BarcelonaThe latest PISA report has shown that the level of mathematical competence of Catalan students has plummeted. In just four years, 21 points have been lost in the OECD tests, a drop equivalent to going back an entire school year. Beyond the poor position of Catalonia in the international ranking, several voices have raised their cry to heaven, assuring that it is difficult for them to understand how 15-year-old teenagers could not solve “apparently easy” mathematical problems. But what has gone wrong to get to this worrying situation? We asked two high school mathematics teachers and a mathematics teacher trainer.
“Apart from the effect of the pandemic, in Catalonia there is a very specific problem: the vast majority of mathematics teachers do not know how to apply or do not believe in the new curriculum that places more emphasis on the need to work on mathematical competence” points out the professor of mathematics at the Vidreres Institute, Raül Fernández. The teacher, who is also president of the Association of Mathematics Teachers of the Girona Regions (Ademgi), criticizes that in most classrooms they continue to bet on rote work and repetition, but forget – or have little account – problem solving, and “it is precisely this aspect that PISA values the most”.
Students know how to make equations and algorithms, but do not know how to use them. ”
This vision is also shared by the president of the Federation of Entities for the Teaching of Mathematics in Catalonia (FEEMCAT), Carme Vicens. “The problem is big and it must be faced in a brave way,” he warns. Vicens, who is also a mathematics teacher at the 3 d’Abril high school, explains that the OECD tests promote “deep mathematical reasoning”, which is in the same line as the latest approved curricula. However, in Catalonia these have not “curdled” among the teaching staff. “We feel more comfortable working the way we learned, which may be better or worse, but it’s what we know,” he acknowledges.
The result of this discrepancy between curricula and methods is as follows. “Students know how to make equations and algorithms, but they don’t know how to use them,” points out Lluís Mora, mathematics teacher trainer and recently retired secondary school teacher. Mora explains that, at present, in most classrooms, mathematics exams are given in which, out of ten questions, eight are to solve equations directly (be it exercises for calculating fractions, divisions, multiplications, etc.), and only two questions are problems. “We understand a problem as something with a statement that you have to interpret, translate it into mathematical language, and know how to connect that with your knowledge to see what mathematical tools you’ve already learned to use that you can apply to find the solution. And then know how to justify why you did it that way,” explains Mora.
To translate what the trainer explains on a theoretical scale, Vicens gives a practical example. “You can work on the calculation of areas by putting a list with a series of figures and have them calculate them. This may be good for them at a given moment, but it does not help them to face a real situation if they have never practiced it” , raises On the other hand, the teacher points out that if the calculation of areas is first worked theoretically and then they are asked to solve a problem, in which “they have to set up the party at the end of the year, they have a yard with specific dimensions and they have to see how many people they can fit and what shape and size the chairs are,” the situation is much more complex. “Apart from calculating the area, they have to reason about what shape the chairs are and how to place them. So they continue to practice how to calculate an area, but they see the meaning and in the future they will be able to find the connection between the problem that they have in front of them and the tools they know,” he insists.
Fernández also points out that to achieve this connection there must be a significant effort from everyone: “Obviously, making problems is more difficult and costs them much more, but we have to make them see that solving them is what’s cool, and knowing how to do the equation is only the beginning. But for that they have to do a lot of problems in the classroom, but also at home.”
The hole between the excess and the defect of theory
The three teachers explain that it takes a lot of time to be able to do these exercises of applying the tools learned to real problems. “The classes are still the same, and the time we used to spend purely on teaching content, we now have to divide it between that content and its practical application. The result of this is that less progress is made in mathematical knowledge more traditional,” Vicens describes. Both the president of FEEMCAT and Fernández explain that this is one of the reasons why at home parents have the feeling that their children are not learning enough mathematics and they hear complaints that some students are not memorizing the multiplication tables. A situation that Fernández clarifies: “It’s clear that if they know the multiplication tables, everything will be easier for them; but for those who don’t, we now also teach strategies so they know how to find the solution to problems.”
But then, if PISA is more competitive and is now opting for this route, why haven’t better results been obtained? “Those who are now in ESO have already experienced this change of working more with skills, but those who took the tests in 2022 had done all of primary and secondary school with a system that did not work so much on this resolution of problems and this, he explains, is partly because the results are what they are,” suggests Vicens. And here Fernández adds one more fact that explains why the level of mathematics has dropped everywhere (although more markedly in Catalonia). “The isolation of the pandemic has increased math anxiety because these teenagers have had to learn without interacting with anyone and therefore have been left alone with the problem. You can learn history alone at home, but math is almost impossible,” he says.
This scenario could lead one to think that in the PISA tests of 2025 the results should go back up, but Mora warns that in order to achieve this, the competence training must reach all teachers and not only those who “believe in it”. In addition, the trainer also insists that it is necessary to accompany and follow up to ensure that the application of these methodologies is effective. “It’s one thing for them to learn how to do it and the other for them to be able to apply it in the classroom every day,” he warns.
2023-12-14 06:46:04
#teach #solve #equation
