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La evaluación del aprendizaje de las matemáticas: ¿Qué propósitos y sentidos legitima? — Transcript

by UED – Educación Matemática · 2,045 words · 341 segments · language en · Watch on YouTube

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0:00I reiterate my good morning to the
0:02professor, to Professor Olimpia,
0:04Professor Ángel, and Pedro Gómez.
0:08Thank you for the invitation and to
0:10Paola for all the management, and to
0:12the students and professors
0:14accompanying us. I want to point out
0:18that the purpose of this participation
0:20is to establish a framework for
0:22reflection on the link between learning
0:25assessment and the aims of the
0:27education project. mathematics. I seek
0:32to highlight the ethical-political
0:34nature of assessment in order to
0:37problematize the absolutization of
0:40assessment judgment, both in
0:42standardized tests and in the
0:44mathematics classroom. I will use as a
0:50methodological strategy performing two
0:52analyses first. One on how the
0:57absolutization of assessment judgment
1:00interrelates with social and cultural
1:02inequalities, and then in secondary
1:05mathematics classrooms, how students
1:07are constructed by the meaning of
1:10assessment. And finally, to close with
1:15the possibilities and tensions of a
1:17project that tries to relate assessment
1:20to the purposes and meaning of
1:22mathematics education. This
1:27presentation, let's say, this
1:29reflection, is part of the initiatives
1:32of a study group that began in the 90s
1:34with stud-mathematics professors,
1:41students of the Master's in Mathematics
1:44Teaching at the National Pedagogical
1:47University, with references to the
1:50social and political dimensions
1:52proposed by Valero, by S-as you, by
1:55Candia Morgan, by Chevallard, who also
1:58problematizes assessment and its
2:01ethical meaning, and others like Rogel
2:04Gutiérrez. So, we began to make a
2:08shift in the understanding of the
2:10assessment problem to establish and
2:13analyze the conditions that shape the
2:16learning of mathematics as part of the
2:19evaluable process. We have conducted
2:24empirical research in mathematics
2:26classes located in public secondary
2:28education and situated in contexts of
2:30poverty. Here we integrate all the
2:36research that has been done in Latin
2:39America on teaching and learning in
2:41contexts of poverty, because it is also
2:44a research question whether or not
2:47these contexts require and demand other
2:49pedagogies and other strategies. The
2:55research, the mathematical knowledge
2:57that we have related to the proposal is
2:59everything that in Colombia, in
3:00curricular guidelines, is called
3:02variational thinking. This is a
3:06publication we made, the first on
3:08assessment practices in the mathematics
3:11classroom in basic education, and some
3:14of the student teachers who have
3:16accompanied us. Well, the first, the
3:20first analysis on the absolutization of
3:23assessment judgment and its
3:24interrelation with social and cultural
3:27inequalities. I want to tell you that,
3:32in the 90s, with globalization,
3:34international educational policies
3:37focused on efficiency, performance,
3:40accountability, and effectiveness were
3:44implemented in the region, and the
3:47World Bank required all Latin American
3:50countries to establish national
3:53evaluation systems, since having
3:57information on the efficiency and
4:00effectiveness of the systems was
4:02carried out through a test, a
4:05standardized test introduced or related
4:08to the notion of competencies. Well,
4:13Colombia had already set up an
4:16institution that had begun a national
4:20passing test toward higher education
4:23with the installation of the national
4:27evaluation system and the test. So,
4:31studies began to be carried out to turn
4:34the results into information. This is a
4:37publication that circulated, which was
4:39one of the first that circulated in
4:412008 at the national level, where
4:47evaluators economists tell us, tell me
4:52what you score and I'll tell you what
4:54socioeconomic bracket you're from. In
4:57the state exams for high school
4:58graduates in the area of mathematics,
5:01students from bracket 6 have
5:03performance levels that can be 50%
5:05higher than those from bracket 1. I
5:08want to tell Professor Olimpia and
5:11Professor Ángel that the population in
5:13Colombia is also stratified by economic
5:16status. In this way, the stratification
5:21of students begins to be made public
5:23and related to their social and
5:25economic conditions. And it begins to
5:30be shown that learning mathematics is
5:33part of the production of educational
5:36inequalities, but it is also part of
5:38the reproduction of social inequality
5:41that constitutes all of our Latin
5:43American countries. The ICFES then also
5:50begins to rank schools, educational
5:53institutions generally speaking, and
5:56from the first test it began generating
5:59the ranking of the 100 best schools
6:03every year and publishing it. And so,
6:09of course, this publication, this
6:13ranking, leads schools to want to be
6:16included. All public and private
6:21institutions, I will call them schools,
6:24want to be among the 100 schools, which
6:28are also stratified by the conditions
6:31of the possibility of being selected by
6:34parents. And it begins to generate a
6:39movement to seek to be among the top
6:42100. And so the movement of the
6:46institutions will focus on the
6:48knowledge of the test, on the handling
6:51of the test, and in turn, this movement
6:54will trigger something like a renewal
6:56in the teaching of mathematics and, I
6:59imagine, in language teaching as well,
7:02to study how the test is created. Then,
7:06outside of schools, companies will also
7:09be created, testing companies that will
7:13show that schools are efficient, right?
