Sunday, August 5, 2012

Guided Math: Chapter 8

This post is part of my Guided Math Book Study. I will discuss each chapter in two sections: an overview of the chapter and my learning/wonderings and how this learning will affect my mathematics instruction. You can read the entire series of posts by clicking here. (Graphics for this post provided by Scrappin' Doodles.)

Assessment in Guided Math

Information gathered through assessment not only provides information about where to begin instructionally, but also guides future instruction and the students' learning. (Sammons, 2011, pg. 227)

Teachers need to know how to assess their students in order to help students make growth as mathematicians. Instructional effectiveness is lost when instruction does not mirror student needs. How is this obtained? Assessment. 

Teachers constantly gather evidence about their students--from observation, conferences, work samples and more. This evidence provides teachers with a framework upon which to build instruction, matching student needs to instructional content. It is a win-win situation. However, students need to be taught how to self-assess as well. This will allow them to monitor their own learning and hopefully be more mindful of the work they are doing as they are working.

Assessment can not only happen at the end of a unit of instruction; it needs to be embedded throughout the curriculum to allow for
-continuous information for instructional decision making
-continuous assessment of student strengths
-discovering what students can do independently and with teacher support
-documenting progress
-summarizing student achievement
-reporting data to various stakeholders (administration, etc)

The above rationales focus first on LEARNING. This is vital. Learning is the most important thing that happens in any classroom. The first three factors are dependent upon each other; one needs the other to thrive. When teachers can manage this, they know their students well and are able to make instructional decisions frequently and accurately that will meet their students' needs.

When teachers assess more frequently, they can ask themselves the following questions:
-How well did my students master the curriculum or standards?
-Are students ready to move on?
-How the the whole class perform on this assignment/standard?
-Does anything need to be retaught, in part or whole, before I can move on with instruction?

When teachers ask these questions, they are able to focus and refine their teaching toward student LEARNING. 
I don't know anyone who doesn't have to keep some kind of data notebook of some sort to document student progress. I also know many teachers who simply stick the data in the notebook and don't use it except when they have to present it to a review board. By USING the data and allowing STUDENTS and PARENTS to see, understand and use the data, students will be more successful. If little Joe is struggling with fractions even after remediation, the teacher should know this based upon observation, work completed and conferencing with the student. All of that information will allow the teacher to pursue even more intervention, as needed, to help this child to master concepts that are giving him difficulty.

Standardized testing does not provide enough feedback for students to make it meaningful. In Michigan, we take our MEAP standardized test in the fall (October) and usually get results back in March. Not helpful. With the new MAP test that we've implemented in the last several years, students (and teachers) get feedback within 24 hours. That is data that I can use, from a standardized test, that will allow me to change my instructional focus. However, it's only given three times per year. While I DO use this information and I DO love how much information it provides me (and my students), it isn't enough. You have to have data from YOUR DAILY TEACHING in order to be the most effective at teaching to your students areas of weakness as well as their areas of strength.

Assessment and Learning in Guided Math

In short, teachers must assess frequently AND manage the data from the assessment effectively in order for the assessments to be worthwhile in guiding student learning.

Using exemplars and other criteria can teach students what SUCCESS looks like. When students are going blindly into a problem without a clear path as to what will make their answer a successful one, they are more apt to struggle. Students who struggle frequently probably do not fully understand what is expected of them. To help combat this, there are three steps for providing descriptions of the expectations (Davies, 2000, as cited in Sammons 2011):
1. Describe what the students need to learn in a language the students will understand
This could be in the form of I-can statements in terms of the objective and short statements of HOW the students will use the objective to learn. eg. I can make equivalent fractions by comparing fraction cards from the Everyday Math program.
2. Share the description with the students and how it relates to success in life after school
Always relate what kids are doing to something beyond the current classroom. (You will need to know this so that next year, you can build upon it in X-grade or If you ever want to build anything, you will need to understand fractions to the 1/16ths.)
3. Use the descriptions to guide instruction, assessment and evaluation
Once students know what the expectation is and have exemplars, they must be used in evaluation and assessment! You can't throw a curve ball and suddenly grade based upon a criteria you didn't explain to your students.

Establishing Criteria for Success with Checklists and Rubrics

Before planning for instruction, teachers must have a clear vision of what they want their instruction to accomplish: what standards do students need to learn for this unit of study? We often use rubrics and checklists for literacy, so why not also use them for math?

