Contributed by Rita Janes and Elizabeth Strong
While visiting a classroom where the teacher had introduced a new topic in mathematics, I asked her how the children’s understanding of the topic was progressing. She said that she did not know because the children had not written the unit test. Her response perplexed me because she was interacting daily with the children but was unaware how they were doing. I think she really did know but did not have the confidence to say until she had the children’s unit test results.
Since then, when working with teachers, we discuss the importance when planning a lesson to think about what they will be observing when their children are involved in the learning experiences. Such observations will let them know if their children are learning and if their instructional plan needs changes. As well, I encourage the teachers to prepare collaboratively, with a colleague(s), either face to face or with electronic discussions, observation questions appropriate for their lessons.
Here are sample observation questions teachers prepared to accompany a learning experience using How Do You Count A Dozen Ducklings (Chae) as a resource and designed to meet the following learning expectation:
- Skip count a number of objects accurately and know that the count is the same as if counted by 1s.
One teacher’s observation and interventions are shared below.
Learning Experience: Children are engaged in an activity related to How Do You Count A Dozen Ducklings where Mama Duck counts her ducklings by 2s, 3s, 4s and 6’s and children relate the counting to the illustrations and the total number of ducks. They explore the misuse of language in the book to describe a mathematical situation, as in the lines, “She (Mama Duck) sorted her ducklings in new little lines so she could count them three at a time. This way when she counted, she only had to count to FOUR.”
Teacher Observation Questions:
- Can the children count accurately the 12 eggs and 12 ducklings by 1s, 2s, 3s, 4s, 6s?
- Do they understand that counting by 2s, 3s, etc. to 12 gives the same count as if they counted by 1s?
- Do they understand that when they count pictures, themselves or objects into equal groups that the total count does not change? Or do they make the same mistake as the Mama Duck and think that when she sorted into groups of three she only had to count to four? Do they know this is not correct?
Teacher Observations and Intervention:
- Several children did not count accurately the pictorial representation of ducklings whether counting by ones or by multiples. The teacher decided to provide tubs of blocks and ask children to count a set of 12 by counting the blocks by ones, then count another set by counting by 2s and so on by 3s, 4s, 6s. This was repeated many times and sets were compared until the teacher knew children were counting accurately.
- The teacher observed when children counted a set of 12 blocks by 2s, etc., they were not always sure they had 12 blocks and often checked by recounting the set of blocks by ones.
- Children sometimes when counting a set of 12 ducklings by 4s, saying, 4, 8, 12, they would say there were 3 ducklings. They were making the same mistake as Mama Duck. Having the children count classmates helped greatly in allowing them to see that whether you count the set by 1s, 2s, 3s, etc. the final count will be the same, and not the number of number words said.
- Teachers observed that just because children could skip count a number of objects they did not always understand that the count was the same as counting by 1s. Children were not always confident that skip counting was a suitable way to count a set of objects.
After repeating this activity for different numbers (8, 16, 24, etc.), the teacher knew that the children were now ready for writing equal groups as addition and multiplication equations, relating the two, and introducing commutativity of multiplication. Complete details of these lessons along with Observation Questions may be found in Number & Stories: Using Children’s Literature to Teach Children Number Sense.
Chae, I. S. (2006). How Do You Count A Dozen Ducklings? Illustrated by S. H. Rew.
Park ridge, IL: Albert Whitman.
Janes, R. C. & Strong, E. L. (2014). Number & Stories: Using Children’s Literature to
Teach Young Children Number Sense. Thousand Oaks, CA: Corwin.
Rita Janes was a teacher at all levels of schooling and most recently involved in professional development with elementary school teachers where she promotes the use of rich problem solving tasks, mathematical discourse, and asking of good questions to ensure inquiry-oriented classroom environments for children. Rita has served on the Board of Directors for the National Council of Teachers and the National Council of Supervisors of Mathematics and chaired the NCTM Professional Development Services Committee.
Elizabeth Strong’s career began as a primary-elementary teacher, then elementary school administrator, school district curriculum coordinator and university professor. Her focus areas are literacy, language arts and children’s literature. She is an international, national, provincial and regional professional development presenter and facilitator. She has served on such boards as the International Board on Books for Young Children and the Prime Minister’s Awards for Teaching Excellence in Science, Technology and Mathematics. She holds a Ph. D in education from The Ohio State University.