Design Meaningful Math Lessons Using the Task/Question/Evidence Process
- Rebecca DiBuono
- Nov 17, 2025
- 5 min read
The TQE process, crafted by Dr. Juli K. Dixon, is a framework for teachers to create engaging and meaningful math lessons that help students explore and understand mathematical concepts, procedures, or relationships. Originating from the Making Sense of Mathematics for Teaching series, this process guides educators in designing lessons.
In this blog post, I'll describe the phases of the TQE process and how I use it to create a lesson to introduce the exploration of related division facts with dividends up to 144, aligning with the Florida B.E.S.T. standard, MA.3.NSO.2.2.
Generating Tasks
Tasks are designed to elicit evidence of students' reasoning and understanding by engaging them in solving authentic, challenging problems. These tasks are crafted
with the intention of not only assessing students' knowledge but also providing insights into their thought processes and problem-solving strategies. By presenting students with real-world scenarios and complex questions, educators can observe how students apply their prior knowledge and skills in practical contexts.
Authentic tasks encourage students to engage in higher-order thinking. Rather than simply recalling facts or performing calculations, students are prompted to analyze text, determine an appropriate strategy, and develop coherent arguments. This shift from passive learning to active engagement fosters a deeper understanding of the material, as students must navigate through complexities and uncertainties that mirror real-life situations.
When designing a lesson on understanding the concept of division, I started by choosing a specific division fact for students to solve and connected it to a theme. To create a real-world scenario, the task focused on distributing cookies among friends.
One of my preferred tools for generating tasks is Magic School AI. This platform provides a range of tools aimed at helping educators and students by saving time and enhancing learning. In Magic School AI, I created a custom tool that generates tasks for the TQE process.
Developing Questions
To effectively prepare questions, I referenced Florida's BIG-M standards guide to address potential misconceptions. For example, a common error when exploring division describes difficulty relating word problems and real-world scenarios to models, expressions, and equations. Specifically relating to division, students may be confused when an amount in each group is given and the number of equal-size groups needs to be found. These potential misconceptions provide teachers valuable insight to prepare questions when providing supports.
"When scaffolding is provided before students have the opportunity to make sense of a challenging task without the extra help, students are inhibited from developing productive perseverance." - Dr. Juli K. Dixon
Dr. Dixon highlights the critical distinction between "just in time" supports, which are immediate and responsive, and "just in case" supports, in her blog on DNA Math. When teachers follow the gradual release model of I Do, We Do, You Do, typically there is scaffolding built into the lesson. In contrast, following the TQE Process puts the responsibility of learning with the students by presenting a task without supports before solving. The teacher actively monitors as students begin making sense of the task and developing an action plan to solve. When a misconception arises, the teacher presses to build connections and develop mathematical reasoning.
Teachers often utilize six types of questions to improve understanding during mathematics instruction:
1. Probing Students' Thought Processes
These questions aim to encourage students to articulate their reasoning and thought processes. Students should elaborate on their own thinking for deepening their own understanding and for the class. For example:
“Explain how you arrived at that answer.”
2. Exploring Mathematical Meanings and Relationships
These questions help students make connections between different mathematical concepts. For example:
“How does the concept of division relate to multiplication?”
3. Fostering Discussion
These questions promote dialogue and collaborative learning among students. For example:
“Do you agree or disagree? Why?”
4. Eliciting Procedures or Facts
These questions focus on retrieving specific information or procedures. This question type may also be used to reference specific math vocabulary. For example, when referencing a four digit number and their values, you may ask:
“What is the value of the digit in the thousands place?”
5. Inquiring About Other Mathematical Concepts
These questions encourage students to think about how different areas of mathematics are interconnected. These questions do not need to directly relate to the task or math ideas for the lesson. For example, during a conversation about graphing data in a table, you may ask:
“What title would you label this graph?”
6. Posing Nonmathematical Questions
These questions do note relate to the teaching and learning of math, but may reference the context of the lesson or task provided. For example:
“Do you want to use a white board or graph paper?”
Evaluating Student Evidence
Students support their solutions and clarify their thoughts by using reasoning that is appropriate for the lesson focus. This approach encourages deeper understanding and fosters a more engaging learning environment. By emphasizing the importance of reasoning, students learn to articulate their thoughts clearly and effectively, which is crucial in academic discussions.
In my classroom, students or partner groups present their whiteboard work using a document camera, allowing them to discuss their reasoning and the methods they utilized to solve the task at hand. I intentionally choose students whose evidence can be connected in a meaningful way, facilitating rich mathematical discussions. To deepen their understanding, I challenge them with questions that press them to identify connections or relationships between the various examples of shared evidence.
This collaborative approach not only enhances their critical thinking skills but also reinforces the value of teamwork in problem-solving. By fostering an environment where students actively engage with each other's ideas, they develop a more comprehensive understanding of the subject matter.
Changing the Game
The task/question/evidence process is a game-changer in mathematics instruction, dramatically enhancing the learning experience for students! By focusing on crafting challenging tasks, using strategic questioning techniques, and actively gathering evidence of understanding, educators can create a vibrant and dynamic classroom environment. This approach not only boosts student engagement and motivation but also caters to diverse learning needs and nurtures a growth mindset. By embracing this method, teachers can more effectively guide students on their mathematical journeys, ensuring they develop both the skills and confidence needed for success!
Resources
Dixon, J. K., & Nolan, E. C. (2016). Making Sense of Mathematics for Teaching, Grades 3-5. Solution Tree Press.
Providing Scaffolding Just in Case by Juli Dixon [Part 3 from the (Un)Productive Practices Series] - DNA MATH. (2018). DNA MATH. https://www.dnamath.com/blog-post/five-ways-we-undermine-efforts-to-increase-student-achievement-and-what-to-do-about-it-part-3-of-5/
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