User:Meghandill
Return to: ETAP 623 Spring 2018 Section 6476 | Student-Led Error Analysis Discourse in Mathematics Classrooms
About Me
Education: I graduated from SUNY Geneseo in 2013 with a Bachelor of Science in Education: Childhood/Special Education and an English Concentration. Currently I am working on a Master of Science Degree in Curriculum Development and Instructional Technology from SUNY Albany.
Personal: I am originally from Buffalo, NY but I currently reside in Rochester, NY. I have worked as a fifth grade Math teacher at a local charter school for the past five years and I am also the 5th grade - 8th grade Math Department Chair at my school. During my free time, I enjoy traveling, spending time with my husband and rescue dog, Maggie and attending ballet classes.
My Topic and Purpose
As a mathematics teacher, I believe that 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.
Learning Outcomes
Upon the completion of this course, students will be able to:
-Summarize the importance of error analysis in the classroom
-Conduct and implement student-led discussions in the classroom around error analysis
-Develop mathematics error analysis lesson plans for instruction
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.
Error Analysis Needs Assessment Survey and Data
Twenty-eight participants responded with the following results:
1. I have or would like to use student-led discussions in my classroom to combat misconceptions
Agree: 100%
Disagree: 0%
2. I plan for anticipated errors prior to teaching my lessons
Agree: 85.71%
Disagree: 10.71%
Other: 3.57% (Response did not indicate a reasoning for this choice)
3. I address student errors:
Through Whole-Group Discourse: 35.71%
Through Private Conversations: 32.14%
After the Exit Ticket: 0%
Other: 32.14% (Responses indicated that educators used a combination of the strategies listed above.)
4. I believe error analysis discussions deepen a student’s understanding
Agree: 100%
Disagree: 0%
5. I believe discussing misconceptions in the classroom prepares my students for future lessons
Agree: 92.86%
Disagree: 7.14%
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.
Analysis of the Learner and Context
The learner of this course is a mathematics teacher in a K-12 setting. Participants should have access to the Internet and basic computer skills. Participants should also have access to lesson plans that will be taught during this course. For this mini-course, the learner does not have to have prior experience facilitating student-led error analysis discourse but they should have knowledge of their mathematics curriculum.
Performance-Based 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
Task Analysis
Part 1: Goals
Terminal Goal:
Participants will be able to facilitate student-led discussions based on analyzing errors in mathematics classrooms.
Enabling Goals:
Participants will be able to summarize the importance of error analysis in a classroom setting
Participants will be able to analyze existing lesson plans and determine potential student misconceptions
Participants will be able to create and implement student directed prompts into lesson plans to emphasize student discourse
Part 2: KASI
Knowledge:
Know effective questioning prompts for student-led discourse
Know the importance and impact of error analysis in classroom curriculum
Attitudes:
Believe that student-led discourse and error analysis can enhance student understanding
Willingly implement the techniques of error analysis and student led discourse in their lesson plans
Skills:
Ability to analyze mathematical curriculum and potential student misconceptions
Ability to use technology and communicate with participating peers through the Internet
Ability to adapt lesson plans to support student’s needs
Interpersonal Skills:
Actively participate and reflect on peer’s implementation of mini-course skills
Effectively and respectively communicate best practices and experiences throughout the mini-course
Part 3: Pedagogical Approach
Unit 1:
The first unit will be primarily a instructivist pedagogy approach where the participants will learn about the positive impact that error analysis can have on student understanding and what types of student directed prompts can enhance student-led discussions.
Unit 2:
The second unit will be a combination between a constructivist and instructivist approach. In this unit, participants will learn how to pre-plan for potential student misconceptions in a mathematics classroom and then they will practice this skill and reflect on how this skill could enhance student understanding.
Unit 3:
The final unit will primarily be a constructivist approach where the participants will plan a student-led discourse moment within an existing lesson plan based on a potential student misconception and then reflect on the planning experience.
Curriculum Map
References and Resources
Barlow, A. T., Watson, L. A., Tessema, A. A., Lischka, A. E. & Strayer, J. F. (2018). Inspection-worthy mistakes: which and why? Carefully select and leverage student errors for whole-class discussions to benefit the learning of all. Teaching Children Mathematics. 24, 384-391.
Bill, V. & Speranzo, L. (2017, July 17). Using talk to make sense of mathematics. National Council of Teachers of Mathematics. Retrieved from: https://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Using-Talk-to-Make-Sense-of-Mathematics/
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.
Curriculum Associates. (2018). Let’s talk math: 20 power sentence starters & questions. Retrieved from: https://www.weareteachers.com/wp-content/uploads/final-student-poster-8-15.pdf
Curriculum Associates. (2018). Why mathematical discourse matters: And how it can help your students. Retrieved from: https://www.weareteachers.com/wp-content/uploads/ready-tips-math-discourse-infographic.pdf
Gojak, L. M. (2013). The power of a good mistake. National Council of Teachers of Mathematics. Retrieved from: https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/The-Power-of-a-Good-Mistake/
Herter, R. (2015, August 13). Growth mindset for math – mistakes. Retrieved from: https://www.youtube.com/watch?v=LrgpKjiQbQw
Hill, Z. (2016, August 15). Mathematical discourse, part 2: Planning for the task. National Council of Teachers of Mathematics. Retrieved from: https://www.nctm.org/Publications/Teaching-Children-Mathematics/Blog/Mathematical-Discourse,-Part-2_-Planning-for-the-Task-(Anticipating,-Selecting,-and-Sequencing)/
Hoffman, B. L., Breyfogle, M. L. & Dressler, J. A. (2009). The power of incorrect answers. Mathematics Teaching in the Middle School. 15, 232-238.
Kersaint, G. (2015, September 29). Talk math: How to engage students in mathematical discourse. Getting Smart. Retrieved from: http://www.gettingsmart.com/2015/09/talking-math-how-to-engage-students-in-mathematical-discourse/
Lemov, D., Hernandez, J., & Kim, J. (2016). Teach like a champion field guide 2.0: A practical resource to make the 62 techniques your own. San Francisco, CA: Jossey-Bass.
Rumsey, C. & Langrall, C. W. (2016). Promoting mathematical argumentation. Teaching Children Mathematics. 22, 413-419.