Takeaways from Jo Boaler: Assessment

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Josea Eggink, Kennedy High School, Bloomington, MN

In July, Mark Coté and I attended Jo Boaler’s three-day workshop “Mindset, Mathematics, & Common Core Transition” in San Marcos, CA. Below is the third in a series of articles sharing highlights from our three days in San Marcos.

During the workshop, Jo commented that students in the United States are over tested in math. She said the USA’s mistaken idea that testing will help students improve is analogous to thinking that measuring someone’s height will help them grow. She also pointed out that the countries that do the least amount of testing (Finland, for example) rank highest in student math performance.

Although we need to lessen the amount of highstakes testing, Jo encouraged teachers to increase their use of a different, and immensely valuable, assessment: Assessment for Learning. The purpose of Assessment for Learning is to help students understand where they are, where they need to get to, and how to close the gap. It provides students with the knowledge and tools to become self-regulatory learners. Jo stated that if more teachers incorporate Assessment for Learning in their classroom culture, the United States could jump from the middle to within the top three in international math rankings.

The following are four Assessment for Learning strategies that Jo shared during the workshop:

Self- and peer-assessment. In a research study conducted by White and Frederiksen, students who engaged in self- and peer-assessments outperformed students who did not engage in these activities. Also, the greatest gains were made by students who had previously been considered low-achieving, suggesting that many low-achieving students are low-achieving simply because they do not know what they are supposed to learn. Jo added that in order for students to understand what meets the criteria, the goals of the unit should be stated in kid-friendly language. Then we can better engage students in reflecting whether they have learned the concepts.

You can also have students self-assess their use of the mathematical practices. Jo showed us the Thermometer Student Rubric Self-Assessment created by Exemplars, that you can use.

Diagnostic feedback. Jo cited a study conducted by Butler that compared three conditions: giving students grades, giving students diagnostic feedback, and giving students both grades and diagnostic feedback. The students who received only diagnostic feedback later outperformed students from the other two groups. Elawar and Corno had similar findings in their research study involving eighteen 6th grade classes. The students receiving diagnostic comments on their homework (with no scores) learned twice as fast as the students who did receive scores, the achievement gap between male and female students disappeared, and student attitudes improved.

Have students design assessment questions.

Questioning. Questioning students during class is a wonderful way to assess their understanding, and we are fortunate that the CPM materials provide suggestions and support for effective questioning in the teacher notes. Jo reminded us that our questions need to focus on student ideas and to give ample wait time before inviting responses from students.

Jo also shared thoughts on grading. She said grades should reflect more than how many problems students get correct. Grades should also reflect aspects of students’ mathematical thinking such as how they see representations and how they ask questions. Jo recommends giving students the opportunity to resubmit summative assessments for a higher grade after they spend more time on the material. (The goal, after all, is learning.)

You can visit Jo’s website to find more insights, research, and resources, and be sure to check out Jo’s keynote presentation at CPM’s conference this February in San Francisco!

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Algebra Tiles Blue Icon

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.