Thoughts on Rubrics

Karen Wootton, Director of Assessment

I hear teachers talk about rubrics with mixed tones. Some love them and swear by them, others just do not bother with them. Often the common ground is a lack of understanding about rubrics and how they can be used to further student learning.

For some teachers, rubrics are a means of communicating expectations. Teachers use rubrics to outline what would be a higher quality response, and this is a component of formative assessment. This gives students targets to aim for when completing a task. Other teachers use the rubric as criteria for grading, or summative assessment. These point-value rubrics, typically a 4-point or 6-point rubric, help teachers assign points based on how the response fits with the details of the rubric. Rubrics can be used for either purpose.

Suppose a teacher plans to use a 4-point rubric. Here is a typical descriptor for a score of three in a 4-point rubric: “Substantially accomplishes the purpose of the task. Student work shows essential grasp of the central mathematical idea(s). Recorded work in large part communicates correct thinking.” Usually, the score of a 3 is not much different from the score of a 4 in the description. But, for many teachers, entering a “3 out of 4” in the grade book, meaning the student earned a 75%, doesn’t seem to be in agreement with what a three stands for in a 4-point rubric. Doesn’t the description seem to fit a student who is doing better than “C” work? To help with this incongruity, in the assessment tab of the CPM teacher binder, CPM has suggestions for rubric grading, including percentages (2 as 70%, etc.) for translating a rubric score into a grade book percentage (eBook ? Assessment ? Grading and Scoring). For some teachers, this eases concerns of the rubric score being fair.

If you are considering using rubrics but have scoring concerns, you can still use rubrics by making some small changes and not translating to a percentage. One easy change is to switch from a 4-point rubric to simply assigning A, B, C, D, or F. Most students and parents know what those letters represent and can translate the letter into a level of competency Another alternative would be to switch to words. A 4-point word rubric might be Unacceptable, Marginal, Proficient, Distinguished. A more simple one: Developing, Competent, and Exemplary.

Rubrics can be used for many different assessment items. The research is clear though that for formative assessment (or Assessment for Learning) to be effective, you want to stay away from grades or percentages, and offer feedback. Feedback does not need to be long or detailed. In fact, you do not want to “tell” students how to do the problem in the feedback, but ask questions with your goal being to make the student think further about the problem. For example, you could write on a student’s paper “What prompted you to multiply by three? Where did you get 3 from the problem?” or “There was something we realized we needed to do when multiplying both sides of an inequality by a negative number. Do you remember? Why did we do this?” Even students who have solved a problem correctly should be offered the opportunity to think further and learn. Feedback for such a student could look like “This is very detailed and clear, but I am wondering if you could do the problem if the problem asked you to consider an octagon rather than a hexagon. What do you think?” In thinking through the problem and the mistakes the student has made, the student learns.

If you are using the rubric for a summative assessment, you might want to abandon that plan. For a summative assessment, do what most math teachers do: come up with an appropriate number of points for the problem to be worth, and then delineate how many points each “part” is worth. (e.g. “-2 for forgetting to flip an inequality…”) Most teachers are required to give summative assessments for the purpose of filling a grade book. Develop a system that works for you and is fair and appropriate for students.

One more thing to remember: you do not need to hide rubrics from your students. Share them and all your expectations for each task you give. Student learning will advance when you take this open approach to expectations and learning.

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Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.