Assessing conceptual understandings & strategies
The best way I've experimented with over the years to assess student learning in maths as a summative is to simply give them the central idea and some time to record their understandings and make connections.
Some of the advantages in these sorts of summatives:
° Every child feels like a successful mathematician.
(Unlike traditional maths tests, no one is made to feel stupid and no one is denied the opportunity to really show what they are capable of as is the case in most traditional maths assessments)
° They feel proud when they see all their understandings.
° It becomes a meaningful reflection especially when they are making connections.
° It gives them an opportunity to process more deeply what they have been exploring.
° It caters to all levels of understanding and abilities; the high-fliers can go for gold and those that might struggle a bit can still have the opportunity to show what they do know and can do. (Unlike traditional maths tests which tend to always cater for the 'middle' learners with the challenge questions at the end of the test to 'cater' to the higher achievers)
° From observations and taking notes throughout the unit, I already know their strengths and areas of weakness in the maths topic so I don't need to give a traditional test as a summative.
° My personal philosophy on student assessment is that if I am not going to use the data from an assessment to inform my teaching or the students' learning, then there is really no point in assessing. This style of a summative makes a happy compromise for me. The students are doing a summative, but it is a meaningful learning experience for them as they make connections. I can use the data from this style of assessing to see which students need extra support in some areas of conceptual thinking in our next maths unit regardless of what the maths topic might be. This data tends to transcend maths topics.
° When they take this home to share with their parents, it is likely they will have a discussion about their thoughts and so the reflective learning continues with a different audience outside our classroom. I can't imagine kids having much of a discussion with their parents when sharing a traditional maths test covered in ticks and crosses and if there is a discussion its likely to be negative with parents pointing out why they got certain answers wrong.
° They get an opportunity to see the big conceptual understandings in maths.
° It reflects the discussions and inquiry-based learning happening throughout the unit.
° It is fair to all students. Differentiating inquiries throughout a unit and then suddenly giving a child who has been struggling the same test as everyone else in the class is cruel and unnecessary. I can't see why a teacher, who knows student X and Y are struggling, would give them a traditional test that they know they will struggle with. It hardly sends an encouraging message to those students. This style of summative though caters to the differentiation that has taken place throughout the unit.
° It is student-led learning.
° It is an enquiry-based learning activity by piecing together how concepts or skills connect.
We recently completed our unit into measuring time. Our central idea was:
By understanding astronomy, we have been able to create ways to measure time.
We started by drawing diagrams that explained astronomical features that help us measure time such as:
° The Earth takes 24 hours to rotate
° The Earth takes 365 1/4 days to the orbit the Sun (hence why we also have a leap year)
° How there is a full moon approximately every 28 days and that is partly why our Gregorian calendar has 12 months
° How the Earth is divided into 24 time zones as 360° divided by 24 is 15 and therefore each line of latitude is 15°
° Why places like Europe have 4 seasons and places near the Equator have 2.
We were given images that we could either choose to use or not. We used the images to make connections either explaining how the astronomical feature allowed that system for measuring time to be created or how those systems connect with each other.
Closes up of the above example:
On the next day, we looked at one of our lines of inquiry we had explored:
Function: Strategies we can use when measuring time.
We reflected together on different strategies we had explored during our unit. They selected three strategies that were either new to them or that they felt they had got stronger at.
They then tried to visually explain how the strategy worked.
Finally, they complete a short reflection as seen at the bottom.
Together with the summative, each child receives the following sort of feedback.
I've been experimenting this year with assessing students in maths using the PYP Learner Profiles. I'm loving it so much. It brings the Learner Profile to life for the children and they are being assessed on their attitude towards their mathematical thinking rather than being told they are smart or not so smart at the mathematical thinking involved.
To see another example of a maths summative using a central idea, scroll to the bottom of this blogpost to see how it looks for a unit on measuring angles:
Measuring angles summative