One of the most important understandings in calculus is that functions have values which can be positive and negative but that those values are also changing, and that change can be in a positive or negative direction. Slope isn’t just for straight lines!
For example, when you’re getting out of student loan debt, the total value in your bank accounts might be negative, but the rate of change of your money is positive.
Or for another example, the value of the gross domestic product of the United States is always positive and the rate of change of the GDP is almost always positive so it makes more sense here to look at the rate of change of the rate of change. What is the rate of change of the increase? How does it compare to the increase of previous decades or other countries?
Because of the importance of these questions, calculus teachers frequently ask students questions about rate of change. Given a function, what is its derivative? Give a second derivative, what might the first derivative look like?
We give students a function and its first and second derivative, without revealing which is which. We ask them to label the derivatives accurately and then we give them feedback on their thinking.
But then we bring in a Challenge Creator and invite students to create their own function and label its derivatives. If they do that successfully, they can enter it into the gallery to challenge their classmates.
You get one function from us and then dozens more from your classmates. A calculus class that is social and creative! That’s why we’re here.
Calculus teachers who ignore this, or see it but don’t give it a try…I don’t know…this is a pretty nice activity produced by the @desmos team.
These couple of weeks have been quite controversial for me. I don’t want to get into this “hard life” and “hard job” thing; I am grateful for the things I have. Also, I have worked my ass of for this, so I will not give up. Anyway, in August I have started teaching in a new school; new school comes with new rules, ideas and concepts. Therefor, I was expecting a couple of hard months. In the past weeks, a question has appeared in my head over and over again: What am I teaching for?
Am I trying to make them like maths? If you asked me this last year, my answer would have been yes! At the moment, there is a shadow over my mind and soul. I like maths!! I LOVE maths!! Therefor, I thought that I could share my passion with my pupils and try my best to show them some interesting parts of maths. It is hard to do this, but I believe I can do it. Even if one pupil out of 20 likes maths in the end, then I feel good about it.
Am I teaching for the test/exam? A couple of weeks ago, I received an answer for this: “Stop thinking about passion and think more at the exam; they have to pass the exam – there is no passion in that.” I have been thinking at this for a while now… It is true, they have to pass the exams to get to college, university, to get a job and so on. Also, there is no passion in passing an exam. But is this everything? Do we have to forget about everything else? I have been reading about these exams like I have never done before in my life; I use mostly past paper questions in all of my lessons (starting with S3 – 13/14 years old). The department is actually thinking of using past paper questions for lower classes, but they didn’t find a suitable method yet. How important are these exams? Do we have to work for them years and years on end? We cannot survive if we don’t get A, but B? Do we need absolutely everyone to pass, even if they have absolutely no idea what are they doing? I am trained to use just one specific method to solve a question, as if there are no other methods, as if they are not able to understand more. The pupils just do the same thing over and over again: the same question with different numbers.
In a way, I refuse to think that this is my only purpose here. Helping someone pass an exam makes me a good teacher; is that right? I have been raised in a culture where exams are everything and I understand their importance, but sometimes it’s just to much. Why do we have to forget about the fun, beauty of maths? Why do we have to simplify a question so bad, just to make sure they do the minimum do get full marks in a question?
At the moment the situation is quite strange for me. I know that I will not forget that maths is my passion; that I am doing maths to make me happy; that I read maths books in my free time; that I write and share about maths. I just miss doing some problem solving with the kids. I miss giving them a question and letting them THINK about it just to see what they come up with. (I cannot stand the expression “IDK” or “I haven’t done this before”) I miss showing them different methods to solve a questions and then decide which is the best and why (or let them chose their favorite method). I miss doing an art related activity. I miss showing them a short video (TED-ed or Numberphile were my favorite for this).
So, here are a couple of my questions for today; I would love to know your opinion on this. Feel free to comment bellow with your answers:
How important are these exams?
How many years do we need to prepare for just on exam?
How many exams do we need to show we are successful?
How good is teaching just one method and them practicing blindly?
What should I do? What do YOU do?
Hope I didn’t bore you with this topic. If you have a question for me, or what to talk about this more just send at email at lthmathematics@gmail.com Have a great day.
