Abstract
This project was designed for my freshman CP-Algebra 1 course. This year I had been struggling with reaching various ability levels, far more diverse than the previous years.
Changes that were made to my previous assessment practices included pre-tests and more complex assessments. Pre-tests are now going to be used to activate prior knowledge. Complex assessments, such as projects, provided my students with the opportunity to synthesize and demonstrate their mathematical knowledge.
Over the course of second semester, I developed differentiated quizzes and gave only feedback. This practice encouraged deeper understanding of concepts for all ability levels and was fair to grade. I currently still use this grading practice for all quizzes.
All three of these new practices have greatly benefited my students understanding and motivation this semester. Implementation of these practices will continue next school year.
Changes that were made to my previous assessment practices included pre-tests and more complex assessments. Pre-tests are now going to be used to activate prior knowledge. Complex assessments, such as projects, provided my students with the opportunity to synthesize and demonstrate their mathematical knowledge.
Over the course of second semester, I developed differentiated quizzes and gave only feedback. This practice encouraged deeper understanding of concepts for all ability levels and was fair to grade. I currently still use this grading practice for all quizzes.
All three of these new practices have greatly benefited my students understanding and motivation this semester. Implementation of these practices will continue next school year.
What I've Learned...
This project has been very rewarding for me, as well as my students. The focus of this project changed slowly from solely differentiating assessments to learning from the quizzes, tests and projects.
This assessment project was designed to challenge my previous beliefs of assessments and force me to try alternative assessments. At the beginning of the last school year a few of my colleagues started giving pre-tests in their Algebra 1 classes but I immediately wrote off the idea, not seeing the purpose. So, my first goal was to develop a pre-assessment for each chapter in order to better understand my student’s strengths and weaknesses. As discussed in my updated assessments, I felt a lot of frustration after administering the first pre-test because after the assessment was graded the students them acknowledged that they had seen the Pythagorean Theorem, distance formula and midpoint formula before. Because the students did poorly on the pre-test I was not able to target sections that students needed more work on, my goal of giving the pre-test, because they all did very poorly on the pre-test. After going through this process, I realized that it is important to trigger previous knowledge. For next year, I plan on creating a Webquest in which students review material covered in their pre-algebra class: the Pythagorean Theorem, distance formula and midpoint formula. The aim of the Webquest is to help students access their previous knowledge, in addition to master the three formulas. The students will then take a short quiz on Moodle. All my students have learned these concepts before so a Webquest will allow them to review the material at different depths. For example, a strong student may only need a few examples to pass the Moodle quiz. On the other hand, another student may need numerous examples and practice problems before they take the quiz. To remediate any missing questions, the Moodle quiz will provide feedback based on the wrong answer they chose. For instance, if a student chose B a response would say "Close! Be careful - you switched your x and y values" so they can easily find their mistakes.
I plan on creating pre-assessments for all Algebra 1 chapters. Whether the pre-tests are worksheets, Webquests or online quizzes, I now realize how important it is to access my student’s prior knowledge. The new pre-tests will have two objectives. The first objective will be to activate previous knowledge of my students. Approximately half of the pre-test will contain skills and/or concepts that the students have already learned. It will be essential that students master these skills and it would be advantageous to have some sort of remediation for students who still struggle with these prior skills. I also have learned that it is important for students to make connections between old and new material and understand its importance. For example, when my students are learning how to solve systems of equations a portion of their pre-test will be graphing linear equations, an important step in solving systems. In class I spend a lot of time reviewing how to graph linear equations during the actual lesson. Thus, my hope is by requiring students to pass a pre-test requiring graphing skills, I can then spend more time on the actual lesson of solving systems of equation by graphing rather than reviewing.
The second objective of a pre-test is to show students how much they have actually learned throughout the unit. The second half of the pre-test will consists of problems taken from the chapter objectives. I will then ask similar questions on the chapter test, demonstrating to students how much they have learned. I tried this practice out on the pre-test I administered. I took questions directly from the pre-test and placed them on the chapter test. After the test, the students and I then had a discussion about how great it was that over a course of just two weeks, they can now answer the pre-test questions. While this concept seems very minute, I have learned that it is important to encourage students and confirm how much they have accomplished and learned.
