Practising the skill of analyzing primary mathematics curriculum for students of Primary Education

34 HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1075.2018-0166 Educational Sciences, 2018, Volume 63, Issue 9, pp. 34-41 This paper is available online at PRACTISING THE SKILL OF ANALYZING PRIMARY MATHEMATICS CURRICULUM FOR STUDENTS OF PRIMARY EDUCATION Nguyen Chien Thang 1 and Nguyen Thi Phuong Nhung 2 1 School of Natural Science Education, Vinh University 2 Faculty of Education, Vinh University Abstract. Educational curricula have an important role in ensuring educational qualities of a nation and of every school. Analyzing educatinal curricula therefore must be one of core competencies of teachers. That is why teacher students should be formed and practised the skill of analyzing educational curricula at the stage of training their profession at undergraduate level. In this paper, we present the need and the role of analyzing curricula in general, analyzing primary mathematics curriculum in particular. We then find out the real status and the reasons for practising the skill of analyzing mathematics curriculum at primary level. We thence propose measures to practise this skill for students of Primary Education major. This will contribute to improve pedagogical skills for students of Primary Education major and help them be able to adapt with the development of mathematics curricula at primary level in the age of globalization and the new industrializing revolution. Keywords: Students of Primary Education major, skill, analyze curricula, mathematics, primary level. 1. Introduction Of primary subjects, along with Vietnamese, mathematics plays an important role in the teaching and learning process. Primary mathematics has a variety of applications in life and is essential for learning other subjects. Therefore, in order to teach mathematics at primary school effectively, students of Primary Education major must be trained many specific pedagogical skills, of which the skill of analyzing curricula is a basic and core one. Many researches on practising pedagogical skills have mentioned curicula, the analysis of primary curricula and textbooks in general, of primary mathematics in particular, such as [2, 3, 5, 7, 10, 12, 13], However, there are not many studies that offer specific measures to guide students to practice. In this paper, we focus on practising the skill of analyzing primary mathematics curriculum for students of Primary Education major the practice of students of Primary Received May 5, 2018. Revised July 11, 2018. Accepted September 5, 2018. Contact Nguyen Thi Phuong Nhung, e-mail address: [email protected] Practising the skill of analyzing Primary Mathematics curriculum for students of Primary Education 35 Education major through the primary teacher education program. We simultaneously analyze the real status of primary teachers about this skill. With the proposed measures we would like to develop the teaching ability for students of Primary Education major, help them teach the knowledge strands better and soon adapt to the development of the Mathematics Program at elementary level. 2. Content 2.1. The skill to analyze the primary mathematics curriculum Mathematics is a compulsory subject at primary level that helps students systematically grasp the most necessary mathematical concepts and rules for all, as the basis for academic study at next levels or it can be used in everyday life. The structure of the mathematics curriculum at primary level is “spiral concentric” (concentric, extended and gradually enhanced), revolves around and integrates four strands of knowledge: arithmetic, algebraic elements and statistical element, quantitative and qualitative elements, geometric elements, solving word problems. The contents of primary mathematics subjects have been developed based on the viewpoint, the spirit of modern mathematics in accordance with each stage of students' perceptions. Knowledge and skills of mathematics subjects at primary are formed primarily by practicing and are constantly reviewed and consolidated [1]. The skill to analyze mathematics curriculum at primary school is one of very important skills in the system of teachers’ skills. The effectiveness of the teaching process depends very much on the teacher's understanding of the main idea of the curriculum, the scientific basis of the content, methods, means, forms of organisation of teaching and how to assess the learning outcomes of the curriculum. When analyzing the mathematics curriculum at primary school, it is necessary to meet some basic requirements, such as: clarifying of what grade the objectives and contents of the concerned mathematics curriculum are, including what issues; What the focal points in it are; Background knowledge and relationships with other knowledge; What the minimum level required in the process of teaching that content is; Methods and means to be mobilized, If students of Primary Education major are trained in the analysis of primary mathematics curriculum, then after graduation they will be able to elicit the most relevant areas of knowledge that will help students mobilize in time to comprehend new knowledge, in addition, they can properly implemented the standard of knowledge and skills for primary school students in the teaching process ([5]). As a result, the skill to analyze mathematics curriculum at primary school plays an important role in helping primary teachers understand the overall structure and structural characteristics of the curriculum; Know the objectives, the basic content of each knowledge strand, the relationship between the knowledge strands together and see the role, location, meaning of each knowledge strand; Know the location of the content and the teaching periods in the curriculum system and the interrelationships between them; Understand the required level of knowledge, skills in each chapter, each section to each lesson. In addition, the analysis of the curriculum can help teachers identify the pedagogical intent of the curriculum and textbook authors. Thereby, teachers have the basis for selection of content, Nguyen Chien Thang and Nguyen Thi Phuong Nhung 36 selection of teaching methods to develop teaching plans in the direction of positive students as well as design tests to assess the results of learning mathematics in a suitable way. It is also a condition to promote and promote the creativity of teachers in the requirement of the current educational innovation. 