Teaching Math in Primary Grades PDF

TEACHING MATH IN PRIMARY GRADES =============================== 1. **Kids need Math to be able to count.** Counting is something they will need every single day of their lives. From the little things to the big things in life, counting is in every aspect of our lives. 2. **Math will help...

TEACHING MATH IN PRIMARY GRADES =============================== 1. **Kids need Math to be able to count.** Counting is something they will need every single day of their lives. From the little things to the big things in life, counting is in every aspect of our lives. 2. **Math will help your child get their numerals right**. One of the most important things a child will be working on figuring out for a huge chunk of their adult life is money. Not to mention shopping and dealing with change which requires basic Math skills such as adding, subtraction, multiplication, and division. 3. **Many essential life skills fall under Math.** Skills like being able to read a clock to tell the time, calculating time in terms of hours, days, weeks or months, reading temperature and so much more. A lot of flights could be missed if one is unable to calculate military time. 4. **Math is the basis for a whole array of other subjects, ranging from Accounting to Statistics to Economics and even certain Sciences such as Physics and Chemistry.** Without knowing Math, a child's options of higher studies narrow down. 5. **Math helps develop critical thinking skills, a skill which is a huge requirement once kids enter the real world.** With the ongoing competition in the job market, developing and excelling in Math is becoming more and more of a requirement to get ahead. The Learning Trajectories (Paths) Approach ========================================== 1. **Learning substantial math is critical for primary grade children.** The early years are especially important for math development. Children's knowledge of math in these years predicts their math achievement for later years---and throughout their school career. Furthermore, what they know in math predicts their later reading achievement as well. Given that early math learning predicts later math and reading achievement, math appears to be a core component of learning and thinking. 2. **All children have the potential to learn challenging and interesting math.** Primary grade children have an often-surprising ability to do abstract math---that is, math that is done by reasoning mentally, without the need for concrete objects. Listen to the worries of this first-grader. 3. **Understanding children's mathematical development helps teachers be knowledgeable and effective in teaching math.** Children's thinking follows natural developmental paths in learning math. When teachers understand these paths and offer activities based on children's progress along them, they build math learning environments that are developmentally appropriate and particularly effective. A useful tool in understanding and supporting the development of children's mathematical reasoning is a math learning trajectory. There are learning trajectories for mathematics at all age levels, from birth throughout the school years, and for learning all kinds of content---from specific math concepts such as number and operations to specific science concepts like understanding electricity. Learning Trajectories ===================== - Math learning trajectories have three parts: a mathematical goal, a developmental path along which children's math knowledge grows to reach that goal, and a set of instructional tasks, or activities, for each level of children's understanding along that path to help them become proficient in that level before moving on to the next level. Let's examine each of these three parts. - **Goal**. The first part of a learning trajectory is the goal. Goals should include the big ideas of math, such as "numbers can be used to tell us how many, describe order, and measure" and "geometry can be used to understand and to represent the objects, directions, and locations in our world, and the relationship between them of knowing how to solve a variety of addition and subtraction problems. - **Developmental path**. The second part of a learning trajectory consists of levels of thinking, each more sophisticated than the last, leading to achieving the mathematical goal. That is, the developmental path describes a typical learning route child follow in developing understanding of and skill in a particular mathematics topic. - Learning trajectories are important because young children's ideas and their interpretations of situations are different from those of adults. Teachers must interpret what the child is doing and thinking and attempt to see the situation from the child's viewpoint. Knowledge of developmental paths enhances teachers' understanding of children's thinking, helping teachers assess children's level of understanding and offer instructional activities at that level. Similarly, effective teachers consider the instructional tasks from the child's perspective. - **Instructional tasks**. The third part of a learning trajectory consists of sets of instructional tasks or activities matched to each level of thinking in a developmental progression. The tasks are designed to help children learn the ideas and practice the skills needed to master that level. Teachers use instructional tasks to promote children's growth from one level to the next. Role of a Teacher ================= - is to create an engaging encouraging environment for young learners to thrive in. - Math Classroom - Peer teaching in math - Conducive to learning environment - Be creative in giving some activities - Have a resourceful and creative Learning Materials - Give appropriate activity according to their level of learning and understanding (not so difficult and so easy) - Have groupings in some activities Who are the primary grades? =========================== - In the Philippines refers to kindergarten until Grade 3. Generally, primary grades completers are expected to have a good sense of number, perform simple operations like addition and subtraction, have the capacity progress from using physical examples and written calculations to carrying out operations mentally, and have the ability to identify proper strategies and techniques needed to come to conclusions and carrying out calculations when solving mathematical problems. Why do we teach Mathematics? Three Major Reasons ================================================ 1. **Necessary Mathematics** - mathematics for school, employment and economy. 