Creating Open-Ended Math Tasks

Regardless of your class size, designing instruction for everyone’s ability is a complex endeavor, students come into the classroom with different funds of knowledge, experiences, and beliefs about themselves as a learner. Despite these differences, you must prepare students to meet grade level standards and access state adopted curriculum.

While traditional math textbooks often provide the structure for students to practice procedural skills, they often lack the flexibility to scaffold instruction based on students' needs and interests.  Just like a doctor needs to focus on the patient's needs, lifestyle, and symptoms, so must the teacher individualize instruction based on their students. This is where designing open-ended tasks for your students can move your instruction from "why do we need to learn this" to "when can we work on our task." 

There are two main types of tasks: close-ended and open-ended tasks. Close-ended tasks are predictable, focus on one way of thinking, and have a single right answer. In contrast, open-ended tasks are unpredictable, provide students with opportunities to explore ideas more broadly, have multiple solutions, and incorporate many ways of thinking and decision-making. There is often ambiguity in open-ended tasks, as such they are frequently referred to as ill-constructed questions or problems. Open-ended tasks require more cognitive effort from students and therefore engage them in higher levels of thinking and learning. Students must draw from their knowledge in broad ways to figure out potential solutions.

Another difference between open-ended and close-ended tasks lies in the type of thinking required when determining a solution. Close-ended tasks often draw on narrow ways of thinking that rely on procedure or previously memorized information, while open-ended tasks draw on students’ broad conceptual knowledge (Stein & Smith, 1998). The path to the solution of an open-ended task requires effort, multiple steps, and application of broad conceptual knowledge, rather than rote memorization.  

So are you ready to infuse Open-Ended Tasks into your classroom practice? In this video I am demonstrating how I introduce an open-ended  task of a Scavenger hunt to identify arrays in this second grade classroom.  Students have been working with arrays by constructing models using a variety of manipulatives.  In this activity they are extending their thinking to identify an array in their class. 

The flexibility of open-ended tasks allows students to work in their "Zone of Proximal Development" (ZPD) while providing you with the knowledge of where student understanding lies in an authentic task.  

Free Template

Technology can also support students in ways of showing and expressing what they know about a concept.  Using free tools such as SeeSaw or Flip Grid students can create a video to explain their thinking.  This type of activity also allows students to create, apply and synthesize learning in a meaningful way.  As an extension of this activity students were required to identify arrays in their home. 

When creating Open-Ended Tasks you must ground the task in students' interests, funds of knowledge and ability.  This will support you in creating a hook, that will capture students' attention and support them in making mathematical connections.  Holiday's and school events are also a perfect way to build on students' fund of knowledge.  In this gift giving guide activity, students were able to select a gift to get ratings from their peers.  The concepts of ratios, percents, and division were all included in this open-ended task.  Once students completed a hard copy of their gift guide they then completed a digital version which was shared with families.  

Ratio Gift Guide

Creating open-ended tasks are a perfect way to keep students motivated to "do the math" and apply the concepts they are learning about in a meaningful context.  When the recess bell rings and kids are still motivated to work on this open-ended task, you know it's worth the investment. Create your own open-ended tasks with this planner and invited Dr. Dickenson to your school for Professional Development in curriculum and design.  

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