4 Ways To Assess 3-Act Tasks

One of the most common concerns about implementing 3-Act Tasks (also known as problem-based lessons, application problems, or math modeling problems) is “How do you assess them?” Here are the four ways I use most often:

You don’t grade every single classwork assignment, do you? So, similarly you shouldn’t feel compelled to have to grade these types of problems either. While it may seem obvious, some teachers avoid using these problem because they feel like it will be too time consuming to assess them later. If that’s what’s stopping you, then just skip the grading part because not using them at all is even worse.

This is the most commonly used option and is relatively easy to implement if you need to get through a pile of 180 papers like secondary math teachers often do. The rubric originally came from the Smarter Balanced Assessment Consortium (SBAC) and consists of one point for a correct answer and one point for sufficient reasoning to justify the answer. Since I use this Problem Solving Framework when I do problem-based lessons, I just grade the “conclusion” section where students must write down their answer and explain how they got it.

One realistic concern with this rubric is that sometimes it’s hard to choose between assigning one point or zero points for a student’s explanation. So, this rubric can be easily modified to go from 0 to 5 points for correct answer and 0 to 5 points for sufficient reasoning to justify the answer. In that case, a student who gets the correct answer but whose reasoning is just OK might get a 5 for a correct answer but 2 points for his reasoning. Another issue with this method is that different teachers might give the same student different scores. This is a big concern if the problem is being used for a common assessment and leads to a need for Option #3.

This rubric is time consuming to create and use but is essential when consistent scoring is required. The process begins by determining what aspects of the problem solving process are worth assessing. This may include criteria such as:

• Getting the correct answer
• Using the correct units
• Explains the formula used
• Writing as a narrative with complete sentences

This rubric is something of a hybrid between a general purpose rubric and a problem-specific rubric in that it applies to virtually all problems but it also gives you more specific information.  It is called a practice rubric because you are evaluating students’ use of the Common Core State Standards’ Practice Standards.  So, some of the criteria might be:

• Monitored and evaluated progress and changed course if necessary. (MP 1)
• Checked their answers to problem using a different method. (MP 1)
• Explained correspondences between equations, verbal descriptions, tables, and graphs. (MP 1)
• Justified conclusions, communicated them to others, and responded to the arguments of others. (MP 3)
• Stated the meaning of the symbols chosen. (MP 6)
• Carefully specified units of measure. (MP 6)
• Calculated accurately, efficiently, and expressed numerical answers with a degree of precision appropriate for the problem context.  (MP 6)

If you liked those criteria and want to see a much longer list you can pick from, then check this out.

To make this more concrete, I will implement the three rubric options on three students’ responses to my sinkhole problem.

You can immediately see the problems with assigning 1 or 0 points with this first student.  This student stated 342,119 feet when it should be cubic feet.  I could make a case for 0, 0.5, or 1 point for correct answer.  Let’s say 1 point though.  Next comes the reasoning point.  I would have wanted to read more about the process the student used.  For example you don’t plug the width (diameter) of the hole into the formula.  You plug half the width (radius) so I would give them a 0 for sufficient reasoning.  So, if it was me I would give the student 1 point total.

This student is easier to grade.  The answer has the correct value and units, so 1 point for that.  The reasoning is sufficient as well so another 1 point for that giving a total of 2 points.

Like the second student this student earns 1 point for a correct answer.  I’d also give the student 1 point for sufficient reasoning for a total of 2 points.

Let’s assume that we want to assess the four criteria listed below.  Next I have to assign point values to each criteria.  Obviously determining these point values will depend on the people making the rubric.  For this example I will use:

• Getting the correct answer – 3 points
• Using the correct units – 1 point
• Explains that the radius is half of the diameter – 2 points
• Writing as a narrative with complete sentences – 2 points

Let’s revisit the first student now using this rubric:

• Getting the correct answer – 2 points
• Using the correct units – 0 point
• Explains that the radius is half of the diameter – 0 points
• Writing as a narrative with complete sentences – 2 points

He didn’t quite get the right answer because of the units so I took a point off of “Getting the correct answer” and another point off of “Using the correct units”.  He didn’t explain anything about the radius so he lost two points there as well.  4 points total.

Next is the second student:

• Getting the correct answer – 3 points
• Using the correct units – 1 point
• Explains that the radius is half of the diameter – 2 points
• Writing as a narrative with complete sentences – 2 points

This student included every aspect I was looking for and earns all 8 points.

Finally we have the third student:

• Getting the correct answer – 3 points
• Using the correct units – 1 point
• Explains that the radius is half of the diameter – 2 points
• Writing as a narrative with complete sentences – 1 points

This was a tough one.  I took off one point for writing the conclusion as a narrative but I could see assigning full points too.  Obviously calibration would be critical to determine exactly what it would take to earn each point level.

Let’s assume that we want to assess the four criteria listed below.  You might pick these if they were the things you valued and wanted students to do more of.  Next I have to assign point values to each criteria.  Obviously determining these point values will depend on the people making the rubric.  For this example I will use:

• Student explains how equations, words, pictures, and/or symbols are connected. – 2 points
• Student does not just state steps taken, but convinces reader that the steps they took are a correct way to approach problem. – 2 points
• Student carefully specifies units of measureand uses it consistently in conclusion. – 1 points
• Student accurately calculates a numerical value for the answer. – 3 points

Let’s revisit the first student now using this rubric:

• Student explains how equations, words, pictures, and/or symbols are connected. – 0 points
• Student does not just state steps taken, but convinces reader that the steps they took are a correct way to approach problem. – 0 points
• Student carefully specifies units of measureand uses it consistently in conclusion. – 0 points
• Student accurately calculates a numerical value for the answer. – 3 points

This student did not do a good job connecting the context with the math content so he get 0 points for explaining how they are connected.  He somewhat justified his conclusions and lost a point for not using the correct units.  He did calculate accurately so he got full points for that.  4 points total.

Next is the second student:

• Student explains how equations, words, pictures, and/or symbols are connected. – 1 points
• Student does not just state steps taken, but convinces reader that the steps they took are a correct way to approach problem. – 2 points
• Student carefully specifies units of measureand uses it consistently in conclusion. – 1 points
• Student accurately calculates a numerical value for the answer. – 3 points

This student did a good but not perfect job of explaining how his equation connected to the context so I took off a point for that.  I wouldn’t argue too hard against full points here though.  She justified her conclusion well for another 2 points.  She used the correct units (cubic feet) and explained why.  Finally she calculated accurately.  7 points total.

Finally we have the third student:

• Student explains how equations, words, pictures, and/or symbols are connected. – 0 points
• Student does not just state steps taken, but convinces reader that the steps they took are a correct way to approach problem. – 1 points
• Student carefully specifies units of measureand uses it consistently in conclusion. – 0 points
• Student accurately calculates a numerical value for the answer. – 3 points

This student’s conclusion is light on a narrative that explains how anything is connected.  There isn’t much of a convincing argument either.  So, 0 points and point for the first two criteria.  No units are specified, so 0 points there.  Finally she calculated accurately.  4 points total.

A couple of final notes:

• With any rubric being used as a common assessment, you’ll need to go through a calibration process. A team of teachers that plan to use the rubric should find exemplars that show what it would take to earn each of the scores for each category. Clearly this process will take time, but once every grader is on the same page, the scores are much more likely to be comparable and reliable.
• Remember that you can always mix it up and have students check out the rubric and/or evaluate themselves.  For example, if you showed them the rubric after they solved the problem but before they explain their reasoning, that would send them in the right direction.  Alternatively, you could show it to them after they are completely done, and this would give them a chance to make adjustments.

I hope that at least one of these assessment methods resonated with you.  What do you agree with?  Where have I missed the mark?  Are there any other options for assessing 3-Act Tasks that I missed?  Please let me know in the comments.