Practices of Didactics of Mathematics in LatinAmerica
Mariana Bajonero,Angela Barba, Daniela Murillo 551032A_1144
Math is very important nowadays
Due to globalization and the increased use of technology, math is very important nowadays. All over the world, there is a great need for teaching good mathematics- Math is a key school subject; because students' thought process is affected in a positive way. It provides a set of unique skills such as logic, abstract concepts, methodical thinking, and it helps to fully comprehend many science concepts as well. Additionally, math fosters emotional aptitudes, intelligence and personality; because this field encloses all human activities.
In LatinAmerican and Caribbean (LAC) countries students are falling behind because they are not being taught at the level needed in today’s world. Students perform poorly in international evaluations suchs asTrends in the International Mathematics and Science Study (TIMSS) and the Program for International Student Assessment (PISA). In many countries, low mathematics results correlate with low language results.
Many studies have reported that teaching math is a big issue in LAC countries. In the same way they share many similarities, for example, the literacy rate among young people is about 90%. However, they do differentiate in things like each country's income, poverty rates, life expectancy, etc. and there are big gaps. In theAncient World, some of these countries had talented civilizations such as the Incas and the Mayans, cultures that were advanced and had a great math knowledge.
Mathematics education in LAC a reality to be transformed
Math in Colombia
The international evaluationTIMSS (Trends in the International Mathematics and Science Study) and the PISAtest (Program for International Student Assessment) provide accurate results regarding measuring students' achievements in this region.The tests show that most students lack the ability to solve a problem, including ones containing basic algorithms. For example, in 2006 the results for Colombia were poor, with reading 385/556 and math 370/547.The students' proficiency level on the mathematics scale is very low seeing as about 50% of students perform below level 1.
But what is level 1? It is a basic measurement for students to answer questions where all relevant information is present and questions are clearly stated. Students can understand clear information. In other words level 1 has to do with the basics.
This situation shows that Colombian math teachers are not prepared for meeting the present circumstances. One way to fix these problems is to have qualified teachers, people who know the subject vey well and have the tools to teach competently. Once graduated, teachers need to continue growing professionally and to have a vast knowledge of their subject.And students need to not just learn about a specific subject, but also which specific learning method works the best for them.
In many countries, as well in Colombia, low math results are a result of low reading comprehension. Experts have pointed out this language/math relationship. Is it clear a student cannot solve a math problem if he lacks the required skills of his own language? Furthermore, how can a student express math concepts properly without good vocabulary?Thus, to get better results in math, teachers need to work hard on improving language literacy.
In Colombia, like most countries in LAC the government provides education for everyone and the literacy rates are high among young people. However, quality is not the same as quantity, and in most cases it is quite low.Ashort term solution is not easy, the countries need to train their teachers better. In other words better teachers, better conditions, better students.
To reach these goals, mathematicians have to be involved in teachers training, because their participation is almost zero. When this is achieved math will be improved in our country.
Nevertheless, there are some efforts to improve mathematics in the country. For example, since the year 2000 Colombia has participated in the Bolivarian Mathematics Olympics.The country has hosted one of the oldest math national events in the continent,The Colombian Mathematics Olympics,which started about 30 years ago. In recent years, the country has invited students from neighboring countries of the region and it promoted the first Iberoamerican Mathematical Olympics. One can see that most nations are trying to improve by offering mandatory classes covering most of their population, but it is not enough.
How to improve math in Colombia
Find ways to improve math and language education all together.
Connect professional mathematicians with school teachers to get a better vision of the field.
Keep a detailed report of students performance in international testing like the PISAorTIMSS.
Use technology to provide access to teachers and students to more resources.
Write minimum standards for math education from elementary through high school.
Universities need to associate mathematicians to help teachers in training with their pedagogical and didactic skills; providing new teachers with a bigger teaching tools box with supporting materials namely sensorial stuff, new resources, teaching techniques to reach all types of students, etc.
For new teachers
Strict policies for teaching training and selection.
Raising teachers salaries to attract more people.
Deeper knowledge of the subject taught.
Offering professional development during vacations.
Create mentoring programs between research mathematicians and new teachers.
For In-service teachers
Offering programs related to didactics and better practices. Perhaps using online classes.
Training teachers in the correct use of technology.
Giving teachers a sabbatical to use this time to prepare better.
… more ideas…
School-based national Olympics
Emphasizing the use of the competition to create a link between mathematicians and teachers. Leaving aside the models that only focus on selecting the best students.This situation requires government support to fund these projects making sure researchers could be linked with these types of events. The sustainable development goals are an urgent call to action for all countries, goal #4 refers to ensuring everyone receives an excellent quality education. Math is part of these goals, as is understood as a basic right for all students and it is needed for today’s world. Half of the Colombian students barely reach Level 1 in international tests.The country needs to act and provide better teachers to raise their students' standards.
Math in Chile
Chilean education has a unified organization in schools, the administration is in charge of municipal and private institutions, and the State has the responsibility to verify and maintain the system in operation, thus generating the highest academic quality in Latin America.The most challenging mathematical activity is the demonstration, this program aims to provide presentations of the activities proposed in the curriculum.This is a general approach that is incorporated continuously during the educational process, it is a mathematical process to learn how to think.
