We are on week two of the math blogger initiative and one of the prompts this week is to share one worksheet/assessment/etc. Since my last post was on how we grade using a rubric, and I referenced how we format our assessments I thought this would be a good time to share one. Obviously I don't want to post an exact assessment as my students may read this! Instead I have posted a review worksheet, which is virtually the same as the exam. The level 2 and 3 questions will simply have different numbers/values. I tell my students that level 4 can be anything related to the outcome, so these two questions are simply sample level 4 questions.

N9.1A Reassessment Binder Review

You will notice that we include the rubric on the assessment. We feel this is important as the students are then asked to reflect on their learning when the assessment is returned. The rubric will help them to see what they know and what they still need to work on.

We have also decided to be transparent in the level of each question. What this does is ease the student into the assessment. If you put a difficult question at the start (which I have done in the past!) you may increase the anxiety of students and some may not be able to continue even though there will be questions they know. Some people might worry that students will only answer the level 2 and then quit. This happens very rarely in my experience. Because we focus on learning and improving, most want to do as well as they can and they realize there is no punishment in simply trying. This format also makes it really easy to score! We are currently working on re-formatting all of our assessments this way.

## Thursday, August 23, 2012

## Monday, August 20, 2012

### Grading with a Rubric

In an earlier post (here) I talked about the 4 point rubric that we use. Now that we have the rubric, we need to make sure everyone understands how to grade with it! What we discovered early on is that there were some misunderstanding to this process and some were still grading each question /4 and then finding an average of all of the scores. This is not the way we want to be using the rubric. In fact, one thing that should be pointed out is that at no point do you ever want to see a #/4 on an assessment. Mathematically this can be confusing, as students will convert to a percent and the rubric is not about a fraction/percent "grade" but a level of understanding.

In Robert Marzano's book

This has been difficult for some students to understand. They might have the same quantity of questions correct, but score different from a peer and wonder why. It has taken a lot of teaching to have them understand that they need to read the rubric to see where their level of understanding is consistent. I have given back assessments to my students that does not have a score on it. I have corrected the assessments and recorded in my gradebook their score, but have not written it on their papers. I ask them to go through their assessment, read the rubric and score their assessment. I then take them back in to see what they think. Most students are bang on. The ones that aren't we then have a discussion. Some have even convinced me that they deserve the score they gave. These conversations show me that their level of understanding is maybe higher than I thought. I would like to do more of this with my students this year.

A couple of my colleagues and I created a couple of short videos to help others understand how to grade with a rubric. These were done a couple years ago and the look of our assessments have changed, and the rubric has changed but the idea of how to grade has remained the same. The videos are here and here.

This year our math department will meet on a regular basis to do common grading. I believe this is also important to make sure we are all interpreting the rubric consistently and to see if any need tweeking because we are too far apart in our interpretations.

In Robert Marzano's book

*Formative Assessment and Standards Based Grading*he spends a whole chapter (3) talking about this scale and showing how to score with it. He talks about organizing assessments into three sections - one for score 2.0 content, one for score 3.0 content and one for score 4.0 content. (Page 46) We now do this on all of our assessments. The students are well aware of where each question fits on the level of understanding rubric. Marzano then goes on to say that "to score this assessment, the teacher would look at the pattern of responses across the three sections. If a student correctly answered all items on the test, she would receive a score of 4.0. If she answered all items correctly in section A (level 2) and B (level 3) but not C (level 4), she would receive a score of 3.0. If she answered all of the items correctly to section A but not B and C, she would receive a score of 2.0. If she could answer no items correctly on her own but could answer some items correctly with help from the teacher, she would receive a score of 1.0." (Page 46) This is exactly how we grade with our rubrics. The challenge lies with those students who have some questions correct in a level but not all. This is where our half points come in to play.This has been difficult for some students to understand. They might have the same quantity of questions correct, but score different from a peer and wonder why. It has taken a lot of teaching to have them understand that they need to read the rubric to see where their level of understanding is consistent. I have given back assessments to my students that does not have a score on it. I have corrected the assessments and recorded in my gradebook their score, but have not written it on their papers. I ask them to go through their assessment, read the rubric and score their assessment. I then take them back in to see what they think. Most students are bang on. The ones that aren't we then have a discussion. Some have even convinced me that they deserve the score they gave. These conversations show me that their level of understanding is maybe higher than I thought. I would like to do more of this with my students this year.

