Using a Journal Article as a Professional Development Experience
Title: Disequilibrium & Questioning in the Primary Classroom- Establishing Routines That Help Children Learn
Author: Susan Carter
Journal: Teaching Children Mathematics
Issue: October 2008, Volume 15, Issue 3, pp. 134-137.
Rationale for Use
The author, a grade one teacher, shares her experience helping children have success in learning mathematical concepts by having them come to an understanding that struggle is an essential part of learning. Teachers often wonder about if and when they should allow their students to struggle in mathematics.
The article reinforces a statement under the Learning Principle (Principles and Standards for School Mathematics, NCTM, 2000, p. 21): “When challenged with appropriately chosen tasks, students become confident in their ability to tackle difficult problems, eager to figure things out on their own… and willing to persevere. … Students view the difficulty of complex investigations as a worthwhile challenge rather than as an excuse to give up”.
- Provide copies of the article for each participant so they can either read the article beforehand or at the beginning of the session.
- Small group: Invite participants to discuss their understanding of the word “disequilibrium” and share their own experiences with it either in their own learning or in observing children in their classrooms.
Whole Group: Continue sharing and discussion of ideas shared in small groups with particular consideration to classroom experiences of participants. Record observations made on chart paper.
- NOTE: If you think it is necessary, highlight examples of the meaning of disequilibrium as stated by the author. For example, “Jean Piaget (1970) defined disequilibrium as a conflict between new ideas and current conceptions (p. 135)” or “Understanding that disequilibrium is normal gives students a foundation from which to struggle and move toward understanding ( p. 136)”. These could be placed on chart paper or electronically displayed for all to see.
Reflect on the statement Carter poses in the article: “When I began teaching mathematics to first graders, I based the success of my lessons on the happiness of my students…If students became unhappy, got stressed out, or seemed frustrated, I was known to actually stop a lesson and start an activity sheet…. The focus in my classroom was not on worthwhile tasks but on tasks everyone would succeed with - at varying speeds. (p 135)”. (This excerpt could be posted on chart paper or shown on an Overhead or PowerPoint slides). Discussion could focus on
- worthwhile mathematical tasks and the amount of support that a teacher should provide to help students think through a task; and
- the importance (role) of worthwhile tasks in children’s learning.
Several times in the article the author talks about the importance of allowing student’s to struggle with mathematical ideas. At the end of the article she says: “teaching my students how to acknowledge and pursue the struggle and process of learning resulted in worthwhile, meaningful mathematical experiences for me and my students”.
Invite participants to discuss:
- Their feelings and experiences with allowing student’s to struggle with mathematical ideas; and
- Strategies they have used to help students struggle with mathematics.
The author suggests that as children work in a classroom where disequilibrium is established, they learn to delve into mathematical concepts because they have no fear of failure.
Invite participants to:
- Share ideas they have used to help children overcome a fear of failure in the mathematics classroom.
- Suggest ways for establishing a risk free classroom environment where children feel free to express their thinking, ask questions of other students and the teacher.
Carter relates her students’ conversations as they explored a new mathematical concept- place value. She illustrates how it was used “to help student’s identify disequilibrium for themselves (p. 136).” Participants could reread this section before proceeding.
- Discuss how the ideas expressed by the author might be incorporated into participants’ classes.
- Ask participants before meeting for the next session:
- To choose a concept they are teaching and keep a record of how disequilibrium was nurtured.
- Read the questions used by the author during class discussion (p. 137) and use, if appropriate, while teaching the concept. Keep a record of other questions used and what was noticed about the childrens’ learning?
What would you have done differently if you re-taught the lesson?
- Plan to share experiences and reflections at the follow-up session.
The Learning Principle (PSSM, NCTM, 2000) states:
Students understanding of mathematical ideas can be built throughout their school years if they actively engage in tasks and experiences designed to deepen and connect their knowledge. Learning with understanding can be further enhanced by classroom interactions, as students propose mathematical ideas and conjectures, learn to evaluate their own thinking and that of others, and develop mathematical reasoning skills (p. 21).
- Discuss the above excerpt in light of what the author shared in her article about the importance of establishing disequilibrium in helping children learn.
- Relate to your classroom experiences.
- What suggestions do you have for promoting classroom interactions as suggested by the author in the above quote?
Connections to Other NCTM Publications
- Behrend, J. L. (2001, September). Are rules interfering with children’s mathematical understanding? Teaching Children Mathematics, 8, 36-40.
- Buschman, L. E. (2005, August). Isn’t that interesting! Reflect and discuss. Teaching Children Mathematics, 12, 34-40.
- Kline, K. (2008, October). Learning to think and thinking to learn. Teaching Children Mathematics, 15, 145-151.
- Kurz, T. L., & Batarelo, I. (2009, March). Aligning theory with practice. Teaching Children Mathematics, 15, 404-409.
- National Council of Teachers of Mathematics (2000). Principles and Standards of School Mathematics. Reston, VA: Author.
- National Council of Teachers of Mathematics (2007). The Learning of Mathematics: 69th NCTM Yearbook. Reston, VA: Author.
- Weiser, E. T. (2008, September). Students control their own learning: A metacognitive approach. Teaching Children Mathematics, 15, 91-96
- Zambo, R., & Zambo, D. (2007, December & 2008, January). Mathematics and the learning cycle: How the brain works as it learns mathematics. Teaching Children Mathematics, 14, 265-270.