An excellent mathematics program ensures that assessment is an integral part of instruction, provides evidence of proficiency [for teachers and students] of important mathematics content and practices, includes a variety of strategies and data sources [which are instructionally sensitive], and informs feedback to students, instructional decisions, and program improvement.”
(NCTM, 2014, p. 89)
Assessment to Inform Instruction supports teachers in answering the question What comes next in learning?
Among the various methods of assessment for learning are listening to student contributions (both responses and questions students ask to the teacher and of their peers) and analyzing their written work and using that information to interpret student understanding and determine next steps in instruction. An image of student work below shows that the student recognizes there are 16 ounces in a pound and that this problem is multiplicative in nature.
In elementary mathematics, researchers have developed progressions that describe the likely development of student mathematical thinking for a given concept, what we call big ideas in mathematics. For example, addition and subtraction and multiplication and division are big ideas in mathematics. These progressions can guide teachers in making instructional decisions based on a student’s progress as compared to the progression. Below are progressions for grades Kindergarten through Fifth Grade whole number concepts.
Diagnostic Assessment can be used to identify a students’ strengths as well as areas for improvement, can form the basis for interventions and is often shared with multiple educators in order to plan supports to improve the student’s learning. This short interview-based assessment provides the teacher with information related to the students’ understanding of number, addition and subtraction, place value, and multiplication and can be used to determine if the student is performing at grade level as well as to determine areas of strength or weakness.
Interim (Unit) Assessments support teachers in answering the questions Which standards are our students consistently not mastering? Where can we improve instruction? Which students need specific help? (Stiggins, 2010).
Interim assessments should identify content standards that students are struggling to master as well as the students struggling to meet those standards. Teachers can use this information to improve their own instructional practices aimed at those standards. Additionally, these assessments can help teachers and students focus on identifying student strengths and areas of improvement so they can intentionally plan interventions.
Assessment of Learning supports teachers, schools, and districts in answering the questions What standards are our students consistently not mastering? Where and how can we improve instruction next year? (Stiggins, 2010).
Summative assessments evaluate student learning against intended outcomes. These assessments provide evidence of student achievement and can identify the percentage of students meeting performance expectations on state content standards (Chappuis, 2015).
In Michigan, students are assessed summatively in the spring of each year, starting in 3rd grade. MDE houses sample assessment items for 3rd - 7th grade M-STEP
Secondary students are assessed using the PSAT or SAT. Released items can be used in a variety of ways to inform the work that students are doing in the classroom.
The Formative 5: Everyday Assessment Techniques for Every Math Classroom (Fennell, Kobett, & Wray)
Teaching Number in the Classroom for 4-8 year olds (Assessment and Intervention)
Developing Number Knowledge: Assessment, Teaching, and Intervention with 7-11 year-olds