On October 6th, it rained at my house [click on the image to see the video].
So I saw, immediately, the chance to make some questions:
Do you have the whole activity here: in english and in catalan
[1] Meyer, D. Category: 3acts. 2016. http://blog.mrmeyer.com/category/3acts/.
[2] WikiHow. How to calculate the distance from lightning. 2016. http://www.wikihow.com/Calculate-the-Distance-from-Lightning.
Recently, I discovered a analogy about mathematical activities: what kind of writing task do you do?
You just complete the calligraphy copybooks: follow the marked line with pencil. So you are not able to write free content nop form.
You could write a formal application to Government for example [2]. With this kind of document, you are restricted with a lot of format constraints but you could freely write the content.
And finally, you could write a book [3]. You are not restricted to form or content.
Following 5 Practices for Orchestrating Productive Task-Based Discussions in Science [1] these categories rise up the demanding of knowledge. And I think that students really “write a book” if they do Project-based learning.
I give you an example of this analogy for practicing fractions as operator. I want students to calculate \(\frac{3}{4}\) of \(16\).
Divide this plot to verify this requeriment"
Update: I change the book analogy from this:
Can you find three different ways to divide this plot verifying this requeriment?
What is the division which has the minimum cost? (each fencing side has a cost of $10)?
Can you compare yours with your neighbours’?
Can you find out what is the minimum cost division among all possible divisions?"
to above.
[1] Cartier, J.L., Smith, M.S., Stein, M.K., and Ross, D.K. 5 practices for orchestrating productive task-based discussions in science. National Council of Teachers of Mathematics, 2013.
[2] Govern de les Illes Balears. Llibre d’estil. amadip.esment, 2006.
[3] Wikipedia. El ingenioso hidalgo don quijote de la mancha. 2016. https://es.wikipedia.org/wiki/Don_Quijote_de_la_Mancha#/media/File:El_ingenioso_hidalgo_don_Quijote_de_la_Mancha.jpg.
Try and failure, \(\frac{3}{4} \cdot 16\), equations (\(3x+x = 16\)), etc.↩
Does the cost vary if we choose joined (arc-connex) regions than disjoint areas?↩
More thoughts about flipped classrooms….
[1] Cultura de les Illes Balears, C. d’Educació i. Orientacions per a l’elaboració de la concreció curricular i de les programacions didàctiques. http://weib.caib.es/Documentacio/orientacions_elaboracio_cc_pd/orientacions_concrecio_curricular_i_programacions_didactiques_25-02.pdf.
[2] Kirch, C. Flipping with kirch. the ups and downs from inside my flipped classroom. The Bretzmann group, 2016.
[3] Kirch, C. Flipping your math classroom: More than just videos and worksheets. how i got time back in my classroom to support all learners and deepen the learning experience for students. 2016. https://www.bigmarker.com/GlobalMathDept/Flipping-Your-Math-Classroom-More-Than-Just-Videos-and-Worksheets.
[4] Wikipedia. Flipped classroom. 2016. https://en.wikipedia.org/wiki/Flipped_classroom.
It does not mean method of learning.↩
It is not exclusive about Flipped classrooms. Other pedagogies show direct instruction is not working anymore.↩
In some cases, these 20 hours could be reduced when you are the department chief^{3} (3 hours), tutorials, etc. In my case, this season I teach only 14 hours in classrooms (37% of my working time). I do not complain about the number of hours of teaching^{4} but I complain about the efficiency of non-teaching hours. In the majority of our non-teaching hours, we spend (read waste) time discussing about irrelevant things for students. It’s sporadic to mention how to improve teaching or what specific mesures we could adopt for engage students in our meetings. We spend time discussing things like:
Things which are, mostly, not really important. We spend almost 30% of our (permanence) time on improductive meetings or burocracy. And the most disappointing thing is that it is marked by law or by tradition. But I think we could (and should) spend (invest) this 30% of our time doing valuable things, things for students, things for improving our school, things for free us of filling forms, etc.
What are your situation? How much time do you spend to unproductive tasks?
[1] Cultura de les Illes Balears, C. d’Educació i. Intruccions per a l’organització i el funcionament dels centres docents públics d’educació secundària obligatòria per al curs 2015-2016. 2015. http://www.caib.es/sacmicrofront/archivopub.do?ctrl=MCRST4905ZI147029&id=147029.
In my opinion, it’s an euphemism for “doing nothing” for bad teachers because these hours are not controled. Good professionals spend more than 10 hours per week at home for preparing classes↩
teaching staff meetings, inter subject department (Comissió de Coordinació Pedagògica in catalan), school board, etc↩
you are the boss of all teachers teaching the same subject↩
Politicians use it for abusing and deteriorate working conditions many times.↩
In a certain city, gas service is paying 15 € fixed a month and 0.75 € for each cubic meter consumed.
- How much do you pay for \(3 m^3\)? And for \(5 m^3\)
- Plot the function which relates consumed cubic meters and the cost of the service
When do you need the formula of the relation there? Clearly you could get (a) without a formula. And you could plot the points using value table (with previosly calculated values in (a) if you want) but you need the formula of the relation (\(cost = 15 + 0.75 meter\)) for assuring that you could join the points with a straight line (using the theoric fact that: afine functions correspond to straight lines). Otherwise you would not know if the plot is a straight line or a curve.
My students understood more clearly the connection between plots and functions when I ask them for which step needs here the formula.