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1. An authentic assessment that I find really useful are brief written tasks that include error analysis.  The students are provided with a scenario and asked to "be the teacher" and tell where that student made their mistake.  This is a great opportunity for students to practice writing, which was discussed in the previous two chapters, and really prove that they understand the concept.  I like to use these frequently at the end of a daily lesson to do a quick check of student understanding.  I can then provide feedback to students during small group time.  I also think that using common assessments among grade levels is very important.  As a third grade team, we have worked hard to develop our common assessments to make sure that all third graders are being held accountable to the same standards.
2.  I think the best way to approach assessment is to use multiple methods.  Some students are just not good test takers, and I would love to have more time/resources to be able to complete more projects and oral presentations with students so that everyone could experience a more individualized approach to assessment.  Tests and quizzes certainly have their place to help drive instruction, but there are definitely a lot of methods would be very useful and more meaningful to students.

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1. Our whole group lessons include word problems and the students show their thinking on whiteboards. This is a formative assessment that gives us the opportunity to identify misunderstandings, give some guided instruction for individuals, and get an overall assessment. Small group instruction is a great opportunity to break down the skill and/or provide enrichment. I think that providing purposeful centers and small group instruction is a way to gather data to grow students. Feedback could be given to students in small groups-students with similar misunderstandings. Students would not always be with same classmates in their groups. Another thought is that feedback could be sharing what was a good way to solve or show their work. It could also be to have the student try it again - after a whole group review.
2. I like the idea of projects in place of "end of unit assessments." The students should be able to choose from choices of ways to show their knowledge. Some students are artist and some like technology. The choice would give the students ownership and the opportunity to use a media that is of interest to them.

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1. In third grade our daily whole group lessons teach skills through word problems.  The kids work out their answers on white boards which allows the teachers to walk around and ask the children questions about their thinking and also monitor their outcomes.  Small group instruction allows for even greater monitoring of the students understanding of the various skills.  The teacher can break the skill down further to help struggling students understand better or enrich those students who need enrichment.  Rotations using eSpark, math games, and worksheets can also be used to monitor understanding.  2.  One project based assessment that the students complete is a graphing project.  After the students have learned all about the different types of graphs they use this knowledge to design a question, collect data (surveying the students in various classes), then they create their graphs and display them on a poster.  Finally, they present their poster to the class.  The kids really love this project and it gives me a lot of information about their understanding of graphs.
I would love to do more project based assessments that allow the kids to choose how they would like to present their knowledge of the skills.  The kids could record their understanding, design a poster, create a powerpoint, demonstrate their understanding through a presentation, or come up with their own idea for showing what they have learned.

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1. This chapter was very interesting to me in that for my kiddos quizzes and tests end up taking days to complete, only for a grade to be given, and onto the next the concept- often the new concept is started in class even before they finished the assessment. Which raises the question, is this type of assessment informing instruction? Does this involve the students in taking an active role in their learning? Do students know what they know and what they are working on knowing? I think having students actively engaged in working toward their learning goals would be the ideal. Could this possibly be achieved by a change in our thinking about the way we assess what students know? I think yes. If students take small 2 question exit tickets that are mix of computation, error analysis, open ended tasks that allow students to model and then explain their thinking would all give powerful insight into where students are. And if we pair those exit tickets with powerful feedback provided by conferencing with students during small groups, our students would be empowered to know then what their focus should be during the practice of the concept that follows- because they know what they are doing well, and what they need to work on still. And there is no reason to be upset by their mistakes, because they understand they have the time to continue to grow and learn in this concept.

2. Honestly, with standards based report cards, we have the ability to assess students through multiple modes and replace typical unit tests with opportunities for students to show their thinking in a multitude of ways. The text gave examples of students could be given a choice of math tasks that would be completed during independent center time. That would be another way that they could be assessed, both formative and summative. For summative assessments, the deeper problem-based tasks that are discussed earlier in the text that involve combining several skills would be a great way for students to show what they know. And they could even collect these as well as exit tickets and written responses in a math portfolio to show growth- which in turn could be reflected in what number goes on their report cards.

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I think we need to thoughtfully incorporate a variety of formative assessments into our daily instruction so that we can assess our students in the moment.  This can include using white boards, exit tickets, and observations during our small groups.  We should be able to use the information we gather from these daily assessments to guide / adjust our instruction and to help us differentiate to meet our students' needs.  I know that I need to work on using more specific feedback to help my students grow.

I feel that we need a variety of assessments in order to get a good sampling of the students' learning. It would be great to see more project-based assessments where the students are using what they have learned and applying it to real-world situations. Choice boards would be a great option to allow our students to demonstrate their understanding through various activities that they select. This allows them to incorporate their learning styles and interests to show what they know.

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I feel like my small group teacher center is one of my best options for both assessing student understanding and providing them with immediate feedback.  I love when I hear my kiddos say just as their centers time with me is coming to an end, “Can’t we do just one more problem??” or “I wish we could stay with you for another rotation.”  This tells me that the interactions we are having and the feedback that they are receiving really are making an impact on their learning.  Another thing I love, are some of the awesome ideas shared by my math buddies in the posts for this chapter!!  Since finding a dedicated amount of time for exit slips at the end of each lesson can often be difficult, Rachael’s idea of incorporating exit slips into the independent center is a great one.  The students get to practice the skill, show what they know, and we get a quick snapshot of their understanding.  I especially like the idea of then using the exit slips as discussion starters and feedback opportunities during our teacher center.

