AMANTEMARY_ACTIVE_LEARNING_STRATEGIES.pptx

Teaching Strategies

1. ACTIVE LEARNING STRATEGIES MARY U. AMANTE

2. What is Active Learning? “Say goodbye to passive learning and embrace the power of active learning.” Active learning strategies have evolved through contributions from various educators and theorists who emphasized the importance of engaging students in the learning process. From Socratic questioning to contemporary technology-enhanced learning environments, the core idea remains that students learn best when they are actively involved in constructing their knowledge and understanding. Active learning strategies are instructional approaches that engage students in the learning process directly through activities and discussions, rather than passively listening to lectures. In a math classroom, these strategies can enhance understanding, retention, and application of mathematical concepts.

3. Importance in Education Boosts students engagement and participation- active learning involves students in interactive activities, increasing their involvement and attentiveness in the learning process. Develops critical thinking and problem-solving skills- Through active learning methods, students are encourage to analyze, evaluate and apply knowledge to solve real-world challenges. Enhance collaboration and communication abilities- active learning fosters group discussion and teamwork, improving students’ interpersonal skills and communication. Empowers students to take ownership of their own learning process- by engaging in active learning, students become active participants in their education, driving curiosity and motivation to explore and learn independently. Improve long-term knowledge and retention- active learning methods, discussions, hands-on activities, and problem-solving skill, have been shown to enhance memory retention and recall of information over time

4. Active Learning Strategies 1. Think-Pair-Share - Students first think about a question or problem individually, then pair up with a partner to discuss their thoughts, and finally share their conclusions with the class. Example: In a lesson on solving quadratic equations, the teacher might pose a problem such as . Students first solve it individually, then discuss their methods and solutions with a partner. After the pair discussions, selected pairs share their solutions with the entire class, discussing different methods such as factoring, using the quadratic formula, or completing the square. 2. Peer Instruction - Students answer a conceptual question individually, then discuss their answers with peers, and finally answer the question again. Example: During a unit on probability, the teacher presents a question: "What is the probability of drawing an ace from a standard deck of cards?" Students first respond using clickers or paper, revealing varying levels of understanding. After discussing the question and their reasoning with peers, they answer again. This process helps clarify misconceptions and deepen understanding.  

5. Active Learning Strategies 3. Collaborative Problem Solving - Students work together in small groups to solve a complex problem or complete a task. Example: For a topic on linear equations, the teacher provides a real-world problem such as: "A company sells two products. Product A sells for $20 each, and Product B sells for $30 each. The company needs to earn $600 in sales. How many of each product should they sell to reach this goal?" Students collaborate in groups to set up and solve the system of equations representing the problem. 4 . Math Stations - Different stations are set up around the classroom, each with a unique activity or problem. Students rotate through the stations in groups. Example: In a geometry class, stations might include activities like: - Station 1: Constructing and measuring different types of angles. - Station 2: Solving problems involving the Pythagorean theorem. - Station 3: Identifying properties of different polygons. Students spend a set amount of time at each station before moving on, promoting varied and active engagement with the material.

6. Active Learning Strategies 5. Flipped Classroom - Students learn new content at home (e.g., through video lectures or readings) and use class time for engaging in hands-on activities, problem-solving, and discussions. Example: Before a lesson on derivatives, students watch a video explaining the concept and basic rules of differentiation. In class, they work on a series of challenging differentiation problems in small groups, with the teacher available for guidance and to answer questions. 6. Gallery Walk - Students solve problems or create posters on large sheets of paper, which are then displayed around the room for classmates to review and provide feedback. Example: For a statistics unit, students might create posters showing different data sets and their corresponding histograms, box plots, and summary statistics. As students walk around reviewing each other's work, they leave sticky notes with comments or questions, promoting peer learning and discussion.

