value. For students who struggle with completing the mathematics computation, this will give me the opportunity to see if they understand what they should do but just cannot physically do the calculations. Through the second and third prompt, I would be look for an original equation that responds to the prompt and to see if the students indeed know when they will only have one solution or any solution. For the fourth prompt, I will be looking for an original equation without the supporting work. When an equation with absolute value has a negative number on the other side of the equation and just the absolute value on one side, there is no solution and I would hope that my students can recognize when they can put no solution and not have to worry about solving the entire inequality. For the last prompt, I would look for student’s responses to include something dealing with extraneous solutions or not every number will make the inequality true. I would use this as an exit slip for the students and it will give me an idea of who really understands the material, who is thinking on a higher level, and who might need a little more work. These prompts would be graded as either a check for completion, a check plus for excellent responses, or a check minus for incorrect responses or lack of explanation.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Assessment #3: Observations with checklists **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Through this assessment I would put the students into pairs with 5 sample problems to work on. As I walk around I would have a checklist with me to see if the any of the following topics or comments come up while the pairs are working regarding the problems.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">If there is a negative on the other side of the equation, then there is no solution.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">If the equation has a zero on one side, then there is only one solution.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">You need to write two equations when there is an absolute value because it could negative or positive.

- <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">You have to check your answers to make sure that both work (or there aren’t any extraneous solutions)

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">If the pairs have talked about or mentioned all of the four above points, then I would award them with a 10 for having mentioned the above points. If students are able to recognize the above points then the rest is basic algebra to solve. Afterwards I would collect their papers and give them a grade based on how many they got right and wrong for a total of 15 points (one point for each of the five problems). The main focus is on the understanding of the process so that is why the conversation and team work is weighed more than the actual problem itself.

**<span style="font-family: 'Times New Roman',Times,serif;">Excel Chart and Graphs **
===<span style="font-family: 'Times New Roman',Times,serif;">The following represent each individual question and the percentage of students who got 0 points, 1 point of 2 points. As you can see from the graph more students received the full amount of points (2) on problem 1 while in problem number 2 students struggled the most, only receiving 1 point. Problem 3 was fairly even on the number of students who received full credit and those that received partial or no credit. ===


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">NCTM 6 Assessment Standards – Reflective Narrative **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> I feel that each of my assessments address the standards fairly well. When I look at the three assessments I designed I feel that they all measure the mathematics to some extent. I feel the rubric and the observation/checklists activity measures the mathematical computations so I can see who can apply the concepts to particular problems. I feel however that all three measure the mathematics as a whole. The reason I say this is because through each you can hope to observe the thought process of how students are thinking about solving equations with absolute value. I feel that each method is fair in assessing a student. Not only does it take the written work of a student but also the communication made between two students (through observations) and also how they are thinking about the material and seeing how they think to solve a problem (through journal entries). These cover the Mathematics and Equity standards found in the National Council of Teachers of Mathematics Six Assessment Standards.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;"> As for the Openness standard, the rubric will be available to students before they complete the assignment. This way, students will know what they will be graded on. Also, if necessary, when a parent is questioning why a student scored a particular way, I can present the rubric to them and explain how and why a student received a particular score. For the observations, I would let the students know that I hope and expect to hear conversations that are focused on the material and how to solve the problems they are assigned. By vocalizing what is expected students can know or adjust their conversations to fit such expectations. For the Inferences standard, I feel that each assessment is well-rounded. One is about how they can perform and be detail about their approach (rubric). Another is how they can effectively communicate individually key concepts about equations with absolute values (journals). The last method promotes dialogue between students and an opportunity to express vocally how they understand how to set up and solve a problem (observations).

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">I feel that if all three of these are met at a high level, then students deserve to move on to the next level. If they falter in one or more areas then it is up to the teacher to recognize where the lack is and do whatever is necessary to fix it before a bigger assessment takes place. By doing so the Learning standard is used so that teachers can determine gaps in understanding and target those areas for intervention when making instructional decisions. If all these standards can be met then the Coherence standard has been accomplished as well since it is an accumulation of all the standards.


 * <span style="font-family: 'Times New Roman','serif';">UbD Assessment Matrix **

<span style="font-family: 'Times New Roman','serif';">Evidence: Detailed work with all steps shown with accuracy playing a key role in assessing. || <span style="font-family: 'Times New Roman','serif';">Chapter 7 – details of understanding <span style="font-family: 'Times New Roman','serif';">Chapter 8 – presented criteria and validity || <span style="font-family: 'Times New Roman','serif';">Application || <span style="font-family: 'Times New Roman','serif';">Valid <span style="font-family: 'Times New Roman','serif';">Reliable <span style="font-family: 'Times New Roman','serif';">Sufficient || <span style="font-family: 'Times New Roman','serif';">Accomplishes understanding of how to apply the information learned. || <span style="font-family: 'Times New Roman','serif';">Evidence: Effective communication of response to questions with particulars as mentioned in the assessment rundown. || <span style="font-family: 'Times New Roman','serif';">Chapter 8 – validity of responses in understanding the material <span style="font-family: 'Times New Roman','serif';">Chapter 9 (Brahier) – assessors role and variety of assessment strategies || <span style="font-family: 'Times New Roman','serif';">Explanation <span style="font-family: 'Times New Roman','serif';">Interpretation <span style="font-family: 'Times New Roman','serif';">Empathy <span style="font-family: 'Times New Roman','serif';">Self-Knowledge || <span style="font-family: 'Times New Roman','serif';">Valid <span style="font-family: 'Times New Roman','serif';">Reliable || <span style="font-family: 'Times New Roman','serif';">Accomplishes how to communicate concepts through written responses. || <span style="font-family: 'Times New Roman','serif';">Evidence: Communication between the student pairs with mention of particulars as mentioned in the assessment rundown. || <span style="font-family: 'Times New Roman','serif';">Chapter 8 – validity of communication between students. <span style="font-family: 'Times New Roman','serif';">Video Workshop (Teacher Insights) – monitor student conversation for quality of work. || <span style="font-family: 'Times New Roman','serif';">Explanation <span style="font-family: 'Times New Roman','serif';">Interpretation <span style="font-family: 'Times New Roman','serif';">Application <span style="font-family: 'Times New Roman','serif';">Perspective <span style="font-family: 'Times New Roman','serif';">Empathy <span style="font-family: 'Times New Roman','serif';">Self-Knowledge || <span style="font-family: 'Times New Roman','serif';">Valid <span style="font-family: 'Times New Roman','serif';">Sufficient || <span style="font-family: 'Times New Roman','serif';">Accomplishes how communication between others can be helpful and a way to assess knowledge instead of through just strictly a written response. ||
 * **<span style="font-family: 'Times New Roman','serif';">Key Design Questions **
 * <span style="font-family: 'Times New Roman','serif';">What is the evidence of the desired results?
 * <span style="font-family: 'Times New Roman','serif';">In particular; what is appropriate evidence of the desired understanding? || **<span style="font-family: 'Times New Roman','serif';">Chapters of the Book **
 * <span style="font-family: 'Times New Roman','serif';">Chapter 7 – Thinking like an Assessor
 * <span style="font-family: 'Times New Roman','serif';">Chapter 8- Criteria and Validity
 * //<span style="font-family: 'Times New Roman','serif';">Other resources // || **<span style="font-family: 'Times New Roman','serif';">Design Considerations **
 * <span style="font-family: 'Times New Roman','serif';">Six facets of understanding
 * <span style="font-family: 'Times New Roman','serif';">Continuum of assessment types || **<span style="font-family: 'Times New Roman','serif';">Filters (Design Criteria) **
 * <span style="font-family: 'Times New Roman','serif';">Valid
 * <span style="font-family: 'Times New Roman','serif';">Reliable
 * <span style="font-family: 'Times New Roman','serif';">Sufficient || **<span style="font-family: 'Times New Roman','serif';">What the final Design Accomplishes **
 * <span style="font-family: 'Times New Roman','serif';">Lesson (unit) anchored in credible and useful evidence of the desired results ||
 * <span style="font-family: 'Times New Roman','serif';">Assessment 1 (Rubric)
 * <span style="font-family: 'Times New Roman','serif';">Assessment 2 (Journal)
 * <span style="font-family: 'Times New Roman','serif';">Assessment 3 (Observations and Checklist)

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">After completing the analytic rubric and compare the data on the original grading scale to the one using the rubric, there was greater achievement with the original grader results than from the rubric. What I noticed is that the original grader assigned one point for anything that was not almost perfect. That included attempting the problem (whether on the right track or not), solving for one equation and not two, forgetting to changing the sign of the constant, etc. In the analytic rubric, one point was assigned for attempting the problem, however two points were assigned if the students remembered to write two equations but either not solving correctly or not setting up the second equation correctly. However the results did show a higher percentage of success with student who knew that they needed to have two equations (however setting them up incorrectly). I feel the rubric shows more of an achievement in the standard of being able to solve equation involving absolute values. This shows that student knew that two equations are necessary however re-teaching is needed to correct the errors that they originally made. Also, the original grader gave full credit for problems that were not completely correct. For example, if the student added instead of subtracted a number, the original grader assigned full credit. However in the analytic rubric two points were assigned for students who made this error. I feel that allowing students to think that they are 100% correct when they are not can cause an equity issue. This could lead to the same errors being made later throughout the academic school year and resulting in a much greater penalty, say on a final examination. With that being mentioned, I feel that in the long run, greater achievement of the standard is seen through the rubric because not only does it allow students to see where and why the received the grade but it also allows for the teacher to recognize and highlight what they might need to go back over later.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Gap Analysis **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Grade Book Example **

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">The electronic grade book that I plan on using is Easy Grade Pro. I have used Easy Grade Pro in the past and it is an excellent electronic grade book. I can insert students names and keep record of their turned in and missing assignments. I can also keep track of their attendance through Easy Grade Pro. When I want to print out their grades, it allows me to do so by category (tests, homework, class work, etc.), individually (by student) or as a whole class by their student ID numbers. Easy Grade Pro also allows me to insert the weight of each assignment and it does the calculations for me whenever I insert an assignment. For example, if tests are worth 70% of their grade and homework is worth 30%, I can label an assignment as homework and it will weigh it appropriately to the rest of the grades that particular student has.