Assessments in Math Reflection

Assessments in Math Reflection:

Traditional  

In all subject areas, teachers are constantly assessing students, but are they assessing students in the best possible way? In math methods, we talked a lot about different ways teachers can assess their students in math. Teachers can assess students through traditional tests and quizzes, but there are so many other valuable ways to assess students. Many teachers get stuck in the mindset that students need a cut and dry, formal test where they circle or indicate their answer. While traditional assessments can be used, I learned (from discussions and activities in class and from the assessment articles) that teachers could also use many other types of assessments.

Open-Ended Assessments

First, I learned that teachers could conduct open-ended assessments. I think it is awesome that many schools are realizing the importance and value of open-ended assessments and are starting to gear towards more authentic and exploratory assessments. It is great when there are various strategies that can be used to solve a problem and when there are various solutions that could be considered correct. Students can and should use reasoning, problem solving, and communication skills (math is more than formulas, it is conceptual too). While developing open-ended assessments may be challenging and time-consuming for teachers, the more practice they get with open-ended assessments, the more they will see their value and reward. Teachers can gain a better understanding of how students are comprehending the material and better recognize if they need to reteach or review certain material. Also, teachers benefit from the following: variety of solutions from students (shows how all students think differently and how a problem can be solved in various ways), engage students who do not typically like to write or who do not like math, the strong connection between math and literacy may be more comforting for teachers who are not as comfortable with math instruction but more comfortable with literacy instruction, samples of student work on open-ended assessment problems is a helpful tool for communication (teacher can convey a child’s progress to parents in a parent-teacher conference; they can show them exactly what their child is understanding in certain topics), share examples of student work with teaching colleagues (teachers can communicate how students are learning), and special education teachers or support teachers might find it valuable to have a student’s work so they can look at specific examples and areas of strengths/weaknesses. Students also gain benefits from open-ended problems: Their confidence, willingness to participate, pride in their ability to explain their thinking, and eagerness to help others will likely increase. Open-ended tasks allow students more freedom to use their own methods/strategies/approaches. This engages and motivates students because they are able to have ownership and comfort in the strategies they choose to demonstrate/express a math idea. When students respond to these open-ended tasks, it provides teachers with evidence of students’ understanding of problem-solving and communication skills.

 I think open-ended tasks are extremely important to implement when teaching mathematics because it helps students dig deeper and find more meaning in the content. Instead of looking at “What’s the answer?” students are able to think about “Why is that my answer? How should I go about solving this? Does this make sense?” Teachers also can better analyze the students’ thought processes, strategies, and solutions, and gain a better understanding of what students still struggle with, which helps guide future instruction. I will use open-ended assessments in my future classroom because I think it takes student learning to a whole other level and is a great way for students to learn from each other and for the teacher to see where students are at. I also want to make sure I provide feedback to ALL of my students on their work. I feel it is important to acknowledge all students’ level of understanding and comment on what you would like to see them work on or accomplish in future work. Even if a student mastered the skill, there should be feedback provided to the student letting him or her know what they should continue to work on so they are always able to achieve the best work possible and to their highest potential. I can make comments on their work directly and/or use a rubric or checklist. Moreover, I hope to encourage my students to use visuals during open-ended tasks to help them express and develop their math knowledge. Many young students are still trying to grow with their writing skills and have trouble conveying their thoughts in a written explanation so visuals can be beneficial. Lastly, I know that open-ended tasks may be complicated and uncomfortable for students in the beginning. It takes time and practice for students to learn to write and express their thoughts. Therefore, I want to introduce the idea of open-ended assessments early on in the year so there is lots of time to practice. With more opportunities to participate in open-ended tasks, students will be able to practice how to effectively explain their thought process.