2.2. Types of curriculum analysis There are two types of curriculum analysis ([5]): + Horizontal analysis: is the analysis of the content of mathematics teaching in each class, each semester, each chapter, each section, each week; + Vertical analysis is the analysis of the content of mathematics teaching in the knowledge strands in all classes in which the knowledge strand is arranged; it is also possible to analyze the content of that knowledge strand for one academic year or one semester. Whether analyzing the mathematics curriculum at primary school in the way of “vertical” or “horizontal” then students need to perform some basic practice operations, including: 1. Learn about the curriculum: Read the mathematics curriculum carefully (the part that needs analysis), look at the corresponding content in the mathematics textbook, summarize the main content in a sequential order, list the number of periods per content; 2. Analysis: It is necessary to clarify the objectives and levels of requirements of each core knowledge area in the curriculum part analyzed; Justify the arrangement, the pedagogical intent and the relationship between the units of knowledge in each chapter, each section, each part; clarify the notes in teaching which are the relevant background knowledge while implementing the content, teaching methods often used, the means of support when necessary and the appropriate form of teaching organization, For example, analyze the mathematics teaching curriculum of the second semester of 5th grade (“horizontal” analysis). What need to do to analyze the mathematics teaching curriculum of the second semester of the Grade 5 Mathematics are: - Read the mathematics teaching curriculum of the second semester of the Grade 5 Mathematics, view the textbook (from the "trapezoid" to the end) to see the curriculum manifestation, learn the total number of periods, summarize the main content. - Analyze to see: + The core objective of the second semester curriculum of the Grade 5 Mathematics is to formulate the concept of some geometry figures; use formulas for calculating area, volume of figures and generally apply knowledge (on arithmetic, quantity and the measurement of quantities, ) to solve mathematics problems. + The difficult knowledge which is noteworthy is the notions of volume of a figure, of a unit of volume, of calculations with time measurement and of problems of regular motion. + The main method of teaching when forming the formulae of calculating geometric areas and volumes is the "intuitive" approach combined with the “Open-minded Practising the skill of analyzing Primary Mathematics curriculum for students of Primary Education 37 approach” and "Practice - Exercise". Using incomplete induction helps students acknowledge formulas reasonably. + Background knowledge (relationships with previous knowledge units): The form of formulae for calculating the lateral area and the surface area of a rectangular parallelepiped and of a cube based background knowledge are the formulae for calculating the areas of rectangles and squares in Mathematics 3. Calculations with time measurement are closely related to time unit conversions, thus knowledge of the relationship between time units from grades 2, 3, 4 should be systematized again. The solution of word problems at the end of Grade 5 has the following background knowledge: Natural numbers; fractions; decimal numbers; geometric formulae; units of measurement and relationships between units of measurement, methods of solving specific types of mathematics appeared in grades 3, 4, + Skills need to be strengthened such as: the skill to calculate on the system of decimal numbers; the skill to convert and calculate measurement of time in different units of measurement; the skill to identify and distinguish geometric figures and formulas of calculating magnitudes of geometric quantities; the skill to solve word problems of regular motions, in percentages, about geometric elements. + The teaching facilities should be prepared as models of some geometric solids, some summary tables. 2.3. Some aspects of the real status of the primary mathematics curriculum analysis skill of current primary teachers Firstly, observing the reality of teaching mathematics in primary schools today, we find that there have been some problems for the primary mathematics curriculum analysis skill of current primary teachers. It is that they have not been aware of the importance of the analysis of the curriculum in general and the curriculum of mathematics in particular, have no sense of cultivating this skill. Most teachers only use mathematics textbooks and the knowledge-skill standards promulgated by the Ministry of Education and Training to plan your lesson plan for each class. Less emphasis is placed on identifying a holistic view of the objectives, the content structure of the curiculum, and the scientific basis of the curiculum's implementation method. Thus, it leads to more confusion in the mathematics teaching process. For example, implement this curiculum but from the perspective of the other curiculum; conduct teaching activities without understanding why to do so; do not understand the intent of the textbook, teaching does not "hit" the target of the lesson, do not explain the problems in the lessons. On the other hand, when instructing students to review, there appears a situation that teachers have not yet generalized the strands of the knowledge and skills in the whole curriculum as well as the curriculum of each class logically, have not yet generalize the types of questions, exercises and the purpose, the meaning of each type, leading to the process of instructing students to carry out gloomy, overlapping, much time consuming and affecting the development of students' thinking. In addition, poor curiculum analysis skills also affect test design skills and the conduct of asessing students’ mathematics learning results. By failing to understand the direction and objectives of the curiculum, the assessment may be misaligned to the Nguyen Chien Thang and Nguyen Thi Phuong Nhung 38 objectives and the implementation. For example, the basic objectives of the current mathematics curriculum is to form and to develop students' thinking ability, reasoning ability, mathematics problem solving, the ability to use tools and means of learning mathematics,...; to develope key knowledge and skills, especially, to create opportunities for students to experience and apply