We would like to share how the idea of a child’s growth mindset led us on a journey to improve number sense in the early years. Our inquiry focused on how to support the development of number sense in struggling young learners. Come explore and examine hands-on activities designed to boost skills in counting, quantity and relationships. We will share ideas for diagnostics and assessment that worked. The focus was on kindergarten to Grade 2 learners.
Toronto District School Board
Toronto District School Board
Professional Learning Goals
We began our journey by understanding that there was a significant gap in mathematic skill in the kindergarten to Grade 2 levels. We wanted to know what that gap was and why it was occurring so readily in our community. In order to figure this out, we had to create a diagnostic, using current research, which helped us to isolate missing skills and understandings in our students. During the process of developing this diagnostic, we learned a great deal about how children learn math. A child learns to walk by crawling, then standing, then walking, so too must a child develop their math competency.
Once we figured out what developmental benchmarks in mathematics were missing, we were able to gather many different activities for the student to do to gain that missing skill and continue a quick and easy progression.
Activities and Resources
First, we studied the current writings of Small, Clements and Van de Walle, the Guides to Effective Teaching, and the Ontario Curriculum and Exemplars. When we were better versed in the commonalities and the differences between documents, we were able to decide what direction our assessment for learning should take. We chose an age-based developmental continuum, based on Clements’ writings, to use as the basis of our diagnostic. We then tested our assessment and once we confirmed its viability, we proceeded to find activities that would help students develop their skills in these missing early mathematics understandings.
The biggest challenge of our project was getting the assessment right. We developed and tested six versions until we finally settled on the seventh one. This took more time than we expected and we were concerned about how much time was left for the actual “activities” part, which was our focus.
Enhancing Student Learning and Development
After many trials and refinements, we found that the students we worked with who had initial difficulties in early math concepts, with practice became more competent in their understanding of mathematics at their grade level. These targeted activities can be done with entire classes, in small group or one-to-one. Children who have the skill will move on quickly while students who do not can use these activities through centres, with the teacher and peers, or at home.
When we completed the project, we presented it at the Ontario Association of Mathematics Education (OAME) conference, this past May. It was well-received. We have been invited to share it with our school and another elementary school in our district this fall. We plan to initiate its use in all primary classes at our school in October. We are also sharing it here.
It will be useful for teachers who are teaching mathematics in kindergarten to Grade 2, and is best presented in a hands-on way, sharing some of the theory behind it through our presentation.
It is possible to do it with or without materials and training as all that is needed are the materials in the attached files.
We feel our project was a real success as it has garnered a lot of interest through our presentation of the materials. It has also stimulated a lot of questions about mathematics education that our team wishes to investigate further.
Our goals were met and we determine the success by the fact that we have a comprehensive package of materials that will identify missing mathematics concepts and provide targeted activities to bridge these gaps.
We spent a lot of time in the beginning, struggling to decide a specific direction to go with our concept. I think next time we’ll jump right in and allow the process to guide us as we move through developing the concept.
- Clements, Douglas H. and Julie Sarama. (2009). Learning and Teaching Early Math: The Learning Trajectories Approach.
- Ontario Ministry of Education. (2003). A Guide to Effective Instruction in Mathematics.
- Burns, Marilyn. (2000). About Teaching Mathematics: A K-8 Resource, Second Edition.
- Small, Marian. (2009). Making Math Meaningful to Canadian Students, K-8.
- Van de Walle, John A. (2006). Teaching Student-Centered Mathematics: Grades K-3.
(See the annotated list of Internet sites, Apple apps and Android apps included in the uploads.)
These resources will open in your browser in a new tab, or be downloaded to your computer.
#3 OAME Materials for Assessment
These are the "in-a-bag" manipulatives for new teachers or teachers with limited resources.
#4 OAME Activities
This is the list of activities that target specific parts of kindergarten to Grade 2 math skills, listed by manipulative.