Student-Centered Assessments

            I also learned the value in creating student-centered assessments. I think creating inquiry-based, exploratory, and authentic assessments is an important duty of a teacher in order to gain the levels of student understanding.  In student-centered assessments, students are engaging and participating in math activities that deepen their knowledge, and the teacher can gauge student understanding. In other words, in a student-centered classroom, assessment should focus on helping the students to learn math content and provide valuable information to teachers and students (they should help the teacher with future instruction). Students should benefit from assessment opportunities (should help guide/scaffold students to explain their thinking and gear them towards deeper reasoning of math content). When teachers create an effective assessment, they should think about using multiple assessment techniques, focus on specific math goals, and consider how students will think about/respond to the math. Meaningful assessments should show what we want students to know/be able to do (objectives/goals). Assessments are in a sense like a performance; students get to perform what skills they know and this helps convey their thought process/strategies. Designing student-centered assessments are very valuable for both students and teachers. Students gain a better understanding of math content and teachers can better gauge students’ thought processes/strategies/understanding, which helps guide future instruction.

I think it is really important to provide many opportunities for student-centered assessments because I think it is more engaging and motivating for students and allows them to have a sense of ownership of the content. Also, communicating is an important life skill, and students get to practice communicating by conveying their knowledge and reasoning to their peers and teachers showing their understanding for the concept. I believe that sometimes teachers assume that assessments should be used at the end of a unit, but really assessments can and should be used throughout the whole unit (before, during, and after). This way teachers are constantly able to monitor students’ progress. Also, while student-centered assessments may take a lot of critical planning from the teacher and may be time-consuming for the students, they are a meaningful tool where students can show how they are problem solving. I hope to implement student-centered assessments in my future classroom to engage students, deepen their math knowledge, and guide my instruction.     

Conversations as Assessments

           

Moreover, I learned how important conversations could be. A simple conversation that a student has with another student or teacher is an easy and valuable way to access students. Students are constantly talking, and it’s the teacher’s job to purposefully listen to student conversations so they can learn about students’ thought processes. Conversations can show faulty reasoning, mistakes in computations, and misunderstanding of content, all of which can be used by the teacher to guide future instruction. Through questioning, one-on-one, small group, or whole class discussions, presentations, or interviews, teachers can learn about students understanding. With this knowledge, teachers can then ask follow-up questions, teach impromptu or planned lessons, better plan for future instruction, revise planned instruction, and adapt instruction to meet the students’ needs. No matter what the environment of the school or classroom is like, conversations are a tool that can always be used. Whether teacher-to-class, teacher-to-student, or student-to-student conversation, tons of valuable information is expressed through conversation and teachers can use this informal conversation as an assessment to better grasp what students do and do not understand. Furthermore, getting students to participate in conversation is not always an easy task. Therefore, teachers should try to wait an appropriate amount of time after asking a question before calling on a student for a response, and they should encourage all students to think/share ideas. [I also believe teachers should give students praise for participating even if their answer is incorrect to make students feel safe and more willing to participate in the future.] Moreover, students cannot converse if teachers do not provide students enough opportunities to do so. Having students think, pair and share, and/or talk in a small group before sharing their ideas aloud to the whole class allows them adequate time to think about the question, prepare an answer, and feel more comfortable. Lastly, teachers should make sure their classroom is set up in a manner that promotes collaboration (i.e. table groups, open floor space, etc.)

I strongly believe that the idea of conversing in a classroom cannot be stressed enough. Conversation is such a simple assessment tool that is informal and requires no planning. Conversation in a classroom is a win-win; through conversation, students are participating and learning from each other, and teachers are listening/assessing as the students converse. With conversation, teachers can truly assess students' math understanding and knowledge and what areas students still struggle with. This will help teachers guide their future instruction, where they need to reteach, and what parts of their future lessons they need to revise. In addition, conversation helps students understand their own mistakes! By sharing their thought process with a peer or teacher, often students catch their own mistakes and are able to correctly adjust their thought process. I always find it amazing to listen to the diverse responses in which students share, because sometimes students share such creative approaches that deepens their own math knowledge as well as their peers. I think conversation is useful in a classroom because students can learn from their peers as well as understand the significance of participating and clearly conveying their thought process. I hope to provide multiple opportunities for my students to collaborate with their peers as well as myself and use this as an assessment tool.

