My last blog of the year is dedicated to the teachers of Highland and John Wetten Elementary Schools. They came through a pretty stressful and at times disheartening school year with grace and fortitude. It inspired me to work harder to find resources and answers to their questions. In this blog, I’d like to share some of the answers we’ve discovered together.
First of all, it is critical to have a clear and coherent vision of mathematics instruction. There are many balls a teacher needs to juggle simultaneously. I chose to use a stool to illustrate to our teachers what I believed were the essential components. On one leg of the stool I placed the caption Conceptual Understanding. It is critical that classroom teachers have a deep understanding of the mathematics of their grade level standards. We created curriculum maps to identify which standards at which time of year we would focus instruction around. Once that was in place, we looked through all the resources available to us to find the best instructional materials to teach those standards.
On the next leg of the stool I placed the label Problem Solving. At the top of each map mentioned above is a reminder of the importance of teaching using all the process standards identified in our Oregon 2007 Mathematics Standards, including mathematical problem solving (Or Mathematical Practices for the maps aligned to the CCSS standards. See below for more on them). I shared problem solving tasks (including the Making Sense of Problem Solving materials) that teachers can use to check students’ ability to apply math skills in context. I also did a series of classroom demonstration lessons focused on this topic and a staff workshop that introduced teachers to Oregon’s Mathematics Problem Solving Scoring Guide. This scoring guide has been revised over the last few years and was just adopted by the our Oregon State Board of Education this last week.
The third leg of the stool represents Computational Fluency. If you’ve been following this blog for any time, you know that several entries were devoted to discussions of this critical component. (February and March 2010). This is a topic we’ve just begun to come up with grade level agreements on for how teachers will monitor students’ progress towards the fluency standards at their grade level.
Then I added three rungs to the stool. The first rung that supports the stool and makes it strong is labeled Assessment. We wanted to find efficient and effective ways to gauge student’s instructional levels and progress towards proficiency in mastering their grade level standards. And for those who were not proficient, we needed assessment tools to hone in on their gaps so we could adjust our instruction to better meet their needs. We knew the earlier we intervened the better to close the gaps while they were still small, but when we started this journey all we had available were Oregon Assessment of Knowledge and Skill (OAKS) data reports and the assessments that came with our primary math curriculum materials. OAKS data came too late in the game for early intervention and the published assessments we had available through our math curriculum materials were not aligned to our grade level standards.
So, we’ve come up with an assessment system that is multifaceted. For older students we learned how to better analyze the data available to us from the OAKS assessment by exporting, sorting and color-coding the data (and those reports have gotten better over the years since we started, too). An article I co-authored with Winnie Miller in The Oregon Mathematics Teacher (TOMT) journal called “Super Spread Sheets“ helps detail how we did that. But that was not enough information to really help us accomplish what we needed. I put together a Progress Monitoring Assessment (PMA) that surveyed the breadth of the standards. We wanted this tool to be something that would take minimal time away from instruction and be easy to correct. We also wanted to give it to students with enough frequency that we could track growth and areas where we needed to adjust instruction. Instead of reinventing the wheel, I utilized an assessment resource that was already available and aligned to the Oregon 2007 Math Standards, the ezCBM assessments. On this site they have .pdf files of assessments available for a free download or to use in their online version of the assessments after you sign up for a school or individual teacher account. I pared down their huge bank of assessments to 3 assessments of 10 items each for all three CORE grade level standards for grades 1-6. Through trial and error, we came up with a timeline that we thought might work best. We started with a Baseline PMA in the fall. Then we used the first of the three variations of the EZCBM PMA that aligned with the grade level CORE standard we were focusing on for that trimester to be given as a pretest, the second was given midway through the trimester to monitor and adjust instruction and the third one was given as a posttest. We also gave students the previous grade level baseline assessment and used the information from that and their grade level PMA’s to assign all students to work on identified skill practice areas on a computer program both districts have subscribed to called IXL.
