Assessment for Learning Practices
Wiliam (2011) states that professional development should focus on formative assessment, as a regular assessment-teacher-action cycle produces substantial increases in student learning. Teacher learning should include:
- understanding base knowledge of assessment practices.
- planning for implementation of strategies to respond to the assessment; and
- discussing instructional changes made and results on student learning.
Mathematics concepts build over time. While the focus for many provinces, school divisions, and schools is to increase student achievement in mathematics, that requires increased opportunities for students to be able to engage in grade level mathematics. This can only occur through opportunities to fill gaps in skills and understanding, which begins with identification of those gaps.
The first step in providing the opportunity for students to engage in grade-level mathematics is to identify which essential skills students are proficient at and which skills are barriers to engagement. A grade-level Pre-Assessment built on Essential Learning Outcomes is a tool that can help inform students, teachers, and parents. A Pre-Assessment can be administered in its entirety at the beginning of the school year, or broken apart into concepts needed as pre-skills for each unit of study in the new year.
The structure of a continuum of Pre-Assessment Diagnostics is
The questions in a Grade 3 Pre-Assessment are identical to those questions in the Grade 3 Post-Assessment. In addition to those core questions, concepts from Grade 3 are added. A suggestion is that the Post-Assessment would be administered in early May to allow for reteaching and redirection in order to best prepare students for the next grade level.
Not all concepts are included in these diagnostic assessments. Only those concepts that are skill based are included. For instance, the concept of Area is not included, as a student can understand the concept of area as an application of multiplication. Multiplication appears in the PreAssessment, but knowing the area of a rectangle does not.
These assessments are meant to be formative only. They are not meant to be a part of a reporting document, as they do not fully test conceptual understanding in the depth that curriculum requires. These are only a tool to know which preskills students are struggling with, and which preskills students are proficient with.
The diagnostics below were created by a working group from our Mathematics Community, including: Dulcie Puobi, Victoria MacMillan, Jennifer Brokofsky, Michelle Naidu, Lisa Bryden, Sharon Harvey, and Terry Johanson.
The Kindergarten to Grade 2 Diagnostics Numeracy Assessments have a different format than the Grade 3 and up. First of all these assessments are interview based and are intended to take no more than 15 minutes per student to administer. Secondly, these assessments include a set of cards, a recording sheet and a rubric to support identification of students current level of understanding.
The Diagnostic Numeracy Assessments will not measure grade level concepts in enough detail to allow you to determine a report card grade. The outcomes that are represented on this diagnostic are skill based outcomes that fall into the strands of Number and Operations as well as Patterns and Relations and therefore, do not assess the mathematics curriculum in it’s entirety. For this reason, using these assessments for reporting purposes would be inappropriate and is not recommended.
The Kindergarten to Grade 2 Diagnostic Numeracy Assessments were created by a working group of teachers from our K-5 Mathematics Community including: Rhonda Wacker, Rosemary Vinet, Kelly Massier-Anderson, Elizabeth Phipps, Tracy Schnell-Persson, Wendy Macleod, Jennifer Hamon-Adair, Jodie Wachs, Dulcie Puobi, Jennifer Brokofsky, and Cassandra Neufeld