7:18Because they handle the test. So, the
7:22methodology used, this methodology of
7:24the, sorry, this methodology of the...I
7:27lost my train of thought for a moment.
7:33This method of the test goes toward a
7:36policy that also shares the same
7:43because that mirage of effectiveness in
7:46technical validity is created. Thanks
7:49to it, one will achieve better
7:53performance on the test. In the year,
7:56like in 2009, we did a study precisely
8:01to look at the effects of introducing
8:05the test into the teaching of
8:08mathematics, and we considered and
8:12found that several students that,
8:22effectively, sorry, that effectively
8:24the students had already mastered the
8:27test, how the exam was. This is an
8:32answer from a fifth-grade student when
8:35we asked him to invent a numerical
8:38problem, and look at the structure of
8:40the statement, which is very nice and
8:43very well done, and he also already
8:46knows that you have to select a single
8:49answer. Look, the structure says: if
8:53every bear is born weighing 2 kg, how
8:55much will the bear weigh in 3 years if
8:58it gains 2 kg every month? It is truly
9:02a very good, a very good problem
9:05structure. Well, currently, let's say
9:10the strategy to update teachers with
9:13the test is called "Evaluation to
9:15Advance." What does it consist of? Well
9:20, it consists of experts teaching the
9:24attending teachers which competency is
9:28selected for the test, how the context
9:32is built, which is like a problem the
9:36teachers have, what the mathematical
9:39content component is, what it evaluates
9:43, which is the correct answer and why,
9:49and also how the answers that are
9:52incorrect are made. A belief is thus
9:57being installed, right? That the best
10:02teaching systems are due to having
10:05better assessment tools, to the extent
10:08that students can truly respond to that
10:11external demand that is being made to
10:15modify the teaching of mathematics. And
10:21to this effect of the national exam, we
10:24must also add the effect that the
10:27external PISA test already has in the
10:30country, but the external PISA test
10:32also begins to release results,
10:35establishing a relationship between
10:38those results and the project it must
10:40answer to. That is to say, it notes
10:45that if 70.2%of students do not reach
10:49the level required by PISA to be active
10:52in society, for example. So, that
10:57begins to reveal that learning outcomes
11:00are related to the fact that the
11:03education project should aim to form
11:05active subjects to participate in
11:08society. Well, the other research we
11:14have conducted is in secondary
11:16education math classes and, as I was
11:19saying, configuring and studying
11:21everything that shapes learning. We
11:26have carried it out in schools located
11:29in what are called areas of social risk
11:32. And here is a classroom; this is
11:37research we did, and as you see, the
11:39professors who conducted the study,
11:42Alberto Martínez and Nora Rojas, write
11:45that the classroom has no didactic or
11:48audiovisual resources, nor does it have
11:51school textbooks. It is a
11:55non-prototypical classroom for research
11:57, since the course is made up of 39
12:00students. The physical space of the
12:05classroom does not allow for a
12:08comfortable space for students, nor for
12:11organizing group work. And you can see
12:16in the photo how the classroom is also
12:19used to store the desks that are
12:24already broken. What do we find in the
12:27culture of the math class? It is also a
12:31culture stratified by capabilities, the
12:34mathematical capabilities that students
12:36must have. We can easily say that the
12:41class culture can be described using
12:43the north-south metaphor, and spatially
12:46, it is fulfilled in the front as well.
