Stage 4 (Final Project Report )

 This report will present a detailed description of my project related with the three major changes in my assessment practices.

Through the item analysis on Quadratic Functions, I hoped to attain a better understanding of student knowledge gaps. This helped me in two ways. After returning the work to my students, we went over the problems with the most number of incorrect answers. We then reviewed the problems, and they were able to determine what they had done wrong. I also noticed that one of the questions had almost no right answer from my students. I looked at that question and I did not see anything wrong with it. I tried solving the problem myself and realized that the answer provided by the test editor was incorrect. Students pointed it out to me too. I have never checked the answers from these tests, because I thought the publisher should be authoritative. The last part of this assessment was the retaking of an equivalent test the next day. This reassessment showed improvement in scores, but the improvement occurred mostly for the students who do well in my math classes.

The second change I made was that I began pre-assessing the required skills for newly taught lessons by using open-ended or short answers assessments. A pre-assessment reveals what needs to be covered before new lessons. This can help discern the amount of teaching time allotted for each topic.

The last change was in the manner I assessed trigonometric functions. A formative open-ended assessment was replaced with a complex performance. Students were required to graph the trigonometric functions, sine and cosine. After graphing, they had to use their graphs for establishing new values for the above functions. Detailed directions were given for setting up the graph window and locating the new values, as students were unfamiliar with this kind of graphing calculator. Students also wrote a reflection about the difficulties they encountered, and what they learned while working on the project.

A summative multiple choice test was replaced with six essay questions. Students had to explain how they recognized the specific sides of a right triangle, decide on the trigonometric function to be used, discuss the applicability of trigonometric functions in the real-world, and finally to create a real-world problem that requires the use of a trigonometric solution.

Because our school’s administration wants writing to be integrated into the math curriculum, these new assessments required the creation of two rubrics. Therefore I had to use a rubric for math knowledge, and another to address writing mechanics. The first assessment also contained a rubric for the quality of their reflections as well.

The reflection revealed that students:

·        helped clear-up graphing problems from the past due to this hands-on assessment.

·        would use this graphing calculator in the future assignments and other graphing-related projects.

·        preferred the visual computer-based assessments to the traditional graphing paper and pencil assignments.

My direct observation was that students needed more practice in answering and writing essay questions into well-developed sentences. Students might have had creative ideas, but their responses were simplistic. This proved to be consistent in all of their assessment reflections. On the other hand, their writing mechanics were generally very good.

What I learned while working on this project

1. While using the item analysis, I determined that:

• all given tests should be checked by the teacher prior to administration, because often textbook questions may prove to be confusing for students. Instructions may not be clear, and teachers can clarify these issues before students begin the exam.
• I should never assume that the book’s assessments and answers are always right. I discovered that through checking the assessment problems in advance, I can correct the mistakes and retain the validity of the test.
• increasing the feedback helps students mostly if they use it after feedback was given, and not by just letting them know what was wrong in their work. That happened when an equivalent test form was given to students after the item analysis.

2. Pre-assessment is an important aspect for teaching math skills. I learned that I should never assume students have the necessary knowledge for new topics. A short open-ended quiz reveals whether I need to spend more time on reviewing the skills needed for new topics. Open-ended assessment is preferable to multiple-choice quizzes, because guessing can be an influential factor. In this way, students become familiar with the required terminology and procedures, and this helps remove the effects of their previous knowledge gaps. Through this, I also learned that students become more involved in the learning process and are less likely to become passive and eventually give-up.

3. From my changed assessments I learned that:

• by developing a scoring rubric, students can see what is expected from them in order to earn a high or low grade, and improve their own self-assessment methods.
• other teachers will be able to make suggestions for rubric improvement.
• I should not assume that students can determine on the manner in which to perform the assessment. Ample and sequential directions must be given to students, especially when the assessment is of a new kind.
• the time bestowed for the completion of assessments should be taken into consideration, because the intent is to measure their math knowledge; not how fast they solve the problems.
• time pressures lower the assessment’s validity.

4. Student reflection could bring viable suggestions for needed assessment changes and improvement. Once these suggestions are implemented, students feel that they have a say in their assessment process and take more responsibility for their learning.

Things I would do differently

1. I would perform a second item analysis after the reassessment. This should prove if the first analysis helped, especially for those questions with a small number of correct answers, or whether or not the improvement occurred due to other reasons.

2. I would check the assessment before it is given to the students, so mistakes can be removed and clarifications made.

3. I would explore other methods to use, other than open-ended quizzes, to predetermine student mathematical abilities and knowledge for new topics.
    
4. I would add a few problems from the new topic into the pre-assessment to check for the likely probability of student knowledge and accordingly incorporate it in my teaching practices.
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5. I would go over the use of the graphing calculator utilized in Graphit before giving the assessment. Many of the students had problems with basic PC skills and wasted time setting their graph’s window.
    
6. If possible, a practice similar to the assessment should be given to students before the assessment, so they would be familiar with a new test format. I would also create a display of exemplary student work and projects.

Questions

While working on this project I had difficulties with:

•  establishing realistic time limits for new assessments. I would like to attain some feedback from other teachers on methods to determine appropriate time limits for assessments to ensure that they reveal what students actually know.

• acquiring a full understanding of the necessary skills needed for a new lesson. I would like to receive some feedback on how to handle  this problem and also how to spend the least amount of time for this issue.

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