Thursday, 15 October 2015

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:







17 comments:

  1. Very refreshing, Graeme. I am most certainly going to Try this! Thank you!

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    1. Thanks for the feedback Lindy! I hope it helps. My kids really loved it a lot and are no w showing this new risk-taking approach to enquiring into numbers. One child said today in a number investigation, "It doesn't matter if my theory is wrong, numbers are just a made up system anyway" - This bravado stemmed from this unit. Let me know if you need any help with it :)

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  2. Graeme, thank you so much for sharing this! We are just starting to build PYP stand-alone math planners and your examples answer so many of our questions about what they look like in action. We are definitely going to use many of your practices when designing our math summatives.

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    1. Thanks so much for your feedback Taryn. That's really thoughtful of you! Kids really start enjoying maths with this approach. Let me know if you need any help! :)

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  3. All words and not a single number. Is this a writing assignment?

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  4. I like to think that when kids are given an opportunity to explore how and why their number system works the way it does, they can use it far more confidently. BTW, why can't maths learning take on an historical edge? This is what the kids wanted to find out, so that's what we found out. :)

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  5. Graeme,
    Thanks for sharing, as always. Your photos inspire me (to copy you)! I plan to do this with the Central Idea for all we do. Please keep sharing!

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    1. That's really sweet of you Megan. I've been trying quite a few of your ideas you share on Twitter. Would be amazing to be on the same team as you!!

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  6. Thanks for sharing. I do agree that maths assessment is not only focus on how to do but also why we do something mathematically.

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    1. Thanks Tatik. The 'whys' can often be forgotten in maths learning, but when we see those 'light bulb' moments go off in kids when they discover the 'whys', we can see how important they are to really have a deep maths understanding ü 'how's' in maths summatives could merely be showing a child's ability to rote learn, but when we give them a chance to explain why, I think that's when the real and deep learning takes place.

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  7. I've been thinking about this idea for a while now and I like its potential for showing understanding. What sort of prompts (if any) do you give to ensure students demonstrate a depth of understanding rather than just surface connections to the central idea. For example, do you ask, "How can you show that using numbers?" or "Why is that the case?"

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    1. Hiya. Thanks for the feedback. A strategy I often use is always helping the children to understand that WHYs of maths are more important than the HOWs. We often discuss the importance of this and so they begin to understand that in their summative reflections, they should always try to explain the WHYs. Hope this makes sense? Your prompt question ideas are great and would also help the children to dig deeper into their thinking!

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  8. I've discovered your brilliant blog whilst researching this summer. I think your assessment ideas are really interesting and something that I have been pondering for a while. I'm definitely going to be trying out lots of your approaches with my Y6 maths class in September. Thank you so much for sharing your hard work - I hope my pupils are as inspired as yours!

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    1. Thanks so much for your feedback and compliment Alison. It's lovely of you to take the time to give feedback. Let me know if you need any copies of assessments etc. Always happy to help. :)

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  9. Thank you Graeme for sharing very engaging ideas! I completely support the idea of rescuing children from worksheets!!

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    1. Thanks for your feedback. Hope some of these ideas help :)

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  10. Thanks Graeme. This is very useful to me. I am a math consultant and such ideas help us a lot in providing PLD to teachers!! Thanks for sharing. I have been using the Inquiry math attitude to develop student understanding in mathematics. :)

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