At the end of each unit is the end-of-unit assessment. These assessments have a specific length and breadth, with problem types that are intended to gauge students’ understanding of the key concepts of the unit while also preparing students for new-generation standardized exams. Problem types include multiple-choice, multiple response, short answer, restricted constructed response, and extended response. Problems vary in difficulty and depth of knowledge.
Teachers may choose to grade these assessments in a standardized fashion, but may also choose to grade more formatively by asking students to show and explain their work on all problems. Teachers may also decide to make changes to the provided assessments to better suit their needs. If making changes, teachers are encouraged to keep the format of problem types provided, which helps students know what to expect and ensures each assessment will take approximately the same amount of time.
In longer units, a mid-unit assessment is also available. This assessment has the same form and structure as an end-of-unit assessment. In longer units, the end-of-unit assessment will include the breadth of all content for the full unit, with emphasis on the content from the second half of the unit.
All summative assessment problems include a complete solution and standard alignment. Multiple-choice and multiple response problems often include a reason for each potential error a student might make. Restricted constructed response and extended response items include a rubric.
Unlike formative assessments, problems on summative assessments generally do not prescribe a method of solution.
Design Principles for Summative Assessments
Students should get the correct answer on assessment problems for the right reasons, and get incorrect answers for the right reasons. To help with this, our assessment problems are targeted and short, use consistent, positive wording, and have clear, undebatable correct responses.
In multiple choice problems, distractors are common errors and misconceptions directly relating to what is being assessed, since problems are intended to test whether the student has proficiency on a specific skill. The distractors serve as a diagnostic, giving teachers the chance to quickly see which of the most common errors are being made. There are no “trick” questions, and the phrases “all of the above” and “none of the above” are never used, since they do not give useful information about the methods a student used.
Multiple response prompts always include the phrase “select all” to clearly indicate their type. Each part of a multiple response problem addresses a different piece of the same overall skill, again serving as a diagnostic for teachers to understand which common errors students are making.
Short answer, restricted constructed response, and extended response problems are careful to avoid the “double whammy” effect, where a part of the problem asks for students to use correct work from a previous part. This choice is made to ensure that students have all possible opportunities to show proficiency on assessments.
When possible, extended response problems provide multiple ways for students to demonstrate understanding of the content being assessed, through some combination of arithmetic or algebra, use of representations (tables, graphs, diagrams, expressions, and equations) and explanation.
Rubrics for Evaluating Student Answers
Restricted constructed response and extended response items have rubrics that can be used to evaluate the level of student responses.
Restricted Constructed Response
- Tier 1 response: Work is complete and correct.
- Tier 2 response: Work shows general conceptual understanding and mastery, with some errors.
- Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Two or more error types from Tier 2 responsecan be given as the reason for a Tier 3 response instead of listing combinations.
- Tier 1 response: Work is complete and correct, with complete explanation or justification.
- Tier 2 response: Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
- Tier 3 response: Work shows a developing but incomplete conceptual understanding, with significant errors.
- Tier 4 response: Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Typically, sample errors are included. Acceptable errors can be listed at any Tier (as an additional bullet point), notably Tier 1, to specify exclusions.
Each unit has a culminating lesson where students have an opportunity to show off their problem-solving skills or apply the mathematics they have learned to a real-world problem. The end unit assessments, combined with students’ work on the culminating lessons, will show a multi-faceted view of students’ learning over the course of the unit.