The second goal of this project was to assess chapter objectives through various types of question and projects. I have learned that editing tests and making points proportional to importance of sections is not easy and it takes a lot of time. More specifically, I have reflected on the practice of multiple choice and partial-credit on my chapter tests. The apex of each chapter is a formative, criterion-referenced chapter test. At the beginning of the semester, I only used multiple choice on the semester final and quarter summative assessments. I did not like multiple choice questions because it gave students no room for error or partial credit. However, I have come to find that multiple choice is an appropriate type of question because it forces the student to derive the correct answer. Why had I been focusing so much on partial credit? In reality, it is extremely important for students to arrive at the correct answer, not the 75% correct answer. Multiple choice forces students to work through the entire problem correctly. One of my co-workers recently instituted a “no partial credit” testing policy. Similar to multiple-choice right/wrong answers, students received zero or full points on a test question and they are allowed one re-take. In many conversations we have had over this policy, she has expressed how this has positively affected her students. Not only are their grades higher, they are working harder on math both inside and outside of class. I am entertaining this possible grading policy for my chapter tests next year.
I have also learned that projects are important, when done appropriately – a perfect assignment does not happen on the first try. I really like projects because they are complex assessments and require students to synthesize material and apply their knowledge in ways other than formal assessments. From the M&M activity, I learned how important it is to have clear, well-defined directions. Over the past three years, I have tweaked the lab and this year worked the best. The students reached their objectives of the lab, as demonstrated by their chapter 8 test. Also, I shared the lab with my co-workers and we edited it together which was very beneficial. I will continue to work on these complex-assignments in all of my classes. I have learned that it is important to keep refining and reflecting each project.
From my third goal, to differentiate my formative assessments in order to cater to various ability levels, I found the key to both deeper understanding for my students and fairness. I decided to start with differentiation – just quizzes. By creating two quizzes with varying difficulty, I was concerned that my grading was not going to be fair. I subjectively chose who received each quiz (based loosely on grades) – what if I gave someone too hard of a quiz and they failed? What if I gave someone the easier quiz and they aced it?
As the semester advanced, one of P. Black’s assessment ideas in “Working inside the Black Box: Assessment for Learning in the Classroom” really stuck – grading with feedback only. Not assigning scores and instead providing constrictive feedback first started as an experiment stemming from our class discussion. This procedure is the single best enhancement I have made to my assessment practices. It has changed my assessment practices for the better. I return each quiz with feedback and they can then earn 100% once they complete all of their corrections and turn it in before the chapter test. Now, I am comfortable using differentiated quizzes because grading is fair; all students have an opportunity to learn and it alleviates all teacher bias.
At first, I was concerned with changing my grading policy in the middle of the year but the student response was encouraging. After our “trial” feedback-only quiz I had a lot of discussion with my students about their motivation and the importance of learning from their mistakes. We decided together that it was in their best interest to continue the feedback-only quizzes and I soon adopted it in all of my classes. My honors-level students are now being challenged on their assessments; they sometimes have to work very hard at some problems, which is new from first semester. On the other hand, my weaker students are doing better. I currently have no F’s in my class because their test grades are improving with each test. Rarely do students fail their tests because they spent time making corrections on their quizzes. I feel that the pace of my class is now appropriate for all levels. Also, my students’ work ethic has changed for the better and I enjoy seeing my students proud of themselves when they get the correct answer on the quiz corrections. My quizzes are now truly assessments for learning.
Obviously, I learned that there are some disadvantages to this practice. First, I am concerned that if I implement this for every quiz some students will stop studying for quizzes because they realize they can earn full credit even if they fail the first time. Second, my new grading policy states that if students do not have the quiz turned in 100% complete, they earn zero points. I struggle with this practice but I can not think of a better practice. Nevertheless, I like my current grading policy because it forces students to correct their mistakes and focus on the content more than the quiz grade.