A couple of my colleagues and I created a couple of short videos to help others understand how to grade with a rubric. These were done a couple years ago and the look of our assessments have changed, and the rubric has changed but the idea of how to grade has remained the same. The videos are here and here.

This year our math department will meet on a regular basis to do common grading. I believe this is also important to make sure we are all interpreting the rubric consistently and to see if any need tweeking because we are too far apart in our interpretations.

## Wednesday, August 15, 2012

### Learning Logs

I have signed up to be a part of the math blogging initiative and have been given my first "assignment". I am looking forward to this initiative and learning from other teachers!

One of the choices for our assignment was to blog about one or two specific things that we plan on doing differently this year. One change I am planning on implementing with my math 9's is to incorporate learning logs into the classroom. I feel that I have managed to find an opener for class (My favorite formative activity) that works well, but I don't have a good closer. Typically the students are completing practice until the bell goes.

I have been reading

My students have duo-tangs that are left in the classroom where they keep their continual progress reports (click here to see these), and assessments. I am also going to include sheets for their learning log in these. That way if they stay in the classroom I can sit down and read through them when I have time (my goal is once a week!). The suggestion in the book is that you provide them with the following prompts and the students are to choose no more than three to respond to that day. I am not sure if I will give the complete list or if I will choose one or two each day for the students to respond to. I am also not sure if I will ask them to choose only one a day or allow up to three. I plan on doing this with 5 minutes left in class. Any suggestions on how to proceed would be appreciated!

The prompts suggested in the book are:

Today I learned...

I was surprised by...

The most useful thing I will take from this lesson is...

I was interested in...

What I liked most about this lesson was...

One thing I'm not sure about is...

The main thing I want to find out more about is...

After this session I feel...

I might have gotten more from this lesson if...

I really liked this idea when I read about it. I hope to have it become part of our daily classroom routine.

One of the choices for our assignment was to blog about one or two specific things that we plan on doing differently this year. One change I am planning on implementing with my math 9's is to incorporate learning logs into the classroom. I feel that I have managed to find an opener for class (My favorite formative activity) that works well, but I don't have a good closer. Typically the students are completing practice until the bell goes.

I have been reading

*Embedded Formative Assessment*by Dylan Wiliam (a great read by the way) and found the idea of a learning log (page 157). A learning log is a way to get students to reflect on their learning. I also think it will help me improve my skills as a teacher by reading what works well and what doesn't for the students. My goal is to implement this with my math 9 class in semester 1. My math 9's have always been my guinea pigs. They are willing to try new things and we have more flexibility with time to work out kinks. Assuming it goes well I will implement it with all of my classes in semester 2.My students have duo-tangs that are left in the classroom where they keep their continual progress reports (click here to see these), and assessments. I am also going to include sheets for their learning log in these. That way if they stay in the classroom I can sit down and read through them when I have time (my goal is once a week!). The suggestion in the book is that you provide them with the following prompts and the students are to choose no more than three to respond to that day. I am not sure if I will give the complete list or if I will choose one or two each day for the students to respond to. I am also not sure if I will ask them to choose only one a day or allow up to three. I plan on doing this with 5 minutes left in class. Any suggestions on how to proceed would be appreciated!

The prompts suggested in the book are:

Today I learned...

I was surprised by...

The most useful thing I will take from this lesson is...

I was interested in...

What I liked most about this lesson was...

One thing I'm not sure about is...

The main thing I want to find out more about is...

After this session I feel...

I might have gotten more from this lesson if...

I really liked this idea when I read about it. I hope to have it become part of our daily classroom routine.

## Sunday, August 12, 2012

### Redos

When making a shift to learning for all, one of the discussions/debates is centered around whether or not to allow "redos". This is a tough one for a lot of people. Four or five years ago I didn't believe in redos. I felt that if the student worked through the unit, did the assignments, asked for help, completed the review, which I always set up as a pre-test, then they should be ready for the unit exam. If they weren't then they hadn't tried hard enough and too bad. Now I feel bad for my students of that time period! Once you make the shift to "learning for all" and "moving learning forward" for the students, then redos/reassessments make sense! Why wouldn't we want our students to be able to demonstrate understanding of an outcome, even if it is two months after the formal lessons in class? Ultimately the goal of the course is for students to have demonstrated learning in all outcomes. Why we have set dates for this to happen is beyond me! The curriculum states that the student will demonstrate an understanding of.... by the end of the course, not by October 15, when I have decided to give a "unit exam"!

Rick Wormeli has a great video where he shares his views as to why we should allow reassessments. You can click here to watch part one of this video. Click here to watch part two.

Here are some of the hurdles that I hear to giving reassessments and my solution to them:

Well in some cases this is true. However, I have discovered that if you present this in a certain way then those will be minimized. I tell my students that it is important to do the best you can on the first try because in the end, if you jump around with your levels of understanding then I will look for the most consistent level. They know that if they consistently improve, then I will give them their final score, so the first ones won't count, but if they jump around ie. 2, 3, 2, I tell them I have to look at consistency and now that first assessment holds some weight. Because of this, most students will do the best they can on the first attempt. But yes, there are those that won't... we simply have to worry about what we can control!

In three years of experience I have yet to come across this. I am not saying it won't happen and we might have those one or two students who do this. I say let's cross that bridge when we get there. I think that with the way things are now set up this won't be a problem. But I might be wrong!

It is about the student's learning. The ultimate goal is that students will learn. We don't go and ask our doctors how many times they had to write the medical exams before they passed. They are all doctors now and it doesn't matter. Some babies learn to walk at 6 months and some not until 18 months. Should we penalize the late walker and say they can never play sports? A level 3 is a level 3, no matter when they achieved it. Ultimately they now know the material.

Well there is a cost associated with reassessing. I don't allow my students to walk into my classroom and say "I want to rewrite outcome 5." They have to show me that they have done some work in preparing for this outcome. Whether it be making the corrections on their last assessment, or showing me that they have now completed all of their practice questions, or doing an extra set of practice questions, or simply having a conversation with me, they have to have put in some extra time before they get to reassess. It's not a revolving door where they write, get back a low score and walk in to write again. There has to be work done in between. This work must be shown at least one day prior to wanting to reassess. As far as creating these, yes, it is a little extra work, but ultimately I feel my job is about helping students learn and this is one part of my job. With math, it is pretty easy to change numbers in a question. Level 2 and 3 questions which tend to be process problems, are easy to change. The level 4 do require a little more thought on my part, but when I am developing the learning plan I try to create a bank of level 4 questions so that I can easily pull from this. Depending on the outcome and the extent of the misunderstanding in the first assessment, sometimes I simply do an oral reassessment. If I have a conversation with the student and they are able to explain their understanding then that is good enough for me. It is really not a lot of work and in the end it benefits the student. It also makes my job easier in following classes when I get these students as they now have a higher level of understanding than if I didn't allow for the reassessments and learning to occur.

Yes, this was a problem. However another colleague and myself have found a solution that has worked. We have set up a reassessment policy that is communicated to the students and signed by the students and their parents. We have set up contract dates at the start of the year. They are 3 - 4 weeks apart. At each date, any student who is below a level 2 on any outcome is placed on contract. They then have until the next contract date to attempt this outcome again. The other colleague and I each take a noon hour a week to supervise these reassessments, so the student has two days a week to complete this. This keeps the students more organized and spreads out the assessments over the course of the semester. We also have a final reassessment date about 2 weeks prior to the final exam. After this, there is no reassessing. The final exam is the reassessment. The students are all aware of these dates and it keeps things moving smoothly.

Well that is actually false. There are many instances where people have redos! Going for a drivers license is one that most people will experience. Not everyone passes on their first attempt, yet that isn't held against them when they go the next time. We don't have stickers on our vehicles that say "I passed on my fifth time". Airplane pilots did not land an airplane on their first attempt. They practiced hundreds or thousands of times in a simulator before attempting with a real aircraft. Accountants have more than one chance to write their exams. Lawyers have more than one chance to pass the bar exam. This list could go on and on. School is about learning. Failure is a part of learning. Moving forward and becoming better is a part of learning.

Reassessments have worked well for me when a student walks in on an assessment day and says that they are not ready for the assessment. I now tell them that it is okay, they can try the assessment, do the best they can and then we'll know what they still need to work on. Usually the student is more prepared than they think. Test anxiety is removed when they know there is another chance if needed. Many times the student doesn't have to reassess, they simply weren't confident enough and are still programmed that all assessments "count" towards their final grade. With that not being the case anymore, the student is more relaxed and often finds that they are more prepared than they thought!