2. **Social and Personal Mathematics** - mathematics for personal and social relevance. 3. **Appreciation of Mathematics as an Element of Culture** - the importance not only of appreciating mathematics itself, but also its role in history, culture and society in general. Necessary Mathematics in School =============================== - Science - Music - Social Studies - Home Economics - Language -- on how many syllables, words, phrase, sentence etc. **K to 12 Curriculum Guide MATHEMATICS (Grade 1 to Grade 10) Conceptual Framework of Mathematics Education** CONCEPTUAL FRAMEWORK ==================== - Mathematics is one subject that pervades life at any age and in any circumstance. Thus, its value goes beyond the classroom and the school. Mathematics as a school subject, therefore, must be learned comprehensively and with much depth. - The twin goals of mathematics in the basic education levels, K-10, are Critical Thinking and Problem Solving. - Critical thinking, according to Scriven and Paul (1987) is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. - On the other hand, according to Polya (1945 & 1962), mathematical problem solving is finding a way around a difficulty, around an obstacle, and finding a solution to a problem that is unknown. - These two goals are to be achieved with an organized and rigorous curriculum content, a well-defined set of high-level skills and processes, desirable values and attitudes, and appropriate tools, taking into account the different contexts of Filipino learners. - There are five content areas in the curriculum, as adopted from the framework prepared by MATHTED & SEI (2010): Numbers and Number Sense, Measurement, Geometry, Patterns and Algebra, and Probability and Statistics. - The specific skills and processes to be developed are: knowing and understanding; estimating, computing and solving; visualizing and modelling; representing and communicating; conjecturing, reasoning, proving and decision-making; and applying and connecting. - The following values and attitudes are to be honed as well: accuracy, creativity, objectivity, perseverance, and productivity. - We recognize that the use of appropriate tools is necessary in teaching mathematics. These include: manipulative objects, measuring devices, calculators and computers, smart phones and tablet PCs, and the Internet. - We define context as a locale, situation, or set of conditions of Filipino learners that may influence their study and use of mathematics to develop critical thinking and problem- solving skills. Contexts refer to beliefs, environment, language and culture that include traditions and practices, as well as the learner's prior knowledge and experiences. - The framework is supported by the following underlying learning principles and theories: Experiential and Situated Learning, Reflective Learning, Constructivism, Cooperative Learning and Discovery and Inquiry-based Learning. The mathematics curriculum is grounded in these theories. - Experiential Learning as advocated by David Kolb is learning that occurs by making sense of direct everyday experiences. Experiential Learning theory defines learning as \"the process whereby knowledge is created through the transformation of experience. Knowledge results from the combination of grasping and transforming experience\" (Kolb, 1984, p. 41). Situated Learning, theorized by Lave and Wenger, is learning in the same context in which concepts and theories are applied. - Reflective Learning refers to learning that is facilitated by reflective thinking. It is not enough that learners encounter real-life situations. Deeper learning occurs when learners are able to think about their experiences and process these, allowing them the opportunity to make sense of and derive meaning from their experiences. - Constructivism is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connect them to new ideas. - Cooperative Learning puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. - The mathematics curriculum allows for students to learn by asking relevant questions and discovering new ideas. Discovery Learning and Inquiry-based Learning (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships, and concepts. BRIEF COURSE DESCRIPTION ======================== - Mathematics from K-10 is a skills subject. By itself, it is all about quantities, shapes and figures, functions, logic, and reasoning. Mathematics is also a tool of science and a language complete with its own notations and symbols and "grammar" rules, with which concepts and ideas are effectively expressed. - The contents of mathematics include Numbers and Number Sense, Measurement, Geometry, Patterns & Algebra and Statistics and Probability. - Numbers and Number Sense as a strand include concepts of numbers, properties, operations, estimation, and their applications. - Measurement as a strand includes the use of numbers and measures to describe, understand, and compare mathematical and concrete objects. It focuses on attributes such as length, mass and weight, capacity, time, money, and temperature, as well as applications involving perimeter, area, surface area, volume, and angle measure. - Geometry as a strand includes properties