This assessment project was designed to challenge my previous beliefs of assessments and force me to try alternative assessments. At the beginning of the last school year a few of my colleagues started giving pre-tests in their Algebra 1 classes but I immediately wrote off the idea, not seeing the purpose. So, my first goal was to develop a pre-assessment for each chapter in order to better understand my student’s strengths and weaknesses. As discussed in my updated assessments, I felt a lot of frustration after administering the first pre-test because after the assessment was graded the students them acknowledged that they had seen the Pythagorean Theorem, distance formula and midpoint formula before. Because the students did poorly on the pre-test I was not able to target sections that students needed more work on, my goal of giving the pre-test, because they all did very poorly on the pre-test. After going through this process, I realized that it is important to trigger previous knowledge. For next year, I plan on creating a Webquest in which students review material covered in their pre-algebra class: the Pythagorean Theorem, distance formula and midpoint formula. The aim of the Webquest is to help students access their previous knowledge, in addition to master the three formulas. The students will then take a short quiz on Moodle. All my students have learned these concepts before so a Webquest will allow them to review the material at different depths. For example, a strong student may only need a few examples to pass the Moodle quiz. On the other hand, another student may need numerous examples and practice problems before they take the quiz. To remediate any missing questions, the Moodle quiz will provide feedback based on the wrong answer they chose. For instance, if a student chose B a response would say "Close! Be careful - you switched your x and y values" so they can easily find their mistakes.
I plan on creating pre-assessments for all Algebra 1 chapters. Whether the pre-tests are worksheets, Webquests or online quizzes, I now realize how important it is to access my student’s prior knowledge. The new pre-tests will have two objectives. The first objective will be to activate previous knowledge of my students. Approximately half of the pre-test will contain skills and/or concepts that the students have already learned. It will be essential that students master these skills and it would be advantageous to have some sort of remediation for students who still struggle with these prior skills. I also have learned that it is important for students to make connections between old and new material and understand its importance. For example, when my students are learning how to solve systems of equations a portion of their pre-test will be graphing linear equations, an important step in solving systems. In class I spend a lot of time reviewing how to graph linear equations during the actual lesson. Thus, my hope is by requiring students to pass a pre-test requiring graphing skills, I can then spend more time on the actual lesson of solving systems of equation by graphing rather than reviewing.
The second objective of a pre-test is to show students how much they have actually learned throughout the unit. The second half of the pre-test will consists of problems taken from the chapter objectives. I will then ask similar questions on the chapter test, demonstrating to students how much they have learned. I tried this practice out on the pre-test I administered. I took questions directly from the pre-test and placed them on the chapter test. After the test, the students and I then had a discussion about how great it was that over a course of just two weeks, they can now answer the pre-test questions. While this concept seems very minute, I have learned that it is important to encourage students and confirm how much they have accomplished and learned.
The second goal of this project was to assess chapter objectives through various types of question and projects. I have learned that editing tests and making points proportional to importance of sections is not easy and it takes a lot of time. More specifically, I have reflected on the practice of multiple choice and partial-credit on my chapter tests. The apex of each chapter is a formative, criterion-referenced chapter test. At the beginning of the semester, I only used multiple choice on the semester final and quarter summative assessments. I did not like multiple choice questions because it gave students no room for error or partial credit. However, I have come to find that multiple choice is an appropriate type of question because it forces the student to derive the correct answer. Why had I been focusing so much on partial credit? In reality, it is extremely important for students to arrive at the correct answer, not the 75% correct answer. Multiple choice forces students to work through the entire problem correctly. One of my co-workers recently instituted a “no partial credit” testing policy. Similar to multiple-choice right/wrong answers, students received zero or full points on a test question and they are allowed one re-take. In many conversations we have had over this policy, she has expressed how this has positively affected her students. Not only are their grades higher, they are working harder on math both inside and outside of class. I am entertaining this possible grading policy for my chapter tests next year.
