Representing student mastery mathematically is not straightforward. Not only are there several different ways that people often want to "slice" or "group" the data, but there are also a variety of opinions over how (or even whether or not to) average student scores over multiple assessments, standards, standard types, units, and courses. JumpRope offers a number of options and tools to help you get the number that you're looking for, but it is important to understand where the numbers come from as you consider your curriculum and your conversations with students.
Calculating Scores for Standards (at the directly assessed level)
The most important numbers in JumpRope are the directly assessed standard level calculations per student. These are based on one or more assessments, and answer that most-important question: given all of the evidence, what level of mastery has this student demonstrated? However, the way the number is actually calculated is controversial to say the least! Some teachers believe that all scores should be averaged. Others believe that growth should be rewarded and that early assessments shouldn't be punished. Still others assess in a way that means that the highest score ever given is the score that matters. Some want a combination of these, a best-fit line, or the ability to choose standard-by-standard how to calculate the averages. In JumpRope, we call these the calculation types.
We believe that there is merit to each strategy, and we choose not to legislate in our software. Rather, we give schools and districts the ability to pick a default calculation type.
- Weighted Average: This calculation type takes an average of all assessments for each student on each learning target. If teachers assign a weight to an assessment, this will incorporate the appropriate weight when calculating the average. This method is the easiest to understand, since it is close to traditional grading systems.
- Max Value: This calculation type simply takes the highest score ever achieved by each student on each learning target. In this way, the highest level of mastery ever demonstrated is what is considered the final level of mastery on a standard. It works well if teachers are only using robust summative assessments of learning within the JumpRope system, but breaks down if scores are entered for less-robust assessments.
- Power Law: This calculation type is based on research on cognitive development. It is a time-based average, and automatically adjusts assessment weights to give higher weight to the more recent assessments. In this way, it more closely represents true student learning progress. However, it is more difficult for students to understand or teachers to predict because the formula is very complex. If you're interested and mathematically-inclined, we'd love your input on the power law's exact algorithm; check out the attached file below. You may also wish to check out this article on the Power Law which includes some practical tips.
- Most Recent: This calculation type carries the most recent assessment score achieved, based on the date assigned to the assessment (rather than the date the score was entered). As with Max Value, this works best when all assessments are robust or when a final assessment is guaranteed to be robust. This article contains more details and tips on using the Most Recent calculation.
- Decaying Average: This calculation type assigns progressively-decreasing weights to older assessments. Working backwards, each assessment is worth 66.667% of the teacher-assigned weight, compounded exponentially. In effect, newer assessments automatically "count more" in the overall score. Teacher weights still apply.
- Final Rating: somewhat different from the other four types, this type can be set and enforced at a school-wide level. In fact, it must be enabled for the whole school in order to be used. This is partly due to the fact that it can get a little bit confusing as it completely overrides any other method that has been selected. Here's the deal: if made optional at the school level, teachers can create a special assessment type known as a Rating. Each student that receives a score on a Rating for any given standard will be given that score (the one received on the Rating) for their overall mastery on the standard. If no score is entered for any given student - or if no Rating is created for a given standard with this calculation type, a value of "Unrated" will apply and the standard will not count towards course grades at all. If your school has chosen to make Ratings required, a Rating assessment is created automatically for every standard and you must enter scores for each student or their average on that standard will show as a U (for unrated) regardless of other times that the standard may have been assessed. This allows teachers and/or entire schools to make a habit of manually reviewing and rating student mastery for each standard - a potentially valuable process.
Each of these average types is applied at the standard grouping level only. Once the appropriate standard average is calculated, the total "weights" of the underlying assessments are also added up. The calculated "average" is shown on reports at the standard level. Any groupings above the directly assessed standard level are calculated as described below. Note: because teachers and schools can choose various different "Grouping Schemes" when creating progress reports, the explanations below have some additional complexity. Please let us know in the forums if you need further details!
Averaging Units (note: not all schools use the concept of units in their reports)
Unit averages are calculated as weighted averages of the underlying group - almost always standards. Standards are not all given equal weight. Rather, the weight given to each standard "bubbles up" from underlying assessments (a standard with three assessments weighted as 4, 1, and 1 will carry a weight of 6 when calculating the unit average). The mastery level that is used for each standard comes from the average type selected above. When units are averaged together to calculate higher-level average (such as a course average), they also carry the total weight of all underlying standards and a weighted average is calculated.
Course averages are calculated as a weighted average of the underlying values. When courses are averaged together to calculate higher-level average (such as a standard type average), each course can optionally be given equal weight based on a setting in the Admin Console. This is because teacher's weighting systems do not always "play nice" with one another (one teacher may have higher weights or simply more assessments that add up to higher weights) - this would lead to overall averages that were unequally-weighted to certain courses or teachers.
Averages on Standard Types
Each Standard Type average (such as Overall Academic Mastery and Overall Character Mastery) is calculated as a weighted average. When standard types are averaged together to calculate higher-level averages (such as overall student grades), they follow the rules explained in this post.
Thanks for taking the time to further understand how mastery averages are calculated in JumpRope!