Mth 502 Methods and Techniques in Teaching Mathematics PDF

West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City MTH 502: Methods and Techniques in Teaching Mathematics KHEMME LAPOR UBIAL 2024M0049 Master of Arts...

West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City MTH 502: Methods and Techniques in Teaching Mathematics KHEMME LAPOR UBIAL 2024M0049 Master of Arts in Education major in Mathematics 1st SEMESTER, A.Y. 2024-2025 Page 1 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City NOTES in MTH 502: Methods and Techniques in Teaching Mathematics KHEMME LAPOR UBIAL 2024M0049 Master of Arts in Education major in Mathematics 1st SEMESTER, A.Y. 2024-2025 MIDTERM “Commit to the Lord whatever you do, and he will establish your plans.” (Proverbs 16:3) MIDTERM EXAMINATION (Topics from Unit 1 – Unit 4) OUTPUTS NEEDED TO SUBMIT: 1. Required Task 1 (Individual) - Personal Introduction - Personal Pledge/Commitment (to maximize participation in this course) You can identify the possible barriers or struggles and how you will address these. 2. Required Task 1 (By Pair) - 10 Habits of Effective Teaching and Teacher’s Thriving Kit (Edit and layout thriving kit) 3. Required Task 4 (By Group) - Share the Humanized Realistic IM in Mathematics to the Class 4. Required Task 3 (By Group) - Summary Sheet (Describing how critical thinking skills, problem solving, constructivism, and Dale’s Cone of Experience strategies can enhance Mathematics teaching and learning) 5. Required Task 4 (By Group) - Using 2-3 approaches, design sample of each of the following: a. motivational learning activities b. classroom management routine c. instructional materials to be used (innovative/improvised IMs) (No duplication of approach) d. presentation/demo-teaching (5-7 minutes) UNIT 0: PRELIMINARIES 1. Student Engagement a. Teacher/Student Introduction b. Course Orientation 2. Who Am I? / All About Me a. My Philosophy in Life b. Family c. Strengths and Weaknesses d. Word/Symbol that Best Represents Me e. Rule/Quote/Philosophy that Inspires me to keep going no matter what Questions for Reflection: 1. What is the most meaningful experience in your mathematics classes? 2. Mention the best teaching practice of your most favorite mathematics teacher that helped you a appreciate/love Mathematics (or your best teaching practice that made your students love Math) 3. Cite one difficult lesson in Math you learned the most. How did your teacher present this lesson? (or share one of the most difficult topic in Math and how did you present this to your class for meaningful learning?) Page 2 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City UNIT I: HUMANIZING MATHEMATICS INSTRUCTION 1. Reasons, Views, Observations, Experiences, and reflections of Teachers a. Reasons for Teaching 1. Energizing Environment It’s virtually impossible to be bored or stagnant with a job as challenging as teaching. Your brain is constantly engaged in creative ways as you work to solve a multitude of daily problems that you’ve never faced before. Teachers are lifelong learners who relish the chance to grow and evolve. Moreover, the innocent enthusiasm of your students will keep you young as they remind you to smile through even though the most frustrating moments. 2. Your Personality and Humor The greatest asset you bring to the classroom each day is your own unique personality. Sometimes in cubicle of life, there’s a need to blend in and tone down your personality. However, teachers absolutely must use their individual gifts to inspire, lead, motivate their students. And when the job gets tough, sometimes it’s only your sense of humor that can keep you moving forward with any sanity. 3. Job Security The world will always need teachers. If you are willing to work hard in any type of environment, you will find that you can always get work – even as a brand-new teacher. Learn your trade, earn your credential, become tenured, and you can breathe a sigh of relief knowing that you have a job you can count on for decades to come. 4. Intangible Rewards Most teachers find themselves encouraged and uplifted by the little joys that accompany working with children. You’ll cherish the funny things they say, the silly things they do, the questions they ask, and the stories they write. 5. Inspiring Rewards Each day when you go in front of your students, you never know what you will say or do that will leave a lasting impression on your students. We can all remember something positive (or negative) that one of our elementary school teachers said to us or the class – something that stuck in our minds and informed our viewpoints for all these years. When you bring the full force of your personality and expertise to the classroom, you can’t help but inspire your students and mold their young, impressionable minds. This is a sacred trust we are given as teachers, and definitely one of the benefits of the job. 6. Giving Back to the Community The majority of teachers enter the education profession because they want to make a difference in the world and their communities. This is a noble and valiant purpose that you should always keep in the forefront of your mind. No matter the challenges you face in the classroom, your work truly does have a positive ramification for your students, their families, and the future. Give your best to each student and watch them grow. This is truly the greatest gift of all. For reflection: Which of these reasons you can relate the most? Why? Page 3 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City b. Views of Teaching There are three common views of what constitutes teaching according to (Miller, 1996): 1. Teaching as a TRANSMISSION From this perspective, teaching is the act of transmitting knowledge from Point A (teacher’s head) to Point B (students’ heads). This is a teacher-centered approach in which the teacher is the dispenser of knowledge, the arbitrator of truth, and the final evaluator of learning. A teacher’s job from this perspective is to supply students with a designated body of knowledge in a predetermined order. Academic achievement is seen as students’ ability to demonstrate, replicate, or retransmit this designated body of knowledge back to the teacher or to some other measuring agency or entity. 2. Teaching as a TRANSACTION From this perspective, teaching is the process of creating situations whereby students are able to interact with the material to be learned in order to construct knowledge. Constructivism is an educational philosophy consistent with this view. Here, knowledge is not passively received; rather, it is actively built up or constructed by students as they connect their past knowledge and experiences with new information (Santrock, 2004). And just as each students’ past knowledge and experiences are different, so too is the interpretation, understanding, and meaning of the new information that each ultimately constructs. Teachers are not expected to pour knowledge into the heads of learners; rather, they assist learners in their construction of knowledge by creating experiences where students’ old information can transact with new information to create meaningful knowledge (knowledge that is connected to something students already know). Academic achievement from a constructivist perspective is seen as students’ ability to use this knowledge to solve real-world problems or to create products or performances that are valued in one or more cultural settings. 