w4d1 5.5 Cases From the Classroom

Assessment is the process of collecting information to find out what students are learning. As we have examined different instructional models throughout this course we have learned about evaluating instructional objectives. Read the observation notes from Dr. Zwijac located in section 5.5 in your textbook and answer questions 2, 5, and 6 (bulleted below). Keep in mind you will need to read the entire chapter to be able to apply the principles therein to end of chapter discussion questions. 

· Help Ingrid to understand how the district’s CFA can assist her instructional efforts. Given her current second-quarter goals, offer one suggestion for an appropriate formative assessment strategy in Language Arts and in Math.

· What advice would you give Melanie for developing assessments for learning that encourage and bring smiles to her kindergartners?

· Discuss how and why formative assessment is considered assessment for learning, and why summative assessments are considered assessment of learning. What advice would you give these teachers to help them consider the advantages of each?

5.5 Cases From the Classroom

From the Desk of: Jeff

December 6

Hola, Dr. Z.—

This week you wanted to know how we use assessments in our teaching. Well, in our district, we have organized middle school math around a system of Common Formative Assessments (we call them CFAs). These are tests that were developed by the district teachers and curriculum coaches for us to use near the end of each major unit. The curriculum pacing guide gives a suggested date for when these tests should be given, and then a 2-week window for re-teaching or enrichment.

After giving the last CFA, I sat down with Meredith, the other 6th grade math teacher at my school, and we sorted the results into categories. Which problems did a lot of students miss? Which problems did all students get correct? What concepts need to be re-taught and to whom? How can we enrich these concepts for those who are ready? Then, we shared what we had with the 7th and 8th grade math teachers in our PLC, and they did the same with their results. I like this process. At first I didn’t get it—it seemed like just a lot of meeting time. But as the year has gone on, I am beginning to see how we are working together to help each other out. The upper-grade teachers are interested in the 6th graders learning so they can move forward in their own curriculum—and I am able to see first-hand where my own students are heading next year and the year after. From these CFA results, we organized student support groups and planned out who will do what and when. We also brought the CFA results (and our analysis) to the district math meetings, and worked in grade level teams to see how everyone was doing. We adjusted the pacing guides and calendar somewhat, and worked on enrichment activities for those who understood the concepts, and re-teach activities for the others. Since we have 2 teachers for the 6th grade in my school, this was do-able for us.

To me, the test wasn’t formative enough. What I learned from this process is that waiting until close to the end of the unit to adjust based on the CFA was too late for me to know what is really going on with the students. In-class assignments and homework helped me to see who is getting the answers right, but I didn’t know how they understand the concepts. When I looked at the first CFA results, I was disappointed. I had taught that skill, why hadn’t they remembered? I was surprised by what they didn’t know. And I must admit I was angry—probably at myself more than them, but I really had an emotional reaction to less than 50 percent of the students making a “proficient” score. I realized that I needed a quicker way of knowing what was going on.

I figured this out when it came to the unit on dividing fractions. The big idea that it was important to know which operation was appropriate. So, we reviewed what they knew about addition, subtraction and multiplication of fractions. I began with a question that I wanted them to solve alone and show their work (big so I could see it) on their dry erase boards.

You did 8 loads of laundry by filling the detergent cup 3/4 full. How many loads of laundry could you have done if you filled the detergent cup to the top for each load?

Their answers were all over the place! Some recognized that this was a multiplication problem, and showed the correct answer, 6. Others though it was an addition problem, and some subtracted. But what I saw amazed me. If I hadn’t asked them to write big and hold up their white boards so that I could see all the answers at once, I might have missed this. Most of them drew a butterfly in order to work out the math! Some multiplied using the numbers in the butterfly and got a beautifully logical but wrong answer, others added or subtracted. And no one could tell me their thinking behind the numbers. They had learned a procedure, but did not understand the meaning. To them, getting the answer was the most important thing. And getting the right answer was more important than understanding the meaning behind the math. I think that some of the tricks they use to get at what they hoped would be the right answers end up confusing them even more.

