If you're a teacher in a state that will take the PARCC or Smarter Balanced common-core-aligned assessments next spring, you know by now that the performance tasks for math are going to be hardlikely much harder than standardized test items your students have seen in the past.
But just how difficult will they be? And how many different skills will each task assess? Some teachers have seen these types of problems in field tests and online practice items, but others have had little exposure to them yet.
Yesterday, as part of a two-day professional-development event hosted by the Maryland State Department of Education, a handful of math educators took a close look at a 4th grade performance task, and several were surprised by the level of advanced thinking it required.
Here's the math problem, which was released as part of a "prototype project" by the Partnership for Assessment of Readiness for College and Careers and its university partners (it's available on the The Mathematics Common Core Toolbox website).
The attendees spent a few minutes looking over the problem ("This is tough," said a math coach. "I'm surprised this is 4th grade," remarked a teacher-educator). Afterward, the group listed what students need to know and be able to do in order to complete it. Here's what they came up with:
- The definitions of perimeter and area
- How to find perimeter and area
- The definition of a square mile
- The properties of a rectangle
- How to solve for an unknown in a perimeter
- Multiplication (up to multi-digit)
- Addition and subtraction (up to multi-digit)
Depending on how a student chooses to solve the problem, they may need even more math skills (division, for instance). And this is not to mention the reading and writing skills students need for this type of problem. (I admit that when I initially read the problem, I was thinking that 42 miles referred to the area of the park. It wasn't until I re-read it that I realized it was the perimeter.)
The teachers then looked at the scoring rubric below. It shows that students get credit for finding the missing side length, for finding the area of the park, and for calculating the final number of deer. They can also get partial credit for each piece if they make minor calculation errors (the tasks will be graded by hand).
Surely, there are a lot of skills crammed into this one problem. In fact, the task touches on at least three domains from the Common Core State Standardsalgebraic thinking, number and operations in base 10, and measurement and data. And unlike the problems students may be used to seeing, this one doesn't lead them through the solving process by asking scaffolded questionsthere's no part A, B, and C, but rather a singular question.
However, when I compare the bullet points above to the scoring rubric, the rubric does seem to capture this information, as well as offer ample room for students to demonstrate isolated knowledge. For example, perhaps they know perimeter but not the area. If that's the case they'll get at least 1/3 credit. The rubric also notes that students who make a calculation error early on will lose credit for that miscalculation but can still receive credit in subsequent parts using the miscalculated value.
One skill I'm not seeing measured in the rubric is whether students know that "square miles" refers to the area within a mile. But perhaps that's seen as tied up in knowledge about area.
Would be great to hear back from other educators on this in the comments section below. What are your thoughts on the 4th grade question? And the scoring scheme? Have you started presenting students with problems like this, and if so how have they done?