3. Teaching as a TRANSFORMATION From this perspective, teaching is creating conditions that have the potential to transform the learner on many different levels (cognitive, emotional, social, intuitive, creative, spiritual, and other). Transformational teaching invites both students and teachers to discover their full potential as learners, as members of society, and as human beings. The ultimate transformational goal is to help develop more nurturing human beings who are better able to perceive the interconnectedness of all human, plant, and animal life (Narve, 2001). For reflection: Can you share your thoughts on these views? As of now, how do you view your own teaching? What are your own views of teaching? - RITA PIERSON – “Every child deserves a champion: an adult who will never give up on them, who understands the power of connection and insists they become the best they can possibly be.” Page 4 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City - MAYA ANGELOU – “People will forget what you said. People will forget what you did. But people will not forget how you made them feel.” - Teaching is heart work. - “A teacher affects eternity; he/she can never tell where his influence stops.” (Henry Abams) - “Teaching is tiring but inspiring and rewarding career. Teaching is challenging but satisfying and fulfilling profession.” (Sir Rigz) For sharing: What are your own views of teaching? Video summary: We Are Teachers and We Do More Than Teach! https://youtu.be/ZnAGgWqG6yo Summary Teachers are multifaceted leaders who inspire, nurture, and empower students, shaping their futures and fostering creativity and resilience. Highlights - We are teachers and leaders, shaping young minds. - We inspire creativity through arts and sciences. - We teach essential skills: reading, writing, and problem-solving. - We cultivate compassionate global citizens. - We provide keys to success and self-discovery for our students. - We thrive in chaos, balancing many responsibilities daily. - We love and support each student as if they were our own. Key Insights - Diversity in Teaching: Teachers come from all backgrounds, bringing unique perspectives to the classroom, making education richer and more relatable. Page 5 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City - Failure as a Teacher: Emphasizing that mistakes are valuable learning opportunities encourages resilience and critical thinking in students. - Performance in the Classroom: Every day is a performance, where teachers engage and motivate students, sometimes deserving recognition for their efforts. - Controlled Chaos: Teachers master the ability to manage a dynamic environment, showcasing their adaptability and multitasking skills. - Igniting Passion: Teachers spark curiosity and wonder, ensuring students remain hopeful and engaged with their learning journey. - Not Just Babysitters: Teaching is a dedicated profession that goes beyond supervision; it is about nurturing growth and potential. - Global Citizenship: Educators instill values of compassion and awareness, preparing students to navigate and contribute positively to the world. c. The Habits of Effective Teaching Habit – a behavior that is repeated regularly and tends to occur unconsciously 1. Establish Mathematics goals to focus learning Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions. 2. Implement tasks that promote reasoning and problem solving Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies. 3. Use and connect mathematical representations Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools from problem solving. 4. Facilitate meaningful mathematical discourse Effective teaching of mathematics discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments. 5. Pose purposeful questions Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships. 6. Build procedural fluency from conceptual understanding Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. 7. Support productive struggle in learning mathematics Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. 8. Elicit and use evidence of student thinking Page 6 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning. (NCTM, 2014). “Let everything you do be done as if it makes a difference.” The ABCs of Good Character - Availability – we are always there to help each other - Brave – we face challenges head on - Content – we are happy with what we have - Dependable – we do what we say we’re going to do - Empathetic – we feel each other’s joys and sorrows - Forgiving – we don’t hold a grudge - Generous – we give cheerfully - Humble – we don’t brag about our victories - Industrious – we figure things out where we need to - Joyful – we find joy in life and in each other - Kindhearted – we lovingly care for each other’s needs - Loyal – we are here for each other in good times and bad - Mannerly – we behave in a way that is thoughtful of others - Neighborly – we love others with a smile and greeting - Obedient – we obey our parents - Patient – we show patience to each other - Questioning – we approach life with interest - Responsible – we do everything to the best of our ability - Self-controlled – we control our words and actions - Thankful – we are grateful for what we have - Unwavering – when we set our mind to something, we see it through - Virtuous – we aim to be pure - Wise – we make smart choices - Xcited – we ae excited about every new day of life - Yielding – we give up our personal rights with a desire to serve others - Zealous – we approach life with energy and zest For Sharing: 1. What for you is effective teaching? 2. Can you share your own habits of effective teaching? Or habits that need to be developed for effective teaching? 2. Humanizing Mathematics Instruction a. Teachers Sensitivity What is your idea of teacher’s well-being? Teacher’s well-being is reflected in a positive attitude toward teaching that stem from supportive relationships with colleagues and students. The belief that one’s personal and professional needs and expectations are met. Why is a teacher’s well-being important? The social, emotional, and physical health of teachers is a shared responsibility and a critical component of student learning and overall community well-being. When teachers feel supported, they are able to: o Manage the daily stresses of teaching Page 7 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City o Establish and maintain effective classroom management strategies that are productive for learning o Cultivate supportive and caring relationship with students As a teacher, how well are you? Are you happy? Excited? Thriving? Engaged? If not, Take care of yourself. Whether that means taking a mental health day once a month. Leaving at contract time. Eating lunch in your classroom. Not taking any work home. Eating all of your candy stash. Walking away from a negative co-worker. Or crying in your classroom at the end of the day. BREAKTHROUGH TEACHING “The Powerful Teacher” “I’ve come to a frightening conclusion That I am the decisive element in the classroom. It’s my personal approach that creates the climate. It’s my daily mood that makes the weather. As a teacher, I possess a tremendous power To make a child’s life miserable or joyous. I can be a tool of torture or an instrument of inspiration. I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis Will be escalated or de-escalated And a child humanized or dehumanized.” “Self-care isn’t selfish, it’s necessary.” Teacher Sensitivity According to University of Virginia Center for Advancement Study of Teaching and Learning, teacher’s responsiveness to students’ academic and emotional needs. According to Madison Below, it includes an awareness of individual students’ academic and social emotional needs in a way that allows teachers to anticipate areas of difficulty and provide appropriate and effective learning opportunities and levels of support for all students in the classroom. Lack of sensitivity Contribute to the atmosphere of anxiety in the classroom and may have behavioral and intellectual consequences for students. Concretizing Mathematics Concrete representations of abstract ideas not only make a significant contribution to the learning process but they provide the opportunity for restless learners to interact with the materials in an enjoyable way. Competition in Mathematical Class Competition, which is energizing for some students, sets up conditions under which other students may feel vulnerable and exposed. Creating a Positive Learning Climate for All Students Page 8 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City It is important for the teacher to help all students feel confident about their ability in Mathematics. Teachers need to have a variety of strategies for a class of students. Problem Solving A classroom in which problem solving plays a central role that can provide environment for mathematical learning to flourish. Small Group Learning Small learning groups minimizes competition and allow students to work together in a non-threatening environment. Assessment Strategies Written tests provide only one evaluation measure. Portfolios, projects, logs, journals, and expository and creative writing are all excellent alternatives that enable the teacher to assess mathematics learning. Sensitivity to Students’ Feelings In classroom everyone’s contributions should be valued, sarcasm must be avoided, and praise and encouragement should be used generously. Providing Time for Questioning The teacher should recognize this impulse and should pose questions that elicit rather than answers, to encourage students to deliberate and to understand the problem. - Do not allow the same students to dominate every discussion. Break up gendered monopolies by eliciting responses from others. - Avoid the temptation to call only