Portfolios as Assessments

Furthermore, I learned about how portfolios can be a wonderful assessment tool. Portfolios are an alternate and authentic way to assess students in math. The teacher can decide what categories students will have in their portfolios (i.e. mathematical attitude, problem-solving, mathematical growth, mathematical writing, mathematical connections). Sometimes it’s important to realize that students need more than just a grade; they need to understand their strengths and progression. In the portfolios, students can collect pieces of their work (that demonstrated problem-solving, communication, and connections). Portfolios can be done each math unit, per quarter, per semester, or one time a year. Additionally, the teacher may decide to have students write a reflection (explaining the category that their piece is in as well as why they chose that piece). The teacher may also choose to have students keep a learning log, write a math autobiography, and write introductory reflections for each portfolio piece. The benefits of using the portfolios is that the students are being provided more opportunities to write, problem solve, and complete projects in which both the teacher and the students can analyze their thinking. Also, the students reflect on their learning and solving more realistic problems that require reasoning. The portfolio can be assessed based on the organization and on the students’ learning and mathematical understanding. The portfolio could weigh just as much as a traditional assessment. However, the goal of the portfolio is to understand the level at which students comprehended the concepts and how well they are able to succeed. The teacher may also choose to design a portfolio checklist or rubric to help appropriately assess the students. Portfolios are time consuming to put together and time consuming to grade. However, it is an authentic and effective way for the teacher to be able to assess student learning and see where they (the teacher) can adapt future instruction so students can be more successful in math. Portfolios allow students to analyze their own learning, growth, and understanding of math

            Portfolios are excellent assessment tools that stray away from the “typical” and often ineffective traditional tests. I think students can learn more from a portfolio that they put together than from a test. In addition to teachers assessing student understanding, the students themselves can evaluate their own level of understanding and progress.  I really like how students are able to have the freedom to pick what pieces they put in their portfolio as well as write a reflection on those pieces that they chose (makes students think about what is good about that piece of work/why they are proud of it). I believe the portfolio is like a book that the student has written; it contains various work samples created by the student. I think portfolios create a sense of ownership and confidence in students and help them evaluate their own learning and understanding of math. Moreover, I think portfolios are an amazing concrete example that teachers can use in parent-teacher conferences to show the student’s progress, level of understanding, strengths, and weaknesses.

Formative Assessments vs. Summative Assessments

Additionally, we discussed the difference between formative and summative assessments. Formative assessments are ongoing and regularly being used (i.e. warm-ups, questioning, class discussion, observing students, etc.). Summative assessments are at the end of a lesson or unit and see what student’s learned/understand about the concept. These summative assessments, which may be tests, quizzes, or projects, determine grades. As a teacher, I plan to use a well-balanced mix of formative and summative assessments. I think it’s important that students are informally assessed (such as through conversation, observation, or activities) but that they are also more formally assessed (such as through a test, project, or portfolio). By having a mix of these assessments, not only does it provide the students multiple opportunities to experience different assessments, but it also helps the teacher compile nice and reliable notes/statistics on each student’s progress.

Assessing my Own Work

Throughout the various assignments in this summer session, I was able to assess my own work. As I was working through an assignment, I would observe my own work, re-read what I wrote, and question myself to see if it made sense or if I could improve it. After each assignment, I would again observe my own work, re-read what I wrote, and question myself to see if it made sense or if I could improve it. In addition, for every assignment I would check the criteria on the rubric to ensure that I was meeting the requirements and incorporating everything I was supposed to. Also, just as we had to assess or “evaluate” our own work, I think students could do this as well (especially as students get older). It is important for students to identify areas of strengths, weaknesses, and what can be improved upon.

