Positive Maths Assessments- Fractions / Decimals / %

What is the purpose of a summative assessment?

If we don't use the data gathered from them because that unit isn't going to be reviewed, what's the point of them?

I have wondered this a lot over the years.  I believe the only real purpose of any form of assessment is to inform the teaching or learning.  Data gathered in traditional maths test summatives are often not used. 


A traditional maths summative:

° set of closed questions with distinct right or wrong answers

(These right / wrong questions send the wrong message to our young mathematicians. 

 Maths is not a right/wrong subject. It is scientific thinking where we create a hypothesis and      test the strategy/s and then assess their effectiveness.  When we give right/wrong          questions to kids in maths, we are sending the wrong message about what mathematical thinking is about. Failed strategies we test should be celebrated because they teach us why another strategy could be more useful. Enquiry-based maths classrooms are not about getting 'right' answers. They are rich, celebratory learning environments where kids are testing and creating strategies, making connections, questioning and reasoning. Shouldn't our summatives reflect the type of learning during the unit?)

° catered to a grade level expectation average

( Just as we all learn to ride a bike, lose our first tooth, say our first word etc at different ages, comprehending mathematical concepts comes to us all at different ages when our minds are ready. When we give the traditional maths test, we are telling children- If you can't answer this question I have given you, you are clearly dumb at maths because this is the type of question a student in Year 6 should be able to answer.  When we then think about the way we differentiated the learning activities during the unit to cater to each child's levels of understanding, why would we then give them questions we know they aren't likely to answer? Is it not a form of abuse on some level to the child?  Equally, the students we know who are exceeding that grade level expectation are being dumbed down in traditional maths tests except for those typical 2 or 3 questions at the end of the test that cater to those at that end of spectrum)

° gives negative feedback to what they learnt in the unit, not celebrate

( We then traditionally send these maths tests home to share with parents.  What parent celebrates with their child the correct answers they got in the test?  Surely the majority of parents focus on the crosses and discuss these with their child.  So, the child firstly receives negativity towards their learning and who they are as a mathematician from the teacher who gives them a test they know they won't be able to answer and then receives extra negativity from their parents who focus on their wrong answers.  How is this beneficial? And because it is a summative, the student isn't given the opportunity to improve on those 'wrong' answers because we aren't exploring that particular maths concept again for the year.  And so the continual negative cycle keeps spinning for each child.)

Maths pre and formative assessments are crucial to helping student learning. We can use the data to help students with misconceptions or what steps they are mathematically ready for.

To make the summative meaningful, I give the students our maths central idea and during the unit, we pause and reflect on what we have learnt about it as we progress.  In addition to providing valuable reflecting time for the learner to consolidate their own learning, it allows me to see during the unit what each student is gaining in understanding and so it serves as a key formative. 

Here are some samples from our recent fractions,decimals, and percentages unit exploring the central idea: 
        

The reverse side reflection always fascinates me as it gives a big tell of what really stood out the most for each learner:

Another sample:

         It fascinates me to read what stands out in each child's mind as the unit progresses.

Though it is simple, the 'I used to think.......but now I know........' thinking strategy helps children to think deeply about their own learning and can be a powerful reflective tool.  It also fascinates me what stood out the most in the minds.

Some other student samples:

I used to think that fractions were of no use and you can't use them in real life situations.

Now I know that fractions, decimals and percentages are used all the time in real life situations such as shopping, banking etc

I used to think it wasn't possible to add, subtract, multiply or divide fractions.

Now I know that they can be added etc and that we do add them in real life.

I used to think that percentages are not easy to calculate in your mind (mentally)

Now I know there are easy strategies we can use to calculate them mentally.

I used to think that when you see a % discount, you just subtracted that number from the price.

Now I know you need to calculate the % of that number first and then subtract.

I used to think that fractions, decimals and percentages were completely different.

Now I know that they are basically the same thing- just expressed in different ways.

I used to think that decimals were useless and only used at school.

Now I know we use decimals in so many different ways in our real lives- length! map ratios! even money! and so much more!

I used to think that adding or subtracting decimals in our head is too challenging.

Now I know they are really easy to do especially when you use the compensation strategy. 

I used to think that if you add, subtract. multiply or divide decimals, you can just forget about the decimal point

Now I know that you can't forget the decimal point because it changes the size of the number!

Reading through these, it also makes me realise the power of a PYP central idea especially when it includes a reference to how we use that maths in real life.  So many children in my class now seem to be seeing the relevance of enquiring into fractions, decimals & %.  When children don't have the opportunity to see how a maths concepts can relate to their lives, so much engagement is lost. 

An EAL student sample:

This style of summative:

° is open-ended so each child is able to explore their own mathematical concepts they are building

° allows each child to feel like a successful mathematician

° provides valuable reflecting time during the unit to strengthen understandings of the concepts or skills

° allows the learner to see their learning develop as they add more ideas during the unit

° provides a growth mindset as mathematicians

° caters to all levels of mathematical understandings- not just the grade level expectations. It caters to all the differentiating that occurred during the unit.

° allows the learner to celebrate their own learning rather than being judged by a set of grade level expectations

° gives me, as the teacher, valuable insights as a formative during the unit that helps me see where each learner is developing and where they can be helped for their next steps

° the parent sharing is a celebratory experience.  Parents cannot focus on 'wrong' answers with their child. they are forced to focus on what they child has achieved and so additional positive messages are given to the child as a mathematician.  

° the last question asking the child to think about what they feel they need to focus on next time they learn about that particular maths concept provides an opportunity for the child to take ownership and responsibility towards their own learning

This is essentially a positive celebration of learning and helps instill the values we create in our maths learning.