the most talkative students. Appreciate aggressive women as you would aggressive men, but be aware of the effects that each has on others and the group. How do young children learn may NOT be the same as how students learn, but still, we may consider the following: - Children are curious, inquisitive, and always excited about learning new things. Learning for them comes naturally and the best way to teach children is to build on play and their natural learning styles. - Children learn though interacting with friends. - Children learn in a positive environment. - Children learn though play. - Children learn though their language. - Children learn though imitation. - Children learn by doing. - Children learn by moving. - Children learn through repetition. - Children learn through their senses. - Children learn by being motivated. - Children learn by experimenting. - Children learn at their own level. - Children learn though praise. - Children learn through exposure. When the above guidelines are followed, children will become more independent learners who are excited about school and are enthusiastic Page 9 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City about learning. They will have a strong foundation, confidence in their abilities and lifelong skills that will help them continue to learn. “Tell me, I’ll forget. Show me, I may remember. But involve me and I will understand.” (Chinese proverb) BECAUSE WE KNOW WE DO Children learn though their senses We provide real, three-dimensional objects for them to manipulate. Children need time to organize We provide long periods of their thoughts uninterrupted time for them to explore. Children have different attention We provide flexible schedule so spans children can move at their own pace Children are frustrated easily We provide an environment and materials that are accessible and easy for them to manage themselves Children are egocentric, only We do not force them to internalize seeing things from their own someone else’s point of view point of view Children want what they want to We listen to them and provide know ways for them to learn it. Children learn from making We allow mistakes to happen. mistakes Children learn from accomplishing We let them try without rushing in hard tasks with our solutions Children construct their own We provide a way for them to knowledge “teach” themselves. EXPERIENCE ENVIRONMENT Collecting Manipulatives Counting Puzzles Estimating Games Recording Brain Teasers Ranking Task Cards Comparing Graphing Paper Contrasting Clock Analyzing Ruler and tape measure Graphing Weighing Scale Evaluating Calculator b. PERMA, Care Theory/Care Pedagogy For reflection and sharing: 1. Can you share your idea about positive education? 2. What is meant by PERMA? Precious Moments: When do you feel the HAPPIEST? How can you incorporate that into your daily schedule? “Optimism is a happiness magnet. If you stay positive good thinsg and good people will be drawn to you.” Page 10 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City “Think Positive, Talk Positive, Feel Positive” How are you? - What does it mean to be HAPPY? - Do I have a positive outlook in life? - Do I have a supportive community to journey with? - Do I find purpose and fulfillment in what I do? - Do I feel proud about the things I do? What is Positive Education? - Approach to education that draws on positive psychology’s emphasis of individual strengths and personal motivation to promote learning. - The combination of traditional education principles with the study of happiness and wellbeing. - It aims to increase the experience of positive emotions in our students and encourage them to engage their strengths for personal and community goals. - Promote flourishing or positive mental health within the school community. PERMA by DR. MARTIN SELIGMAN – Father of Positive Psychology P – Positive Emotion E – Engagement R – Relationships M – Meaning A – Achievement/Accomplishment Video about PERMA: https://www.youtube.com/watch?v=jqqHUxzpf Summary The script discusses the PERMA model of positive psychology, emphasizing the importance of relationships, meaning, and engagement for happiness and well-being. Highlights - PERMA model includes five elements crucial for well-being. - Engagement through activities like music can enhance happiness. - Strong relationships are vital for personal and professional fulfillment. - Meaning and purpose in life contribute to overall satisfaction. - Positive psychology has gained traction with millions participating in assessments. - Measuring flow and engagement is essential in educational and workplace settings. - Techniques for building relationships can be learned and applied by anyone. Key Insights - The PERMA model serves as a comprehensive framework for understanding happiness, encompassing Positive Emotion, Engagement, Relationships, Meaning, and Accomplishment. Each element contributes uniquely to overall well-being. - Engagement, particularly through creative outlets like music, fosters a state of flow, enhancing life satisfaction. This highlights the importance of finding personal passions. - Relationships are foundational to happiness; investing in strong, supportive connections can lead to greater fulfillment and emotional resilience. - Meaning and purpose are crucial aspects of a well-lived life, encouraging individuals to contribute to something larger than themselves, enhancing life’s significance. - The rise of positive psychology has led to widespread participation in assessments, indicating a collective interest in mental health and well-being. Page 11 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City - Schools and workplaces are becoming more aware of the importance of measuring engagement and flow, leading to environments that support growth and satisfaction. - Learning techniques for building and maintaining relationships can empower individuals in various settings, enhancing both personal and communal well-being. P – POSITIVE EMOTION Experience happiness, joy, hope, love and gratitude What makes you good? Playing games? Watching movies? Physical exercise? Reading books? E – ENGAGEMENT Being completely engrossed in whatever you are doing What activities make you lose track of time? Board games? Meditation? Baking? Studying? R – RELATIONSHIP Having authentic and loving connections Who brings you joy, peace and support? Family? Friends? Colleagues? Teacher? M – MEANING Living with a sense of purpose What causes and pursuits do you find important and worthwhile? Helping your family in need? Engaging in spiritual activities? Sharing knowledge to others? A – ACCOMPLISHMENT Having a sense of achievement What are your goals? How can they achieve? Changing work-life balance? Learning something new? Why is it important to develop a positive attitude in learning mathematics? - Enable them to persevere in more-challenging problems, to take some responsibility for their own learning, and to develop good work habits in mathematics. How to implement Positive Education into the classroom? - Build up students’ confidence by using uplifting language - Honest feedback makes a stronger improvement - Motivating the students “Just like an angle of elevation, be someone who aims for the top, but whenever you reach the top, never ever look down on anyone else. Remember, life is like a WHEEL. Sometimes we’re up, sometimes we’re down.” “Who among you are feeling happy or excited today? How about, who are feeling down or sad today?” Investigate Feelings THINK and DRAW one thing/person/event that can uplift your mood and one thing/person/event that can sadden you. c. Humanizing Mathematics Teaching Page 12 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City d. Teacher’s Thriving Toolkit Teachers play an important role in the educational community. It is important to think about and promote teacher’s well-being in a holistic way in order to achieve better outcomes for learners and teachers. As a teacher, you will act as an ambassador to promote the teachers' well-being in your school. You can create a Personal Thriving Toolkit in Teaching Mathematics to note your challenges and needs, how you cope (it can be your self-care kit) for sharing your fellow teachers as well as the school’s support for wellness. Educators, you are superheroes. But even superheroes need to be taken care of! We know you pour out everything you have into your role, but how can you avoid burnout? How might you re-ignite a positive atmosphere in your school and lead your students to love learning? What are some ways you might be able to cultivate healthy relationships with