I have also learned that projects are important, when done appropriately – a perfect assignment does not happen on the first try. I really like projects because they are complex assessments and require students to synthesize material and apply their knowledge in ways other than formal assessments. From the M&M activity, I learned how important it is to have clear, well-defined directions. Over the past three years, I have tweaked the lab and this year worked the best. The students reached their objectives of the lab, as demonstrated by their chapter 8 test. Also, I shared the lab with my co-workers and we edited it together which was very beneficial. I will continue to work on these complex-assignments in all of my classes. I have learned that it is important to keep refining and reflecting each project.
From my third goal, to differentiate my formative assessments in order to cater to various ability levels, I found the key to both deeper understanding for my students and fairness. I decided to start with differentiation – just quizzes. By creating two quizzes with varying difficulty, I was concerned that my grading was not going to be fair. I subjectively chose who received each quiz (based loosely on grades) – what if I gave someone too hard of a quiz and they failed? What if I gave someone the easier quiz and they aced it?
As the semester advanced, one of P. Black’s assessment ideas in “Working inside the Black Box: Assessment for Learning in the Classroom” really stuck – grading with feedback only. Not assigning scores and instead providing constrictive feedback first started as an experiment stemming from our class discussion. This procedure is the single best enhancement I have made to my assessment practices. It has changed my assessment practices for the better. I return each quiz with feedback and they can then earn 100% once they complete all of their corrections and turn it in before the chapter test. Now, I am comfortable using differentiated quizzes because grading is fair; all students have an opportunity to learn and it alleviates all teacher bias.
At first, I was concerned with changing my grading policy in the middle of the year but the student response was encouraging. After our “trial” feedback-only quiz I had a lot of discussion with my students about their motivation and the importance of learning from their mistakes. We decided together that it was in their best interest to continue the feedback-only quizzes and I soon adopted it in all of my classes. My honors-level students are now being challenged on their assessments; they sometimes have to work very hard at some problems, which is new from first semester. On the other hand, my weaker students are doing better. I currently have no F’s in my class because their test grades are improving with each test. Rarely do students fail their tests because they spent time making corrections on their quizzes. I feel that the pace of my class is now appropriate for all levels. Also, my students’ work ethic has changed for the better and I enjoy seeing my students proud of themselves when they get the correct answer on the quiz corrections. My quizzes are now truly assessments for learning.
Obviously, I learned that there are some disadvantages to this practice. First, I am concerned that if I implement this for every quiz some students will stop studying for quizzes because they realize they can earn full credit even if they fail the first time. Second, my new grading policy states that if students do not have the quiz turned in 100% complete, they earn zero points. I struggle with this practice but I can not think of a better practice. Nevertheless, I like my current grading policy because it forces students to correct their mistakes and focus on the content more than the quiz grade.
What I Would Do Differently...
I would incorporate technology, primarily Moodle quizzes, into my pre-tests. This will help make analyzing results quicker and more efficient.
I will work on incorporating more appropriate projects into my curriculum. Along with this, I will use my co-workers as resources. Collaborating with my co-workers on the M&M project was very beneficial. Along with this, I will encourage my co-workers to try these projects out with me.
I would focus on one goal for the project – not three – so I could spend more time on that specific aspect. I sometimes felt that I was scrambling to create new quizzes, tests, and projects. Instead, I should have picked one to focus on. As the project developed, I did spend more time on the quizzes.
I will work on incorporating more appropriate projects into my curriculum. Along with this, I will use my co-workers as resources. Collaborating with my co-workers on the M&M project was very beneficial. Along with this, I will encourage my co-workers to try these projects out with me.
I would focus on one goal for the project – not three – so I could spend more time on that specific aspect. I sometimes felt that I was scrambling to create new quizzes, tests, and projects. Instead, I should have picked one to focus on. As the project developed, I did spend more time on the quizzes.
