As one of my favorite blogroll authors does, I’ve decided to write a post every time I upload a new activity. Or at least when I upload an interesting one. Thus I could explain why I would choose this activity and how I would made it. And people who are subscribed to my blog could discover new activities (I remember that you could also subscribe to my set of activities)
On October 6th, it rained at my house:
So I saw, immediately, the chance to make some questions:
Recently, I discovered a analogy about mathematical activities: what kind of writing task do you do?
Following 5 Practices for Orchestrating Productive Task-Based Discussions in Science (Cartier et al. 2013) 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 of .
Activity: "Two farmers want to divide a 4 x 4 plot but the first should have three times surface than the second.
Divide this plot to verify this requeriment"
Students response:
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.
Cartier, Jennifer L., Margaret S. Smith, Mary Kay Stein, and Danielle K. Ross. 2013. Discussions in Science. National Council of Teachers of Mathematics. http://www.nctm.org/store/Products/5-Practices-for-Orchestrating-Task-Based-Discussions-in-Science/.
Govern de les Illes Balears. 2006. Llibre d’estil. amadip.esment. http://www.caib.es/conselleries/relinst/sgtrelinst/llibrestil/00index.html.
On 25th August, I received the book “Flipping with Kirch. The Ups and Downs from inside my flipped classroom” by Crystal Kirch (Kirch 2016a). I bought after seeing Global Math Department conference by Crystal Kirch (Kirch 2016b). I recommend you. I’m on page 23 (of 215) but it’s very good written with direct and chick-to-chick style. She anticipates what you are thinking while you read the book. She insists that Flipped classrooms are not just about students learning theory outside classrooms and making exercises at classrooms. It’s about switch between teacher-centric classroom to students-based time. It makes possible to have more time to support the thinking of your students than with direct instruction.
More thoughts about flipped classrooms….
Conselleria d’Educació i Cultura de les Illes Balears. 2010. 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.
Kirch, Crystal. 2016a. Flipping with Kirch. The Ups and Downs from Inside My Flipped Classroom. The Bretzmann group.
———. 2016b. “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.” Global Math Departament. 2016. https://www.bigmarker.com/GlobalMathDept/Flipping-Your-Math-Classroom-More-Than-Just-Videos-and-Worksheets.
In Spain public schools, secondary teachers have a legal stablished working time per week:
In some cases, these 20 hours could be reduced when you are the department chief (you are the boss of all teachers teaching the same subject) (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^{3} 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?
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.↩︎
Politicians use it for abusing and deteriorate working conditions many times.↩︎
I posed this problem in class:
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 ? And for
- 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 () 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.
]]>If an athlete is running at 6.833 meters per second in 1500 meters race, at which speed she would run in 3000 meters race?
This activity is very uninsteresting. It does not bring nothing to our students. How can we enrich that? In my case, I think I acomplished it incorporating as much as actions I could in the activity. In the original activity, our students just calculate. No more. In the evolved activity they do more things than that. Perhaps, the evolved activity were not interesting and it would not engage our students. I don’t know, but at least it touches more aspects of the reality. Knowledge is about connections and one way to connect is to do diffents things (or same thing in different ways).
No more preambles. Here is my activity:
You can download as pdf (Bordoy 2016).
It involves:
I hope my students would consider it interesting.
PS: Sorry for orthographic mistakes in animation. I corrected in pdf.
Bordoy, Xavier. 2016. “Athletics Records.” http://canterano.somenxavier.xyz/bitacola/blog/athletics-races.pdf.
I came across this problem (in castillian) from Brian Bolt “Aún más actividades matemáticas” (Bolt 1989) which consists of finding the fastest path between two points with different velocities in various regions:
As it is expressed in its solution this problem involves an optimization problem of a radical function, which obviously does not match the level of my students:
But I have liked the problem very much. So I decided to transform this to a more simple one: changing the metric in from usual metric to taxi metric^{1}. With this discretization, the problem is more easy (even it could be solved with try-and-see tactic): students just have to minimize an afine function. The moral of the tale is that we have to maximize the trip with the highest velocity.
