Testing and Scoring Math

Much of what I do throughout the day deals with summative test creation and assessment.  Listening, helping, doing...it doesn't matter.  In one way or another it is always interesting.  The beliefs about tests vary greatly from one grade level to another and from one PLC to another.  

There are a number of teachers who are still holding fast to the "100 point" test where points are assigned to each problem to add up to 100.  This makes for easy grading, fairness throughout all the assessments, and easy student understanding of scoring protocols.  Lets just make it easy and say I disagree with all 3 statements.  There are other teachers who want to make the assessment standards based but want points assigned to the assessment for each problem (seems to be a theme here).  Finally, there are others who want nothing to do with "points" but want to focus on understanding.  This is clearly the group I like to hang out with.

Since the "fairness throughout all the assessments" comment doesn't fit anywhere else in this blog lets address it here.  Throughout the year some topics are more important than others.  I would challenge any teacher to debate that the first topics of the year in math are more important than content taught in the 2nd semester.  Why then should all topics have the same weight.  In fact, don't put them in one group.  Make them standards based and this whole debate is moot.

Lets be clear, none of the teachers are inherently wrong in their stance but are on different stages in the growth process towards understanding how a test can help drive instruction.  Trying not to waste time or digital paper, here is what I see as a quality assessment and scoring process.  

1. The assessment needs to assess different levels of understanding.  We use Webb's DOK levels as our benchmarks.  A student needs to be able to perform well on DOK 3 questions in order to earn what is recognized as an A.  Note, it is not perfect performance but performing well that is used for terminology.  I'll explain that in more depth later.
2. The assessment can offer few DOK 1 (basic) level questions but cannot be dominated by them.  We need our students to think analytically.  Just performing the skill level of the question isn't going to help them apply it in the future.  Is this necessary...absolutely.  However, not on the summative assessment.  It needs to be on formative assessments that will help determine if students understand what we were teaching.  Checking this for the first time on the assessment means the teacher is not teaching to the students but is teaching topics.  We have to make sure students understand these questions prior to the summative assessment.  If we have done that, we don't need them on the summative assessment.
3. The best are standards based but I am giving in that at the 9-12 grade level this is much harder than in earlier grades.  Even if we ignore the terminology "standards based" and make it topic based the result is the same.  We need to have questions that will demonstrate understanding at different levels of Webb's DOK to a specific topic.  This is an easy way to determine if students know the skill, can apply the skill, and can explain or demonstrate their understanding of the topic.
4. Grading/Scoring needs to give a clear perception of how students are doing.  I struggle when we take a point off for an addition error if the topic was finding the perimeter of an object.  Are we assessing addition or understanding perimeter?  Now, I know that the error is an issue and needs to be addressed.  Therefore, look over the whole test.  If the student is making many of these "oops" errors throughout the test then they don't deserve an A.  However, it tells us they understand the topics but are probably going too fast, not checking their work, or losing focus after the problem has been started.  These are good things to know.  Here are some basic scoring guidelines.
1. A student that can do the DOK 1 questions has demonstrated they understand the skill we need them to understand.  This student will probably earn at least a C.  
2. A student that can do the DOK 1 and DOK 2 questions has demonstrated they understand and can begin to integrate several concepts into one.  Students at this level are proficient, They have confirmed they should earn at least a B.      
3. A Student that can do the DOK 1, DOK 2 and DOK 3 questions has demonstrated they should earn an A.  They get the skill, can apply it, and can explain it.  What wouldn't they get an A.
4. Don't assign points to the problems.  Instead, look at the questions that apply to a topic.  How did they do.  Then think about that in terms of #1 - #3 above.  Where would the student fit?  This portion takes a good deal of training to understand but makes grading not only more accurate but easier.

Testing is immensely important.  However, too many teachers see it as the end when in reality should be the beginning.  It is important for students to do well but in the end, don't we need to alter our instruction to fix issues students have had.  Having a test that encourages that is a major step in moving education forward.  

The problem is it takes a long time and a lot of training to do right.