Article Discussions on Assessment

Getting Started with Open-Ended Assessment

Found in Teaching Children Mathematics, April 2005

This article discussed the high points and low points of utilizing open-ended assessment in the classroom. Open-ended problems are those where multiple strategies can be used to solve, and multiple solutions may be correct or accurate. These types of problems allow students to better demonstrate their actual understanding of a topic in mathematics. Instead of just finding an answer and writing it down, students must additionally explain their thinking and reasoning using detail. Open-ended problems do not rely on content-based mathematics. Instead, they require students to not only find a correct solution but also explain their process and reasoning for finding that solution. It is important for open-ended problems to utilize meaningful mathematics, allow for multiple strategies/solutions, and have the perfect medium of too little and not too much information provided. It was noted by a featured teacher in this article that creating and implementing open-ended problems can be very time-consuming and difficult. However, they can be very beneficial to students and their overall learning in mathematics. They require students to do a lot of work in justifying their answers, which may be a new concept for students. This featured teacher also suggested to not grade these problems at first, which will allow students to be more comfortable completing them. Additionally, she found it beneficial to show student samples on an overhead (with names removed) and talk about the pros/cons of each sample response to a problem. She explained that after using open-ended problems for an extensive period of time, she saw gains in student confidence and willingness to share their answers to peers. She also noted that as the teacher, she felt this provided her with a more concrete method of assessment, which helped her explain student achievement to parents.

This was an interesting article to read. I have heard of open-ended problems before, but have never really given them a lot of thought. It is obvious that they can be quite difficult to create and implement, but the benefits do seem to be great. I believe that using open-ended problems helps students to really look into their thinking and make sense of their strategies and processes for finding answers to problems. Open-ended problem solving takes a lot of effort on both the student's and teacher's part, but it is a very useful tool that can help students to take more meaning from mathematics.

Discussion Questions:

1. What are some ways that you could potentially implement open-ended problems in your future math lessons?

2. Could you implement open-ended problems into other curricular areas?

A Smorgasbord of Assessment Options

From Teaching Children Mathematics - April 2010

As teachers, we are faced with the task of creating authentic assessments to gauge our students' learning. Creating these types of assessment can be very challenging. To add to the challenge, there are an array of assessment options to choose from in which we can utilize in our classrooms. This article talked about one type of assessment, called student-centered assessment. This format benefits the students because they are participating in meaningful mathematics, but it also benefits the teacher because it helps to gauge student understanding and their level of learning. Mathematics is a process, and students must heavily rely on building upon prior knowledge as they work through concepts. In this article, a class of students who were working with understanding geometric shapes and solids was discussed. In this class, students were at a variety of levels of understanding in regards to geometric shapes. Regardless of their individual level, students used both knowledge and reasoning to come to various conclusions about geometric shapes they were working with. A "mastery" indication of these concepts occurred when students were readily able to communicate their thinking and reasoning to their peers. It was noted in this article that in order for student-centered assessment to be effective, modes of both formative and summative assessment must be utilized. It was also suggested that they best way of creating student-centered assessment is to first identify the standard, then select a target achievement level, and finally create assessment options for students to demonstrate their understanding of the concept.

Student-centered assessment seems to be a very valuable tool for teachers to use in the classroom. It not only get students focused and motivated on a topic, but it has them thinking more deeply and communicating their thoughts and reasoning to their peers. I think this is a very important skill for students to be able to master. Once they communicate their thoughts and rationale, it is a clear indication that they truly understand a subject themselves. It is definitely evident that creating these authentic, student-centered assessment is very time consuming and not exactly "easy". It takes a lot of planning and thought on the teacher's part, and it takes a greater amount of time to implement in the classroom. However, the benefits outweigh the downfalls, and student-centered assessment is definitely something I would like to use in my classroom to help engage my students.

Discussion Questions:

1. Can you think of any specific student-centered assessments that could be utilized in a mathematics lesson?

2. Are there any other benefits you have seen through observations/field experience that display student-centered assessment?

Understanding Student to Open-Ended Tasks

From Mathematics Teaching in the Middle School - April 2000

This was another article in regards to the use of open-ended tasks in mathematics classrooms. Open-ended tasks allow for student choice in the strategy to use for solving, and also allows (usually) for multiple correct responses. This allows students flexibility in solving, and using strategies that they are comfortable with. While open-ended tasks sound to be beneficial to students, they often are hard for students to grasp and understand. Some students have little experience or practice in actually communicating their reasoning, which open-ended tasks require. This article described some sample responses from 6th graders working with an irregular area task. Several responses were shown, some being incorrect and others being correct. The teacher of these students seemed to be pretty hard on giving feedback for all of the responses. In addition, students she thought understood the concept of area extremely well performed poorly on the task. Alternatively, students that she thought were struggling easily grasped the problem and explained their reasoning adequately. It was noted that the students who made great use of words, pictures, and diagrams to aid in explaining their thinking performed better on the task. The teacher had been working with this group of students over the course of a year, and felt that her feedback was allowing her students to generate more detailed and supportive responses when completing tasks like the one posed in the article.

