Open-ended Assessments: Part 1

By Brea Ratliff, Secondary Mathematics Research Coordinator

As schools prepare for standardized testing this spring, many educators often wonder which instructional strategies will be most effective in terms of ensuring student success.

Beyond the scope of content, state mathematics assessments are measuring students’ ability to problem solve, recognize appropriate conjectures, communicate and analyze knowledge, and understand how mathematical ideas connect.

In short, these tests evaluate whether or not students are able to demonstrate the appropriate processing skills necessary for mathematics at each grade level.

On the STAAR Mathematics assessment for grades 3-8, mathematical processing skills are “incorporated into at least 75% of the test questions…and [are] identified along with content standards” (TEA, 2013). In order for students to perform well on an assessment designed this way, they should show success on formative assessments where they are challenged to apply their content knowledge while confidently using these skills. Over the next several weeks, we will explore a variety of open-ended formative assessments for students in grades 5 and 8, and students who are taking Algebra 1. These assessments can be implemented in a variety of ways. Depending on the makeup of your classroom, they could be a bell ringer, or the performance indicator during or following direct instruction. Many teachers also use them to start meaningful discussions with their students, as well as for an exit ticket or homework assignment. The possibilities are endless.

This week, let’s begin by looking at a few open-ended assessment ideas for 5th grade – all of which build upon student expectation 5.10(C) from the TEKS:

5.10(C) – The student is expected to select and use appropriate units and formulas to measure length, perimeter, area, and volume.

Level 1 – Assessments designed to develop proficiency in one student expectation. Assessments build around one particular skill are often helpful after when introducing a concept, or providing targeted intervention.

 Level 2 – Assessments designed to develop proficiency in two or more student expectations. The assessments for this level can vary in degree. While some may be designed to assess a combination of content skills, others may be written to include process skills. In this next example, we continue to look at 5.10(C), but also student expectations 5.3(A) and 5.3(B):

5.3(A) – The student is expected to use addition and subtraction to solve problems involving whole numbers and decimals.

5.3(B) – The student is expected to use multiplication to solve problems involving whole numbers (no more than three digits times two digits without technology).

For this next example, we assess students’ logical reasoning while addressing student expectation 5.16(A):

5.16(A) – The student is expected to make generalizations from patterns or sets of examples and nonexamples.

This assessment covers two content standards we have already addressed [5.3(A), 5.10(C)], and introduces two standards from Probability and Statistics and Underlying Processes and Mathematical Tools:

5.13(B) – The student is expected to describe characteristics of data presented in tables and graphs including median, mode, and range.

5.14(B) – The student is expected to solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.

These are just a few examples to use with your students, but they are guaranteed to challenge your students to apply what they know about length, perimeter, area and volume in a new way.

Texas Education Agency. (2013). STAAR Assessed Curriculum, Grade 5. Retrieved from http://www.tea.state.tx.us/WorkArea/linkit.aspx?LinkIdentifier=id&ItemID=2147488330&libID=2147488329