Thursday / April 25

As teachers we want to use rich tasks to support our students in acquiring conceptual understanding that leads to stronger procedural fluency. Sometimes when we are caught up in our routines, we may not pause to consider if a task is significant enough to impact student learning. There are six questions we can use as we review a task to decide if it is, in fact, a rich task.

1. #### Does the task connect to important algebra content and mathematical practices, in reference to your algebra content standards?

Rich tasks should connect to important algebra content and reference content standards.

1. #### How does the task develop, build on, or connect to important understandings in algebra?

Rich tasks should relate to or add to important understandings in algebra.

1. #### Does the task connect to additional mathematical topics, and if so, how?

Connections among and within topics is one way to ensure that students are constructing understandings that form a cohesive knowledge base.

Strong connections minimize the amount of reteaching that we have to do.

For example, students often do not see the connection between simplifying an algebraic expression and using equivalent equations to find a solution to the equation. They may not see the relationships evident in multiple representations used, such as a table, graph, and equation. Rich tasks make the math visible so that students can form these connections.

1. #### Does the task provide multiple solution pathways for your students?

Our classrooms represent a diverse range of learners with varying strengths and opportunities to learn. To provide access to engage in the task, there must be opportunities for students to use different solution strategies. Additionally, there are connections between the different pathways to a solution that students can identify and continue to use.

1. #### Does the task engage your students in understanding and building concepts?

Curricula tend to focus on a procedural-based approach to algebra, with less time spent on conceptual knowledge that supports retention and deeper understanding. Even though we do need procedural fluency, it is even more important that students understand at a deeper level so that they are able to apply those understandings in more complex topics.

1. #### Does the task require higher-level thinking and reasoning?

If students can complete a task by using only procedural knowledge, then the task does not support higher-level thinking and reasoning and thus is not a rich task. A task is not an exercise—i.e., something that can be solved with an algorithm. A task should ask students to think through questions that may:

• Challenge students’ misconceptions
• Motivate students to construct generalizations
• Require students to compare and contrast solution methods
• Prompt students to use multiple representations
• Apply previously learned concepts and procedures to new topics
• Shift the task to a more complex level as students work through it

Using these six questions to analyze a task is a precursor to the rest of planning for a task. The next most important step is to actually do the task without looking at the solution first. As you work through it, consider the strategies your students will use to complete and how those strategies can be leveraged to build student understanding. Then, consider the instructional sequence and decide where the task would fit best.

Barbara J. Dougherty is the past director of the Curriculum Research & Development Group and a professor in the College of Education at the University of Hawai‘i at Mãnoa. She is a former member of the board of directors of the National Council of Teachers of Mathematics and is the
co-chair of the Mathematics/Special Education Workgroup, a partnership between the NCTM and the Council for Exceptional Children. She served on the author panel for the What Works Clearinghouse Practice Guide on assisting elementary school students who have difficulty learning mathematics for the U.S. Department of Education Institute of Education Sciences. She is the author or coauthor of approximately 22 book chapters, 29 articles, and 36 books, including Classroom-Ready Rich Algebra Tasks, Grades 6-12: Engaging Students in Doing Math (2023). Her research, funded by more than \$11.5 million in grants, emphasizes supporting students who struggle in middle and high school, with a focus on algebra. She holds teaching certifications in middle and high school mathematics and K–12 special education.

Linda C. Venenciano is a professor in the School of Learning and Teaching at Pacific University, where she teaches and supports early childhood through high school preservice teachers in mathematics education. She is a former classroom teacher and has taught mathematics to students from first grade through undergraduate. She previously served as the interim director of the Curriculum Research & Development Group and as an associate professor of mathematics education at the University of Hawai‘i at Mãnoa. She is the author or coauthor of 21 peer-reviewed publications and 12 books, including Classroom-Ready Rich Algebra Tasks, Grades 6-12: Engaging Students in Doing Math (2023). Linda is currently serving on the editorial board of Investigations in Mathematics Learning and has served as a program chair for the annual meeting of the Research Council on Mathematics Learning and as a guest editor for a special issue of Educational Studies in Mathematics.