SPED 2 Portfolio: Developing Number Sense

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 Number sense is a topic I wanted to explore since it sets the foundation for all mathematics. In the progression video called “Early Numbers and Counting” Graham Fletcher discusses the skills children usually have when they enter school in kindergarten and the progression. He first mentions that students might be able to subitize (recognize a quantity visually) but states that students might not know how to explain how they know the quantity. He explains that when students arrive in kindergarten they arrive with some skills usually in subitizing and “more and less” and develop their math skills in the following progression:

1. Subitizing
2. More and Less
3. Rote counting 0-100 forward and backward
4. One-to-one correspondence (counters: being able to count a predetermined number of objects and producers: being able to put a predetermined number of objects aside if asked, but if asked how many objects were put aside would have to go back and count again)

Strategy for one-to-one correspondence: matching a number of bear or other object to something other than a number. Such as 8 bears to 8 beads.

5. Cardinality: count and last count sequence is the number the items represent

Strategy: Help students with their counting by showing them how to line them up while counting them, so they don’t count one item twice, and that the last item they count is the number of the quantity

6. Hierarchal Inclusion: Numbers are within other numbers, for instance if you have 5 eggs, you must also have 4 eggs, 3 eggs, 2 eggs, and 1 egg.

Strategy to assess: If students have 5 eggs, and you ask them to put 4 eggs in a bowl, notice if the student counts out four eggs or if the student just removes 1 egg and places the 4 in the bowl.

7. Number conservation and decomposition
8. Conceptual subitizing

(Fletcher, n.d.)

 

I think this progression video and the following one about addition and subtraction are so interesting and informative to watch. I’m sure I’m not the only one that has thought “where do I start!?” when students encounter challenges at the most foundational level and sometimes it’s tough to figure out what students aren’t understanding. In the early primary years especially, students are often not working from a program or textbook so there really is very little guidance in the progression of skills and not being very strong in math myself I had a lot of difficulties figuring out where to start. I think this video really breaks down the skills and provides some insight into how the skills build on each other. 

Some strategies found on this website to build number sense include:

 

The Sound of Imaging: https://gfletchy.com/2015/05/12/the-sounds-of-imaging-numbers/

Items needed: unifix cubes, container

-Ask students to close their eyes and listen as you drop unifix cubes into the container at different speeds and see if they can guess based on sound how many you have in the container

This can be used for 1-to-1 correspondence and cardinality and adapted in a variety of ways to meet other learning objectives

 I have used this one before in my class and students really enjoyed this activity. I used it as in the video with base ten.

3 Act Tasks: https://gfletchy.com/3-act-lessons/

These are problem-based lessons that are divided into 3 parts to them, the first one is always a provocation usually to begin a number talk.

 These are great additions to number talks and cover a range of math units and grades.

Reference:

Fletcher, G. (n.d.). Progression Video. G-Fletchy. https://gfletchy.com/progression-videos/