# Assessing for Understanding rather than Fluency

In classrooms around the country gifted mathematics students are hiding in support maths.  They have been overlooked by our current Fluency assessment – left back, seeming to struggle and falling behind.

Here are some simple questions that I use as a very quick diagnostic tool for students working in different grades:

1. Prep:  Can you make me five fingers, but using both of your hands?  Can you make me five fingers, but with a partner?
2. Prep-2:  Holding an opaque cup, count 6 counters into it.  Shake the cup and ask students, How many now?  Shake the cup again and ask the question.  Watch for students who have a solid understanding about what changes a number and what does not change a number.
3. Year 1-2:  Tape a masking paper strip across the floor.  Place 1 unifix cube at one end, and 10 joined together at the other end.  Ask the students to place 2, 4 and 7 on the line.  Watch for the concept of relative size.  How big is 7 compared to 1 and 10?
4. Year 1-3:  Draw some blank squares that are joined together in a cross shape.  These are meant to represent parts of a hundreds chart.  Write one number (e.g. 16) at the top of the shape, and see if the students can work out what the other numbers are.  The serious extension question is to start with a 30 in the middle and then include four squares on the corners.  See the picture on the left of Rohan, a Prep student, in March of this year.
5. Years 3-4:  Tape a masking paper strip across the entire length of your floor.  Place 1 MAB cube at one end, and 1000 MAB cube at the other end.  Ask the students to place 10 and 100 on the line.  This task is a “must” for any grade 3-4 teachers as it also gives you a real assessment of low understanding from other students.  For seriously gifted students, change the starting number to 200 and the ending number to 1300.  Try placing 500 and 1000 on the line.
6. Years 3-6:  Using an A4 piece of paper, make the weirdest half that you can that is still actually a half.  Then ask students which half is the biggest (hopefully getting them to prove that all of the halves are actually the same rather than thinking that one is bigger).
7. Years 5-7:  Ask students to make 23.7 out of MAB.  Watch for students who seem confused, and ask them if they could do it if you gave them scissors.  Most students, even in high school, simply make 23 then draw a dot and then make another 7.  Separating 30 blocks is not the same as 23.7.  Decimal numbers are about relative size, not about a dot.

Have fun finding out what your students really understand and really don’t understand.  I firmly believe that it is not until we know about students’ intuitive understanding of mathematics and their connections between numbers that we can truly teach the student rather than the content.

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