I was working at school today on some assessments for the math department at the high school, and reflecting on how far I have come since my early days of teaching and writing tests. Way back in the day, my biggest concern about writing tests was making sure it would come out to 100 points. Over time, my focus shifted to having a greater emphasis on determining the content I was testing and much less concern on the number of possible points.

With the reading I did this past spring, combined with the first of the Math Leadership courses I am taking through UMF, I’m now finding the number of points is somewhat irrelevant. Rather, I’m carefully designing assessments to determine exactly what skills I want to measure.

Math Assessment


The starting point, of course, is determining what standard you wish to assess. Using my work today, one of the standards I was writing an assessment for was CCSS.MATH.CONTENT.HSN.RN.A.1:

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. 

Once this was determined, I needed to decide what basic skills students needed before they could reach this level of knowledge and skill. I came up with the following five specific items that I felt students needed to be able to do, before they could actually successfully show mastery of the standard. Those items are:

  • Understand the meaning of a positive integer exponent
  • Understand the meaning of a zero exponent
  • Understand the meaning of a negative exponent
  • Understand the multiplication property of exponents
  • Understand the division property of exponents

Once these pieces were in place, I was ready to build a “Proficiency Scale” for this standard.

Proficiency Scales

The work I’m doing is based on the work done by Dr. Robert Marzano. According to his website, “A proficiency scale, in simplest terms, represents a progression of learning goals with three levels of difficulty: (1) the target (level 3.0) content; (2) the simpler (level 2.0) content; and (3) the more complex (level 4.0) content.”

So, in this case, the statement of the standard above is the target, and a student successfully completing that level of problem would earn a score of a 3. The 5 bullet points listed above are considered simpler content, and earn a score of 2. Finally, the creation of a problem more complex than the stated standard would allow for a student to earn a score of 4.

Many versions of the proficiency scale allow for intermediate scores (2.5, 3.5), as well as scores of 1 (student needs help to achieve the 2.0 level questions) and 0 (even with help student cannot achieve the 2.0 level).

Putting these together gives this proficiency scale:

Here is a link to a blank Proficiency Scale as a Google Doc that you can use for a template.

Once this scale was built, I moved on to writing the assessment.


Because of the work I had already done on creating the proficiency scale, this impacted my work on designing the assessment. I started by creating an Assessment Blueprint. An Assessment Blueprint lists the skills in the proficiency scale. It includes a listing of the type of questions, as well as what level they were at on the proficiency scale. This blueprint came out as follows:

Each item now has a description of the type and number of questions to go with it. This blueprint will be provided to students, along with the proficiency scale, at the beginning of the unit so that students know exactly what they need to accomplish and how they will be measured.


I’m not actually going to post the assessment here. After all, it is one that we plan to utilize and I don’t want to make the specific questions public! What I can say, however, is that once these steps were done, the actually writing of the assessment went quickly. I didn’t concern myself with “how many points are on the exam”. Nor did I worry whether I had asked all the questions I wanted to. I simply followed the blueprint and created the assessment.

Additionally, it becomes quite easy to create additional assessments for the same content. One of the expectations of the proficiency based system is that students have multiple attempts to show proficiency. Assessments should not be treated with a “once and done” approach. Think, for example, about taking a driver’s test. If a person fails the test the first time, they are not barred from ever having a license. They are able to repeat that test as many times as needed in order to show mastery. The same concept (within the constraints of our school year and age of students, of course!) applies to a Proficiency Based system. If students are not proficient when they first take the assessment, they do not move on. Rather they need to continue studying and learning and retake the assessment, until they show proficiency.

Anyone have thoughts or questions on the process I just described? Feel free to ask them in the comment section below!