I thought it was interesting how the teacher's viewpoint of student understanding was drastically changed after giving her students this task. The students that she was not concerned about turned out to be the ones who did not comprehend this task or provide adequate reasoning for their responses. Alternatively, the students she was concerned about really pulled through on this task to provide a correct answer and use supportive reasoning. I think that this was a clear indication that the teacher really needed a way to look further into her student's thinking and mathematical processes. I like that it was also noted within the article that any teacher beginning to provide students open-ended tasks like this one need to expect reasonable results. Students are not going to adequately explain their thinking on the first try, and will need a lot of practice in order to respond to these types of tasks correctly.

Discussion Questions:

1. What do you presume were some of the benefits that students experienced when working with open-ended tasks like the one described in the article?

2. Do you think this teacher was too harsh on her student's responses?

Assessing Students' Understanding through Conversations

From Teaching Children Mathematics - December 2007/January 2008

Conversation as an assessment tool is often an underrated element in the classroom. However, conversation is used as a method of assessment much more frequently that any other form of assessment. Why is this? I believe that it is because conversation is informal, for the most part. It is easy to participate in, and it allows for a lot of information to be exchanged between teachers and students. Conversations over mathematics can truly gauge what students do and do not understand about the topic at hand. This article talked about three different situations in which conversation was critical to understanding student knowledge. One 3rd grade teacher used informal conversation to gauge the true understanding of one of her students working with place value. Another 5th grade teacher used conversation to understand the mistakes made by a group of students on a geometry quiz. Another teacher used conversation during a lesson on measurement to realize that students were struggling with the basic concepts of measurement. All of these examples showed how critical conversation was to the lesson, because the teacher was much better able to gauge student understanding. This article also talked about promoting conversation in the classroom required that students feel safe in the environment. Students should feel comfortable sharing their thoughts, and be respective of others doing the same.

Conversation is such a valuable assessment tool, in my opinion. It is something I plan to use very regularly in my classroom. The reason that I like conversation so much is because it takes little planning, but it can still yield so much information. I believe that conversations as a class can also yield student participation, which is crucial in a classroom. This article discussed the idea of participation, and also the utilization of wait time in order to obtain responses from all students. Conversations about mathematics can not only gauge understanding, but can help students to find errors in their problem solving or clear up any misconceptions they may have. Conversation as an assessment tool is very useful to any classroom teacher.

Discussion Questions:

1. Can you think of any times during observations/field experiences where you have seen conversation being a great assessment tool?

2. How will you work conversation as assessment into your future classroom and lessons?

An Experiment in Using Portfolios in the Middle School

From Mathematics Teaching in the Middle School - March 2008

This was a very interesting article to read about the implementation and use of portfolios in a middle school mathematics classroom. The teacher featured in this article wanted to display her student's knowledge in a different way than traditional quizzes and tests. Therefore, she turned to the use of student-made portfolios. Over the course of several weeks, the teacher had the students collect pieces of their work. Students were to have sections of their portfolios discussing their mathematical attitude, problem solving, mathematical growth, mathematical writing, and mathematical connections. Students worked to select specific pieces of work for each of these areas. The portfolios additionally required a lot of student reflection on their choices, and rationale for picking these items. Once completed, the portfolios were sent home for parents to view and answer some questions about. The teacher assessed these portfolios by organization and the overall learning and understanding of mathematics that the student received from creating the portfolio. She used a checklist to do this. As far as benefits of utilizing the portfolios, the teacher explained that she began writing her lessons so that they were able to be included in the portfolios. She did this by creating assignments that involved more writing, real-world connections, and problem solving. She also noted that by reviewing the portfolios, she was better able to see what students had learned and where they experienced the most growth in their learning.

I really like the idea of using portfolios as a form of alternative assessment. I have made numerous portfolios myself for college courses, and they really are more meaningful than taking a final exam. They allow a student to examine their progress and reflect upon their work in various forms. I think that the students in this featured class seemed to take a lot away from creating their portfolios. In addition, the teacher required the students to reflect on why they choice certain pieces. The teacher also discussed how she had students write in learning logs after completing each assignment. Students were to write what they did and did not understand. This helped students when creating their portfolios to select pieces of their work that really represented their knowledge and understanding. Portfolios are a great form of assessment, and I would really like to use them in my future classroom.

Discussion Questions:

1. Where have you seen portfolios being used in the classroom?

2. Why would having students create portfolios be beneficial to use during parent-teacher conferences?


References:

Bacon, K.A. (2010). A smorgasbord of assessment options. Teaching Children Mathematics. 16(8).

Leatham, K.R., Lawrence, K., Mewborn, D.S. (2005). Getting started with open-ended assessment. Teaching Children Mathematics. 11(8).

Maxwell, V.L., Lassak, M.B. (2008). An experiment in using portfolios in the middle school. Mathematics Teaching in the Middle School. 13(7).

Moskal, B.M. (2000). Understanding student to open-ended tasks. Teaching Mathematics in the Middle School. 5(8).

Vanderhye, C.M., Zmijewski Demers, C.M. (2007/2008). Assessing students' understanding through conversations. Teaching Children Mathematics. 14(5).