The following conversation is one that could readily occur when a student brings home a report card under our traditional grading system.

Congratulations! You got an 89 in your Algebra 1 course! That sure represents a lot of hard work.

Can you please tell me, from that grade, what topics you mastered and what topics you need more work on?

What’s that? You don’t know? So what exactly does that 89 mean?

This is a not-too unrealistic conversation that could readily happen to any student after receiving their report card. What, after all, does 89 actually mean? How does it help you to know what topics you have failed to master yet?

In a Proficiency Based Education (PBE) system, part of the premise is that there is clear communication about what topics have been mastered and what topics still need to be worked on. Imagine seeing the following report card for your high school math courses.

Proficiency Score Description
4 Exceeds the Standard
3 Meets the Standard
2 Partially Meets the Standard
1 Not Yet Met the Standard

To see more detail on the standards, please click the “+” sign in front of the standard. Please note that “PI” means “Performance Indicator”.

#### Standard 1: Number and Quantity: 3.375

PI 1: Extend the properties of exponents to rational exponents – 3.0
PI 2: Use the properties of rational and irrational numbers – 3.5
PI 3: Reason quantitatively and use units to solve problems – 4.0
PI 4: Perform arithmetic operations with complex numbers – 3.0

#### Standard 2: Algebra: 3.429

PI 1: Write expressions in equivalent forms to solve problems – 3.0
PI 2: Perform arithmetic operations on polynomials – 4.0
PI 3: Understand the relationship between zeros and factors of polynomials – 4.0
PI 4: Understanding solving equations as a process of reasoning and explain the reasoning – 3.0
PI 5: Solve equations and inequalities in one variable – 3.5
PI 6: Solve systems of equations – 3.5
PI 7: Represent and solve equations and inequalities graphically – 3.0

#### Standard 3: Functions: Not Assessed

PI 1: Understand the concept of a function and use function notation – 3.0
PI 2: Interpret functions that arise in applications in terms of the context – 3.0
PI 3: Build a function that models a relationship between two quantities – Not Assessed

#### Standard 4: Geometry: 3.917

PI 1: Experiment with transformations in the plane – 4.0
PI 2: Understand congruence in terms of rigid motions – 4.0
PI 3: Make geometric constructions – 3.5
PI 4: Understand similarity in terms of similarity transformations – 4.0
PI 5: Find arc lengths and areas of sectors of circles – 4.0
PI 6: Explain volume formulas and use them to solve problems – 4.0

#### Standard 5: Statistics and Probability: Not Assessed

PI 1: Summarize, represent, and interpret data on a single count or measurement variable – Not Assessed
PI 2: Summarize, represent, and interpret data on two categorical and quantitative variables – Not Assessed
PI 3: Interpret linear models – Not Assessed

Notice the detail given in this report card. First, you can see that certain standards have already been met – specifically, standards 1, 2, and 4. Secondly, clicking the “+” symbol in front of each standard provides more detailed information. For example, clicking the “+” in front of Standard 3 shows that two Performance Indicators have been assessed, with a score of 3.0, while one Performance Indicator still needs to be assessed.

Furthermore, Standard 1 shows a score of 3.375. Clicking the “+” shows that the four Performance Indicators have scores of 3.0, 3.5, 4.0, and 3.0. These scores were averaged to come up with the Standard 1 score 3.375.

Now, look at the same student report card a couple of years later:

#### Standard 1: Number and Quantity: 3.375

PI 1: Extend the properties of exponents to rational exponents – 3.0
PI 2: Use the properties of rational and irrational numbers – 3.5
PI 3: Reason quantitatively and use units to solve problems – 4.0
PI 4: Perform arithmetic operations with complex numbers – 3.0

#### Standard 2: Algebra: 3.429

PI 1: Write expressions in equivalent forms to solve problems – 3.0
PI 2: Perform arithmetic operations on polynomials – 4.0
PI 3: Understand the relationship between zeros and factors of polynomials – 4.0
PI 4: Understanding solving equations as a process of reasoning and explain the reasoning – 3.0
PI 5: Solve equations and inequalities in one variable – 3.5
PI 6: Solve systems of equations – 3.5
PI 7: Represent and solve equations and inequalities graphically – 3.0

#### Standard 3: Functions: 3.0

PI 1: Understand the concept of a function and use function notation – 3.0
PI 2: Interpret functions that arise in applications in terms of the context – 3.0
PI 3: Build a function that models a relationship between two quantities – 3.0

#### Standard 4: Geometry: 3.917

PI 1: Experiment with transformations in the plane – 4.0
PI 2: Understand congruence in terms of rigid motions – 4.0
PI 3: Make geometric constructions – 3.5
PI 4: Understand similarity in terms of similarity transformations – 4.0
PI 5: Find arc lengths and areas of sectors of circles – 4.0
PI 6: Explain volume formulas and use them to solve problems – 4.0

#### Standard 5: Statistics and Probability: 3.5

PI 1: Summarize, represent, and interpret data on a single count or measurement variable – 3.0
PI 2: Summarize, represent, and interpret data on two categorical and quantitative variables – 4.0
PI 3: Interpret linear models – 3.5

Notice that this student now has shown that they have met all required math standards. Like before, you can click the “+” symbol to see the details within each standard.

## Multiple Attempts

It’s important to note that in a true proficiency based grading system, students are not limited to one attempt in meeting the requirements. In fact, in this example, a student only has a score recorded at all if they have at least met the indicator. Students who have not yet met the indicator are simply given additional instruction, and then additional attempts at meeting proficiency.

In an earlier article, I gave an example of a driver’s test. People are given as many opportunities as needed to show mastery on their driver’s test. The same concept applies here in a PBE system – students are given multiple opportunities to show they have met the required indicators.

What we end up with is a system that is highly transparent, showing the areas students still need to work on and master. Students are not penalized if they take longer to learn and master material under this system, and they will be able to graduate from high school with evidence to show they are truly proficient in the content areas.