Reassessments are not a bad thing. I now not only allow reassessments, but encourage them. I want my students to WANT to learn and WANT to show mastery. I encourage them to be the best they can be. I apologize to my students in the past when I didn't allow reassessments!

Rick Wormeli has a great video where he shares his views as to why we should allow reassessments. You can click here to watch part one of this video. Click here to watch part two.

Here are some of the hurdles that I hear to giving reassessments and my solution to them:

**"If I allow reassessments then kids won't try hard the first time"**Well in some cases this is true. However, I have discovered that if you present this in a certain way then those will be minimized. I tell my students that it is important to do the best you can on the first try because in the end, if you jump around with your levels of understanding then I will look for the most consistent level. They know that if they consistently improve, then I will give them their final score, so the first ones won't count, but if they jump around ie. 2, 3, 2, I tell them I have to look at consistency and now that first assessment holds some weight. Because of this, most students will do the best they can on the first attempt. But yes, there are those that won't... we simply have to worry about what we can control!

**"If I allow reassessments for everyone then the high achievers will keep rewriting until they get the 4 because they want the scholarships and they might write 10 times to do this."**In three years of experience I have yet to come across this. I am not saying it won't happen and we might have those one or two students who do this. I say let's cross that bridge when we get there. I think that with the way things are now set up this won't be a problem. But I might be wrong!

**"How is it fair that a student who scores a 3 on their third attempt is the same as the a student who scores a 3 on the first try."**It is about the student's learning. The ultimate goal is that students will learn. We don't go and ask our doctors how many times they had to write the medical exams before they passed. They are all doctors now and it doesn't matter. Some babies learn to walk at 6 months and some not until 18 months. Should we penalize the late walker and say they can never play sports? A level 3 is a level 3, no matter when they achieved it. Ultimately they now know the material.

**"It will be time for me to create and score all of these extra assessments. What does the student have to do?"**Well there is a cost associated with reassessing. I don't allow my students to walk into my classroom and say "I want to rewrite outcome 5." They have to show me that they have done some work in preparing for this outcome. Whether it be making the corrections on their last assessment, or showing me that they have now completed all of their practice questions, or doing an extra set of practice questions, or simply having a conversation with me, they have to have put in some extra time before they get to reassess. It's not a revolving door where they write, get back a low score and walk in to write again. There has to be work done in between. This work must be shown at least one day prior to wanting to reassess. As far as creating these, yes, it is a little extra work, but ultimately I feel my job is about helping students learn and this is one part of my job. With math, it is pretty easy to change numbers in a question. Level 2 and 3 questions which tend to be process problems, are easy to change. The level 4 do require a little more thought on my part, but when I am developing the learning plan I try to create a bank of level 4 questions so that I can easily pull from this. Depending on the outcome and the extent of the misunderstanding in the first assessment, sometimes I simply do an oral reassessment. If I have a conversation with the student and they are able to explain their understanding then that is good enough for me. It is really not a lot of work and in the end it benefits the student. It also makes my job easier in following classes when I get these students as they now have a higher level of understanding than if I didn't allow for the reassessments and learning to occur.

**"I'm going to have so many assessments to mark at the end of the semester when all of a sudden they realize they don't have the scores they want."**Yes, this was a problem. However another colleague and myself have found a solution that has worked. We have set up a reassessment policy that is communicated to the students and signed by the students and their parents. We have set up contract dates at the start of the year. They are 3 - 4 weeks apart. At each date, any student who is below a level 2 on any outcome is placed on contract. They then have until the next contract date to attempt this outcome again. The other colleague and I each take a noon hour a week to supervise these reassessments, so the student has two days a week to complete this. This keeps the students more organized and spreads out the assessments over the course of the semester. We also have a final reassessment date about 2 weeks prior to the final exam. After this, there is no reassessing. The final exam is the reassessment. The students are all aware of these dates and it keeps things moving smoothly.

