Monday, 11 May 2015

No more maths tests!!!


Assessing without tests......


Which helps student learning the most?


° Pre-assessment?

° Formative assessment?

° Summative assessment?



If, during an entire maths unit, you were only allowed to do one of those assessment types, which would be of the most use to you?


Pre-Assessment:

For me, the most important assessment in maths is the pre-assessment; those findings inform the enquiries & investigations for the unit.  It tells me where my students are at in both their conceptual understandings and with the skills. It helps me to group children early on in the unit and then to regroup later if needed.

 In the first few days of a new maths unit, when given a short pre-assessment (usually just 6 or 7 questions perhaps based on skills that will be used in the unit or conceptual understanding questions), I always begin by saying:


You are not expected to be able to answer all these questions. If you know how to answer these, that's great.  If you don't know how to answer them, that's equally great.

They find that puzzling the first few times, so I explain that the purpose is for me to find out what I need to do to help everyone take their understandings further.  

Another useful pre-assessment strategy is the KWL chart.  It gives a great idea of where each student is at and gives them ownership of their learning for the unit. 


Formative Assessment:

Most of the formative assessments we do in my class, come from the enquiries and investigations as well as observing the thinking and strategies children are using.  The only time I give a more formal formative assessment is when I feel I haven't got as clear a picture as I need of what each child is able to do.  If I don't think I need the data to inform further learning, then I don't give a formal formative assessment. Continual observations and conferencing during their investigations generally gives me the knowledge needed to scaffold them to their next levels of understanding. 


Summative Assessment:

I'm completely done with those traditional maths tests at the end of a unit. They cater to the middle level with the token extension /challenge questions towards the end to cater to the brighter sparks. If you are learning at a lower level than the middle, the test acts like a form of abuse.  If I know the child won't be able to answer most of the questions, why would I inflict that upon them?  I don't need evidence to know they find those levels too difficult. Equally, for those students working at a higher mathematical level than the middle, a traditional test dumbs down what they are actually capable of. 

The other key point for avoiding tests I think, is that when you are differentiating throughout the unit especially with student-led investigations,  it's basically impossible to create a test that would cater to all the diverse learning that has been going on. 

And lastly, given it is the end of the unit, how much of that evidence gathered would inform my further teaching?  Usually not a lot so then what is the point?


So, why do we continually obese over a summative? I've wondered about this a lot over the years. It seems the only logical answer can be to show evidence to parents.  I would have already gathered plenty of evidence throughout the unit of where each child is at.

So, I started experimenting with ways for my students to do a summative that is meaningful to them. Something that will help their learning and something that could reflect their enquiries.


I've come up with a simple, but I think, powerful idea.  For a summative I simply place the central idea in the centre of an A3 page and the children record everything they understand about the central idea.  They are encouraged to use diagrams, write short explanations of how things work and to make connections between the skills and ideas.   

It takes a few times for the children to fully appreciate what we are doing.  When I notice some are getting stuck for ideas, I might remind them of things we have looked at to help spark memories but without telling them what to write.

A useful strategy is to sometimes begin by brainstorming a list of activities we have done in the unit. The children can then see these on the board and it might jog their memory of what they have learnt and understand. 

I've found that doing this is best to do over two or three 15/ 20 minute sessions. When they return to their page the following day, they are proud of what they have already recorded and feel more refreshed to continue rather than doing an entire 30/40 minute session.






Below are some examples of a summative my class did when they were doing their personal investigations into angles. 

The central idea we explored was:  'When angles co-exist, connections and relationships are formed'


Student A:





I find the advantages of this style of a summative are:


° They all feel successful whilst doing it.

° It caters to every child's learning needs and levels.

° The children are not being told they are 'stupid' because they cannot answer certain questions as given in traditional maths tests

° It becomes a meaningful time to reflect on the conceptual understandings of that maths topic

° It gives them an opportunity to make connections between the concepts and skills involved.

° It gives them an opportunity to show what they do know, unlike a traditional maths test that greatly limits their ability to show what they understand.

° It informs my teaching practise. Knowing they will be reflecting on the central idea means I need to ensure we are constantly discussing the concepts during the unit and continually referring back to our central idea displayed on the wall. These discussions help deepen student understanding and also allows for interesting questions to arise which often lead to new enquiries or investigations.

° Because they are doing different investigations and are given activities at different levels to cater to their needs during the unit, it is really not fair to give them a test with questions I know they probably can't do as they haven't done those activities.  This style reflects & caters to the constant differentiation that takes place during the maths unit. 

° It is fascinating, as their teacher, to read and gain an understanding of where each child is at and to see what stuck out the most in their minds during the unit.

° It takes 5 minutes to make. :)










A quick, but powerful reflection after doing the summative:










Student B:












Student C:





When I read through these, I find it fascinating to see what discoveries they have made from their enquiries and what sticks out the most in the minds when they think of our central idea.

Best of all, they all feel like successful mathematicians because they haven't been given a traditional test that tend to cater to the middle level with the standard extension questions that will cater only to a few in the class.

No one has been forced to feel 'dumb' doing this type of summative and they gain a real sense of pride in all they have achieved in their learning when they see all they have included in their summative. 










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