Thursday, October 13, 2016

Assessing for Understanding

So by now the school year is well underway and you are beginning to learn a lot about the mathematicians in your classes.  As we gather evidence that will eventually serve to provide a grade on the trimester report card, I've had a few questions regarding how to collect that evidence, and how we are scoring assessments this year.

What do I do if the student got it wrong, but I know they can get it right?
You'll see in the email response below that this will be a common scenario.  It's important to remember that we are always formatively assessing our students.  "Formative assessment" is an ongoing process that occurs constantly as you teach your lessons, observe students at work and the discourse they share, and review completed assignments.  Always be looking for evidence of understanding.  If a student makes an error in their journal, or even on an assessment, you can always give them more opportunities to show they really get it.  If it is a careless error, the student may simply need to see the error he or she made, and be given the opportunity to fix it.  If it is an error that is a result of a lack of understanding, the student may need re-teaching.  It might come back in a future lesson (see the spiral!), or you might be able to provide opportunities to revisit the concept and re-assess for understanding.

The items on the test are either correct or incorrect and cannot be given partial credit.  This is true.  Even if there are six answers to #7 (as in, there is a 7a,7b,7c,7d,7e, and a 7f), they ALL need to be correct in order for the item to be marked correct.  Why is this?  Here's how I answered this in a recent email:

If you think a student juuuust missed getting them all [the parts of the question] correct with a careless error, give him or her the chance to look over their work and make the fix.. If he or she can find and fix the error, then adjust the score to a 3.  The other option is to find more evidence elsewhere in the unit or upcoming unit to determine if the student is achieving proficiency or developing.  You can use items on the cumulative assessments for this, the ACIs, alternative test items, or other examples.  (The spiral in the TLG might help you locate where the specific standard is assessed again in the book.)

The more I have learned about scoring assessments, the more I lean toward this kind of scoring.  If the item has 4 parts, EM has essentially designed it that way to assess proficiency.  Students are not proficient until they can get all those right.  And if they don't but you feel they really should have gotten all the answers right, you can give students chances to provide you with that evidence.

Later, we got into discussing specifics.  The items in question were a 5th grade order of operations and grouping problem and a volume-of-a-rectangular-prism problem.  Should students be required to evaluate all for expressions correctly, and then answer the volume problem with the correct units of measurement (cubic centimeters)?  

For #3, the standard is 5.OA.1, "evaluate expressions that contain grouping symbols."  There are four expressions to evaluate, but andb go together and c and go together as they use the same numbers with parentheses in different places.   So if a student got a wrong but b right, that likely demonstrates a misunderstanding of what parentheses mean, as the answer to b would be the same even without the grouping symbols.  The four separate parts to the item help to ensure that the student understands the standard.  5.OA.1 is listed on page 8 (the spiral page) of the Teacher's Lesson Guide as a mastery expectation, so with this assessment item we want to make sure the student gets it.

With units of measurement pertaining to volume of 3D figures, I have mixed feelings!  Yes, it is important that they learn how to compute volume, but we also want them to understand how and why lxwxh=V.  Otherwise, they are just memorizing a formula which is susceptible to becoming confused with area and/or perimeter as they progress down the geometry/ measurement content strands... If the l,w, and h measurements are in cm, then the answer must be in cubic cm.  NOW... That's tough for 5th graders.  So the approach I like is to take those answers that are correct with the incorrect or missing unit of measurement, and bring them back to the student.  "Did you forget something?" ...or, "Is your answer just '40,' or is it '40 somethings...?"  Give the student a chance to demonstrate the unit of measurement.  If the student shrugs his or her shoulders and says "I don't get it, my answer is 40.." then they do not grasp how or why they are using that formula.  The CCSS language is "recognize volume as an attribute of solid figures and understand concepts of volume measurement."  But again, this is hard for 5th grade, so that's why I suggest giving students every opportunity to grasp the concept... You can always re-teach, and give students another chance to demonstrate proficiency.  

Also, there is certainly some subjectivity to scoring these items.  You know your students more and more as the weeks go on, and you will know who needs re-teaching and who doesn't.  The one thing I recommend as you make these judgments, though, is to keep looking for evidence of understanding when you score assessments.  And the more opportunities they have to explore and discover these concepts during the units (to problem solve collaboratively and independently by trial and error and with manipulatives), the more they will achieve understanding.

Lastly, we discussed what can be done in the event we want to find additional evidence to show a student is achieving the standard when the initial assessment item did not:  

Sometimes there might be a domain at the end of a trimester that has minimal assessment items represented... You can certainly base a student's domain grade on more than the two or three assessment items they attempted pertaining to that domain.  Use the items in the cumulative assessment if you like, or the ACIs, or alternative assessments to find more evidence.  I'm always happy to help with this too (and even adjust cover pages if necessary).

More thoughts on all this?  Let me know!