mathematics to real life, thereby forming a positive attitude and belief in mathematics [1]. However, many teachers when developing the midterm, and final examinations tend to evaluate their mastering knowledge of mathematics. Secondly, in the process of training primary teachers at university, we realize that students have been embarrassing when learning this skill. Because of the need to develop analytical skills, students must first acquire the essential knowledge of modern mathematics as well as the knowledge of psychology and education. On that basis, it is necessary to conduct scientifically-practiced activities requiring the ability of logical thinking, analysis, comparison, synthesis, generalization and abstracting to grasp characteristics of the objectives, the overall structure, the directive ideology of the curriculum. Since then, these characteristics can be specified on the content parts, explain how to apply the methods, teaching aids and methods of assessing the mathematics learning outcomes of the students, then specifying on each lesson. 2.4. Some measures to practice the mathematics curriculum analysis skill for students of Primary Education major The process of practicing the analytical skills in general and mathematics curriculum analysis skills in particular is not a simple, easy process. The training activities in this process are highly intellectual, require meticulosity, accuracy, scientificness and knowledgeable stability. Therefore, we propose some measures to practice the analysis skill of the mathematics curriculum in primary schools as follows: Measure 1. Through the basic courses, set up some exploiting directions into lectures to analyze the hidden modern mathematics foundation in the primary mathematics curriculum. The modern mathematics foundation is one of the basic ones of primary mathematics. Analyzing the modern mathematics foundation will help students identify the objects of mathematics at primary, learn languages, mathematical symbols and proofs, explore, discover, deduce, abstract, ... in primary mathematics. Thus, the skill to analyze mathematics foundation in primary mathematics curriculum is an indispensable skill for students of Primary Education major. Therefore, from the early years of learning basic courses (Advanced Mathematics, Elementary Mathematics), teachers should integrate some primary mathematics problems for students to practice this skill. Teachers ask students to discuss and find out their relationship before, during or after each lesson. In addition, the students are required to practice the curriculum analysis skill from the beginning of the course or the basic part in order to help students understand why they have to learn advanced mathematics (elementary mathematics). This helps students initially learn the mathematics curriculum at the primary level, it provides the basis for learning other courses in the primary teacher education program. Practising the skill of analyzing Primary Mathematics curriculum for students of Primary Education 39 Example 1. When teaching the concept of mapping the teacher can lead the students to the concept of mapping by giving the following situation: "Lan has 3 notebooks, her mother gives Lan more ... notebooks. Lan has all ... notebooks. (Math 4, p.6). Ask students to establish the corresponding f between the set A (The mother’s notebooks for Lan) and the set B (All the notebooks she will have). Then the corresponding f is a mapping from set A to set of natural numbers N where B is a subset of N such that f takes each element n into 3 + n. The teacher from there generalize to leads to the concept of mapping. Example 2. Consider the problem "There are 32 students arranged in rows, each row has 4 students. How many rows? [Mathematics 2, p.118]. Determine the equivalence relation that appears in the above problem? Find the quotient set in that equivalence relation. The equivalence relationship here is the "same row" relationship. Students in the same row are in the same equivalence class. The number of elements in the quotient set is exactly the number of rows. So the number of rows is 32: 4 = 8 (rows). Example 3. Define the mappings as the basis for constructing the Multiplication table p.5 (Mathematics 2, p.101) and the Subtracting table in the range of 10 (Mathematics 1, p.86). Are the mappings injective, surjective, and bijective? The symbol [1,10] is a set of natural numbers from 1 to 10. The mapping as the basis for constructing the Multiplication table 5 is f: [1,10] N a 5 x a The mapping f is injective but is not surjective. Measure 2. Create content and self-training activities for students on the analysis of mathematics curricula in primary schools through elective courses. Under the curriculum of training primary teachers with university level, after studying the basic courses, students will be able to take elective courses (arithmetic, quantities, measurement and numerical sets, practive solving mathematics problems; assessment for primary students) in the second and third academic years to initially form the method of teaching the mathematics subject in primary schools. Through these courses, teachers can provide contents and self-training activities of curriculum analysis skills for student by using the knowledge learned in the curriculum survey and finding out the specific objectives of each content. Determining a competency-oriented goal now requires teachers not only to correctly define their mathematical knowledge and skills, but also to visualize and describe in detail the level of achieving some common capabilities or special ability of mathematics subject in the teaching process. This is a new and difficult element for primary school teachers today. Example 1. When learning the course of Quantities, quantity measurement and numerical sets, the teacher introduces the content and asks the students to practice the following contents: + Determine the quantities in the real world. + What quantities of primary mathematics curriculum are introduced? + List the quantities and units of quantity measurement from Grade 1 to Grade 5. + The quantities are introduced in the primary mathematics curriculum. Nguyen Chien Thang and Nguyen Thi Phuong Nhung 40 + State the objectives of knowledge, skills and some competencies acquired in the content of Quantities and quantity measurement. Example 2. When learning the Arithmetic course, the teacher introduces the content and asks students to self-practice the fol