colleagues? Better yet, leaders – how can you implement school-wide support for teacher well-being? – COVID-19: Resilient Educator Toolkit EXAMPLE: - Stay Calm - Move Forward - Be Informed - Embrace Change - Maintain Balance - Think Positively - Self-Care - Create a Plan - Stay Healthy - Stay Motivated Practice to be Positive - Positive thoughts… o About oneself ▪ Do not form your self-concept by comparing yourself to television or movie characters or people from public life ▪ Recognize your limitations and do something to improve yourself. ▪ Do not forget to emphasize your values and abilities. o About the past ▪ Do not blame the past for the difficult situations of today. This is completely useless. ▪ Consider the happiness and successes of yesterday, remember and enjoy them, and your attitude will become more positive. o About the future ▪ Thinking confidently and having hope will increase your probability of a happier life. ▪ If there is something negative that might happen, plan ahead so that distress will not overwhelm you if it does happen. o In relation to environment and people ▪ Put on “tolerance glasses” and observe your surroundings. Page 13 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City ▪ Do not judge people but rather respect them and appreciate the good things they do. - Also… o Choose to think ▪ Things are bad but they could be worse ▪ Perhaps, with some effort and patience I can resolve one thing at a time ▪ Not everything is perfect but there are good things in my life ▪ If I dedicate a little more quality time to my family, I can improve our relationship o Choose to be happy ▪ Most often, joy and happiness are personal choices, being happy is an option ▪ Simple choices, if made with determination, can provide much enthusiasm and prevent discouragement ▪ Optimistic thought is an excellent option for preserving our mental health and reaching our goals. o Looking beyond ▪ Look up! Look to the life of Jesus, considered to be the Greatest Teacher who ever lived. ▪ Stay fresh! ▪ Don’t be afraid to change for the better. ▪ Choose seminars and conventions where you can learn the most. ▪ Learn to use the latest technology to improve your teaching and inspire learning - Ennobling the Noble Professions: Teaching in the Twenty-first Century, H&H 2018 Vol 59 Mindset “My Attitude is (Only Partly) Everything” - Avoid Toxic Traps o Avoid complainers o Avoid gathering areas where negative talk is commonplace o Suggest solutions o Share your burnout efforts o Talk to your educator leaders if toxic conversation derails collaboration time o Identify your burnout triggers - Amend Toxic Thinking o Decide things you cannot control are not worth thinking about o Learn about growth mindset ▪ Growth mindset involves understanding that intelligence and abilities can be developed (as opposed to being “fixed” qualities) and has been repeatedly shown to lead to school success. o Find a healthy place to vent o Journal your frustrations o Play the “swap it” game o Find opportunities to laugh - Adopt Healthy Habits o Exercise o Establish healthy rituals o Get enough sleep o Wash your hands and get outside o Replace emotional eating with healthy rewards Page 14 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City o Play your own soundtrack - Reflection Exercises o What toxic thoughts do you commonly have and what are more positive thoughts with which you will try to replace them? o What unhealthy habits do you have, and what healthy habit or ritual will replace each of these? o Cultivating the pause or any short moments that bring you back – (it could be every time you sit at your desk, or walk to the copy room, or set dedicated moments at scheduled points throughout your day o Breathwork while cutting vegetables o Taking a breath before opening the door o Walking to work or taking a walk during a break o Reaching out to a colleague once a day with a positive comment o Taking five minutes of meditation at lunch instead of checking your phone o Noticing more closely during any sensory moments (wiping the whiteboard clean, pushing in chairs, sorting folders) o Setting an intention or dedicating a day or class period to as to a student o Taking short hallway walks during your plan periods o Devoting self-care time before or after the school day o Inviting a colleague to join you - Whole school Implementation and Support o School wide wellbeing calendar o Breathwork at meeting start o Voluntary Teacher Buddies o Mobilize around the goal, teacher wellbeing, with a sense of urgency o Name a Call-to-Action Design a one-pager: info-graphic, call to action, core beliefs, mission, vision, timeline, and goals o Build a task force of stakeholders with clear directives. Decide upfront how progress will be measured and collect that data (i.e. teacher attrition rats will go down, teacher satisfaction rates will go up). o Provide a menu of well being practices, both individual and social, both relaxing and invigorating (i.e. yoga, mindfulness, game of basketball, coffee with friends, etc.). There is no right or wrong way to access well-being practices; the critical piece is that they become a practice. o Connect students and teaches (tools like Class Catalyst) o Reflect and begin again with a single growth point. A single call to action that everyone can articulate and everyone will be able to see objectively when the goal is reached REFLECTIONS: 1. What moments during the day or week or school year do you notice that teacher self-care is needed most? 2. What challenging areas of teacher’s lives in and out of the school day are opportunities for change and self-care? 3. Imagine what your school community might look and feel like if it cultivates a culture of self-care and wellness. Describe or imagine the details. Page 15 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City 3. Realistic Mathematics Education – RME (Contextualization, Localization, Indigenous Culture, etc.) UNIT II: CONCEPTUAL FRAMEWORK OF MATHEMATICS EDUCATION 1. Goals in Mathematics Education a. K to 12 Curriculum / Matatag Curriculum For Sharing: As an educator, what invaluable treasures or insights do you hope to uncover within the Matatag curriculum that will enrich both your teaching practice and your students’ learning experience? The MATATAG Curriculum The MATATAG program hopes to resolve basic education challenges, namely: MA – Make the curriculum relevant to produce job-ready, active and responsible citizens; TA – Take steps to accelerate delivery of basic education facilities and services; TA – Take good care of learners by promoting learner well-being, inclusive education, and a positive learning environment; and G – Give support to teachers to teach better According to DepEd Order No. 010, s. 2024, a comprehensive review of the K-12 Basic Education Program has revealed several issues, such as: - Overcrowded curriculum - Misaligned learning competencies - Imbalanced cognitive demands MATATAG Curriculum – anchored on the MATATAG: “Bansang Makabata, batang Makabansa” Its goal is to “make the curriculum relevant to produce competent and job-ready, active, and responsible citizens.” CORE VALUES - Maka-Diyos - Makatao - Makakalikasan - Makabansa MATATAG Curriculum has sought to do the ff: a. Ensure every learner is equipped with life skills; b. Instill the value of citizenship and unity in diversity and work effectively with others; c. Educate all Filipino learners to handle challenges of everyday life and respond effectively to disasters and emergency situations; d. Prepare them to thrive in a global human resource market so that they can contribute effectively to nation-building and economic development; and e. Foster critical and creative thinking in Filipino learners by working collaboratively with peers towards identifying problems and challenges that may impact the present and the future, finding and designing solutions for them; and engaging in activities that encourage thinking out of the box. Page 16 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City IMPLEMENTATION OF THE MATATAG CURRICULUM What is the difference of K-TO-12 Curriculum and MATATAG Curriculum in terms of: - Conceptual Framework in mathematics Matatag Mathematics Framework includes: o A robust mathematical content. o A set of strategic skills for applying mathematics in various context o A sound mathematical disposition The Supporting Components o Pedagogy o Assessment o Resources Mathematical Proficiency o Conceptual Understanding – comprehension of mathematical concepts, operations, and relations o Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately o Strategic Competence – ability to formulate, represent, and solve mathematical problems o Adaptive Reasoning – capacity for logical thought, reflection, explanation and justification Page 17 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City o Productive Disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Critical Thinking o The process of purposeful reflective judgement (Factione and Gittens, 2016) o Applies cognitive skills of interpretation, analysis, inference, evaluation, explanation, and self-regulation in an effort to judge what to believe or what to do Problem Solving o Finding way out of a difficulty, a way around an obstacle, attaining an aim which was not immediately attainable (Polya, 1981) o Solving problems is not only goal of learning mathematics but also a major means of doing so (NCTM, 2000) - Main goal in mathematics K-12 Curriculum MATATAG Curriculum The twin goals of mathematics The main goal of the curriculum in the basic education levels, K- is for Filipino learners to become 10, are Critical Thinking and mathematically proficient and Problem Solving. critical problem solvers. - Lesson content K-12 Curriculum MATATAG Curriculum Mathematics CG (2016) Mathematics CG (2023) Numbers and Number Sense Number and Algebra - patterns Measurement involving numbers, Geometry shape, and their Patterns and Algebra attributes; Algebraic Statistics and Probability perspective of numbers; Notions of equations, functions, and analytic geometry Measurement and Geometry - Shapes, their properties, and their geometric measurement; Axiomatic development, advanced concepts, and proofs Data and Probability - Simple collection and representation of data; Understanding the terms “likely”, “more likely”, and “most likely” as simple concepts of probability; Methodical, graphical, and numerical interpretations and computations of data; Experimental and theoretical perspectives of probability; Counting techniques Page 18 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City - Learning areas The learning areas of the K-12 Curriculum intersect the grade levels from Grade 1 – Grade 12. The learning areas are: o Languages: Mother Tongue, Filipino, English o Arts and Humanities: Music, Arts, Physical Education and Health (MAPEH), Edukasyon sa Pagpapahalaga, Araling Panlipunan o Science and Mathematics o Technology and Livelihood Education REVISED K-10 Curriculum Subjects under the Recalibrated Curriculum o Grade 1 ▪ Language ▪ Reading and Literacy ▪ Mathematics ▪ Makabansa ▪ GMRC o Grade 2 ▪ Filipino ▪ English ▪ Mathematics ▪ Makabansa ▪ GMRC o Grade 3 ▪ Filipno ▪ English ▪ Science ▪ Mathematics ▪ Makabansa ▪ GMRC o Grade 4-10 ▪ Filipino ▪ English ▪ Science ▪ Mathematics ▪ AP ▪ MAPEH ▪ TLE ▪ GMRC - Time allotment K-12 Curriculum Note: A one-hour period for Homeroom/Guidance Program is provided for the weekly meeting between the teacher-adviser and the class. Page 19 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City MATATAG Curriculum For Sharing: 1. As a teacher share your experience in implementing the k-12 Curriculum. 2. What difficulty are you encountering in implementing the new curriculum (Matatag Curriculum)? b. Critical Thinking Skills The process of purposeful reflective judgement (Factione and Gittens, 2016) Page 20 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City Applies cognitive skills of interpretation, analysis, inference, evaluation, explanation, and self-regulation in an effort to judge what to believe or what to do. Critical thinking is like using your brain's "superpowers" to make smart choices; - Whether it's picking the right insurance; - Deciding what to do in a job; or - Discussing topics in school, thinking deeply helps a lot. CRITICAL THINKING is the ability to think clearly and rationally about what to do or what to believe. It includes the ability to engage in reflective and independent thinking. 1. Understand the logical connections between ideas. 2. Identify, construct, and evaluate arguments. 3. Detect inconsistencies and common mistakes in reasoning. 4. Solve problems systematically. 5. Identify the relevance and importance of ideas. 6. Reflect on the justification of one’s own beliefs and values. Critical and Analytical Thinking Skills 1. Problem Solving 2. Communicating Mathematically 3. Reasoning 4. Making Mathematical Connections The Importance of Critical Thinking - Critical Thinking is a Domian-General Thinking Skills The ability to think clearly and rationally is important whatever we choose to do. If you work in education, research, finance, management or the legal profession, then critical thinking is obviously important. But critical thinking skills are not restricted to a particular subject area. Being able to think well and solve problems systematically is an asset for any career. - Critical Thinking is Very Important in the New Knowledge Economy Page 21 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City The global knowledge economy is driven by information and technology. One has to be able to deal with changes quickly and effectively. The new economy places increasing demands on flexible intellectual skills, and the ability to analyze information and integrate diverse sources of knowledge in solving problems. Good critical thinking promotes such thinking skills, and is very important in the fast-changing workplace. - Critical Thinking Enhances Languages and Presentation Skills Thinking clearly and systematically can improve the way we express our ideas. In learning how to analyze the logical structure of texts, critical thinking also improves comprehension abilities. - Critical Thinking Promotes Creativity To come up with a creative solution to a problem involves not just having new ideas. It must also be the case that the new ideas being generated are useful and relevant to the task at hand. Critical thinking plays a crucial role in evaluating new ideas, selecting the best ones and modifying them if necessary. - Critical Thinking is Crucial for Self-Reflection In order to live a meaningful life and to structure our lives accordingly, we need to justify and reflect on our values and decisions. Critical thinking provides the tools for this process of self-evaluation. - Good Critical thinking is the foundation of science and democracy Science requires the critical use of reason in experimentation and theory confirmation. The proper functioning of a liberal democracy requires citizens who can think critically about social issues to inform their judgments about proper governance and to overcome biases and prejudice. - Critical Thinking is a Metacognitive Skill Higher-level cognitive skill involves thinking about thinking. Having an awareness in reasoning and be reflective about our own reasoning. Improving ourselves, avoid biases, and maintain objectivity. The mastery of critical thinking is similar to the mastery of many other skills. There are three important components: theory, practice, and attitude. Improving Our Thinking Skills THEORY Thinking correctly needs following the correct rules of reasoning. Theory includes rules. Knowing and practicing basic principles of critical thinking, such as logic, and methods of thinking. By minimizing the probability of doing the same mistakes of other people, we need to follow the correct rules of reasoning. First, this requires some knowledge of typical fallacies. Second, psychologists have discovered persistent biases and limitations in human reasoning. An awareness of these empirical findings will alert us to potential problems. PRACTICE Knowing solemnly will not make you a critical learner, it should be practice and apply them to daily life. There are ways to do this; 1. Perform lots of quality exercises. By engaging in discussions and debates with other people in our daily lives, where principles of thinking can be applied. Page 22 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City 2. To think more deeply about the principles that we have acquired. In the human mind, memory and understanding are acquired through making connections between ideas. ATTITUDES Good critical thinking skills require more than just knowledge and practice. Persistent practice can bring about improvements only if one has the right kind of motivation and attitude. The following attitudes are not uncommon, but they are obstacles to critical thinking… 1. I prefer being given the correct answers rather than figuring them out myself 2. I don’t like to think a lot about my decisions as I rely only on gut feelings. 