Assessing my Peers’ Work

            In addition to assessing my own work, I also had the chance to assess my peers’ work during the summer session. When working in group projects with my peers, we would often divide up the work into different sections to be more efficient. However, after my peers’ would do their portion of the work, I would always assess their work to make sure it flowed. As I did with my own work, I would observe their work, read what they wrote, and question myself as to whether or not it made sense. I would also think about if it was sufficient or if it could be improved. Additionally, when all of our individual work was put together, I wanted to make sure that my group’s work was clear, effective, and organized. Therefore, once combined, I would again observe all of our work, read what everyone wrote, and make sure everything made sense. Additionally, I would check the criteria on the rubric to ensure that my group was meeting the requirements and incorporating everything we were supposed to.

            Moreover, with the problem situation critique assignment, I had the opportunity to assess my peers’ work. Each of my peers created a problem situation, which I then critiqued. I would read their problems, make sure it made sense, see how it could be improved, and determine if they met the criteria on the criteria list. I looked at the following criteria: grade level, use appropriate academic language, age appropriate reading level, level of difficulty (student engagement), can be solved with multiple strategies, relevant/relatable to students, avoids biases (SES, gender, religion, race, sexuality), and clear directions. For each peer I provided (hopefully) valuable comments. I commented on their strengths (what I appreciated about their problem situation) and gave advice as to how they could make their problem better.  The process of critiquing was a great experience. In hardly any of my education classes do I get the opportunity to critique my peers’ work, and quite frankly, I think there should be more of it. Peer-to-peer feedback is crucial because we get to see how others, who are learning about the same material as we are, think about the problem. It is always nice to have teacher feedback, but it is also extremely meaningful to get our peers’ opinions/point of view. My peers had insightful comments for me to consider. Likewise, I tried to put in careful thought to the critiques I gave so my peers could find my comments useful and/or possibly apply my comments to improve their problem situation.

            I also got the chance to assess student’s work. The error analysis student samples and the NAEP analysis of student work were two activities where I got to access student work. In both activities, we had to look at student samples, find what (if any) errors the student made, and how we could provide further support/meaningful feedback (i.e. through verbalization, learning tasks, guided questions) that focus on helping them better understand the area where they were having trouble. With both of these activities (error analysis and NAEP analysis), I learned that if students continue making the same errors without anyone correcting them, they are being set up for failure in the future. This may sound tough, but it is true because if students keep progressing in math while making those same errors, they are going to continually have a misunderstanding of the concept, have difficulty understanding future concepts that build off of the prior concept, and likely get the answer wrong. Therefore, it is vital that teachers step in and guide the students in the proper direction so they understand their error and how to correct it. In my novice experience I got the chance to assess students’ work. However, hopefully I get even more practice with it, since I will constantly be analyzing, interpreting, and understanding my student’s mathematical work. Sometimes it is challenging to jump inside a student’s brain and think about how they thought of the problem. I hope that as I get more practice with analyzing errors, the easier it will be for me to detect and understand student’s errors. Also, in a real-world classroom, I could always talk one-on-one with a student and have them explain their thought process to me.

Assessments Done by the Instructor

           

            My instructor always assessed the work I turned in, which is important so I could see my strengths and weaknesses. Throughout this summer session, I learned the value of creating a clear rubric with obvious distinctions between levels. It is often hard to interpret what students know based on their response, which is why a rubric is a helpful tool. However, as we learned in class, this rubric must be created carefully with clear distinctions between scores so it is easy to determine where students fall. I noticed that my instructor always used clear rubrics when assessing us. Before I turned in my assignment, I would check it with the rubric to make sure I met all the criteria. Then, when my instructor returned my graded work to me, I read through her feedback. I looked through the rubric and comments, which helped me understand her perspective of my work and what could be improved. 

Final Thoughts

            Assessing students is something that I will have to do for the rest of my teaching career. I hope I can create authentic, exploratory, and meaningful assessments where my students are being provided a valuable learning experience and where I can gauge my students’ understanding.

[Some notes were used from my Article Discussion 2 (Assessment) blog post and from my Error Analysis Reflection blog post.

Article references from Article Discussion 2 Post:

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).]