Reviewing Mocks
As a southern hemisphere school we have just had our mock exams, so I thought about way to return them for the biggest impact. I put the question to twitter and got some great responses (given that it was the summer holiday for UK teachers).
As a southern hemisphere school we have just had our mock exams, so I thought about way to return them for the biggest impact. I put the question to twitter and got some great responses (given that it was the summer holiday for UK teachers).
Best ideas for giving back mocks? What do you do? @mathsjem @BracewellMr @BeckyHall75 @mrshawthorne7 @suffolkmaths @MrBlachford @Owen134866 @RufusWilliam @EJmaths @mhorley
— Dan Rodriguez-Clark (@InteractMaths) August 21, 2019
What I ended up doing was giving students back their papers and getting them to go through them and fill in the following template that I printed off. I got this idea from Blake Harvard's post From Unknown to Known in the Classroom.
As they went through the paper I wanted them to write down what their known known's were and, more importantly, what their known unknowns were. I then wanted them to correct their errors, making use of each other first (for most questions at least one person in the class got it right), or referring to my worked solutions.
I found the template useful, but did need to push students to be more thorough and specific in using it. Just writing trigonometry is of no use, they needed to identify what exactly was the problem in trigonometry. Was it spotting the need to use trig? Or applying the rules? Etc. I think for this to be really useful students need to become practiced at using it, and I need to model how to use it well. It is probably too late for my students doing their exams in a month, but for my S5 (Year 12) class with whom I do weekly quizzes, I am going to start building this into the following lesson for them to reflect on the quiz
Trig Relations
At lunch today, a colleague and I were talking about Trig, and one thing that came up in conversation was that if a+b=90 then sin(a)=cos(b). Not that this was something that we did not know, but it certainly was a case of the curse of knowledge as neither of us could think of a time we actually taught this to our students. We both felt this was a useful thing to explicitly teach them.
At lunch today, a colleague and I were talking about Trig, and one thing that came up in conversation was that if a+b=90 then sin(a)=cos(b). Not that this was something that we did not know, but it certainly was a case of the curse of knowledge as neither of us could think of a time we actually taught this to our students. We both felt this was a useful thing to explicitly teach them.
Implicit Differentiation
I had a good lesson (as far as it can be judged at the time) with my IB Higher Level class this week where we started implicit differentiation.
I had a good lesson (as far as it can be judged at the time) with my IB Higher Level class this week where we started implicit differentiation.
The lesson started, as always, with a Last Lesson, Last Week, Last Unit, Further Back.
After that we caught up with our Learning Map. I started this for this unit (an idea inspired by High Impact Instruction by Jim Knight), and have been slowly adding the key ideas to the map as we progress through the unit. It acts as a one page summary for the students when they come to revision, but also acts as a guide to the learning journey. We started the unit by drawing out the overview and main headings to give them an idea of where we were going. I need to make more use of referring to it at the start of each skill.
Then, after teaching Chain, Product and Quotient Rules last week, I had students work on this mathsvenn I put together.
This generated students creating some interesting functions, and different groups interpreted it differently. Some interpreted E as a function that can be differentiated using either the product rule or the quotient rule (so for example rewriting a quotient as a product of the reciprocal) and some interpreted it as a function with a product within a quotient (this was how I had intended it). It led to an interesting discussion
We then moved on to looking at implicit and explicit functions, and I jumped in with the example y2=4x.
I really focused on applying the operator d/dx to each part of the equation, and linked this to solving equations by "doing the same to both sides". We also talked about using the chain rule to split the derivative of y2 wrt x. Students then did a your turn for the equation of a circle.
I discussed the general rule that differentiating f(y) wrt x is the same as differentiating f(y) wrt y and multiplying by dy/dx.
We then looked at an example with a product rule within implicit differentiation.
And set them a your turn.
They all managed to do the differentiation, but none managed the next step to find the turning points. When we had reviewed that, one student asked what the nature of the turning points was. I bounced back with "How would we find that?" to the resounding answer find the second derivative. So, with 5 minutes left of the lesson, that is what I did. I took the opportunity to work it out live on the whiteboard.
The students were enthralled, with all of them staying into lunch to see me finish it. I think they enjoyed seeing me relish the challenge of doing this rather complicated differentiation, but it also served the purpose of showing them that it can be done. I think one of the things that stood out to them was how fast I did it, and this was a good opportunity to remind them of the importance of fluency with calculations to free up working memory. I did change the notation to first derivative to simplify notation, and also rubbed out bits of working as I went (which in a way also showed them the simplification steps more clearly), but what ended up on the board is below).
Of course, after the lesson I realised my error in writing the function as y=. I then wrote up the correct solution and in the following lesson, told the students I had made a mistake in my rush, and gave them the correct version. This was a good opportunity to show them that we all make mistakes.
Revision on the Whiteboards
With my 6B IB Maths Studies class we are revising for the final exams, and we were looking at quadratic functions, a topic they particularly struggle with. I got them to work in pairs to write up all they could remember from the topic on a whiteboard.
With my 6B IB Maths Studies class we are revising for the final exams, and we were looking at quadratic functions, a topic they particularly struggle with. I got them to work in pairs to write up all they could remember from the topic on a whiteboard.
Then I projected an exam question and had them work in pairs on a different whiteboard to solve the problem. As they recalled other things about quadratics, stimulated by the questions, they were to add them to their summary boards
This was a nice way to mix up a brain dump activity, which did not generate much of use, with exam questions, to support the development of connecting ideas. Next time I will get them to add connecting lines between the ideas that are related too.
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