3. I don’t usually review the mistakes I have made. 4. I don’t like to be criticized. The Importance of Critical Thinking To improve our thinking we have to recognize the importance of reflecting on the reasons for belief and action. We should also be willing to engage in debate, break old habits, and deal with linguistic complexities and abstract concepts. In mathematics education, critical thinking skills are integral to achieving several key goals: 1. Understanding Mathematical Concepts: Critical thinking helps students grasp abstract mathematical concepts by questioning assumptions, exploring definitions, and understanding the underlying principles behind mathematical operations. 2. Developing Problem-Solving Strategies: It fosters the ability to analyze complex problems, develop multiple strategies for solving them, and choose the most effective approach based on logical reasoning. 3. Enhancing Logical Reasoning: Critical thinking skills enable students to construct sound mathematical arguments, identify logical fallacies, and evaluate the validity of mathematical statements and proofs. 4. Improving Analytical Skills: Students use critical thinking to analyze data, interpret results, and identify patterns or relationships within mathematical problems, leading to deeper insights and more accurate conclusions. 5. Fostering Intellectual Curiosity: By questioning and exploring mathematical concepts and problems, students develop a sense of intellectual curiosity and a desire for deeper understanding. These goals aim to prepare students not only for academic success and excel in mathematics but also for applying mathematical thinking in various real-world situations "The mind is not a vessel to be filled, but a fire to be ignited". -Plutarch For Sharing: Can you share your experience of how you used critical thinking to make decisions or choices in your life? How does it help you? c. Problem Solving and Problem-based Strategies PROBLEM SOLVING STRATEGIES 1. Guess and Check Page 23 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City o When unsure how to start, guess an answer and then check it. o In the process of checking guess, you may see a way of revising your guess to get closer to the answer or to get the exact answer. 2. Make a table and look for a pattern o Some problems describe relationships that involve regular sequence of numbers or other things. o To solve the problem, you need to be able to recognize and describe the pattern that gives the relationship for the numbers or things. o One way to recognize the information given is to make a table. 3. Solving a similar but simpler problems o By solving one or more simpler problems, you can often find a pattern that will help solve a more complicated problem. 4. Use of logical reasoning o Some of the problems can be solve without the use of numbers. They can solve by the use of the logical reasoning given some information. 5. Working backwards o To solve some problems, you need to start the end result and work backwards to the beginning. 6. Make an organized list o Making an organized list will lead you to work logically and systematically. 7. Write and solve an equation o Algebraic expressions are used to represent information and solve problems. We used a variable for the unknown quantity and expressed the given information in an equation. For sharing: 1. What specific questioning techniques can teachers use to promote critical thinking during problem-solving activities in math class? 2. How does encouraging students to justify their answers and reasoning enhance their critical thinking skills in mathematics? For sharing: 1. Can you share your experience of how you used critical thinking to make decisions or choices in your life? How does it help you? 2. What critical thinking skills and problem-solving strategies have you integrated in your classroom instruction? 3. What are some common challenges students face in developing critical thinking and problem-solving skills in math, and how can you, as a teacher, address these challenges? 2. Constructivism in Mathematics Teaching a. Various Constructivism Strategies in Teaching Mathematics / Best Practices on Using Constructivist Approach For sharing: In your own understanding, what is constructivism, and how does it differ from other philosophies? Page 24 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City What is CONSTRUCTIVISM? - its central idea is that human learning is constructed, that learners build new knowledge upon the foundation of previous learning; - reality is determined by one’s experiences as a learner; - individual experiences make one’s learning unique. Principles of Constructivism - Knowledge is constructed. - People learn to learn, as theylearn. - Learning is a social activity. - Learning is contextual. - Knowledge is personal. - Learning exists in the mind. - Motivation is key to learning. Constructivism in Education In constructivist classrooms… o teacher has a role to create a collaborative environment where students are actively involved in their own learning. o teachers are more facilitators of learning than actual instructors. o teachers must work to understand the preexisting conceptions and understanding of students, then work to incorporate knowledge within those areas. o teachers will also need to adjust their teaching to match the learner’s level of understanding. Constructivist learning is described as follows: o Learning builds on the learner’s prior knowledge and the approach are a constructive process. o Learners are involved in the processes to ensure self-regulated and self-directed processes. o Learning is grounded in the context of the learners and fundamentally social processes. Interaction and communication are open and basic elements of the learning process. o Learning is more than the acquisition of knowledge. It is collaborative, involves interaction and enculturation with a community of practitioners. Collaboration of experts is basic. o The learning process does not only require cognitive but also motivational and emotional domains Constructivist classrooms rely on five key areas to be successful: o Must be learner-centered o Shared knowledge between teachers and students. o Shared authority between teachers and students. o Teachers act as a guide or facilitator. o Learning groups consist of small numbers of students. Constructivism in Mathematics Class In constructivist mathematics class, knowledge is constructed by the learners. To teach is not to explain, not to lecture, and not to transfer mathematical knowledge. Instead, teaching is to create situations that allow learners to form the mental construction. Page 25 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City The following are some recommendations on how to apply constructivism in teaching mathematics: o pose problems that are relevant to the learners o use big concepts than segmented or disjoint topics o create situations that will reveal the learner’s point of view o use authentic assessments, which include interaction between the teacher and the learner and learner and peer. 1. Relating o Learning in the context of one's life experiences ▪ A teacher uses relating when s/he links a new concept to something completely familiar, thus connecting what his/her students already know to the new information. 2. Applying o Learning by putting the concepts to use ▪ Teachers can use realistic and relevant exercises to stimulate a need for mathematics, pose a realistic situation and they demonstrate the utility of mathematics in a student's life, current or future. 3. Experiencing o It is learning by doing—through exploration, discovery, and invention. a. Manipulatives Students move these simple objects around to model abstract concepts concretely b. Problem Solving Activities These hands-on activities engage students' creativity while teaching problem-solving skills, mathematical thinking, communication, and group interactions. c. Laboratory activities Learners may lead to different predictions/conclusions, but through them, they learn that multiple perceptions exist and that even in mathematics, the "right" answer can be a matter of interpretation. 4. Cooperating o learning in the context of sharing, responding, and communicating with other learners ▪ Working with their peers in small groups, most students feel less self-consciousness and can ask questions without a threat of embarrassment. 5. Transferring o using knowledge in a new context or situation ▪ Transferring is especially effective when students use newly acquired knowledge in unfamiliar situations. For Sharing: 1. How have you incorporated any of the mentioned strategies to foster a constructivist environment in your math lessons? What has been the impact on students’ understanding and engagement when using constructivist methods in your math teaching? 