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.

Possible educational value of using phones in schools

Today, I had a very enjoyable conversation with Dr. Kate Highfield about the roles of technology in early education. I've always been frustrated by school technology use in the US- we complain about not having the funds to support a 1-1 technology to student ratio in classrooms, but then spend countless amounts of time and energy preventing kids from brings cell phones into the classroom. We live in a world in which we are close to 1-1 people to technology ratio, and then we ban that technology from schools, and then try to recreate that 1-1 ratio from scratch. Which is why I was very intrigued when Dr. Highfield described how common the BYOD (Bring Your Own Device) policy was in Australian schools.

Putting aside the utility of greater student connectivity, could there potentially be other benefits to letting students use their phone in the classroom? Hear me out for a second. In my work at Iridescent, I found a real value to giving families in our family science program piles of unsorted household supplies to build their machines with. You can give nice fabricated or branded pieces, or "kits" of carefully measured out proportions of household materials, but either of those options tends to give the impression that you need the "nice" stuff or the "kit" to do science, and leads to less making things after the program ends. Nothing beats a random pile of unsorted household materials for giving someone the confidence to do science on their own, at home.

So would the same thinking apply to technology devices? Consider that whatever we do with phones in school, kids are going to be on their phones when they leave school. Wouldn't it be great if kids were spending that phone time on more productive, learning activities? It might be that using a school technology device, like a labtop or a tablet with some preloaded software, gives kids the impression that they need the "technology kit" to learn on their technology device. Maybe they will think that they need the school's computer that has been specifically specced out for learning apps, or the actual pre-installed applications, to really learn on some technology. Maybe they'll see that they can do some of the same stuff on their home computers, if they have one. But, on their phones? What if students actually needed to use their phones in school, in order to view and later use their phones as learning tools?

So here's my question to Dr. Highfield and anyone else- has anyone researched this issue, particularly in a place like Australia where a BYOD policy exists? Does the type of technology used by students in school affect how those same students use their personal technology devices outside of school?

The Four Freedoms of Play and Common Core Standardized Testing

This article is cross-posted on the Iridescent blog.

I was inspired by Scot Osterweil's recent presentation at GLS, in which he presented his four freedoms of play:

• Freedom to Experiment
• Freedom to Fail
• Freedom to Try on Identifies
• Freedom of Effort

What makes this framework most interesting is that to Scot, these are not only the four freedoms of play, but also the four freedoms of learning. Good learning environments also need to contain these freedoms to be effective, an idea very much resonant with James Gee's view on games and learning.

Although these freedoms are not a particularly new idea, it was new to me this year, and it really helped crystalize several previous thoughts I've written about. It definitely resonated with my ideas that agency is not a binary quality of an activity, but that learning activities can contain different degrees of agency. This framework helped illuminate some of those different degrees to which an activity can contain freedom/agency. 

But most interestingly, Scot noted in his talk how school doesn't contain these freedoms, despite the fact that both games and learning do.  His challenge to us was to imagine a school environment that did contain these freedoms. I found it especially interesting to think about in relation to Common Core and standardized testing, which led to the question of this blog post: could a school environment that was constrained by standards ever achieve these four freedoms? Let's try to break down the freedoms and answer that question.

Homemade device to record your iPad with your iPhone using popsicle sticks and rubber bands

This article is cross-posted on the Iridescent blog.

So at Iridescent, we like to live what we preach. We don't just ask kids to make things from scratch, we do it too. Recently I decided that I needed a device to record myself playing games on my iPad (for a separate project to be talked about later). I had done this once before using my iPhone stacked up on a bunch of books and it worked reasonably well. So I decided I wanted the device to hold my iPhone in a position where it could record my iPad. But I also wanted to record myself consistently over the course of a year, so that each time I set it up, it recorded the same way, which meant I needed something better than the stacks-of-books method. It also had to be minimally intrusive in preventing me from using the iPad.

As I thought about this, I realized I had a well-defined design challenge that I needed to solve. Which meant to make things more fun, I decided to use the rule in we use in all of our design challenges: use only low-cost materials.

Additionally, I was always impressed with a Leonardo Da Vinci segment that Bobby Zacharias used in our Be an Inventor program in spring 2012. In the first weeks of that program, students had to design some kind of invention using only the tools and technology available to Leonardo. This meant no glue or machine screws could be used to make connections--things had to be lashed together or connected by pin joints. I always thought that sounded fun, so I decided to put the same constraint on my device.

So, where did that leave me? With a handful of popsicle sticks, rubber bands, and a bunch of ideas in my head.

The final result! Now, how did I get here...

5 Signals that an "Educational Game" Isn't Really a Game

This article is cross-posted on the Iridescent blog.

Kids love games, but why do they hate educational games? The short answer is that most aren't truly games, because being gamelike means a lot more than having flashy graphics and a point system. As an educational game developer, I think one of the most damaging aspects to this industry is when people call things games in order to get kids to play them when they clearly aren't games.

How can you spot the fake games masquerading as educational games? Here are a few signals I've picked up on over time.

1. When walking through a demo of the game, the game designer stops to say "And this part is where the learning occurs."

The learning should be everywhere, not in one part of the game. If you can compartmentalize the part of the game that is about learning, you did something wrong. One such example would be breaking up the game to show a player an instructional video- if you are using a video to teach, then you are not using the gameplay to teach.