**"In the real world you don't get a second chance."**Well that is actually false. There are many instances where people have redos! Going for a drivers license is one that most people will experience. Not everyone passes on their first attempt, yet that isn't held against them when they go the next time. We don't have stickers on our vehicles that say "I passed on my fifth time". Airplane pilots did not land an airplane on their first attempt. They practiced hundreds or thousands of times in a simulator before attempting with a real aircraft. Accountants have more than one chance to write their exams. Lawyers have more than one chance to pass the bar exam. This list could go on and on. School is about learning. Failure is a part of learning. Moving forward and becoming better is a part of learning.

Reassessments have worked well for me when a student walks in on an assessment day and says that they are not ready for the assessment. I now tell them that it is okay, they can try the assessment, do the best they can and then we'll know what they still need to work on. Usually the student is more prepared than they think. Test anxiety is removed when they know there is another chance if needed. Many times the student doesn't have to reassess, they simply weren't confident enough and are still programmed that all assessments "count" towards their final grade. With that not being the case anymore, the student is more relaxed and often finds that they are more prepared than they thought!

Reassessments are not a bad thing. I now not only allow reassessments, but encourage them. I want my students to WANT to learn and WANT to show mastery. I encourage them to be the best they can be. I apologize to my students in the past when I didn't allow reassessments!

## Friday, August 3, 2012

### My Favorite Formative Activity

There are many different definitions and ideas of what formative assessment is. Do you grade it? Is it just feedback? Is it an assessment? A tool? A process? Dylan Wiliam says "Formative assessment involves getting the best possible evidence about what students have learned and then using this information to decide what to do next."

There is a lot of debate as to whether formative scores should be recorded. I've adopted the idea that some of my formative "activities" are simply to collect evidence in an informal way, I will not score these. The activity I am going to describe in this post falls in this category. Other formative "activities" I will record and use these to assist with determining overall levels of understanding, "the summative score". I think that Dr. Marzano best describes this when he says "a specific assessment is neither formative nor summative - it all depends on how the information is used. Theoretically then, the same assessment could be used in a formative sense or in a summative sense."

In my class, I believe all of my formal assessments can be formative in nature. The student has until the end of the semester to demonstrate deep understanding, so if a "unit test" at the start of the semester is improved upon by the "final exam" then that unit test was formative in nature.

My favorite "informal" formative "activity" is one that has been routine in my class for about 5 years. I got the idea from a colleague who did "3 minute reviews" at the start of her class. It is similar to an entrance slip, but instead of testing what will be happening that day, I ask a question about a past skill/process. It may or may not have anything to do with the daily lesson. When the bell rings, there will be a question on the board and the students have 3 - 5 minutes to try and answer it. For four and a half years, I had students put these in a duo-tang that were kept in my classroom. I would look at them usually once a week. They were not graded, just given feedback. Each day, after the students had time to complete the question we would then take it up as a class. Sometimes I would have a student put the answer up on the board, sometimes I would question a number of students on each step of the problem. I loved this activity as I felt it was a great review. I have had other teachers ask what they should do when at the end of a "unit" a number of students are still struggling with the concept. In many cases I don't feel that spending one or two more days will be of great benefit. However if you now do one question a day, for two or three weeks, the students will have the time to sort out their problems, and those who understand it won't be bored. In my math 9 class, three of the first four outcomes that we learn are rational numbers, polynomials and solving linear equations. I now have the entire year to continually review these skills, which are essential to success in math down the road.

In about April this past year, I watched the following video that was posted on twitter from The Teaching Channel. It changed how I went about these entrance slips and has given me better feedback, instant feedback, and it has given the students better feedback, so learning moves forward at even a quicker pace! Click here to see the video. The teacher was doing something very similar to me, except she went one step further. She then turned the activity into an error analysis. Brilliant! It meant a slight change to what I was doing. Instead of using the duo-tangs that I was, or the index cards she used, I took scrap paper and cut it into four pieces and I hand that out to the kids at the start of class. They then hand them back to me as they complete the problem, I quickly sort them into yes or no piles, choose one from the "no" to rewrite on the board. We then spend time going through this solution. We find things that the student did correctly, we try to analyze where their misconception was, and we correct the solution. It is instant feedback for the students and for myself and I find that learning occurs quickly. One of my first attempts with this was when I was reviewing solving linear equations containing fractions. It had been a while since we had done these in class. I put a question on the board and discovered that only about 4 students had done it correctly. The majority of the "no's" had converted the fractions to approximate decimals. We went through the error analysis and discussed why this was not an exact answer. The next day, I put a similar question on the board and I had about half of my class get the question correct. This time only 2 students converted to decimals! We were improving. With this process I know how long I need to spend on the same type of question before we are ready to move to another skill. I also know at the end of it which students now need some extra one on one help with the skill. I love it! This whole process takes 5 - 10 minutes, but it is well worth that time. I don't believe I could accomplish the learning that takes place in this time in one period of extra practice on the skill. I highly encourage trying this with your students!

*Embedded Formative Assessment, Dylan Wiliam, page 50.*I like this statement. I want to find out what my students know and from there I need to make decisions on what to do next to move learning forward.There is a lot of debate as to whether formative scores should be recorded. I've adopted the idea that some of my formative "activities" are simply to collect evidence in an informal way, I will not score these. The activity I am going to describe in this post falls in this category. Other formative "activities" I will record and use these to assist with determining overall levels of understanding, "the summative score". I think that Dr. Marzano best describes this when he says "a specific assessment is neither formative nor summative - it all depends on how the information is used. Theoretically then, the same assessment could be used in a formative sense or in a summative sense."

*Formative Assessment and Standards Based Grading, Robert J. Marzano, page 27.*He goes on to further say that "all assessments are in a sense 'formative'."*page 28.*In my class, I believe all of my formal assessments can be formative in nature. The student has until the end of the semester to demonstrate deep understanding, so if a "unit test" at the start of the semester is improved upon by the "final exam" then that unit test was formative in nature.

My favorite "informal" formative "activity" is one that has been routine in my class for about 5 years. I got the idea from a colleague who did "3 minute reviews" at the start of her class. It is similar to an entrance slip, but instead of testing what will be happening that day, I ask a question about a past skill/process. It may or may not have anything to do with the daily lesson. When the bell rings, there will be a question on the board and the students have 3 - 5 minutes to try and answer it. For four and a half years, I had students put these in a duo-tang that were kept in my classroom. I would look at them usually once a week. They were not graded, just given feedback. Each day, after the students had time to complete the question we would then take it up as a class. Sometimes I would have a student put the answer up on the board, sometimes I would question a number of students on each step of the problem. I loved this activity as I felt it was a great review. I have had other teachers ask what they should do when at the end of a "unit" a number of students are still struggling with the concept. In many cases I don't feel that spending one or two more days will be of great benefit. However if you now do one question a day, for two or three weeks, the students will have the time to sort out their problems, and those who understand it won't be bored. In my math 9 class, three of the first four outcomes that we learn are rational numbers, polynomials and solving linear equations. I now have the entire year to continually review these skills, which are essential to success in math down the road.

In about April this past year, I watched the following video that was posted on twitter from The Teaching Channel. It changed how I went about these entrance slips and has given me better feedback, instant feedback, and it has given the students better feedback, so learning moves forward at even a quicker pace! Click here to see the video. The teacher was doing something very similar to me, except she went one step further. She then turned the activity into an error analysis. Brilliant! It meant a slight change to what I was doing. Instead of using the duo-tangs that I was, or the index cards she used, I took scrap paper and cut it into four pieces and I hand that out to the kids at the start of class. They then hand them back to me as they complete the problem, I quickly sort them into yes or no piles, choose one from the "no" to rewrite on the board. We then spend time going through this solution. We find things that the student did correctly, we try to analyze where their misconception was, and we correct the solution. It is instant feedback for the students and for myself and I find that learning occurs quickly. One of my first attempts with this was when I was reviewing solving linear equations containing fractions. It had been a while since we had done these in class. I put a question on the board and discovered that only about 4 students had done it correctly. The majority of the "no's" had converted the fractions to approximate decimals. We went through the error analysis and discussed why this was not an exact answer. The next day, I put a similar question on the board and I had about half of my class get the question correct. This time only 2 students converted to decimals! We were improving. With this process I know how long I need to spend on the same type of question before we are ready to move to another skill. I also know at the end of it which students now need some extra one on one help with the skill. I love it! This whole process takes 5 - 10 minutes, but it is well worth that time. I don't believe I could accomplish the learning that takes place in this time in one period of extra practice on the skill. I highly encourage trying this with your students!

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