Perhaps this tactic of simplifying could be useful to you with other problems.
Bolt, Brian. 1989. Aún Más Actividades Matemáticas. Labor.
Note that in the city the width and the length of the streets are not the same. So the metric is a modified taxicab: , where and are the width and lentgh of streets.↩︎
Sometimes magic happens in class: good moments of reasoning appear in classroom instantly, without any planification. Sometimes one student asks you for a reasoning validation and then you are marvelled. This happened to me two weeks ago. We were revising homework: sketching graph of quadratic functions with their concavity, their vertex and the cutting points to axes… then, Aitor said:
But it’s needless. We don’t need to calculate the cutting points to -axis because the vertex is “positive”
What?, I said. Can you explain it with more detail?
And then, we put in blackboard what we have known as Aitor’s theorem. We wrote in blackboard its hypothesis and its thesis:
Since then, we have applied this theorem a lot of times for saving us the time to calculate the cutting points of -axis and, more important, my students know firsthand why mathematical reasoning is.
]]>What is the difficulty we need to teach to our students? Sometimes we teach things in a hard way because our teachers, in the past, taught us this way. But perhaps we could think about why we need to teach that way. In general, we could teach one thing more easyly if we don’t need it afterwards and so, we don’t need rules. The rules should be simplifications or generalizations after several rutine repetitions^{1}. I’m going to explain it with an example: how can we teach how to calculate ?^{2}
We could do applying the formula :
But we don’t need it. We surely have got our students confused. And we would introduce a mathematical arsenal that we will not need.
We could do as a product: . So we could apply distributive property.
This reminds our students the “rule” seen before, but surely most of them will have a mess after their application. And surely most of them would not understand what would be doing.
Why not teach simply as we can: . So let’s multiply it.
This reduces the unexpected thing to familiar and known thing: algorithm for multiplying integers.
When does we need to know the formula ? In my opinion, only when our students need to expand expressions like many times or if they needed in order to solve a major problem (in which it is embeded) and they need not to spend their time in calculations (like they do in third way).
Note: for making this article, I used SimpleScreenRecorder for recording an specific area of my desktop while running LibreOffice Writer formula editor and Geogebra. For conversion from webm
to animated gif
I used ffmpeg
.
Update: Fred G. Harwood (@HarMath) suggested we could calculate it also visually. It gets better understanding to students and avoid typical errors.
But sometimes (many more than it should be), the rules are taught before they are needed.↩︎
I need it to teach it because I want it to pass from the form to the form for treating quadratic functions. In particular for representing that in cartesian plane. Yes I know we could represent directly (and more easyly) quadratic functions in the form .↩︎
I notice that this site is stored in Wayback service (belonging to Internet Archive) on date of April 1st. This is good news because this means this site is not so unimportant.
]]>Recently, I bought three books:
Here is a photo of the whole set:
I don’t know if I will have time to read them before next course.
Goyal, Nikhil. 2016. Schools on Trial. How Freedom and Creativity Can Fix Our Educational Malpractice. Doubleday.
Horn, Lani, and Tina Cardone. 2016. The Best of the Math Teacher Blogs 2015. A Collection of Favorite Posts. Amazon Fullfillment. https://www.amazon.com/Best-Math-Teacher-Blogs-2015/dp/1530388902.
NTCM. 2014. Principles to Actions: Ensuring Mathematical Success for All. National Council of Teachers of Mathematics (NCTM).
———. 2015. De Los Principios a La Acción: Para Garantizar El éxito Matemático Para Todos. National Council of Teachers of Mathematics (NCTM).
Fa temps que cerc una manera per organitzar els meus documents de classe, sobretot una manera efectiva d’ordenar les activitats.
Fins ara usava carpetes al meu ordinador, on tenia diverses activitats, separades per nivells. Freqüentment juntava les activitats en documents (sobretot en format ConTeXt). Però amb aquesta organització tenia diversos problemes:
Fa temps que vaig fer-me un script i vaig pujar les meves òperes en tres actes al servidor. Ara bé, això tenia limitacions: havia d’escriure les òperes en format html i només servia per a òperes i no per a altres activitats.
Després de pensar molt i molt, me n’he adonat que l’estructura de blog és ideal per això: una entrada (activitat, document, el que sigui) classificada (normalment usant etiquetes). Així tothom pot trobar fàcilment el que cerca (per exemple “qualsevol cosa relacionada amb funcions afins”). Aquesta darrera setmana m’he posat mans a l’obra i amb l’ús de gostatic
he creat un repositori d’activitats, documents, òperes en tres actes, etc. L’he anomentat "*theque"
per allò de què és una col·lecció ("teca"
) de qualsevol cosa ("*"
).
Encara és una versió beta, però és totalment funcional. Tenc pendent ara passar totes les meves activitats a aquest repositori. Hi podeu accedir aquí: theque.somenxavier.xyz
The use of the arithmetic mean for assess people (in particular students results) is strongly used. But is it the best, or at least optimal, assessment function? What do I mean here? Perhaps we could assess students in diferent way, obtain a number (or [letter](https://en.wikipedia.org/wiki/Grading_systems_by_country “Wikipedia. Grading systems by country. 2016”")) with different procedure. I’m not discussing here the fair of the assessment function (there are a lot of means there) but the didactic aspect of that.
This is my proposition: use additive function. If you have marks, , why instead of calculating arithmetic mean just add them up. This has a lot of advantages:
The only disavantage I know is that you have to be aware of how many test/activities students will get. Because otherwise you could not say “If you get 50 points, you will pass the course”. If students missed tests, then you/they have to re-escale it (perhaps an excuse to talk about proportions ;).
By all these reasons, the additive function will be my next assessment function next course^{1}
Right now I can’t modify the existing rules.↩︎
Estic totalment d’acord amb tot el que diu Eduard Vallory i Subirà a la seva presentació “A disruptive upgrade in education” del TEDxReus [1, 2]:
L’única pega que li veig és la legalitat: es pot assegurar que un professor que imparteixi classe disruptiva no tindrà problemes legals?
En resum, quines garanties (legals) tenim que podrem anar en contra del sistema imperant?
In Spain there are three types of schools:
I only know how the system of public schools works, in where I have teached for 13 years. In particular, the system of Balearic Islands.
There are two types of teachers in public schools: civil servants^{1} or temporary employees. Both kinds of teachers could receive training but they have no obligation to do that. The motivation to get training in both cases are a) getting points to choose the school you want to teach and b) earn more money. The points have a maximum, so it has no sense to get training from a certain moment. This leads to taking courses just for making points. In general, teachers choose easy courses but with no didactic interest.
The courses are offered by the Government itself and private organizations (typically labour unions and universities). When private organizations made a course, the Government has the right to accept or decline. If it’s accepted, the course is homologated. Only homologated courses are valid for making points and, even, to be recognized.
In my opinion que quality of the courses is, at least, arguable. The following are the main categories in which the courses offered, right now, by the Goverment (CEP Manacor, WEIB) and by some unions (ANPE, STEI presencial, STEI distància) belong to (in parentesis the number of courses and the rounded percentage of the main categories):
As you can see, there are not too much courses about making hooking activies (like could be 3-act operas) and making a non-traditional classroom. The research from internet, reading interesting blogs (like Mr. Meyer’s one) and finding MTBoS community is the only alternative that I have found against that. As me, very much people in my region.
I hope in other countries get training could be more useful than in mine. Please comment if you want to share how it works in your country.
They passed a public exam which is made by Government↩︎
I’m not joking: there are several courses just for hiking and, in theory, explain the scientific features of the route. See for example “Excursions per Palma. Les seves manifestacions artístiques” which could be translated as “Trips around Palma. Its artistic manifestations”↩︎
Legally, I have to teach standard deviation . But really I have to teach standard deviation? In low levels of secondary education I do not teach it. I teach mean deviation, . Why:
The only disadvantage I think we would have if we teached the instead of is that we could not take the most references in scientific literature, which use . I thought about it many times. And I think that the reason, the real reason, for which mathematicians use instead is because, as a function, it’s derivable and is not. So it allows getting easy bounds with known distributions (like gaussian ones).
A range of the sample could be another one↩︎
I accustom to pass a (anonymous) poll to my students at the end of the course^{1}. With this, my students can assess me and I can see what are my good points and what have to improve in the next course. I think this time is the only oportunity they have to express their opinion about their teacher (me). I am not scared about any result, because I trust that the mean of the results and common sense compensates the optimal and pessimal opinions.
Here is my poll (translated from catalan):
You can download the pdf and its source.^{2}
Here are my results until now since I have taught in adults school:
I could say that:
So I have to improve the contents (they have to be more real life and interesting contents) and participation (the students lack of participation). For doing that, my plan is to change from traditional manner of doing class to a problem-based one. I do not know how I will do it but now, with the helping resources of MTBoS, the transition will be, surely, more smooth.
On the other hand, another important question is which items you consider important for making a teacher assessment poll? Perhaps you could comment it out…
I completed the assignments of MTBoS mentoring program (aka 2016 blogging initiative).
I think it deserves an informal assessment, at least. After the MTBoS blogging initiative I got:
Update: I decided to create a certificate which accredites that I post 4 of 4 posts (as I can prove):
The logo is made using GIMP from logo of 2016 blogging initiative + Pixabay logo of certificate.
Explore the MTBoS. 2016a. “Week 1 of the 2016 Blogging Initiative!” 2016. https://exploremtbos.wordpress.com/2016/01/10/week-1-of-the-2016-blogging-initiative/.
———. 2016b. “Week 2 of the 2016 Blogging Initiative!” 2016. https://exploremtbos.wordpress.com/2016/01/17/week-2-of-the-2016-blogging-initative/.
———. 2016c. “Week 3 of the 2016 Blogging Initiative!” 2016. https://exploremtbos.wordpress.com/2016/01/24/week-3-of-the-2016-blogging-initiative/.
———. 2016d. “Week 4 of the 2016 Blogging Initiative!” 2016. https://exploremtbos.wordpress.com/2016/01/31/week-4-of-the-2016-blogging-initiative/.
[This post is part of MTBoS mentoring program. This is post number #4 and is related to “Questioning” topic.]
Quadratics is the first unit I have to teach in ESPA 4. This is a course of adults education in Balearic Islands (Spain). What the students should know to do at the end of this unit are:
I have split the unit in three parts according with these aims. So there are three parts, which seem unconnected:
For introducing this topic, I put this problem^{1}:
From this point, we make problems of finding the dimensions of a square with a fixed area.
After that, I put the analogous problem with a rectangle and we see that there are infinite solutions. So we have to restrict the problem: perhaps the height of the rectangle could be something related to the width. For example, the height could be 3 times the width. Also we trait the triangles:
But we restrict our dependency to number times a dimension. In this step all the 2nd-grade equations are of the form .
Then, we make a small change: the dependency of one dimension is a number plus the other dimension:
With this kind of problems, we get complete equations (of the form ). After that we practice solving 2nd-grade equations. Just equations, no problems.
In this part, I remember the cartesian plane and how we could read or write coordinates and points to/from it. And inmediately I teach how to represent quadratic functions and we just “resolve” exercises of representing them:
It is supposed that this section represents the real applications to all of the previous stuff. But I can’t achieve what is pretended. A sample of my problems is this:
(in the last two problems of this sample, the students have just to apply a formula)
I have never been able to find optimization problems which are real, easy and interesting.
Meyer, Dan. 2010. “Will It Hit the Hoop?” 2010. http://blog.mrmeyer.com/2010/wcydwt-will-it-hit-the-hoop/.
Teaching Channel. 2015. “To the Moon!” 2015. https://www.teachingchannel.org/videos/paper-rocket-lesson-plan.
All the problems here are translations from their original ones in catalan.↩︎
[This post is part of MTBoS mentoring program. This is post number #3 and is related to “Questioning” topic.]
“What would you need for making a shoe fabric in your town?”. This is the first question I ask to my students when I start the statistics unit.
They answer several things: a plot for making the building, electricity, machines for making shoes, etc. But, and the end, I say “Yes. All of this stuff it’s needed, but what would you really need for switch on the machines?” and then, if there is no answer to that, then I put a clue “What do you do, first of all, when you go to shoe shop?”. Eventually, the answer becomes “The shoe number”.
And “how is the shoe number that you would manufacture first?”. And then obviously we have to determine what is the most frequent shoe number in our town. So we have to make a poll? But how to do that? I introduce the concept of poll, population and sample. Assuming that our classroom is non-biased sample, we list all the shoe number of my students^{1}. This naturally introduces the frequency table (because we have a middle size sample) and the Mode.
This example of shoe number could be more useful. Depending on the course, then we represent the shoe numbers distribution and see what are the intervals of numbers with are the most frequent (in particular, the median).
This makes me introduce Statistics without having to be so magisterial and, with this, I realized that open questions are always good for introduce topics and engage students.
and usually their parents and siblings too. If you would make a non-inmediate poll, you could send it as a homework.↩︎
[This post is part of MTBoS mentoring program. This is post number #2 and is related to “My favorite” topic.]
I work in an adults school. My official curriculum stablishes that my students of the last course, ESPA 4th^{1}, have to make an scholar’s work about anything which “involves mathematical ideas and procedures” and they have to deliver a memorandum of the following process and their main conclusions. The teacher has to guide them through the process. This is my favorite.
When I change from teenagers education to adults school, this was my main challenge. I had not done this before. After two years in the adults school, I can defend myself against this. My main constraint is the time: the time for doing the work is very limited. My course is just 4-month course and I have to teach 3 lessons. So a month per lesson. And we have one month for the work. And they have to redact in a scientific style the work and they usually do not have any idea of how to do it. So, how do I do?
I have 4 classes per week. In the first month, I spend one class per week to make a mock work^{2}. We try to answer to the question: “Which is the most non-contaminant can in the market?” It serves to us to see the 5 phases in a scientific work:
After this mock work, I push them out for thinking their question of the work. In my opinion “Without question there is no answer to give” and so there is no possible work. After a month, if someone does not have any question, I give them a list of possible questions or topics.
After that, I continue normal classes and I assign them a big homework: start the research and feedback with me any progress, difficulty or decission they’ve made. In this moment I use the theorical authonomy of 18+ years persons^{3}. I encorage to share and ask me anything in any moment, in any class, via email or in the flesh. I remember their duty to deliver the memorandum, I ask them how is their progress once a week and how close is the deadline.
In the final two weeks of the course, they write the memorandum. This is the most difficult thing for them. Telling things in assay mode, reasoning each step, giving reasons of each assertion and being impartial are very difficult things for them because they usually do the contrary. I have to teach them “Linguistics” instead of Mathematics.
At the end, it is worthy: each student ends with an answer to a question. The answer could be less or more “developed” (with more or less confidence in its argument) but each of them achieve to solve the question scientificly^{4}. The following are the titles of some works (translated from catalan, their original language)^{5}:
which I think it is formally equivalent to 10th grade of USA↩︎
My students have not written a scientific work. If I want they to write it, they need at least one chance to learn.↩︎
I suppose that we have to guide the teenagers…↩︎
Obviosly there are students who don’t pass the work, but normally it’s due to their absence of work not due to the lack of reasoning in their argument.↩︎
Any mistake with the translation is mine↩︎
This post is part of MTBoS mentoring program. This is post number #1 and is related to “One Good Thing” topic.
One of the aims of my official curriculum is to discover regularities and patterns. Another one is to plot afine functions and knowing that the formula is associated with (straight) lines and other types of functions correspond to curves. Since two courses ago, I have combined these aims letting students discover by themselves this relation. This is the chronicle of how I have done this year (this week).
Before threating the problem of differentiating curves or lines from the algebraic formula, we need several preliminaries. The first is to know the cartesian coordinates. In the first classes, I explained what is the cartesian plane, what are the axes and I gave some terms like origin and quadrants. Then I gave exercises of reading coordinates from points and to draw points giving their coordinates (see the picture above). Since this point, we will identify the points and their coordinates.
After assuring everyone knows how to read and write points to the cartesian plane, I started to represent functions. I put a simple formula in blackboard (like ) and asked what are the points which satisfy the equation. Then we plotted these points and we got the representation of the formula. We represented several functions: for example , , or , calculating the tables of values of and . We saw the impossibility of knowing exactly what the graph of the function is exactly, because we represented only a finite number of points but the graph itself has infinite number of those. So we had to guess the form of the graph corresponding to one formula.
This is a workout exercise. After that, students know that there are a lot of possible graphs which could generate a formula and they are self-confident representing functions. Then, I asked them:
For knowing that, I asked students to list a bunch of functions (we put in the blackboard) and then I asked them to conjecture their rule (their relation between graphs and formula). The rule could be simple or complex as they want. They choose. If they have not guessed any rule, then I suggest to represent as many function as they need for getting the guess. And if they got the rule, I ask them to prove or falsifying. Falsifying is always possible: we just need two graphs and two formulas which contradicts the rule. But we learnt that it’s impossible to prove the rule with their tools. And even we knew that there are rules more general than others and rules which implies other ones.
This week, the rules are:
Next day, we checked these rules and I informed which “proved” rules are really true or false (read mathematically proved). See graph above (in catalan). Sorry for the quality.
After that, I asked them if there is a rule to know if a functions gets a line or curve. And we deduced that we get a line when the formula is .
After that, because it’s needed only two points for defining one line, then when we would represent a function of the form (that we have learned that is a line), we will need to calculate just two points in our table of values.
I love this experience because it’s very exciting when students deduce their own rules and try to prove or disprove them. We feel like a really mathematicians. I strongly recommend you to apply in your class. Obviously you could use Geogebra or other interactive tools instead of blackboard.
]]>Some time ago, I enrolled in the MTBoS mentoring program^{1}. Yesterday, I received an email from my mentor, Stephen Cavadino (@srcav), to whom I answered. I have a lot of hope with this mentoring program and, surely, he will teach me a lot of things which I could apply into my classroom..
On the other hand, I enabled comments in posts (via isso) for allowing feed-back with blog readers.
MTBoS stands for MathTwitterBlogoSphere↩︎
I decided to study the problem of how to pass from a lesson-based classes to task-based classes. I realized that I need books, articles or some kind of information which provides me the “theory” of how to transform my classes into task-based ones.
For now, I bought “5 Practices for Orchestrating Productive Mathematics Discussions” and “5 Practices for Orchestrating Productive Task-Based Discussions in Science” of National Council of Teachers of Mathematics. I hope these books give me the ideas that I need.
]]>In summer of 2013, I attended XVI JAEM. I went to several conferences of Anton Aubanell and Sergi del Moral. When the JAEM was finished, I planned the classes for the next course. By this reason, I visited the web page of Sergi del Moral^{1} looking for new educational resources. Via this post, I discovered Dan Meyer’s site and I was atonished with the philosophy behind 3-acts activities.
Because I was new in my school and I had not serious experience with adults education, I had no time to incorporate these activities into my classes. However, I decided to do that in some near future. Meanwhile I added Dan Meyer’s site to my RSS reader. One of his posts, pointed me to Greoff Krall’s site and I used his “guide” of how transform routinary activities to interesting ones^{2} for making a matching activity among domains, graphs, algebraic expressions and tables of values (Bordoy 2014).
It is two years since this decision and it is the time to action. I want to teach somehow different, with the minimum of magisterial sessions as I can. Three-acts operas are one way of doing that (Geoff Krall sneaky activities are another). So the plan is to create and use 3-acts operas as well as other non-magisterial activities for improving my classes.
Sharing is great and I appreciate the work of Dan Meyer, Geoff Krall and other teachers who share their work without any other interest but the appropiate credit and community feedback. I want to do the same. So here is my blog. I would be very glad if some material is good for you. Meanwhile, the blog could serve me as a documentary tool.
Bordoy, Xavier. 2014. “Activitat d’emparellament de Domini, Gràfica, Expressió Algebraica I Taula de Valors.” http://somenxavier.xyz/bitacola/blog/01-matching-dominis-grafiques.pdf.