Recently, our district implemented universal screeners for grades 3 – 5 mathematics that are delivered by classroom teachers to students in either one-on-one or small group settings. This post describes the benefits of such individual assessment interviews.
Within the What Works Clearinghouse is a document titled Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools that contains 8 recommendations for the early detection, prevention, and support of students struggling with mathematics. Backed by the first recommendation outlined by the U.S. Department of Education, Institute of Education Sciences: Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk, we developed a plan to administer such assessments in the beginning, middle, and end of the year as part of our RtI plans.
Conducting one-on-one or small group interview-style assessments provides data about the students’ mathematical understandings beyond the answers, but also includes strategies and thought processes used to solve the problems.
In elementary, as students approach fact fluency they move through a developmental progression of numeracy, or a Numeracy Continuum. The steps, or phases, of the continuum include detailed nuances that distinguish one step from the next. These nuances include the specific strategies the students use to solve problems. These strategies, for example, include making 10, doubles, or doubles plus/minus one. In order to more closely monitor student understanding and as a result, more accurately design learning experiences, the teachers must be aware of what method the students use to solve math problems, not only whether the students are correct.
So, how do we collect data on what method the students use to solve problems and what questions to we ask to yield such data? Below are two examples (one more advanced than the other) and the rubric used to score the responses.
1. Read the following question. “Each teacher has two cups. There are six teachers. How many cups are there altogether?” Reread the problem as many times as needed. Students may use scratch paper/pencil if necessary.
- correct by recalling the basic fact (3 points)
- correct by skip counting, repeated addition, drawing a model, etc. (2 points)
- incorrect (1 point)
2. Read the following question. “Pencils come in boxes of 24. The teacher has 3 boxes of pencils. How many pencils does the teacher have?” Reread the problem as many times as needed. Students may use scratch paper/pencil if necessary.
- correct and used a multiplication strategy to solve (3 points)
- correct but used an addition strategy to attempt (2 points)
- incorrect (1 point)
The images below show sample student responses to these questions (question 1 on the left and question 2 on the right).
When interviewing this student, I was able to see for question 1 that she first drew the “thin tens frame” (this was her term), then assigned each teacher two dots, then skip counted by twos to arrive at the solution of 12. This one question showed me, as her teacher, all of this as data regarding her understanding. I also know that she was not able to arrive at the solution by connecting the problem to the basic fact.
On question 2 the student used the traditional algorithm for addition when she added 24 and 24, then the sum of this to the final 24. Because I was interviewing her one-on-one, I was able to notice that she has a misunderstanding of the traditional algorithm (and thus a disconnect between the traditional algorithm and place value) because she added the tens column first, then the ones column.
The feedback from teachers related to the benefits of one-on-one or small group screener assessments include a better understanding of where each of their learners are on the Numeracy Continuum and, therefore, can better support them in goal setting. The goal setting methodology we utilize is S.M.A.R.T. goals which call for specific, measurable, attainable, relevant, and time-bound. Specificity of the goals is related to precisely what learners are able to do in terms of numeracy and what strategies they are able to utilize fluently.
In our journey with Creating a New Vision for Public Education in Texas, we work to more effectively analyze and use assessment results to improve/ change teaching practice and to inform interventions for students who have not demonstrated mastery of the assessed learning standards. Related to Assessment for Learning, the premise we strive toward reads:
III.b Assessments used by teachers are the most critical for improving instruction and student learning, and to be effective must reflect certain characteristics, be interpreted properly in context, and reported clearly. Conducting good assessments is a part of the art and science of good teaching that results from teacher experiences and formal teacher professional development opportunities.
My work to connect our curriculum documents, teacher professional development and understanding of mathematics content and pedagogy as well as Response to Intervention and Instruction is reflected in these initial steps to implement individual assessment interviews in grades 3 – 5 mathematics.