No one ever includes constructions in a Do Now
Why this happens, why it is important, and what to do about it
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I have previously written about why the Do Now should consist of four questions designed to test the retrieval of concepts unrelated to the lesson content. In short, this leads to a structured start to the lesson, where the teacher has a degree of control over how long it lasts, and students can strengthen their memories of concepts they encountered in the past.
A question remains: What topics should these retrieval questions cover?
The answer is obvious: All the things we want our students to remember… which is essentially everything they have been taught.
But that is rarely the case.
I reckon I have seen over 1000 Maths Do Nows in the last academic year, and in all those Do Nows, I am yet to see a question that challenges students to:
Construct a perpendicular bisector
Rotate an object
Plot a quadratic graph from a table of values
Think about your Do Nows. Have you included questions that ask students to do these things?
If not, then why?
Well, one possibility is that these things are not as important for students to remember as things like rounding, negative number operations, solving linear equations, working with fractions, decimals and percentages – the usual Do Now fodder. That is probably true because these topics are the foundation of more mathematical concepts than the absentees listed above. But we don’t want our students to forget how to construct, rotate and plot. And anyone who has marked exam papers will know that many students do forget to do these things.
No, questions on these topics are not included regularly in Do Nows because they are a pain.
They often require equipment that students do not have, or that needs handing out at the start of the lesson. When you are trying to settle students, it is not the time to dish out compasses.
They are a pain to think of on the spot – think of the time it takes to design a loci question, versus a question on adding fractions. Even the great Do Now generators out there, like MathsBot and MathsWhiteboard, avoid these topics.
They are a pain to assess – is that perpendicular in exactly the correct position?
So, I don't think the solution is to include questions on these topics in the Do Now, but students do need opportunities to retrieve them.
In a previous newsletter, I described four key retrieval opportunities:
Do Now
Low-Stakes Quiz
Woven into the current topic
Homework
If the Do Now is not suited to retrieving these kinds of topics, what about the other three?
Well, interweaving is difficult for topics like these. They are certainly more difficult to blend into lessons than negative number operations, FDP work, and forming and solving equations.
Homework may also be problematic. Do students have the necessary equipment at home to answer these questions? If your homework is set online, then these topics are not often assessed the way they would be in the exam due to the limitations of such technology. And the big question: Do enough students do homework to the standard you require to benefit from the act of retrieval?
This leaves us with Low-Stakes Quizzes. I think a weekly Low-Stakes Quiz is the ideal time to assess these sorts of topics. By Low-Stakes Quiz, I mean a 10-question quiz on 10 different topics that the students work on independently for around 20 minutes. The teacher then goes through the answers, the students self-mark, and then create review cards based on their highest-confidence errors.
A low-stakes Quiz is the optimal time to retrieve the topics described in the post because you have more time: more time to give out equipment and more time to model and specify exactly what the answer should look like.
This is why it is so important to make use of several retrieval opportunities. If all your retrieval eggs are in the Do Now basket, then topics will get missed. The same is true if you exclusively use any of the other three retrieval opportunities.
Something like this can work well:
Create a list of all the things students need to remember – use last year’s scheme of work and add to it each time you teach a new topic
Create retrieval questions to assess each of these things
Make a note of which retrieval opportunity these questions have been included in
Keep an eye on any gaps that appear and address them
This way, students should remember how to construct a perpendicular bisector just as well as they remember how to add a fraction.
What do you agree with, and what have I missed?
Let me know in the comments below!
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Thanks so much for reading and have a great week!
Craig
Good morning Craig,
I'm currently writing a new blog post on this subject, here's the draft.
Maths is not a GCSE.
Teach to test mentally has become so intrinsically intertwined with adherence to National Curriculum that teachers of Mathematics have become institutionalised from the outset of their teaching careers.
It is not their fault, my wife is included in this number and has been teaching secondary Mathematics for 25 years if we include her PGCE placements.
As a person diagnosed with ADHD, for me maths is a beautiful and wonderfully complex world of discovery, a view shared by Pythagoras who built a complete religion around it.
Yes, mathematics is the verifiable aspect of science, but it is also art.
It is why STEM became STEAM, the inclusion of art stimulates our fragile human minds like nothing else.
Yes, we can talk about the perpendicular bisector and have students draw clinical fundamentals or we can gift students a pencil, ruler, compass and a set of instructions to recreate artworks that have endured for millenia.
Is this something we have time to achieve in lessons?
We used to, but somewhere along the way our brief was changed and results became all that mattered.
Maths is not a GCSE, it is the framework for seeing and expressing the beauty in the world around us.
Love to you all
BISCUITS_BOX
From my perspective (GCSE re-sit), choice of topics to cover is based on effort and reward. Constructions take time for students to learn, partly because they weren't learned at school, but rarely turn up on an exam paper. Quadratic/cubic graphs and transformations are done weekly as they are always on the paper.
Along with simultaneous equations and trigonometry, all three topics you mention should disappear from the Foundation syllabus and they should be replaced with more problem solving, harder fractions, decimals, percentages and ratios.