What About Assessment and Grading? Part TWO

OVERVIEW, Part One: (yesterday)        (1) Changing Unit Planning     (2) Changing Instruction      (3) Changing Homework

PART TWO: (today)

4. Changing Assessment

PART THREE (tomorrow):   5. Changing Grading

4. Changing Assessment

What are our goals in assessment?

  1. Assessment should provide feedback to us (the teachers) on how student learning is going. Do we need to slow down, or can we move forward on a given topic? Which students need what kind of support?
  2. Assessment should provide feedback to the students on how their learning is going. Do they need to clear up any misconceptions, keep working on something, or get specific help?

That’s it! Assessment is NOT a tool with which to sort students, pacify administrators, or incentivize learning. With this in mind, quizzes should provide a feedback tool, not a method to sort students by speed.

Our quizzes assess all students at all 3 levels.

  • Level One:  Making Meaning of Math – demonstrating understanding at the concrete/pictorial level.
  • Level Two: At Grade Level – transferring understanding to the algorithm.
  • Level Three:  Challenge – apply tools to more complex, challenging problems.

Our goal is success for everyone at Level One and eventually at Levels One and Two for each new concept. We believe that all students can master the visual component of Level 1, which so aptly prepares them for Level 2 and for middle school math in general.   For example, fractions are extremely important to later math, yet many middle school (and high school) teachers complain that a third or more of their students never mastered them. By spending a long time giving students access to Level One fraction problems, we can change that to close to 100% of students mastering fractions by 7th grade.

Finally, we want to challenge the abstract abilities of students who are ready to attempt Level 3. These students breeze through Level One, and even Level 2, and enjoy the challenge and satisfaction of solving challenge problems.

Examples of quizzes:  Quiz 1

(Word Doc here: Quiz-1a and Quiz-1b We give TWO versions of the same quiz, to afford students “privacy”, and to avoid copying. The quizzes are equal in difficulty.

This quiz only has 4 questions, and takes anywhere from 10 minutes to 25 minutes to complete. We use “Puzzle Points” for students who finish quickly. These are logic puzzles, number puzzles, spatial puzzles — anything they seem to like — and they get small rewards when they have done a certain number of them. Rewards are theoretically not necessary, but work great to reel the students in at first 🙂



a)   The student shows good understanding of the problem:


b)   The student shows a developing

understanding of the problem;

he would benefit from drawing

a larger model – using 12ths, not


c) The student shows current lack of understanding;


the student is trying to use a confusing algorithm instead of drawing.

He did much better on Quiz 2, when he

decided to use a drawing instead.



a)   The student shows good understanding

of the problem

at the abstract:


b)   The student shows good


of the problem at the

pictorial level :

c)   The student shows goodprob2ya


of the problem at the

pictorial level : (different

approach than (b) above – she “wrapped

the fraction” into one whole bar first. This makes it easier to see the mixed number answer, while (b) above makes it easier to see the improper fraction. We have no preference! As long as the method makes sense!

d) Student shows developing


understanding. The misconception

is clear — not all the bars are the same

length. She needs to go back to

visualizing Toblerone bars!


The first 2 samples show good thinking, and a willingness to try to figure out the problem. The confusion lies in the fact that – when drawing a model – the FOUR extra liters are not the same SIZE as the other units. This is a common misconception.

The VERY NEXT day, we acted out a scenario in front of the class. One child got a box with an unknown # of blocks inside. The 2nd child got 2 such boxes. The 3rd child got one box plus 4 blocks in her hand. We worked backwards from the fact that there were 60 blocks altogther (most of them hidden), and the light bulb went off for a number of students. There was a similar question on Quiz 2, and more students got it right.

THAT is the whole rationale for assessment.

We had to repeat this enactment after Quiz 2, because there was still confusion apparent. The most common mistake of teachers is to believe that once we have TAUGHT something well, it has been LEARNED well. This is rarely the case! Children are young, their learning path is long, and there is no need for us to judge them on this.

prob3yaprob3nb lya



The first sample is correct, and shows good problem-solving skills, if not yet great form.

The 2nd sample shows good thinking; she might have solved the rest of the problem by writing out more of the facts she already figured out.

(These are the kinds of reflections we hope to see on quiz corrections!)

The third student is honest about finding the problem too challenging at this point in the year.


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