Going for Gold: The "4"

I have had several productive conversations recently about what it means to earn a "4" in mathematics. Many debate the idea of students earning a "3" even in cases in which every answer given is correct. So what more do we want of students if getting all of the answers correct is not enough to earn a "4?"

According to many educational likert scales, a "1" indicates a beginning understanding, a "2" means that a student is working with a more intermediate understanding, a "3" describes a proficient understanding, and a "4" is considered advanced proficiency in understanding and application.

Let's take counting coins as an example. Here is what a scale might look like for counting coins:

1: a student is familiar with the values of basic coins and can recognize and name those coins
2: a student can count a collection of basic coins within 100 and can correctly write the total, including using the symbols for dollars and cents
3: a student can name and count coins within 200, can correctly write the total using numbers and symbols, and can apply their understanding of coin counting to real-world scenarios
4: a student can do all of the above AND can think of and create real-world scenarios in which counting and collecting coins would be relevant; a student can also demonstrate multiple strategies for counting coins (using dimes to count by 10s, for example, then using half dollars to count by 50s); a student can compare and contrast these strategies for counting coins

Here are some great questions to ask students when encouraging them to "GO FOR THE GOLD" and reach that higher-level thinking required to earn a "4":

- can you represent and justify this differently using words, pictures, and/or numbers?
- can you make connections between what you are learning and something else? (math to math/ math to self/ math to world)
- can you create a problem or context using what you have learned?
- can you think of examples AND non-examples in the real world of this particular skill?
- can you explain your thinking clearly to others?

As a general rule, the higher up the ladder of Bloom's Taxonomy we ask students to go, the more likely they are to attain the "4." (See below)