of two- and three-dimensional figures and their relationships, spatial visualization, reasoning, and geometric modelling and proofs. - Patterns and Algebra as a strand studies patterns, relationships, and changes among shapes and quantities. It includes the use of algebraic notations and symbols, equations, and most importantly, functions, to represent and analyze relationships. - Statistics and Probability as a strand is all about developing skills in collecting and organizing data using charts, tables, and graphs; understanding, analyzing and interpreting data; dealing with uncertainty; and making predictions about outcomes. - The K to 10 Mathematics Curriculum provides a solid foundation for Mathematics at Grades 11 to 12. More importantly, it provides necessary concepts and life skills needed by Filipino learners as they proceed to the next stage in their life as learners and as citizens of the Philippines. - K to 12 BASIC EDUCATION CURRICULUMS LEARNING AREA STANDARD: The learner demonstrates understanding and appreciation of key concepts and principles of mathematics as applied - using appropriate technology - in problem solving, critical thinking, communicating, reasoning, making connections, representations, and decisions in real life. KEY STAGE STANDARDS =================== - At the end of Grade 3, the learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 10,000 and the four fundamental operations including money, ordinal numbers up to 100th, basic concepts of fractions); measurement (time, length, mass, capacity, area of square and rectangle); geometry (2-dimensional and 3-dimensional objects, lines, symmetry, and tessellation); patterns and algebra (continuous and repeating patterns and number sentences); statistics and probability (data collection and representation in tables, pictographs and bar graphs and outcomes)as applied -using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. Grade 4-Grade 6 =============== - At the end of Grade 6, the learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers, number theory, fractions, decimals, ratio and proportion, percent, and integers);measurement (time, speed, perimeter, circumference and area of plane figures, volume and surface area of solid/space figures, temperature and meter reading); geometry (parallel and perpendicular lines, angles, triangles, quadrilaterals, polygons, circles, and solid figures); patterns and algebra (continuous and repeating patterns, number sentences, sequences, and simple equations); statistics and probability (bar graphs, line graphs and pie graphs, simple experiment, and experimental probability) as applied -using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life. Grade 7-Grade 10 ================ - At the end of grade 10, the learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (sets and real numbers); measurement (conversion of units); patterns and algebra (linear equations and inequalities in one and two variables, linear functions, systems of linear equations, and inequalities in two variables, exponents and radicals, quadratic equations, inequalities, functions, polynomials, and polynomial equations and functions); geometry (polygons, axiomatic structure of geometry, triangle congruence, inequality and similarity, and basic trigonometry);statistics and probability (measures of central tendency, variability and position; combinatorics and probability) as applied - using appropriate technology - in critical thinking, problem solving, communicating, reasoning, making connections, representations, and decisions in real life. Ano ang gamit ng \"Learning Code\" sa Curriculum Guide? ======================================================= - Dahil nakageneralize ang objective of learning competencies kaya naglagay ng learning code ang deped upang ma-decongest ang nasabing objective or maging specific ang nasabing objective of learning competency. Nasa code kung ilang araw mo ituturo ang nasabing learning competency o learning objective. Hahatiin mo ngayon ang mga content o topic sa isang learning competency. Narito ang tamang paghahati-hati: - Halimbawa sa curriculum guide ng Science grade 3 nakabilog ang learning competency at code sa bandang kanan ng CG. - S3MT-Ia-b-1 - S3 - Science 3 - MT - Matter - I - First Grading - a - First week - b - second week - 1 - competency no. 1 - Marami po ang nalilito dito kung paano ituturo ng guro sa loob ng 2 weeks ang learning competency no. 1. Ide-decongest po ang isang learning competency sa 2 weeks may sample naman po sa CG. kaya need na irevise ang competency no. 1 para kasya sa 2 weeks hindi po ang parts ng lesson plan ang puputol-putulin. - Since hanggang 2 weeks ang pagtuturo isang objective lamang ang gagamitin para very specific to achieve mastery, ang ika -10 days summative assessment which is graded na siya ang formative assessment tulad ng daily quiz ay recorded lamang di pa siya graded. May remediation muna bago yung summative assessment para yung mahihina matuto rin. Kapag nagagawa mo ang tamang pagtuturo maiiwasan ang di makakapasang bata sa klase. Five Contents Areas in K-12 Mathematics Curriculum ================================================== 1. **Numbers and Number Sense** - concepts of numbers, properties, operations, estimations and their application. 2. Measurement =========== - the use of numbers and measures to describe, understand and compare mathematical and concrete objects; attributes such as length, mass and weight, capacity, time, money and temperature, as well as applications involving perimeter, area, surface area, volume and anger measure. 3. Geometry ======== - properties of two and three-dimensional figures and their relationships, special visualization, reasoning and geometric modeling and proofs. 4. Patterns and Algebra ==================== - as a strand studies patterns, relationships and changes among shapes and quantities; use of algebraic notations and symbols, equations, and most importantly, functions, to represent and analyze relationships. 5. Statistics and Probability ========================== - as a strand it all about developing skills and collecting and organizing data using charts, tables and graphs; understanding, analyzing and interpreting data; dealing with uncertainty and making predictions about outcomes. Mathematics Curriculum in the Primary Grades ============================================ - Is not simply a list of competencies. It is logically arranged and organized. For the teachers' reference, content standards, performance standards and learning competencies. The Content Standards ===================== - are broad descriptions of what the students should learn. Performance Standards ===================== - what the student should be able to do once the concepts and skills are taught. The Learning Competencies ========================= - are logically arranged objectives that must be aimed in classroom instruction for the students to achieve the required content and performance standards. The Important Principles in teaching/learning Mathematics ========================================================= 1. **Reflective learning** - is a way of allowing students to step back from their learning experience to help them develop critical thinking skills and improve on future performance by analyzing their experience? This type of learning, which helps move the student from surface to deep learning, can include a range of activities, including self-review, peer review 2. Active and student-centered teaching/learning. ============================================== - focuses on the needs, abilities, interests, and learning styles of the students and has many implications for the design of curriculum, course content, and interactivity of courses. Accordingly, a prominent pedagogy will be teacher-as-coach, to provoke students to learn how to learn and thus to teach themselves, rather than the more traditional teacher-centered learning with teacher-as-deliverer-of-instructional-services, which places the teacher at its center in an active role and students in a passive, receptive role. 3. Communications allowing the learners to articulate or express their thoughts. ============================================================================= - The classroom talk register is well designed to help students articulate ideas and thoughts, particularly when used in the context of discussion. In addition to the conversational probes, like the ones we described in the previous section, there are other ways to support students in expressing their ideas fully and clearly. One way is for the teacher to check repeatedly on her own understanding of students\' contributions as a discussion unfolds. 4. Making connections is so important that prior learning/prerequisite skills are always considered. ================================================================================================= - Prerequisite skills are defined as skills that are necessary as a prior condition for something. else to happen or exist. Therefore, prerequisite skills describe the skills or Mathematics in the context of real-life situation should be the main considerations in designing mathematics activities. ======================================================================================================================== - States that the learning is an active process of creating meaning from different experiences. In other words, students learn best by trying to make sense of something on their own with a teacher as a guide. - According to DepEd, knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connect them to new ideas. Constructivism ============== - Was conceptualized by educational theorist Jean Piaget. He believed that young children learn by doing, constructing knowledge from experiences rather than from adults telling them about their world. - According to Jean Piaget, and others who practice what is known as **constructivist education,** the method most likely to truly educate the students is the one in which they experience their world. Characteristics of constructivist teaching: (Brooks and Brooks, 1993) ===================================================================== - Constructivist teachers invite students\' questions and ideas. - Constructivist teachers accept and encourage students' invented ideas. - Constructivist teachers encourage student's leadership, cooperation, seeking information and the presentation of ideas. - Constructivist teachers modify their instructional strategies in the process of teaching based upon students; thought, experience and interest. - Constructivist teachers use printed materials as well as experts to get more information. - Constructivist teachers encourage free discussions by way of new ideas inviting student questions and answers. - Constructivist teachers encourage or invite student predictions of the causes and effects in relation to particular cases and events. - Constructivist teachers helps the student to test their own ideas. - Constructivist teachers invite students' ideas before the student is presented with the ideas and instructional materials. - Constructivist teachers encourage student to challenge the concept and ideas of others. - Constructivist teacher use cooperative teaching strategies through student interactions and respect, sharing ideas and learning tasks. - Constructivist teachers encourage student to respect, sharing ideas and learning task. - Constructivist teachers encourage student to request. How the constructivist classroom different from a traditional classroom? ======================================================================== **Traditional Classroom** -- ------------------------------- -- Students work primarily alone The Teaching Cycles =================== - The work of a teacher does not start and end in teaching. The teaching process is not a linear activity that starts with planning and end in testing. Instead, it is a cycle of repeating stages until a student acquire an understanding of the targeted concept and skills. You may think of a teaching cycle as a spring-you go through the same process over and over again, but each time with a more informed objective and better understanding of what it means to learn and teach mathematics. There are many models in teaching cycle and it boils down in to 6 common stages: ================================================================================ 1. **Identify objectives** - What knowledge and/or skills do the students need to learn? You must be guided with the content standards, performance standards and the learning competencies that are found in the curriculum guide. 2. Plan instruction ================ - What strategies must be implemented for the student to achieve the objectives targeted in the previous stage? In planning instruction, it is important that you have mastered the content of the lesson that you are about to teach. It is also beneficial to be familiar with your students-what they know, how they learn etc. 3. Implement plan ============== - This is the stage where you conduct the learning activities that you have prepared during the planning stage. A word of advice-even though have carefully and delicately plan for the lesson, you must be flexible with the possible changes that you need to accommodate. How will you know whether change is needed? 4. Checking for understanding ========================== - Teaching is all about helping student learn. During the implementation of the lesson plan, you must every now and then check whether the students have understood 5. Reflecting on teaching ====================== - You must evaluate every teaching period that you finished. Where the objectives achieved? Where the implemented strategies effective? How can instruction be improved? Your answers to the last question will give you an insight on how to improve instruction the next time you teach the same lesson. However, if you answer on the first question is no, the objectives were not met, then you need to plan again. What do you need to do differently in order to achieve the objectives? 6. Assess learning and reflect on the results ========================================== - This stage gives you a concrete measure of what the students have learned. In math, this is usually through a paper and pen examination. However, some authentic assessments may also be implemented. Take note that this stage does not end in assessing learning. You need to reflect on the results. What can you learn about the student learning and teaching practice based on the results? Things to Consider in Planning Instruction in Mathematics in the Primary Grades The 5 Important Elements in Lesson Planning =========================================================================================================================== 1. **Content** - Research the subject matter that you will be teaching. You should consult the curriculum and teaching guides published by DepEd. Aside from books, you can also visit websites which will give you information relevant to your subject area. You should master the contents of your lesson before you teach it. - Remember, you cannot give what you do not have. Moreover, you would not want to teach wrong contents to the student. It is easier to learn than to unlearn; it is difficult to take back wrong contents that already have been taught. You have a big responsibility as a teacher-master your content. 2. Objectives ========== - Before you begin planning, you need to know what specific knowledge and skills you want your students to develop during the lesson or unit. Teachers often focus too much on knowledge, forgetting about developing skills which is the long term are more important than knowing mere facts. So, in planning your instruction, always consider both knowledge and skills. 3. Students ======== - Get to know your students-where they came from, what their interest are, what they already know, their learning style, attention span and special needs. These will all help you determine your students' needs. - Remember that you need to prepare your lessons with all your students in mind and your main goal should be to meet their needs - And offer them enabling environments to learn their preferred way. - Knowing your students will also help you build rapport with them which is important if you want your students to be freely sharing their ideas with you and their classmates. students' mindset. ================== a. Lesson mastery b. Focused objectives c. Comprehensive understanding of students 4. Learning Environment ==================== - Aside from physical environment where the learner takes place, it also important to consider the social and emotional leaning - **Environment of the class**. You need to make sure that you promote a positive environment where students are motivated and are supportive of each other's growth. The students must feel safe to express their thinking, without fear of being embarrassed because of mistakes and different views. - Most importantly, you must create an atmosphere where students are open to learning through the activities you prepared and interactions with their classmates. 5. Availability of resources ========================= - Take into consideration the instructional materials that you will be needing before you write your lesson plan. - Is the blackboard available? If not, can you improvise? Are there specific manipulatives that you need? Where can you get them? Can you make them instead? Do you need technology resources? Have you check whether your devices are compatible with what are available in school? - These are some questions than you can reflect on.