I had to explain my philosophy—I called it the 6th grade rules, now that they are all grown up and in middle school. They are: “Always explain your answers,” and “Wrong answers are part of the process of learning.” A mistake is their opportunity to share what they do not understand before the test. The CFA test is too late. And no more butterflies or other cute stuff that doesn’t have anything to do with math. If the answer works, there is a mathematical reason why it works.

How do I keep up with what they know when I see 90 students each day? I am beginning to use a variety of ways. During class, the students work in small cooperative groups to solve a few problems and develop an explanation using a model or a diagram. For example, I changed the opening question from multiplication to division of fractions to see if they could use the appropriate operation:

You have 9 ounces of laundry detergent. If it takes 3/4 ounce of detergent to wash one load of clothes, how many loads can you do?

Each group reported out by bringing their clearest paper to the document camera for all to see. Then we discussed how that particular answer was derived. Other group members asked questions and added their comments. I like giving these real-life questions, and have started asking the students to compose their own word problems that illustrate what we are working on.

I give independent homework assignments on Monday and Wednesdays. On Tuesday and Thursday, we go over their work and answer questions while students grade their own work. Then, each student scores how they did using the Exemplars Jigsaw Student Rubric. This rubric is neat because it emphasizes problem solving, reasoning and proof, communication, connections and representations—all concepts that work with the math practice standards. Using the rubric also is helping to build self-evaluation skills, which I think are very important. This system helps me to keep up with their work—I can quickly review 90 papers instead of grading each one from scratch.

Thanks for the suggestions on using student work as a formative assessment. I am using the idea from the Teaching Channel, “My Favorite No” (accessed from https://www.teachingchannel .org/videos/class-warm-up-routine). This is a warm-up routine, done in the first 5 minutes of class. I write a problem on an index card and display it on the document camera. Then I hand out index cards to the kids, and give them 5 minutes to write their answer. I quickly sort the cards into 2 piles, yes and no, looking for my favorite wrong answer, and then re-write that answer on an index card and show it on the document camera. It is called “My Favorite No” because it recognizes what they are doing wrong, but also what shows the part that is good math. There is a mistake, but the mistake did not ruin the whole thing, and it shows how far they are from getting it right. I ask questions, such as, “What is good about this answer? What does the person not understand? Where is the mistake?” I like using this idea because index cards are cheap and easy to sort, and I am able to quickly find out what percent of the class knows the concept. I am also able to figure out if the error was one of miscalculation or of misconception, and work on those ideas before moving on. And another thing—I can quickly record these results in the grade book—+ for those that got it, * for those who are still a bit confused but have most of their thinking OK, and - for those that I need to reteach. We never seem to have time for exit cards at the end, so this is a great way to begin the class.

Another thing—I am using those math websites you suggested. It helped me realize that some teaching techniques had nothing to do with evidence-based practice, and I had to be careful what I used. I have banned the butterfly. When using operations with fractions, the students have to show their work by drawing a model, preferably a number line or images made out of squares or rectangles. When we study inequalities (in January, after the break), I guess I will have to ban the “alligator that eats the larger number” (a common way to teach =, <, and > in elementary school). With the new standards, students will be assessed on their understanding of the inequality symbol as a placement (right or left) on a number line. Alligators won’t cut it. We are in the 6th grade now, so we will have to get rid of tricks that may be cute but have nothing to do with math.

So how am I doing? Dang I need a break! The second CFA is scheduled for next week. The results from the first one disappointed me, and I guess for a while I was a bit down over it. I tried not to take it personally, but I really thought I was doing a better job of teaching than that. I don’t want any surprises this time. I have worked hard to develop systems that I can live with that keep me aware of who knows what. I am thinking that a good 80 percent of the students will meet their target scores. The other 20 percent, well, Meredith and I have worked hard to give them the support they need, but they are still pretty inconsistent. So we shall see.

