Monday, February 23, 2015

Bloom's taxonomy in the Common Core Math (part 1/3)

This article is cross-posted on the BrainPOP Educator blog.

Recently, Dan Meyer posted an analysis of what kinds of tasks are expected of students on the Khan Academy and how it compared to the Common Core. Dan used a recently released sample test from the SBAC to describe what the Common Core required, but we were inspired to take Dan's analysis one step further. Instead of interpreting SBAC's interpretation of the Common Core's interpretation of what students should do, we decided to go right to the core, the Common Core. What exact kind of tasks is the Common Core requiring of students? And how do those requirements change across grades?

But, we needed a categorization system to group different kinds of student tasks. Dan used verbs to categorize tasks, but some verbs actually call for similar mental processes, and so probably should be grouped together rather than separated. Additionally some verbs in the standards, like "understand" can have loaded meanings and depending on their context refer to higher or lower order cognitive tasks. To accommodate both of these issues, we grouped tasks using everyone's favorite categorization system, Bloom's taxonomy.

So, this lead to a relatively large task, of going through every standard in every grade and tagging it with one or more levels of Bloom's taxonomy. Our hope is that by doing this kind of work, we can better understand what kind of tasks the Common Core is emphasizing. In this blog post, I'll look at the Common Core Math standards, look for the CCELA and NGSS in followup posts!

Common Core Math

First up, Common Core Math! The results are shown in the two figures below. The top figure shows the percentage of tasks in each level of Bloom's taxonomy, where the lower graph shows pure numbers. The first column in the bottom graph codes the "Mathematical Practices," which are intended to span across all standards, across all grades.

The first two things to notice are that the number of tasks required of students increases with each grade level, and that the distribution of tasks does not change much across grade levels. There is a transition between grades 3-4, in which there are less Understand and more Apply tasks. But in general, there is very little trend across grades. Additionally, for most grades the highest three levels of the taxonomy compromise only 10-35% of the total tasks. For the majority of mathematics tasks students are being asked to do, those tasks are at a relatively low level on Blooms. To be fair, the higher level tasks do take more time than low level tasks, so the allotment of classroom time will be more weighted towards higher level tasks than these standards indicate. But the majority of the standards text actually describe relatively low level tasks.

Another qualification- the Mathematical Practices are much more weighted towards high level tasks than the standards themselves as can be seen in the top figure, and these practices are meant to be infused across the grade level standards. Exactly how this infusing should occur is not clear, but that certainly would weight the scale towards higher level tasks.

UPDATE- You can also check out Part 2 and Part 3 of this series.

Notes on Methodology

In case you are curious how I did this analysis, here some details.

Some grade-specific standards contained multiple parts, or multiple tasks that they required from students. I coded each "task" required from students, which usually was one per standard, but sometimes was multiple tasks per standard.

The standards themselves note that they are overlapping, in that the same content is emphasized and described in different ways in multiple standards. By my analysis, this would give those kinds of semi-repeated tasks more weight, as they would be counted multiple times for each of the various places they appeared. I decided this was ok- things that were more crucial tended to be more often repeated, and therefore should get more weight.

The high school Math standards were not broken up by grade, they were broken up by subject. I felt they confused the graph more than added useful info, so I did not show them here. But I can say that the high school standards were similar to the middle school standards in mostly emphasizing lower order skills in similar percentages. 

To refer back to the original point of Dan's article- the sample test released by the SBAC seems to be testing at a much, much higher level than the 8th grade Common Core standards seem to be calling for, potentially indicating that they had selectively released their best test items, and that the sample test is not a representative example of the test as a whole. Also, the Khan Academy is actually doing quite well compared to the standards themselves! If anything, the Khan Academy tasks were at a higher average level of Bloom's taxonomy than the tasks described in 8th grade Common Core Math standards.

No comments: