Kindergarten: From Counting to Cardinality to Abstraction
Recently, we have been having some discussions about Kindergarten expectations and assessment when it comes to the K.CC standards. We built a Kindergarten task that measured K.CC4.a-c and K.CC5 a few years ago. Unfortunately, the formal assessment was too time-consuming and it was modified. The baby, however, was tossed out with the bath water.
The new task measuring these standards simply asks students to count the abstract pictures on the worksheet, state what they counted (is that really cardinality?) and then write down the total number they counted. Here are the instructions:
- Students should be counting with objects and not abstract representations on a flat piece of paper;
- The new task basically only measures 1-to-1 counting;
- There are higher-order skills and concepts that are more important and we can assume they have 1-to-1 down if they can do these other tasks;
- Students are asked to write the number of “objects” down and they are marked incorrect if they don’t do this correctly (that’s actually standard K.CC.3!).
What Should Kindergarten Teachers Do
First of all, they really need to know their standards. They also need to know the progression of learning that takes place throughout K.CC.4.a-c and K.CC.5. They should accept that if students can do K.CC.5, they can probably fulfill the requirements in K.CC.4.a-c. Students should be given an opportunity to demonstrate “order-irrelevance,” which solidifies the concept of cardinality. Let students demonstrate their understanding that counting applies to any set of items and that these sets may have similar or different attributes (Abstraction Principle). Finally, teachers shouldn’t rely on one isolated task to determine if students have mastered these concepts; they should be living these things every day in the classroom and giving students credit when they perform in centers or other classroom activities.
The new California Math Frameworks for Kindergarten do a great job of detailing the K.CC principals and what students should be able to do. Take a look at this clip from page 9:
Reflective Questions: You can use the comments section to leave some thoughts!
- Do Kindergarten teachers really understand these principles?
- Do these principles need to be taught in order, from 1 to 5?
- What would instruction look like for each of these?
- What foundations for future math do these principles support?