Reading the "NCTM" article made me think of grading math assessments in different ways. So far, I have had very little instruction on how to use rubrics. I really like the analytic and holistic examples that this article provided. In my field placement, the students do traditional tests and they either get it right or wrong. My mentor teacher gives the students grade based on the percentage of problems that they solved correctly. The tests are always in multiple choice format and the students give their best guesses. The "NCTM" talked about easy ways to get these students to develop their math concepts even further by asking secondary questions such as: "Why did you choose the answer you chose?, "What was not right about the other choices?" "What else would you like to add to the question or answer?" (Allen et al). I think that these questions can help the students explain their thinking and help the teacher get a better understanding of how well the students understand the concepts. If it is just multiple choice, students could correctly guess the answer, yet have no idea how they got it or how to do the problem. I feel like these multiple choice tests are not the best way to assess the students.
The "Gaining Insight into Through Assessment" article gives examples of student solutions for three different questions. These questions are more open-ended and the students are required to show their work. For the first problem with the dots, three different student solutions are examined. There is the correct student solution with the correct work, and incorrect student solution with work that does not make sense, and another incorrect student solution that is incorrect, but the work that they did still makes sense. The article talks about whether or not the incorrect student solution with the correct work is still correct. I feel as though he should be incorrect because he came up with the wrong answer, however I do not know if that is the best thing or not. The question I have is, where do you draw the line and how do you determine whether or not the student should be correct or incorrect? It is clear that the student understands some mathematical concepts, but not the ones that the question is looking for. I liked this article and it was interesting to examine the student work. The article talks about the benefits of having open-ended tasks where students have to show their work. They are forced to communicate their ideas about the math concepts and work through them on paper. It is easy for the teacher to see exactly which strategies and approaches that the student is using. These performance tasks also allow students to work through the problem the way that they want to. We have been learning about how important it is to differentiate in math, and that all students learn and think differently. As long as students get the right answer, I feel as though they can do the task whichever way makes the most sense to them.
I think that performance tasks could be more beneficial for both students and teachers. Students are able to solve problems the way they want and think about problems more than just guessing correct answers. Having students explain their thinking and solutions will further their understanding of math concepts, which will help them in the long run. Students are benefited by performance tasks as well because they can see exactly where the student is having misconceptions, or what students are understanding. I would like to use performance tasks in my future classroom.
For my lesson study, some performance tasks could be used without using paper and pencil. I feel as though orally asking students questions can give the teacher a lot of insight to their thinking. They are put on the spot and have to answer your questions, so there is no way for them to make something up. I feel if they are able to answer the questions, it will show that they understand the concepts, and if they are unable to answer the questions, they still have some misconceptions. For my lesson, students are required to use non-standardized tools to measure objects. I can simply ask students what tool would be the best to measure different objects based on size. I can hear what the students answer and assess their knowledge based on their answers.
I found the “NCTM” article very helpful in terms of learning about rubrics and thinking about ways of assessing students. I agree with Colleen when she finds the secondary questions useful for learning how students are answering questions and why they chose a certain question. This article gave me insight on how to use tests. I was not sure about giving test and quizzes in the classroom because they can be very close ended. With the use of the questions that the article provides, it can take a test a step further and really make them worthwhile, not just a grade in the grade book. I liked the idea of students coming up with their own tests. If done correctly, this really allows students to learn the material and can be prepared for what they are going to be assessed on. I do not like when teachers try to trick students with the questions they give on test. The main goal should always be for the students to be learning the information not confusing them. I think the use of holistic and analytic rubrics can be very beneficial for students and the teacher. I really feel like it depends on the task or assignment that is being given that should decide whether the rubric should be holistic or analytic.
ReplyDeleteTo address the questions you posed referencing the article, “Gaining Insight into Through Assessment”, I have the same thoughts about whether a students work should be marked wrong if the answer is wrong but the work is correct. I feel the same and think that if the answer is wrong you would have to mark it wrong. I think this is a great way to connect the two articles and show the importance that a rubric can have. Using an analytic rubric would allow this student to gain points for their work but miss points for getting the answer wrong. If the entire answer were to be counted as wrong, the student may think that the work is wrong and not approach another question the same way. The rubric can help show where the student made a disconnect and where their work is strong.
A performance task for my lesson study could be the same try as yours, where the questions are coming from the teacher and students have to answer right away. I think this can be useful for really understanding what a specific student is thinking where they are not influenced by other students answer. At the same time, students put on the spot like that can get nervous and say they do not know but really just don’t want to speak to be wrong. This is where I would give each student a list of questions to answer after the task was completed. This allows students to show their thinking in writing and they are their own thoughts.
I also found the "NCTM" article to be very helpful in finding new ways to create rubrics and accessing a variety of students. The one thing that I found to be a really neat idea, was having the students create their own math questions. In my math experience, I never had a teacher that would allow for the students to put their input into what type of problems they enjoy (or possibly could write). I think that by having the students write their own math problems would allow for the students to have a closer relationship with their mathematics. I also was interested to learn about the different types of rubrics. Ihave learned about Holistic and Analytical rubrics but it was interesting to see several different examples of them and the list that showed the pros and cons of each. I think this article opened my eyes to new ideas on rubrics and assessment taking.
ReplyDeleteI think that you pose a very good question from the "gaining insight article", I think that many teachers have a hard time drawing a line of when to give credit for the wrong answer but the correct work. I agree with Michelle in the idea of tying the two articles together and giving the students partial credit for the correct work, so they have the understanding that they are not completely incorrect.
I agree with you girls, in the sense that for a performance task I would ask questions and have the students answer them. I think that by doing it more informally, the students would not feel as if they were under pressure and it would also allow for the students to say what is on their mind at that minute.
Overall, I found these articles to be extremly helpful in examining assessments and rubrics.