The general idea is to teach a specific subject in a stimulating environment for learning within the classroom.This process requires theory and practice to know how to develop problem-solving, diagnosing, evaluating and modifying processes for finding a solution.
The pedagogical studies are carried out by the University of Chile in the Faculty of Sciences, Philosophy, and Humanities. It understands the didactics of mathematics facilitating to the teacher an implementation of teaching and learning strategies through different models. By applying cognitive sciences as an effective role through its
Didactic strategies for the development of mathematical skills in Chile.
The didactics of mathematics begin with the training of teachers at each of the levels.The exploration of external activities increases the interest in learning in the classroom, by allowing real problems to be put into practice.The properties of mathematical objects: are treated as a change of cognitive and epistemic attitude in effect. “I can” statements, contribute to knowledge, written, oral and augmentative communication. Applying diverse ideas of Mathematics but explaining and arguing; implementing Toulmin's method, the students build their learning process guided by the teacher, using previous concepts or pre-knowledge.
In recent years, Chile has implemented different projects that promote the use of technology in the classroom, such as (one computer per child). Needless to say that technology by itself does not provide any significant knowledge; thus, it is necessary to implement pedagogical intervention models allowing teachers to properly use these technologies that contribute to learning.The process began in 2009, with a project called "learning mathematics with technology 1:1 laptop”. It is a model in the math curriculum, which integrates 21st-century skills: collaborative work, integration of technology, individual research, mathematical didactics, development of solutions to create interactive, and dynamic learning environments. It also includes permanent training and support for teachers. In the training focusing on designed printed material, interactive digital resources, and assessment of student learning, to increase the assertiveness of the project.
We can conclude that mathematics education in Chile is based on the search for explanatory hypotheses.And it is developed under the problem-solving model, interacting as a group, solving questions, guided by the teacher.
Problem Statement
Based on how the Colombian students perform in the local government ICFES test. It is easy to analyze mathematical skills in Colombia; we can infer that the production of the students is not what is expected by teachers. When is compared with the academic achievement in Chile, a country with the highest math level in LatinAmerica, Colombia is very low.This shows the lack of good reading comprehension.a skills that are developed since early childhood.
Mathematics promotes the understanding of various processes that require a correct use of language. This process allows the students to develop understanding of new concepts more easily. In education, teachers are facilitators for students; they help to build knowledge, understanding, processing and applying different methods to solve the problems.
Possible Solution
To begin with, teachers need a steadfast interest in involving various methodologies to make their teaching a fun and innovative.
Then, students ought to maintain a daily motivation, and be committed to learn new concepts as well.
The Government, in Colombia the Secretary of Education, must maintain constant technological contributions and professional development for teachers.Also they need to connect professional mathematicians with math teachers to share knowledge and good practices to enrich teachers tool box.This will produce a deep impact in students accomplishments in math.
In addition, there is a need of reviewing the evaluation system. Evaluations that really show students accomplishments in a controlled environment.
Math in Mexico
We currently live in a globalized world, which has broken barriers in various fields, social, economic, cultural, educational, among others.Teaching math in Mexico is a two fold parts task; the first, when considering customs and beliefs, there is a misconception of learning procedures and formulas.The concepts are taught, but without being able to understand why and for what it is being learned. In 1992 an academic program was developed with updated contents using the problem approach and creating reasoned teaching. But due to the lack of teacher training and the various atypical styles of training, the goals were not met.
If one considers the evolution education has done through, specifically in math; from the methodological and epistemological point of view; it is necessary to include didactic materials such as books to support children's learning.
Due to the low levels reached by children and young people in terms of learning mathematics in Mexico, in recent years the implementation of academic programs has been proposed to improve the educational level. One of this is the Comprehensive Reform of Basic Education 2007-2012 to strengthen Spanish and mathematics skills.
Regarding the best practices in mathematics didactics, in high school the education tends to take into account approaches such as problem solving. Using research that affect the direction described, and consider the association between problem solving and the use of technology as a mediator in learning.
Because the teaching-learning process of mathematics is complex, teachers must apply the appropriate methodology and strategies to generate a real acquisition of knowledge.
Moreover, there is a new trend using teamwork in the classroom and the use of rubrics for evaluation. However, there is a lack of research about these aspects.And this could be a great opportunity of growth for researchers in mathematics education. This represents an opportunity of growth. Regarding college level, the institutions take advantage of the use of technology as a mediator in the learning process.And they have designed online mathematics courses with the purpose of reaching a larger population. In addition, with these curriculum the students can learn at their own pace.
Although teachers are working with a new academic program 2007-2012 (SEPand SEB 2008). In a school year, the curriculum does not have specify a course of action regarding teaching some concepts like addition and subtraction.
Math in Mexico
The government assumes teachers are well trained and they are able to efficiently teach well all concepts and strategies required in this new academic model.This one refers to the educational program developed in 1992. There are many issues to overcome: like breaking old beliefs, lack of knowledge of concepts, insufficient didactic schemes, etc. (Ávila. 2004; Bernal, Figueroa, Ramírez andTriana, 2006: Carvajal, 2007)
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Lagos, María Ester; Miranda, Hernán; Matus, Claudia; Villarreal, Gonzalo (2011). Aprendiendo matemática con tecnología portátil 1 a 1: resultados de una experiencia de innovación en Chile. Cuadernos, 8, pp. 181-201 .
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