Checklists can provide students with an idea of whether or not they have met requirements for certain things such as problem solving. When students peer-check or the teacher checks, the checklist can be a good starting point to help students to see if they are meeting the minimum criteria for being successful. The problem with a checklist, however, is that it doesn't provide students with feedback on what they need to have to BECOME proficient if they aren't meeting a specific criterion. 

Rubrics allow teachers (and students) to see whether students are meeting the standards in specific areas. In the problem solving example, there could be five criterion: Conceptual Understanding, Reasoning, Computation, Communication and Connections. With each criterion there can be levels of proficiency such as Emerging, Developing, Proficient and Exemplary. Therefore if a student achieves proficiency in all but one or two levels, the rubric provides the student with the information they need to understand how to become proficient.

Descriptive Feedback

Students need to understand exactly what they are doing well and what they need to work on. This is where Descriptive Feedback comes in. Descriptive feedback should occur during and after the learning session, it shouldn't wait until a test or assessment has been administered. It should relate to the learning and be specific so the student can continue to do what they are doing well at and work on mastering concepts they may be using incorrectly. This feedback should be delivered as part of a conversation about the student's learning (CONFERENCES) and provide the student with models of ways in which to show the learning (models, problems on paper, etc).

Marzano, Pickering, and Pollock (2001) (as cited in Sammons 2011), provide four generalizations to help guide teachers in providing descriptive feedback:
1. It should be corrective in nature: if the student work is all exemplary, the student still needs to hear what they are doing that is correct; if the student work is a mixture of correct/incorrect or is all incorrect, they still need to hear what they have done CORRECTLY as well as INCORRECTLY
I think that many of us teachers become so time-pressed we only focus on what is WRONG and don't focus on the positive. I know I have tried over the last year or so to give the student feedback on how they did something WELL no matter how small it is. This is vital in order to keep student motivation up.
2. It should be timely: the longer it takes the child to get the feedback, the less effective the feedback will be. In other words, don't assign a test on Monday and take two weeks to get the results back to the students.
I know this drove me crazy in college. I hated busting my behind on an assignment and not getting feedback on it for weeks or months. Over the last two years, I have honestly tried to ensure that I give a test the day of or before one of our specials classes so I have time to correct the test during that prep time and can provide feedback to my students quicker. Since I haven't really done math conferences before, this will really be vital for me so that I can meet with students who had a lot of trouble on a particular assessment within a day or two and help them get back on track.
3. Should be SPECIFIC: linking the feedback to the criteria that has been established, students will learn what they did well and what they need to keep working on as well as HOW they can become proficient at it.  By using the established rubric, students will know exactly what to do to improve their score (ie I didn't clearly explain my thinking and I need to do that to boost my grade.)
This is something that I do with writing. We have very specific rubrics we model and teach our students. That way when we confer, we can point out where and why the student score was not where we want it to be (ex. I noticed you did [blahblahblah] very well, see this example here in your writing? It really spoke to me. I also noticed that {blahblahblah} was confusing because you aren't using [whatever criteria]...) This would be very easy to transfer to math conferences, especially with rubrics already created for students.
4. Students can add to/provide their own feedback: as students learn the criteria for success, they are more accurately able to assess their own strengths and weaknesses based upon a checklist or rubric. This allows students to peer-correct and self-assess in order to determine where they are struggling and can encourage them to seek extra help and support if they need it. 

Assessment for Math Groups

There are no set assessments for guided math groups the way there might be for guided reading. However, using formative assessments, checklists and rubrics, teachers can determine if the students in their groups are making the progress they want them to make. It is important to remember that this is assessment FOR learning in order to guide the instruction.

I have not used rubrics or checklists for math, ever, and definitely plan to integrate that into my teaching this year. I am all about transferring learning ownership to the students so they can be accountable for their work and the learning they do. This will be a great part of that if I can help my students to learn the criteria for being "successful" at specific math concepts.

I am really getting into the "backwards planning" method as well. We have made "Common Assessments" in our district that don't necessarily match our teaching resources. My thought is that we need to sit down and determine WHAT is in the common assessment for each unit and ensure we are teaching the students those concepts, whether or not they align with our Everyday Math series. In an earlier post in this series, I mentioned the State of Michigan Crosswalks to help teachers link our current Grade Level Content Expectations (GLCEs) to the CCSS. By examining these Crosswalks as well as our end-of-unit assessments, I can better look at WHAT I want my students to learn and then determine HOW I am going to teach it to them. Making rubrics or criteria charts will allow my split grade students to be more independent and work together when I am working with small groups or doing assessments.

Stay tuned for my thoughts and reflections as I wrap up my study of Guided Math by exploring Chapter 9: Putting it into Practice!


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