While I do think that paper-and-pencil tests play an important role in our assessment process, I would love to see some other evaluation options included.  In the past, we incorporated different student projects as a means of assessing student understanding.  I still have past students ask me if we still do the Restaurant Project or the Geo-town Project, and they always express how much they loved these projects and can still remember what they created.  On-going projects like these gave the students a different avenue for expressing their understanding of concepts, allowed me to assess multiple skills at  a time, and provided many wonderful real-world connections.  Unfortunately, again, time plays a factor in implementing this type of assessment.  Dedicating more than one class period to a paper-and-pencil test can cause a time crunch to our very tightly packed schedule, so it is difficult to see how we could devote multiple days to more involved projects.  Another option for putting our great math minds together to see how we could possibly make something like this work! 😊

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I think centers provide a great way to assess students understanding as we go through a unit. Independent work and work they do in small group gives me a good idea of where they are at with the skills we are working on. I also like using check-in slips with a couple questions or error analysis problems to see how students are doing. Giving students feedback during small group on what they are doing well and what they need to improve on. For ideal assessments, I would have multiple ways of assessing students. This could be in the form of end of unit projects, check-ins, and error analysis.

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1.  Our independent center would be a great time to put out exit tickets for our students.  This does not take time from whole group and still gives the teacher feedback.  I also think that they could even be talked about during teacher center, if the centers are planned for this order.  This would give the students immediate feedback and then time to practice the skill.  I know time is the issue her, but it may work on certain days when planned.
2. If we did not have to give grades, wow what a difference that would make! I think we could incorporate more projects into math and centers. I think these projects would be ongoing and incorporate many areas. We could use these projects to drive instruction based on methods and strategies the students used to solve the problems. We could base our small groups on the strategies students presented to keep them moving to more efficient ways of solving problems.

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I like the ideas that were shared that included error analysis. I always felt that the students who could find the mistakes and correctly identify and fix the error showed greater understanding than those who could just simply solve the problem. Also while using the white boards in the classroom to work on problem solving I am quickly able to see who is getting the lesson and who needs help. The students also appreciate the immediate feedback I can provide them when they hold up their whiteboard, when finished, and then I either give them a thumbs up or down depending on their response. While they enjoy the positive feeling they get from a thumbs up, I enjoy seeing their response to my thumbs down when they go into "error analysis" mode and try to find where the mistake was made. This is the point where I also allow students to share their work with partners and discuss agreements or disagreements. The assessment I enjoy working with the most is when I ask the students to come up with a question and set of answers to share with the class. I often reward the student if they can come up with a question that none of the other students can answer (it has to be reasonable). The students also enjoy the challenge and are eager to solve the questions, maybe because they don't want to see the other student get their reward. Kind of backwards thinking but is motivating for them.

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1.  We have been deliberate in using real world problems in our daily instruction in both whole group and small group.  I have focused on vocabulary and building prior knowledge in order to guide the students in understanding what the question is asking.

I prefer immediate feedback.  I am happy to use nonverbal, verbal or written encouragement and guidance,  Using Google Classroom allows be to comment privately to each student and gives them the opportunity to ask questions that only I can see. I also like to incorporate writing with a low floor/high ceiling "brain dump."  For example, "Tell me what you know about fractions."

2. If I didn't have to give formal assessments, I would focus more on small group instruction and forgo whole group instruction. I would create a multi-day project focused on a standard and have the groups report their findings.

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I believe teachers are assessing students constantly whether it is the end of the unit assessment, small quizzes, exit tickets, white board questions asked during a lesson, Kahoot, Prodigy, Espark, classwork, project, or even small group questioning / observing. Teachers need constant assessing to see where their students are at with reaching the targeted learning goal, to adjust their teaching based on constant needs, for parent calls /dojo messages, and for report card time. I think back to when we were doing multiplication and division, almost everyday I would give them an exit tickets of two problems so I knew how to adjust my whole group and station groups for the needs of the students. I do agree with others here that I use white boards many, many times daily.  I verbally tell students they are correct, thumbs up or down, or give one-one suggestions and comments. There is also partner and small group feedback which does take some time to teach the kids to what kind of feedback and how to give appropriate feed back. One of my constant goals is returning my feedback in a smaller amount of time, but this is a struggle for me.  Lastly, I would love to have the day where there was grades to worry about.  If that ever came I do still believe you would have to still do assessments and record keeping to know how to drive your teaching, but to also be able to have effective feed back to parents and to students. I would then enjoy using more projects, more choice activities, and more taking time to help students find out what kind of learner they are (visual, auditory, kinesthetic).

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Again, this is why i love my math stations. I feel like I always have a pulse on what the students know and what they may need more help with. I can watch and see what instruction that I did works or doesn't. Then I can adjust. I take note, work with kiddos one on one. I take all of this in when giving a "grade" at the end. This would be my ideal assessment. But more like a check list form during math station. This is where they have to ongoing, apply what they have learned independently, or with support!