Hey, if I could only relate fractions to the beats on the drum—playing in my rock band is my sanity. We’ll be at The Goat this Saturday night—I put the invite on Facebook. Try to come if you can.

Only 15 more school days until the holidays!

—Jeff

Observation Notes From Dr. Zwijacz

December 7

With the end of the first semester approaching, I decided to focus on assessments and ask the teachers what they are using and how the results change their teaching (or not). So here is a quick check in:

Ingrid (Chapter 1) is busily preparing her fifth graders for the 2nd quarter CFA in math and language arts. She is working with her mentor (Marie) who suggests she concentrate on a review of the major standards for this quarter. In language arts, the test provides passages to read with questions that measure comprehension and are the basis for an informational writing piece. In math, the assessment will include adding, subtracting and multiplying fractions, dividing a whole number by a fraction, and estimating. Students will also have to explain why the procedures for multiplying and dividing fractions make sense. Ingrid is concerned that the CFA results will show how well she is or is not doing as a teacher, even though Marie and the school-based PLC will help her to analyze the results and organize reteaching and enrichment activities. Despite Marie’s reassurances that there is room in the schedule to give students the support they need, Ingrid is pretty still nervous about the upcoming test. Her words: “There is just so much to cover—especially when having to cover so many subjects in the elementary grades!”

Travis (Chapter 3) seems to be getting a handle on his concern about grading papers. He has developed a portfolio system for students to participate in self-evaluation of their work and make a case for their improvement. He is not trying to give a letter grade to daily writing assignments; rather, he is giving targeted feedback and lets the students choose their best work for reading aloud or moving forward for review. With new or difficult tasks, such as reading a particularly hard text, he asks more questions and gives more immediate feedback. He is experimenting with technology here, occasionally having the students post an answer to one thoughtful question on a Google Forms document. He is beginning to realize that formative assessments in areas with more complex skills require more sophisticated approaches than formulaic advice given for more concrete skills. A policy brief from the National Council of Teachers of English (NCTE) helped him to formulate his assessment ideas.

Lori, still involved in the unit on identity (see Chapter 4), has moved on to the extended text, The House on Mango Street by Sandra Cisneros. She is happy with the reading analysis and writing activities the students are doing, but has “no clue how they’ll do on the CFA!” I am a bit concerned about this and will need to reach out to her.

Jeff (in this chapter) thinks he is ready for the next CFA! He said that between the “Favorite No” activity and the use of the student rubric, “I know what they know, and they know what they know and don’t know, and can tell me what they need to do to get better!”

Melanie (Chapter 2) talked about how formative assessments helped her figure out the challenge of teaching kindergarten students all at different levels. Here is an excerpt from her post:

Just because the pacing guide gives a suggestion of what to teach and when, you cannot always follow it for everyone. Some students have mastered that skill, but others may not even have the prerequisites needed to begin understand the concept. Like shapes, for instance. The pacing guide says to teach shapes for 10 days, but I have to keep coming back to shapes for some students. Others already knew it coming in to kindergarten, so I had to move on to what to do with shapes for them. I have to be constantly assessing. That doesn’t mean giving quizzes and tests—because if I did the tension would be so high the children might just cry! Instead, I use a lot of different formative assessments—observations, role play, conversations, counting objects. A checklist is what I use the most. I keep the checklists separated by Language Arts on one clipboard, Math on another, physical and social development on a third. The checklists have abbreviations of the kindergarten standards—like letter recognition, sight words, tracking words, answering questions, counting to 10. So when I observe a child making a rectangle from two triangles, I can quickly mark it off on my checklist and add the date when I observed this behavior. The one thing you can say about kindergarten, it’s never boring. I have to keep on my toes to adjust so that they are not bored because instruction is too easy or frustrated because it is too difficult.

