Meghan Dill: Student-Led Error Analysis in Mathematics Classrooms

From KNILT

Return to: ETAP 623 Spring 2018 Section 6476 | Meghan Dill Portfolio Page


Student-Led Error Analysis in Mathematics Classrooms


Overview and Purpose

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Course Overview:

Misconceptions in the classroom are powerful tools that can be used to deepen student’s understanding. This course will focus on the importance of analyzing errors in the classroom and teach educators how to facilitate student-led discussions around such errors. By asking students to articulate why a solution is incorrect, the educator provides the student with an opportunity to apply their prior knowledge to the concept being discussed and strengthen the conceptual understanding of the topic in the classroom.

Purpose & What to Expect:

The purpose of this mini-course is to develop an understanding of the benefits of misconceptions in mathematics classrooms. By the conclusion of this course, participants will be able to plan for anticipated misconceptions within lesson plans and identify the importance of students analyzing their peer’s errors through student-led discourse.

The first unit of this course will focus on the importance of error analysis in the classroom and introduction to discourse prompts that will aide in the facilitation of student-led discussions. The second unit will introduce how to plan for misconceptions in the classroom and the third unit will conclude with participants developing a student-led discourse moment from an existing lesson plan for future implementation.

Materials Needed:

  • Internet Access
  • Access to K-12 Mathematics Curriculum
  • Journal or Notebook

Needs Assessment

Problem: Student-led error analysis discourse is one of the most effective ways to combat misconceptions in mathematics classrooms. This type of discussion encourages students to use their prior knowledge to discuss whether or not their peers have the correct answer or appropriate mathematical steps and ultimately leads the entire class to a key understanding or conjecture to use in the future after the discussion concludes. However, most educators use private discussions to address student error, which limits the amount of students exposed to the key understanding or teachers do not effectively plan for misconceptions prior to the implementation of their lesson. Both of these strategies ultimately require more class time and often results in the teacher providing the correct answer to the student rather than challenging the student to make connections from the mathematics content to combat their own errors.


Gathering Information on the Problem: A survey was conducted with a set of teachers from a Rochester City School District school.

Twenty-eight participants responded with the following results:


What is To Be Learned:Participants in this mini-course will learn how to effectively plan for misconceptions prior to their lesson and facilitate a student-led discourse surrounding error analysis in their mathematics classroom.


Learners:This mini-course is intended for teachers of any grade level but will primarily focus on K-12 mathematics discussions. The learners in this course will be individuals who intend on using misconceptions in the classroom as learning opportunities and wish to combat errors in an effective amount of time during their classroom instruction.


Instructional Context: This course requires the learner to have access to the Internet and a computer. It is also highly suggested that the learner be involved in classroom instruction, as the mini-course will require the student to implement their understandings from this course directly into an already existing lesson plan.


The Solution: The participants of this mini-course will be exposed to literature surrounding error analysis and video examples of student-led error analysis discourse. The participants will be required to reflect on their understanding of error analysis and determine how it can be effective in their classroom. Additionally they will analyze and plan for an anticipated misconception in an existing classroom lesson and ultimately design a moment for student-led discourse during the selected lesson. The learner will conduct this planned moment in their classroom, reflect on their experience and make alterations if applicable for future lessons.


Goal: By the conclusion of this course, the learners will be able to identify the importance of student-led error analysis discourse in their classrooms, consistently plan for anticipated gaps or misunderstandings in their lessons and facilitate student-led discourse surrounding misconceptions on a daily basis.

Performance Objectives

To demonstrate their learning, participants will complete the following tasks:

  • Summarize the importance of error analysis in mathematics classrooms
  • Develop a plan and implement error analysis techniques into existing lesson plans
  • Analyze teaching objectives to determine potential student misconceptions
  • Create an error analysis student-led discourse moment

Course Units

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This mini-course includes the following units. Click the title of a unit to go to its page.

Unit 1: Introduction to Error Analysis & Student-Led Discourse

This unit of this course will focus on the importance of error analysis in the classroom and introduction to discourse prompts that will aide in the facilitation of student-led discussions.

Unit 2: Planning for Misconceptions

The second unit will introduce how to plan for anticipated misconceptions in the classroom and allow participants to begin reflect on the importance of planning for such moments in the classroom.

Unit 3: Developing Discourse & Implementation

This unit will conclude with participants developing a student-led discourse moment from an existing lesson plan based on Unit 2's potential misconception for future implementation.

Extended Resources

Select or access the following resources to learn more about addressing errors in the classroom and facilitating student-led discussions:

  • Borasi, R. (1994). Capitalizing on Errors as "Springboards for Inquiry": A Teaching Experiment. Journal for Research in Mathematics Education, 25(2), 166-208. doi:10.2307/749507
  • Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Norwood, NJ: Ablex.