All this seemed to be working pretty well for 3rd through 5th grade and teachers were thrilled to have evidence in black and white of the growth students were making, but it still didn’t help us gather information about out youngest students. We found that we couldn’t always tell what primary students were able to do in math using a pencil/paper multiple-choice assessment. In a series of articles I published throughout this last school year in TOMT magazine, I described the process we went through to try out and refine interview assessments that showed student progress toward the grade level standards. These interview assessments are extensive and time consuming but if a child was really puzzling a teacher, they provided one more tool to identify a student’s strengths and weaknesses.
But we still wondered if there were some interview questions that could be used as a quick “screener” to predict which students might struggle in math or need to be offered more challenge and enrichment. This goes back to the April 2009 discussion that was posted on this blog. We think we’ve come up with some ideas and we are currently trying them out with a variety of our primary-aged students. In the fall of next year, I will write one final article in TOMT to share the screening assessment questions our K-2 teachers have been looking at. We’ve been talking about the possibility of training Title teachers and assistants to administer these just like they do the Dynamic Indicators of Basic Early Literacy Skills (DIBELS) reading testing in both our schools. Kindergarten has been looking at ways they might incorporate them into the Gradual Entry or Orientation schedule of activities.
Hand in hand with identifying students’ strengths and weaknesses goes the rung labeled Differentiation and Intervention. I helped put together collections of resources for teachers to better differentiate their math instruction to meet the needs of the ranges present in their classroom based on their requests as they viewed the data reports shared at PLC and Data Team meetings throughout the school year.
We still haven’t made a lot of inroads in creating a comprehensive intervention plan. In one of my schools we’ve played around a little with a Walk to Math Intervention time with different grade levels. In order to move forward it will take a redesign of the daily schedule to insure that grade levels have common blocks of time available to be able to swap students. Once a week I’ve been having halves of two different 3rd or 4th grade classes cycle through me in the computer lab to give all 3rd and 4th Grade classroom teachers an opportunity to design interventions and work with smaller groups of students left in their classrooms while the other half class is in the lab. When they come to me, I reinforce the concepts being focused on each trimester using a wide variety of technology tools. You can track what I’ve done with those groups on the Highland Computer Lab web site. Click on either the 3rd or 4th grade 2010-11 links to see the complete list of lessons. Once a week I also meet with the top third of the 4th grades and for 30 minutes four times a week with the top third of the 1st graders to provide a series of enrichment activities aligned to their trimester CORE instruction. We know there is still a lot more that needs to be addressed in order to create targeted interventions, but it’s a start.
The final rung is labeled Motivation and Positive Attitude. There is an extensive discussion on this blog about motivation in the May 2010 post, so I won’t spend a lot of time going into that here. The only thing I’ll say here is that we had an interesting conversation in one of my schools about the Positive Attitude part of the label. Whose positive attitude did it refer to? Was it the student’s attitude that was critical? There is a lot of research available that shows the importance of students believing they can do math, taking ownership of their learning process and developing persistence to stick with math even when it gets hard. But, I also think it is just as critical that our teachers retain a positive attitude, too. They need to believe that ALL their students can succeed in math and if students are struggling they need to keep trying out different methods and materials. The most important thing I want to stress here is keeping our eyes on what is important here. Although we spend a lot of time looking at numbers throughout the year, the most important numbers to focus on are the ones that show evidence of student growth. It is hard not to fixate on the reported out numbers of the state test but that is only one snapshot look at student progress.Looking at multiple pieces of evidence gives a much clearer picture of students’ growth and their areas of weakness and that is where we need to stand in order to design effective math instruction.
Now, of course, the biggest challenge facing us is that we need to do this whole process again to align to the 2010 adopted Common Core State Standards (CCSS) for Mathematics. In Gladstone we’ve already begun that process. This spring, I worked with K-2 teachers to start the mapping and curriculum alignment process necessary for them to begin teaching to the CCSS math standards in the 2011-12 school year. Now we need to come up with the assessments. This year I have also worked with a team from Teacher to Teacher publications to create Lessons in Strengthening Number Sense for 4th grade that is aligned to the CCSS standards and includes a complete assessment as part of the resources for this intervention material. This summer work will proceed on the Kindergarten through 3rd grade versions of this publication.
I wish you all a fabulous, renewing summer vacation and hope you will check back next fall to learn more about what direction we head in next. As you might imagine, I have some ideas on that score.