I'm not sure if you know this or not, but I am very interested in early numeracy skills. They are the building blocks for future math success. Drs. Sarah Powell and Lynn Fuchs laid out 10 different competencies that make up early numeracy (Powell & Fuchs, 2012). From those 10, I created this graphic showing how they build upon each other. There is some fluidity in this, however.
Everything starts simply. Basic recognition of the numbers and symbols used in mathematics. We all take for granted that when we see the number 5, we know it means 5 objects. We've given that symbol some meaning. Children do not start out with that knowledge. It has no more meaning for them than a picture of a tree. So, we teach context.
I am mostly interested in what is in the green ring. Counting with 1:1 correspondence is a critical skill for moving toward the basic operations. Rote counting is not enough because it does not ensure that students have applied the context we have taught. Rote counting is simply an echoic response to the prompt of counting. It is not uncommon for students to rote count to 100 without having the ability to place a specified number of objects into a bowl. That is why teachers should focus on teaching counting with 1:1 correspondence early.
Why is this important? Simply put, using manipulatives for the basic operations successfully relies on the student's ability to count with 1:1 correspondence. For example, using counting bears with a base sheet to solve the problem 5 plus 4 needs to be able to place exactly 5 bears in one cell and 4 in the other. Then they can count all the placed bears to get the total and solve the problem. Alternatively, students could use tally marks to complete the problem. Yet they still need to use counting with 1:1 correspondence to place the lines in each cell and total them.
So, that is why I focus on this specific skill. However, we can't ignore any of the other 9. Assessing a student's ability is critical to knowing where to start. This can be done with standardized assessments (Dueker & Day, 2022) or with informal assessments. Using simple diagnosis and remediation techniques, teachers can identify where students are making mistakes and target additional teaching to help them reach fluency (Dueker & Grande, 2024). This means doing more than just looking for correct responses. But that is a topic for another blog post.
Dueker, S. A. & Grande, J. D. (2024). Diagnosis, remediation, and error correction for mathematics: How to teach pre-service teachers. Journal of Special Education Preparation. https://openjournals.bsu.edu/JOSEP/article/view/4172
Dueker, S. A. and Day, J. M. (2022) Using standardized assessment to identify and teach prerequisite numeracy skills to learners with disabilities using video modeling. Psychology in the Schools. 59(5), 1001–1014. https://doi.org/10.1002/pits.22473
Powell, S. R., & Fuchs, L. S. (2012). Early numerical competencies and students with mathematics difficulty. Focus on exceptional children, 44(5), 1.
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