Contributed by Rita Janes and Elizabeth Strong
After completing a Mathematics Investigation with my children, I always find it most important and extremely valuable to reflect back over and assess the entire Investigation implementation. Reflection provides me time to think consciously about the strengths and weaknesses of the Investigation, the effectiveness of my instructional plan and strategies, and my children’s successes. It assists me in making my thinking ‘visible’, enabling me to learn from my implementation, and gain greater insights into my own thinking and learning processes. It allows me the opportunity to think about what I have learned, how I might use what I have learned, and what I may need to learn or explore further. At times, I am most fortunate to share and explore my reflections with colleagues who completed the same Investigation. Such collaborated sharing is engaging and thought-provoking and leads us to new understandings about the implementation of the Investigation.
Providing my children time to reflect on their experiences throughout the Investigation is incredibly constructive to them and me. It assists them in actively participating in their learning and connecting their new learnings to their previous experiences. It provides me a greater understanding of their thinking and reasoning throughout their involvement in each mathematical task.
The following is an example of Specific Teacher and Children Reflection Questions related to the Investigation: Doubling Numbers using the children’s book Minnie’s Diner: A Multiplying Menu (Dayle Ann Dodds).
Teacher(s) (If possible share and discuss responses with colleagues):
- Would you recommend Minnie’s Diner: A Multiplying Menu to your colleague(s)? Why or why not?
- Was this an enjoyable, successful Investigation to implement? If so, what made is so?
- Did you have to alter your instructional plan during the Investigation? If so, why? What did you alter?
- How did your teaching strategies increase your children’s opportunities to engage in critical thinking during the Investigation?
- What tasks were most effective? Why?
- Were there new strategies the children used in reading and accomplishing the tasks? If so, what were they?
- Were your children surprised to learn what happens to numbers when they added 2 to them compared to when they doubled them? Did it make sense to them?
Children (Individual, Whole Group, Teacher-Posed Questions):
- Did you enjoy the illustrations? In what way?
- What characters did you like (not like)? Why?
- Have you ever experienced anything that happened in this story? Tell about it.
- Were there any surprises in the story? If so, what were they?
- What did you find most enjoyable about this Investigation? Why? Were you surprised by any of your answers?
- Are you still wondering about: ‘doubling’, ‘twice as much’? Share your wonderings?
The following are samples General Teacher and Children Reflection Questions related to any Investigation and its children’s book:
- What ways do I encourage my children to listen to other’s sharing their ideas?
- Why do I think it is beneficial to learn to… (specific mathematical concept)?
- What did I learn about my children’s reasoning?
- What changes would I make to this Investigation? Why?
- What particular problems did the Investigation pose for my children? Which tasks were easiest than the others? Why?
- How could I change my instructional strategies so more children would accept the challenges presented in the tasks?
- How successful was the Investigation? Did my children learn what I intended them to learn? How do I know?
- Did I provide sufficient time in the Investigation for my children to communicate to each other?
- What instructional strategies do I use to motivate my children to share their reason?
- Did my children find the Investigation challenging? In what way(s)?
- What did I like best about the Investigation? Why?
- Did I find any of the Investigation’s tasks challenging? Which one(s)/ Why?
- What did I learn when I heard my peers shared how they found solutions to the tasks?
- Is the title appropriate for this book? Why? Why not?
- What did I learn ‘new’ in this Investigation?
- If I could change any task in this Investigation, I would change…? Why?
- What did I learn in this Investigation that I nay use in another?
- What questions do I have about the Investigation?
- How do I know I am learning?
- What did I do well? How did I know?
More Investigations including Refection Teacher and Children Questions may be found in Number & Stories: Using Children’s Literature to Teach Young Children Number Sense.
Dodds, D. (2007). Minnie’s Diner: A Multiplying Menu. Cambridge, MA: Candlewick.
Janes, R. & Strong, E. (2014). Number & Stories: Using Children’s Literature to Teach Young
Children Number Sense. Thousand Oaks, CA: Corwin.
Rita Janes and Elizabeth strong have both spent their lives dedicated to teaching. Rita promotes the use of rich problem solving tasks, mathematical discourse and the posing of good questions to ensure inquiry-oriented classroom environments for all children, while Elizabeth’s main focus is effectively using children’s literature in the classroom to encourage young children to discover the delights in books of all genres and to support, extend, and enrich all areas of the curriculum. Both are co-authors of Numbers and Stories.