12:51Very close to the teacher, the
12:53successful students are located, and
12:55toward the back, the south begins, the
12:58students of the south are situated,
13:00excuse me. There is an invisible
13:05contract in the math class that has
13:07also been pointed out by the research.
13:11It is an invisible contract, but one
13:14that establishes values and assessments
13:17of student performance, and that
13:19contract also becomes visible through
13:22the teachers, right? This expression
13:25below, from a professor's research,
13:28pointed out that students do have a
13:31poor foundation, a poor foundation in
13:33values, which is demonstrated in their
13:36gestural, oral, written, and graphic
13:39expressions, and that this poor
13:41performance seems to show that they are
13:44indeed living in permanent scenarios of
13:47physical and verbal aggression. And so,
13:51it also begins to appear, as we saw in
13:54the publication of the results, the
13:58faces of the students who are in the
14:01gap, right? Because there is also a
14:04learning gap in the math classroom.
14:09Look, we then ask ourselves, who are
14:11these students? Well, the students are
14:13young people, right? Because here,
14:15basic education goes from sixth grade
14:17to eleventh grade. Young people with
14:21their own cultures; they are subjects
14:23who have dispositions and intentions
14:26that they have also been building
14:28throughout their learning trajectory,
14:30particularly in the learning of
14:32mathematics. Almost all of them are
14:36certain that they don't have the
14:39capacity to learn, and they have future
14:43perspectives that do not include
14:45mathematics, nor do they include—or
14:49they include with great discouragement
14:52—the move to university, which is
14:55another one of the problems that is
14:58very relevant right now. In the
15:02classroom, we find a sort of transition
15:04of cultures, right? There are several
15:07cultures: the cultures of the youth,
15:10the learning culture that the teacher
15:13intends to impose, or at least link,
15:15aiming to change these subcultures
15:18through learning, but there is a
15:20disconnect in all of these intentions.
15:25We found human teachers with their
15:27ideologies, their feelings—they feel,
15:30well, everything that can happen in a
15:33classroom under these conditions. Hm.
15:38Well, here I am going to tell you about
15:40the possibilities that we have also
15:43started to propose and carry out in
15:45research with master's students for
15:48their theses, now thinking about
15:50possibilities for mathematics education
15:53for all. The framework we have taken is
15:58Valero's, which is about the
16:00relationship between democracy and
16:03citizenship, a citizenship of public
16:05participation in the construction of
16:08social subjects. And so, from school
16:13mathematics, let's say, we selected
16:16what is being called the mathematics of
16:20the social world. We organize the
16:25curriculum through thematic approaches,
16:28because we believe that with this focus
16:31we can build—we have built—
16:33opportunities for learning, and we also
16:36structure the environment and learning
16:39scenarios to foster the building of
16:41communities. Clearly, in this way, we
16:46establish a relationship for all in the
16:49connection between mathematics and
16:51democratic values. So, what are the
16:55tensions? Well, there are several.
16:57First, time—school curricula, right?
17:03The thematic approach requires time,
17:05and there isn't any; you have to cover
17:08the content, you have to ask permission
17:10from schools to organize the curriculum
17:12differently. Teachers feel uncertainty
17:18because they are no longer prepared—
17:20you can't just prepare an entire
17:22didactic unit and follow it; instead,
17:25we have to work moment to moment, as if
17:28we have to restructure the project. Yes
17:33, we do consider it possible to
17:35establish that relationship between
17:38fair assessment and mathematics
17:40education for all. If we start working
17:45on including that recognition of
17:48difference, that participation, and
17:50establishing that this mathematics
17:52education is relevant for everyone.
17:58Currently, I think that as a community,
18:01we should reach a social consensus by
18:04asking ourselves, in a mathematics
18:07education project, why it is important.
18:12Well, thank you very much. Yeah.

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