Meaningful Mathematical Summatives

Meaningful Mathematical Assessments

I see traditional maths test summatives as mostly pointless and grossly unfair to the learner.  

Those traditional tests give the message to a large portion of learners in the class that they are too dumb as mathematicians to be able to answer the set questions or belittle other learners by giving them questions to solve that are too easy for them and therefore deny them opportunities to show what they really do understand. 

Additionally, they are largely focused on HOW to do something mathematically rather than WHY we do something mathematically.  

Furthermore, they counteract the whole process during a unit of enquiry-based learning.

When children take home a maths summative traditional test to share with their parents, we all know that the parents generally highlight all the crosses and seldom focus on what the learner did do well.  This part of the process can then compound in the learner that the whole point of mathematical thinking is to get the right answer and/or that they are 'poor' mathematicians.


To cater to the diverse enquiries taking place during the unit and it to make it a meaningful experience, I've been experimenting the past year with simply giving students the central idea we have been discussing and focusing upon.  At the end of every few maths learning activities, we spend some time reflecting on what we have discovered or connections we have made. This serves as a key part of the student's learning by reflecting on their learning. As the unit progresses, the student also starts to gain a sense of pride in all that they are discovering and understanding. 

Here are some examples from a recent unit of number systems where we explored the central idea:

Mathematicians saw advantages to creating our base 10 number system which extends infinitely in both directions.

Another sample:

I love reading this part of their reflections at the end of the unit.  There are so many unique thoughts shared of what really stood out for them and this gives me a deepened insight into who each student is as a mathematician.  The 'I used to think.....Now I know.....' thinking routine also helps the student to see how their learning and understanding as a mathematician has changed and grown.

The other wonderful and the most important benefit to this sort of summative is that each learner feels successful as a mathematician.

When they take this sort of summative home to share with their parents, they are encouraged to teach their parents what they have learnt.  Parents can't be focusing on possible mistakes their child has made in a traditional maths test, but instead would hopefully become engaged in what their child has learnt. This then serves as a meaningful part of the student's learning cycle where they are reflecting even further on what they have learnt by sharing their understandings.

As feedback, I experiment with different PYP Learner Profile attributes and /or attitudes to help the children gain a deeper sense of how we apply those to learning situations and to hopefully instill in them a sense of reason for focusing on improved attitudes to their maths learning: