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I've been interviewed for the Newsletter the school sends to families, its a way of introducing ourselves to them. The interview can be publicly accessed following this link, I felt like translating and sharing my answers here.
Presentation: Name, position in the school and for how long have you been a member of the teaching staff.
Presentation: Name, position in the school and for how long have you been a member of the teaching staff.
As I tell my students when we meet for the first time: "My ID says my name is Ignacio Santa-María Megía, but I am Nacho". I'm a Secondary Maths teacher and MYP Coordinator (the Middle Years Programme is like Secondary in the IB, the International Baccalaureate), I've been at the school since 2011 also teaching Technology and Entrepreneurship some years.
What made you choose Mathematics as your professional and educational career?
What made you choose Mathematics as your professional and educational career?
As a student I only liked two subjects: Maths and PE, none other. I even used to ask my Maths teacher for extra tasks, but he reminded me to first do the homework of the rest of the subjects (he knew I didn't always finish them). When I got to choose, I knew I wanted to study Maths, nothing else made sense (pun intended).
Luckily by then, nobody wanted to study Maths and it had no cut-off grade, I don't think I'd make it nowadays because they finally realized that what Maths provides goes far beyond knowing a lot of Mathematics. Now, it's one of the degrees with the highest cut-off grade.
As I tell my students: "Maths is about thinking and solving problems" and that's what the degree trains you for. In the past, people thought that studying Maths would only lead you to being a Maths teacher; now we are highly recognized and valued.
In all honesty, and I am clear with my students about this, I never wanted to be a Maths teacher, I wanted to do research at the university. When I finished my degree, I mastered in Mathematical research and started my PhD, but I abandoned when I realized I would have to compete with my fellow PhD colleagues for a position, and they lived for studying; but me not that much. As luck would have it, I started teaching private lessons for my own economic independence while still studying Maths and I started to take a liking to teaching. I wasn't a usual private lessons teacher, I wanted my pupils to understand, not just learn to do things. So I chose Maths but teaching chose me.
It's frequent to fear or even reject Mathematics. What do you do to spark the interest and motivation of the students towards the subject?
It's frequent to fear or even reject Mathematics. What do you do to spark the interest and motivation of the students towards the subject?
In her book Learning to love Math, neurologist Judy Willis states:
"No other school subject pushes emotional buttons the way math does."
"No other school subject pushes emotional buttons the way math does."
This is a very tricky topic. Maths can be ungrateful, effort doesn't always pay off and that's frustrating, this could lead to the so-called "Math-anxiety" which has been largely researched and a lot of time invested in it. I have a theory: aside from the first time we hear a no, when learning to dress up, to put on our socks or to tie shoe laces, it's probable that one of the first times we experienced frustration is with Maths, at least consciously. So, our frustration tolerance and management kicks in.
It has been studied that the frustration caused by not achieving a goal can lead to boredom and disengagement or anxiety and mental blocking, depending on how much we value the target. Additionally, it has also been studied that in order to gain deep understanding there ought to be some degree of frustration, understanding requires a cognitive conflict, something we don't immediately know and that we must "decipher".
As a secondary teacher and mostly of the first years, I'm used to seeing students that believe that Maths is about memorizing and applying recipes. I tell them that I don't teach Maths, I intend to teach them how to think using Maths as an excuse. They complain a lot, I will always remember a student who is now finishing high school that once shouted in the middle of the class "Why are you making us think?!" to what I answered with a loud laugh and a "Thank you for the compliment".
Some students feel like Mathematics is of no value to them, that knowing just the basic operations is enough, they don't understand how it would contribute to their lives knowing how to solve exponential equations, factor polynomials, solve a limit or an integral, etc. They lack the sufficient maturity to realize that it is not about learning to do all of that (though for the SAT it is), but about being able to do it. What I mean is that in order to be able to do all of that, they need to know some rules (ideally understanding them) and use them to solve a problem; and, in life, we are going to do the same with other rules and other problems.
We learn to solve problems (not necessarily math ones) by solving problems (also not necessarily math ones). A problem is a situation I don't immediately know how to solve, otherwise it would be just an exercise.
It is difficult to tackle the lack of interest or motivation towards the subject, some are only interested in their grades, which is a pity on one hand but an entry way on the other. We usually don't like the things we are bad at and we normally like what we are good at, so I try to facilitate the achievement of goals in order to congratulate them and foster a change in attitude towards the subject.
I try to provide each student with the opportunity to answer correctly to questions that require some thinking and if they can't, I think aloud with them so they get a grasp of it and learn for the next time. There is also research about that showing the relationship between effort and progress strengthens certain neuronal connections that can have an effect on self-esteem and shift the attitude towards Maths in particular.
In your opinion, what importance do Mathematics have in a well-rounded education, beyond academics?
In your opinion, what importance do Mathematics have in a well-rounded education, beyond academics?
I believe that I have already answered this question, Maths teaches how to think properly, and what's more important than that?
Furthermore, as I have also said, Maths can be frustrating and learning to deal with that frustration can probably help to learn how to manage frustration in other circumstances of one's life.
What innovative methodologies are you using in your classroom to make Mathematics learning more meaningful?
What innovative methodologies are you using in your classroom to make Mathematics learning more meaningful?
At our school we follow the MYP, it provides a teaching and learning framework with a clear inquiry-based methodology. Additionally, over these years I've had the opportunity to develop professionally with courses like Teaching for Understanding (TfU), Project Based Learning (PBL), Cooperative Learning, Service Learning, Flipped Classroom (FC), Thinking Based Learning (TBL) or Gamification. Thanks to the ideas of Flipped Classroom I managed to pull off the 2019-2020 schoolyear under the confinement because of COVID-19, but I have never used FC again.
I've tried several methodologies and kept the ones I think work better taking into account the characteristics of the subject and my own way of being, I mostly use TBL and TfU.
We are currently following Innovamat 's program in the first two years of secondary (Gr 7 & 8 or MYP years 2 & 3), which are the grades I've been teaching for the last couple of years. This is our third year with them and it is based on the state of the art of Maths didactics, it is about teaching how to think and foster comprehension, just what I was already doing but with a pedagogic, mathematic and design team behind that provides rich and visually attractive resources. Before counting with them, Maths contents in secondary where taught in a different order and depth, so I no longer do some of the things I used to do.
For example, during the confinement I attended a workshop under the XI Escuela de Educación Matemática Miguel de Guzmán about MathCityMap for developing Math routes that crystallized in "De Geometría por Vegueta" which I could do with students the following two years. Also, together with my colleague Iván Pulido we developed the project "Yo sé resolver problemas con ecuaciones" [I know how to solve problems with equations] awarded with the Best Innovative Educative Experience in 2019's SIMO and which I presented in the VII Congreso Internacional sobre Aprendizaje, Innovación y Cooperación (CINAIC 2023), it is based on the research about the benefits of problem posing by Maths students. We both have also developed various gamifications and delivered Break Out EDU workshops in national congresses by the Google Educators Groups Comunidad Profesional para la Transformación Educativa GEG Spain.
For some years I also conducted "Las mil y una demostraciones sin con palabras del Teorema de Pitágoras" [One thousand and one proofs without words of the Pithagorean Theorem] performing oral expressions in Maths Class where students had to put words to proofs without words of the famous theorem. I got to present this activity online in the V Encuentro GeoGebra by Sociedad Canaria de Profesores de Matemáticas (SCPM) "Luís Balbuena Castellano" [Canary Islands Mathematics Teachers Society] and in person in 2023 at the I International GeoGebra Congress.
Now with Innovamat I don't feel the need to innovate to fill a gap anymore, they truly have thought of everything, at least until I come up with a new idea.
What's the influence of technology over the teaching and learning of Mathematics nowadays?
What's the influence of technology over the teaching and learning of Mathematics nowadays?
Like Marcos Marrero says (one of the OAOA movement promoters - Other Algorithms for the Arithmetic Operations - which has just started being applied in the first four primary grades at our school):
"A lot of time has been spent traditionally to improve calculating by hand with big numbers and decimals, but this doesn't make sense anymore since we can use a calculator to do it. No one uses logarithm tables to compute them anymore. Thanks to the calculator we can focus on understanding numbers (the so-called number sense), estimating results to know if we are on the right path or thinking carefully about the most efficient way to solve something."
"A lot of time has been spent traditionally to improve calculating by hand with big numbers and decimals, but this doesn't make sense anymore since we can use a calculator to do it. No one uses logarithm tables to compute them anymore. Thanks to the calculator we can focus on understanding numbers (the so-called number sense), estimating results to know if we are on the right path or thinking carefully about the most efficient way to solve something."
Taking into account that Marcos (and myself) defend the necessity of developing calculation skills, but there is no need to torture with endless worksheets with multiplications of three digits times three digits, it is more important to acquire different strategies to make the same operation in order to make it more efficiently so that calculating by hand would serve, eventually, to improve mental calculation skills. The calculator allows us to focus on what's important.
Aside from the calculator revolution, our present digital technologies allow students to access information (notes, exercises...) just from their pockets and in a classroom from their Chromebook or iPad. Additionally, I can present resources that foster inquiry and comprehension on the smartboard. And, moreover, Innovamat has a weekly digital practice with a personalized itinerary which includes exercises about the last things learned in class and from past lessons that adapts to the performance of each student levelling up or down its difficulty.
It's thank to ICT's that I could develop the resources mentioned above.
Based on your experience, what key skills do students develop when facing mathematical challenges?
Based on your experience, what key skills do students develop when facing mathematical challenges?
If you mean the key competences established in the Spanish law of education (LOMLOE) and recommended by the European Union Council, the ones Maths mostly help develop are the following:
Literacy: Students must have to show their reasoning (as I say to my students: the process is what matters).
Numerical, scientific and engineering skills: Obvious.
Digital and technology-based competences: Thanks, not only to the calculator, but spreadsheets or visualization tools like GeoGebra.
Interpersonal skills, and the ability to adopt new competences: Like I said before, Maths helps to learn how to manage frustration.
Entrepreneurship: The skills required for innovation or entrepreneurship are the ones developed when facing challenges or problems.
What advice would you give to the families for supporting Maths learning from home?
What advice would you give to the families for supporting Maths learning from home?
There is something curious with education in general and with Maths in particular, we all went through the education system and many people believe they are entitled to their opinion. When an electrical appliance breaks at home and you call a technician, you don't think of criticising how the repair is being done. If you have a water leak, you don't give your opinion about how the plumber fixes it. Unless, if for some reason you don't trust the repairman, in which case you'll call someone else, right?
In my opinion, the families shouldn't loosely opine or criticise they way their children are taught, in my view they only show mistrust in the teacher, which the kids perceive, affecting their learning ability. I'm not saying that there shouldn't be criticism, constructive criticism is necessary, but if the criticism is constant and unfounded, I think it is rather mistrust or insecurity.
Families' implication is essential, we must be a team and trust each other. At the school, students acquire knowledge and develop skills, they in fact develop skills while acquiring knowledge. I believe that families' contribution must be with developing skills rather than with the acquisition of knowledge, learning happens at school, not at home. It is fundamental that families support with routines, habits, good manners, even with thinking skills when reasoning or discussing about any topic.
I don't think sitting down at home to explain something taught in the classroom should be a usual thing. There are some specific cases where a student has fallen behind due to an illness absence or because of a special educational need, in these cases I believe it would be justified.
In Secondary, most of the students with private Maths lessons don't need them. They might need someone to help them to sit down for studying or doing homework, someone who sits by their side making sure they do what they have to do, not giving a private lesson. These unnecessary private lessons have an unwanted effect, the students (since they don't need them) can afford the luxury of not paying attention in class because someone is going to tell them at home.
In primary, what sometimes happens is that some students bring their homework perfectly done to class, but are unable to defend it or to do a similar task in the class. Someone clearly helped them, or worse, did it for them. If a student doesn't know how to do some Maths homework task at home, it's better to bring to school the best attempt and tell the teacher about it, it's important that the teacher knows. There is no point explaining at home (it's not the families' role) or telling how to do it, the teacher should know what the students know and don't know, if they come to school with their homework correct, the teacher might think that everything is going well. It may happen that a particular doubt comes up at home, something they know but are unsure of, need a hint or a different approach. In these cases some help could be provided but stepping away if the doubt is more profound allowing them to ask it in class.
After suggesting the benefits of the OAOA movement for several years, I'm now monitoring closely its implementation in our school talking with the teachers. It seems there are some families rejecting it because they don't understand why Maths isn't still taught the traditional way, like they learned it. Truth is that both OAOA and Innovamat feed from the same source, the research in didactics of Mathematics, and there is proof that they improve learning of Mathematics compared with a more traditional way of teaching them.
There is another cite from the book I mentioned earlier which I think is very relevant to this regard:
"Many parents of today's students learned math by doing worksheets and drills, and they expect the same for their children. Parents who were successful in math through repeated memorization skills (rather than strong concept development) may resent alternative math instruction, such as inquiry and manipulatives, for their children. A possible result is that some parents may feel frustrated when they can't help their children with the unfamiliar homework."
"Many parents of today's students learned math by doing worksheets and drills, and they expect the same for their children. Parents who were successful in math through repeated memorization skills (rather than strong concept development) may resent alternative math instruction, such as inquiry and manipulatives, for their children. A possible result is that some parents may feel frustrated when they can't help their children with the unfamiliar homework."
In summary, families can help making sure the students sit down to do their homework or study and even monitoring if they are doing so. They can help studying by asking about the content, arguing... But it doesn't help if they explain the topic, with the exception of those particular cases in which it could be justified, they must let the teachers do their job, and they can't if they think their students know, when it's unreal.
Just one last thing about the private lessons, the objective should be that the students understand and not just learn to do, the objective should be to learn and not pass or getting a good grade which would be a consequence of having learned. This reminds me of the quote "Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime." So lets teach fishing.
And to conclude... Could you recommend a book, a film and a song?
And to conclude... Could you recommend a book, a film and a song?
My favourite book as a child was The Never Ending Story, I couldn't literally stop reading it. If I had to recommend a book nowadays it would be The Infinite Pleasure of Mathematics by Alessandro Maccarrone, it's a book that shatters Maths difficulty, though it is only in Spanish.
Instead of a film, I stick to a show: The Sopranos, like a friend of mine used to say, as a whole, it's the best film ever.
It came to my mind the song A desobedecer [To disobey] by el Kanka, a songwriter from Malaga whom I've watched live several times, the first of which in 2012 a meter away in a room thanks to a series of concerts organized by Cantautores en Vegueta [Songwriters at Vegueta].
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