We will be doing our 2nd quarter CFAs next week. This is a bit of a challenge, because we have to sit with each student individually and give a common probe (like a worksheet with pictures of objects to compare—all the kindergarten teachers have the same sheet). So I have to plan activities for my assistant to do with the class while I call children over individually or in a small group for the CFA. We can really only get away with doing this 30 minutes at a time, otherwise the class gets too hard to handle. I think I did a bit of overkill last quarter, so I am trying to be aware of the time and not have the assessments disrupt our schedule too much. Remember Isaiah? Well, he started mocking me last time we did the CFA. He grabbed one of my clipboards, put on a hat and oversized sunglasses from the dress up area, hovered a crayon over my precious checklist and said in a fierce voice, “Miss Melanie, stand on one foot!” It was funny at the time, but made me realize that I have to work at making the process less ominous for the students. I want these assessments to build confidence, not anxiety.

These teachers are describing a mish-mash of understanding of assessments. Some are describing the use of assessments for learning, while others see the upcoming test as an assessment of learning, despite its original intent. This confusion is plausible however. The Common Formative Assessments as used by this district can best be described as periodic, interim evidence collected over a long term, similar to what others may call progress monitoring, or benchmark assessments. The assessment itself seems to be a measure to see if the students are on track, or an assessment of learning. But the structure of how the test is administered (at least two weeks prior to the end of a unit) and how the results are used and analyzed by a PLC to organize learning activities is a formative use, or an assessment for learning.

The teachers also described short-term (weekly or daily) collection of evidence, a more of a continuous flow of information that they use to target their instruction, or to get students to see what they could do to improve. Ingrid could use some assistance in organizing this form of assessment. Actually, they all could, so I posted some websites for them to look at. These included the following:

Don’t leave out the math—Phil Daro

https://www.youtube.com/watch?v=uyeebGEDtio

My favorite no

https://www.teachingchannel.org/videos/class-warm-up-routine

Fostering high quality formative assessment: A policy research brief produced by the National Council of Teachers of English (NCTE)

http://www.ncte.org/library/NCTEFiles/Resources/Journals/CC/0201-sep2010 /CC0201PolicyBrief.pdf

Daily assessment of students with tiered exit cards

https://www.teachingchannel.org/videos/student-daily-assessment

Inclusion and differentiated instruction: Teachers in the movies do it too

https://www.youtube.com/watch?v=i6rEy3Lqfio

53 ways to check for understanding: Edutopia

http://www.edutopia.org/pdfs/blogs/edutopia-finley-53ways-check-for-understanding.pdf

Wees, D. (2012). 56 different examples of formative assessment

https://docs.google.com/presentation/d/1nzhdnyMQmio5lNT75ITB45rHyLISHEEHZlHTWJRqLmQ/pub?start=false&loop=false&delayms=3000#slide=id.p

Exemplars jigsaw student rubric

http://www.exemplars.com/assets/files/puzzle.pdf

Emotionally, attitudinally, they are all looking forward to the holiday break! Not many complaints now—they all just seem to be hanging on.

—Celina Zwijacz, Ph.D.

Discussion Questions

· Lori, who has “no clue” how her students will do on the CFA, apparently needs some help in using classroom data to inform her teaching. Given her subject area (seventh-grade Language Arts), and suggestions offered by Dr. Z., what strategies for assessment for learning would you initiate?

· Help Ingrid to understand how the district’s CFA can assist her instructional efforts. Given her current second-quarter goals, offer one suggestion for an appropriate formative assessment strategy in Language Arts and in Math.

· Travis has organized a workable strategy for keeping up with the progress of his students and helping them evaluate their own learning more effectively. What other suggestions from the NCTE policy brief would you suggest he use as manageable strategies for formative assessment?

· From your understanding of the relationship between standards, curriculum, and assessment of learning, what conditions should be in place for Jeff’s strategy of assessment for learning to work? What else would you advise that he pay attention to?

· What advice would you give Melanie for developing assessments for learning that encourage and bring smiles to her kindergartners?

· Discuss how and why formative assessment is considered assessment for learning, and why summative assessments are considered assessment of learning. What advice would you give these teachers to help them consider the advantages of each?

· How does working within a PLC help these teachers use the results of common assessments as a vehicle for supporting student learning?