2. Besides the strategies mentioned, what other constructivist approaches have you found effective in teaching mathematics? 3. What challenges have you encountered when implementing constructivist strategies in your mathematics classroom? 4. How can you use constructivism in your future math class? Page 26 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City b. Teaching for Understanding in Mathematics What is Understanding? Understanding is being able to think and act flexibly with a topic or concept. It goes beyond knowing; it is more than a collection of information, facts, or data. It is more than being able to follow steps in a procedure. Mathematical understanding entails knowing, perceiving, comprehending, and making sense of the meaning and connotation of mathematical knowledge. There are two understandings according to Skemp’s Understanding Theory, namely INSTRUMENTAL Understanding and RELATIONAL Understanding. Instrumental understanding is the ability to correctly apply mathematical rules or procedures in solving problems without knowing the reasons for their use and having an understanding limited to memorizing facts without a deeper understanding of a concept. Relational understanding is the ability to apply mathematical rules or procedures correctly in solving problems and knowing the reasons for their use so that they can connect various mathematical concepts. Instrumental Understanding, at the left end shows that ideas are learned, but in isolation to other ideas. At the right end of the continuum is Relational Understanding. It means that new concept or procedure is not only learned, but is also connected to many existing ideas. Teaching for understanding in math focuses on helping students grasp mathematical concepts deeply rather than just memorizing procedures or formulas. It involves the following: Page 27 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City 1. Conceptual Understanding: Emphasize the "why" behind mathematical processes. 2. Connections and Relationships: Highlight the relationships between different mathematical concepts. 3. Problem-Solving and Critical Thinking: Encourage students to apply their understanding to solve complex problems. 4. Real-World Applications: Make connections to real-life situations where mathematical concepts are applied. 5. Active Engagement: Use methods that actively engage students in the learning process. 6. Formative Assessment: Continuously assess students' understanding through various methods and provide feedback to guide their learning Standards for Mathematical practice as ways to develop a deep understanding ▪ Make sense of problems and persevere in solving them To make sense of problems, students need to learn how to analyze the given information, the parameters, and the relationships in a problem so that they can understand the situation and identify possible ways to solve it. ▪ Reason abstractly and quantitatively. This practice involves students reasoning with quantities and their relationships in problem situations. You can support students’ development of this practice by helping them create representations that correspond to the meanings of the quantities and the units involved. ▪ Construct viable arguments and critique the reasoning of others. This practice emphasizes the importance of students’ using mathematical reasoning to justify their ideas and solutions, including being able to recognize and use counterexamples. ▪ Model with mathematics. This practice encourages students to use the mathematics they know to solve problems from everyday life. ▪ Use appropriate tools strategically. Students should become familiar with a variety of problem‐ solving tools and they should learn to choose which ones are most appropriate for a given situation. ▪ Attend to precision. In communicating ideas to others, it is imperative that students learn to be explicit about their reasoning. For example, they need to be clear about the meanings of operations and symbols they use, to indicate units involved in a problem, and to clearly label diagrams that accompany their explanations. ▪ Look for and make use of structure. Students who look for and recognize a pattern or structure can experience a shift in their perspective or understanding. Page 28 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City Therefore, set the expectation that students will look for patterns and structure and help them reflect on their significance. ▪ Look for and express regularity in repeated reasoning. Encourage students to step back and reflect on any regularity that occurs in an effort to help them develop a general idea or method to identify shortcuts. Students’ ideas are key. Mathematical ideas, expressed by students, are important and have the potential to contribute to everyone’s learning. Learning mathematics is about coming to understand the ideas of the mathematical community. ▪ Opportunities for students to talk about mathematics are common. ▪ Multiple approaches are encouraged. ▪ Mistakes are good opportunities for learning. ▪ Math makes sense. Students must come to understand that mathematics makes sense. An understanding can never be “covered” if it is to be understood. - Wiggins and McTighe For Sharing: 1. Share your experience on how teaching for understanding is facilitated in your class. 2. What difficulties you encountered in achieving your goals for teaching for understanding in math? C. Dale’s Cone of Experience Who is Edgar Dale? Edgar Dale (1900–1985) was an American educator and a pioneer in audiovisual education. In his influential work Audiovisual Methods in Teaching (1946). He introduces the Cone of Experiences. Dale's Cone of Experience arranges educational methods along a continuum from the most concrete experiences at the base to the most abstract at the peak. The Cone of Experience Dale's Cone of Experience arranges educational methods along a continuum from the most concrete experiences at the base to the most abstract at the peak. The premise is that learning becomes more abstract as one moves up the cone. The progression indicates that learners start with direct, hands-on experiences (concrete) and eventually move to symbolic, conceptual forms of learning (abstract). Page 29 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City LEVELS OF DALE’S CONE OF EXPERIENCE 1. Direct Purposeful Experiences (Base) These are real-life, hands-on activities where learners actively engage with the subject. For example, conducting an experiment or building something are direct experiences that involve multiple senses. Examples. - Using manipulatives like counting blocks, geometric shapes, or fraction tiles to represent numbers and operations. - Measuring objects around the classroom to teach concepts of length, volume, and weight. - Building models (e.g., constructing 3D shapes) to explore geometry. 2. Contrived Experiences At this level, teachers use simulations or models to create experiences that closely mimic real-life scenarios. These are often controlled environments, such as using a flight simulator to teach pilots. Examples. - Using digital tools and apps to simulate mathematical scenarios, like virtual manipulatives or graphing software. - Role-playing real-world situations (e.g., setting up a mock store to practice addition, subtraction, or percentages). - Creating scaled models to explore concepts of ratio and proportion. 3. Dramatized Experiences Role-playing and dramatization allow learners to enact real life situations in a controlled environment. For example, a mock trial in a law class helps students understand legal procedures through active participation. Examples. - Acting out a scenario where students play the roles of buyers and sellers to understand transactions, costs, and profits. Page 30 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City - Creating stories around math problems (e.g., using a narrative to explain how fractions are used in cooking). - Role-playing as architects to design buildings with specific geometric requirements. 4. Demonstrations Demonstrations involve showing learners how something works, which allows them to observe the process in a structured way. This can involve live demonstrations, videos, or other media. Examples. - Demonstrating how to solve equations step by step on a whiteboard or using an interactive digital platform. - Showing geometric constructions using tools like a compass, protractor, and ruler. - Illustrating probability through experiments (e.g., rolling dice or drawing cards). 5. Study Trips Field trips or study tours allow learners to experience environments outside the classroom. These experiences provide context and help learners understand the real-world application of their classroom lessons. Examples. - Visiting a science museum or planetarium where mathematics is used to explain phenomena. - Touring a construction site to observe how geometry, measurement, and engineering principles are applied. - Exploring nature parks to study patterns, symmetry, and ratios found in nature. 6. Exhibits Exhibits are displays that learners can observe, often without interaction. These are usually found in museums or educational institutions, where learners can see representations of objects or concepts Examples. - Setting up math stations in the classroom where students can explore different concepts, like probability with spinners or symmetry with mirrors. - Displaying posters that illustrate key formulas, theorems, or mathematical patterns. - Using bulletin boards to show visual representations of math problems, solutions, or historical mathematicians' contributions. 7. Educational Television and Motion Pictures Page 31 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City These media forms use video to present information more dynamically than still pictures, helping learners understand processes and events that they might not be able to experience directly. Examples. - Showing videos that explain complex concepts like algebraic functions, calculus, or geometry through visual stories. - Using documentaries about famous mathematicians to inspire students and show the real-world impact of math. - Animations that visually represent abstract concepts, like how a parabola is formed or how graphs of functions behave. 8. Recordings, Radio, and Still Pictures These include audio recordings, podcasts, and photographs. They are more abstract than live experiences because they indirectly represent events and concepts but provide sensory input. Examples. - Incorporating podcasts or recorded lectures that explain difficult concepts. - Using photographs or drawings of real- world objects to teach geometry or scale. 9. Visual Symbols Charts, graphs, and diagrams fall under this category. These visual aids are abstract representations that help learners conceptualize information by simplifying complex realities. Examples. - Using graphs to teach concepts such as functions, slope, and data analysis. - Creating Venn diagrams to explore set theory and logic. - Using pie charts and bar graphs to represent data in statistics lessons. 10. Verbal Symbols (Peak) Verbal symbols are the most abstract form of learning and include written or spoken words. At this level, learners engage with ideas purely through language, without direct sensory input Examples. - Teaching students the formal notation for algebraic expressions, equations, and functions. - Engaging students in problem-solving using only verbal descriptions and abstract reasoning. - Encouraging students to articulate mathematical concepts in written or spoken form, such as explaining a proof or writing about their problem-solving process. Reflection Question: Page 32 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City In your experience as a teacher, how do you ensure that students effectively transition from direct, concrete experiences to more abstract concepts in a way that fosters deep understanding and retention of mathematical ideas? Possible Answers: 1. Through scaffold learning, begin with hands-on activities and gradually transition to more abstract representations. 2. Link abstract concepts to concrete experiences. Relate abstract mathematical concepts to real-life scenarios that students can understand. 3. Promote active engagement. Keep students actively engaged to make learning more participatory and less passive. 4. Frequent formative assessments. Regularly assessing students' understanding of the concepts helps them move forward to more abstract ideas and helps teachers adjust instructions and strategies to solidify students' understanding of the concepts. 5. Foster reflection and metacognition. Allowing students to reflect on their learning process encourages them to move from concrete experiences to abstract understanding. Key Insights The cone emphasizes that learning moves from direct, sensory- rich experiences to more abstract, symbolic forms of understanding. As learning becomes more abstract, fewer senses are engaged. For instance, verbal symbols at the peak of the cone engage only auditory or visual senses, while direct experiences involve all senses. At the base of the cone, learners are active participants, while at the peak, they become passive observers UNIT III: TEACHING AS A PROCESS AND COMMON TEACHING APPROACHES 1. Classification of Teaching Methods/Approaches and Guidelines Involved in the Use of Teaching Methods/Approaches o Teaching Approach - is a set of principles, beliefs or ideas about the nature of learning which is translated into the classroom. o Teaching Strategy - is a long-term plan of action designed to achieve a particular goal. o Teaching Method - is a systematic way of doing something. It implies an orderly logical arrangement of steps. It is more procedural. o Teaching Technique - is a well-defined procedure used to accomplish a specific activity or task Page 33 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City o Examples of Teaching Approaches Teacher-centered Learner-centered Subject-matter centered Learner-centered Teacher-Dominated Interactive Banking Approach Constructivist Disciplinal Integrated Individualistic Collaborative Indirect, guided Direct o Direct/Expository Approach - Direct Instruction/Lecture Method ▪ Is aimed at helping the students acquire procedural knowledge which is knowledge exercised in the performance of some task. ▪ Procedural knowledge - skills needed in the performance task. ▪ It is use for lessons that are factual and non-controversial. ▪ The strategy is teacher- directed. ▪ The emphasis is on the teaching of skill. Each step must be mastered; hence the students gain “how” rather than “what”. ▪ Taught in a step-by-step fashion, it ensures the learning if the entire procedure with no step missed. ▪ This is a form of learning through imitation, sometimes termed “behavioral modeling” ▪ This can also be used to teach facts, principles and laws. ▪ Steps of the Direct Instruction/ Lecture Method 1. Provide the rationale. 2. Demonstrate the skill. 3. Provide guided practice until mastery. 4. Check for understanding and provide feedback. 5. Provide extended practice and transfer. 6. Assess learning at the end. ▪ Guidelines for Its Effective Use (Teaching Skill) 1. The students must be given ample time for practice. 2. They must be included in the planning stage since this technique is highly task-oriented and aimed at mastery of every step. The lesson objectives are student-based. 3. Describing the testing situation and specify the level of performance expected. Page 34 of 35  West Visayas State University College of Education GRADUATE SCHOOL Luna St., La Paz, Iloilo City 4. Divide the complex skills and understanding into subskills or into its component steps so they can be taught easily and with precision. - Demonstration Method 2. Motivation an Essential Tool in Teaching Mathematics a. Sample Motivational Techniques/Activities and IMs on identified competency 3. Describing and Demonstrating Various Teaching Approaches in Mathematics (Conceptual approach/ Concept-Attainment Method, Process Approach, Practical Work Approach, Discovery/Guided Discovery Approach, etc.) 4. Other Approaches in Teaching Mathematics (Use of flash cards/ task cards, worksheets, games, puzzles, trivia, info graphics, storybook, Math Journal, Math Trail, Math Camp, music, poetry, rap, contests/ quiz bee, etc.) UNIT IV: CLASSROOM-TESTED, INNOVATIVE AND INTERDISCIPLINARY MODES OF INSTRUCTION DELIVERY OF MATHEMATICS 1. Consolidation and Practice/Review 2. Exposition/Direct Instruction 3. Lecture-discussion/ Punctuated Lecture/ Interactive Lecture 4. Cooperative Learning Structures 5. Situated Learning/Experiential Learning 6. Socratic Method/ Asking Appropriate Questions 7. Writing to Learn (Construction of sample of the different writing to learn strategies) 8. Reflective Teaching (Reflective Journal Writing, Learning Log, Learning Journal, Reflective Teaching Lesson Worksheet and Sample processing Questions for Reflective Teaching) *NOTE: Each strategy will be discussed in relation to Mathematics teaching with sample classroom management routine and sample instructional materials using this strategy. Page 35 of 35