In order to 'peel back the curtain', as Hubbell & Goodwin (2013) put it, for my students I designed a pre-test, rubric intervention and post-test multiplication and division unit. Following is a breakdown of how the beginning of the unit was administered and analyzed:
Administering and Graphing the Pre-assessment
I administered the pre-assessment to my students and explained to them exactly what it was and what it was meant to do. I told them that this was just a pre-assessment and it was not going to be put into their permanent grade or show up on their report cards. I did this so they would not worry about not knowing some of the answers. I made sure to stress this to them so that they would not have any type of apprehension going into the pre-assessment and I could hopefully gauge their level at a better quality or better rate. I also went over test taking strategies as is normal for me to do with the students. For example, if they did not understand the question then they should skip it and go to the next so as not to get hung up on time.
For the graphing of the results of the pre-assessment data I used an Excel spreadsheet that you will find in Figure 1. Besides for finding it in Figure 1 there is also a OneDrive link to the spreadsheet here:
This spreadsheet I believe is incredibly powerful because it provides a visual representation of the student’s strengths and weaknesses that can be easily digested with just a fleeting glance down to the sheets. As can be seen on or in the Excel spreadsheet, every column that has a green box means that they got the answer correct, if there's a red box with an ‘n’ in it and means that they got the answer wrong, there's also a provision for a partial marks which displays as an off-yellow box with a ‘p’ in it, last there's another provision for unanswered questions and that is yellow box with a ‘u’ in it.
Analysis of Pre-Test Results
The top row of the spreadsheet has question numbers, the row below that is for topic (or standard) of the question. So, for question numbers 1 through 5 underneath you can see the standard was 2-digit by 1-digit division. Almost all of the students were able to get those answers correct and only a few of them got partial credit. Now, when you look at questions 6, 7, and 8, those are the ones you can see that the students had problems with simply by seeing the color isn’t green indicating a correct answer. A look at the topic row shows those questions were over 3-digit by 1-digit division. This is something they have not been taught, but I award partial points for an attempt or for showing work even if the answer is wrong. None of the students got those answers correct so this is something that I will definitely need to direct my focus towards when I'm doing my subsequent lessons on Division. As you move along the spreadsheet, questions 10 to 15 are two digit by one digit multiplication and the results are as I expected: there are some weaker students in my class and I figured they would miss one or two of those but over all the students understand this concept as they have been scaffolded for it fully. As we go towards the end of the spreadsheet, we arrive at question 16 through 18. These are 3-digit by 1-digit multiplication and that required a higher level of regrouping or carrying. As can be seen here, about half of the students got them correct and about half got partial, incorrect, or unanswered. The last four questions on the pre-assessment were division and multiplication word problems. The students have been scaffolded in one step division and multiplication word problems already, so the students were familiar with the format of the problems. The problem areas, again, are exactly what I expected them to be with the weaker students receiving a p, u, or n, and the stronger students being able to get those questions correct. Again, by a simple look at this spreadsheet, after the data had been entered, I can clearly see the focus areas are going to be the division and multiplication word problems, 3-digit by 1-digit multiplication, and 3-digit by 1-digit division. Having this data tool will absolutely help inform my teaching strategies as per teaching this unit.
Rubric and Student Goal Setting
After the data was collected from the graded exams and entered into my data sheet, I created a rubric to give to the students so that they could set their own personal learning goals A representation of this rubric can be seen in rubric pictured above.
The rubric has five different categories based on the unpacked standards informed in part by the research of Berdynaj & Vula (2011) and Hinton et al. (2015). Instead of assigning a numerical value to the different columns, I instead chose to use language that would make the students more engaged in their own learning and goal setting. The lowest level is “Don't Have It”, which means they don't have no idea how to answer the problem. The second level is “Working On It” which means that they might have gotten most of them wrong but they still got partial credit for trying. The third level is “Almost There”, which would mean that they mostly got all of those questions correct for their respective row. Last, the highest and last column is “Mastered”, mastered means they got everything correct within the focus area on the pre-assessment. So, if they got all of “Rewriting Division and Multiplication Problems” correct they could have circled mastered. Next we will move on to how the process of testing and rubric goal setting was carried out.
The process that I chose was I first showed the rubric to them projected on the whiteboard and gave them each a copy. I then explained it to them and answered any questions that they had about how to assess themselves. I told they were going to use their pre-tests to self-assess using the rubric. I highly monitored the process and made sure that they were assessing themselves correctly. With each student I had a discussion about where they wanted to go with their learning. Every single student bought into this idea that they wanted to master the different skills that were required to complete the pre-test. The rubric allowed the students to see where they were in a physical representation and give them a goal to work towards as we work through the unit. The point of this rubric is to gauge where they are and to help develop plans for student interventions (Dixon and Worrell, 2015).
This rubric will be an especially powerful tool to use again at the end of the unit. I am going to administer a post-test and give them back the their rubric that they completed previously and a new copy of the rubric where they can then assess themselves again. Hopefully they will all be able to circle a higher level and on to Mastery if they're scaffolded correctly.
I do believe that the students will experience success by the use of this format of pre-assessment, rubric completion, and goal setting. When students are given ownership over their learning, they can clearly see what's expected of them and can clearly see the path that they need to go down in order to master skills (Hubbell & Godwin, 2013). This empowers them and makes them want to succeed. There is nothing more powerful than a student that wants to succeed and has been given the correct tools with which to accomplish that success. I believe that this process has given my students the tools to accomplish their success.
Dixson, Dante D, and Worrell, Frank C. “Formative and Summative Assessment in the Classroom.” Theory Into Practice 55.2 (2016): 153–159. Web.
Hinton, V., Stroizer, S., & Flores, M. (2015). A Case Study in Using Explicit Instruction to Teach Young Children Counting Skills. Investigations in Mathematics Learning, 8(2), 37–54. doi: 10.1080/24727466.2015.11790350
Hubbell, E. R., & Goodwin, B. (2013). The 12 Touchstones of Good Teaching: A Checklist for Staying Focused Every Day. ASCD.
Lirika Berdynaj, and Eda Vula. “Collaborative Action Research: Teaching of Multiplication and Division in the Second Grade of Primary School.” Turkish Online Journal of Qualitative Inquiry 2.2 (2011): 7–16. Web.
(Singapore), S. E. I. (2014). PR1ME mathematics 3A Teachers Guide. Singapore: Scholastic Education International (Singapore) Private Limited.
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