7. Active Learning Strategies 7. Interactive Simulations and Technology -Using interactive tools and software to explore mathematical concepts dynamically. Example: In a calculus class, students use graphing calculators or software like GeoGebra to explore the behavior of functions and their derivatives. By manipulating parameters and observing changes in real-time, students gain a deeper, more intuitive understanding of the concepts. 8. Case-Based Learning - Presenting students with a real-world case or scenario that requires the application of mathematical concepts to solve. Example: In an algebra class, students might be given a case study about optimizing the layout of a community garden. They use linear programming techniques to determine the most efficient use of space to maximize crop yield.

8. Active Learning Strategies 9. Concept Mapping - Students create visual representations of the relationships between different concepts. Example: After a unit on trigonometry, students create concept maps linking sine, cosine, tangent, and their applications in real-world contexts, such as engineering and physics. 10. Problem-Based Learning (PBL) - Students learn through the experience of solving an open-ended problem. Example: For a unit on exponential growth and decay, students might work on a project analyzing population growth trends in different countries. They gather data, create models, and present their findings, demonstrating their understanding of exponential functions and their applications.

9. FLIPPED CLASSROOM MODEL The flipped classroom model is an instructional strategy that reverses the traditional teaching approach. In a flipped classroom, students are introduced to new content at home, often through video lectures or readings, and then apply that knowledge in the classroom through activities, problem-solving, and discussions. This model shifts the focus from passive to active learning during class time.

10. Key Components of the Flipped Classroom Model 1. Pre-Class Preparation : - Students learn new concepts at home using materials such as video lectures, readings, or interactive lessons. These materials are often prepared by the teacher or sourced from high-quality educational platforms. Example : For a lesson on the Pythagorean theorem, students might watch a video explaining the theorem, its proof, and some basic examples. 2. In-Class Activities : - Class time is dedicated to applying the concepts learned at home. Activities can include problem-solving, collaborative projects, discussions, and hands-on experiments. Example : During class, students work in groups to solve complex problems involving the Pythagorean theorem, such as finding the distance between two points on a coordinate plane or solving real-life application problems.

11. Key Components of the Flipped Classroom Model 3. Assessment and Feedback : - Continuous assessment and immediate feedback are integral to the flipped classroom. Teachers can assess understanding through quizzes, class discussions, and by observing student work during activities. Example : The teacher circulates the classroom, providing guidance and feedback as students work through problems. Quick formative assessments, such as mini-quizzes or exit tickets, can gauge student understanding.

12. Benefits of the Flipped Classroom Model 1. Increased Student Engagement: - Active learning during class time keeps students engaged and motivated. Example : Instead of passively listening to a lecture on solving quadratic equations, students work on solving different types of quadratic problems in groups, discussing and debating the best methods. 2. Personalized Learning : - Students can learn at their own pace at home, rewinding and reviewing materials as needed. Example : If a student struggles with understanding the concept of derivatives, they can rewatch the instructional video or review additional resources provided by the teacher.

13. Benefits of the Flipped Classroom Model 3 . Better Use of Class Time : - Class time is utilized for higher-order thinking activities, such as analysis, synthesis, and application, rather than mere content delivery. Example : After learning about integration techniques at home, students spend class time working on integration problems that involve real-world applications, like calculating areas under curves. 4 . Enhanced Teacher-Student Interaction : - Teachers can spend more time interacting with students individually or in small groups, addressing specific questions and needs. Example : During a lesson on statistical data analysis, the teacher can provide personalized guidance to students who struggle with interpreting data sets or using statistical software.

14. Challenges and Solutions 1. Student Preparation : - Ensuring all students complete the pre-class work is crucial for the model’s success. Solution : Use low-stakes quizzes or reflective questions at the beginning of the class to hold students accountable for their preparation. 2 . Access to Technology : - Students need reliable access to the internet and devices to view pre-class materials. Solution : Provide alternative resources, such as printed materials, or allow students to use school facilities to access online content.

15. Challenges and Solutions 3 . Initial Resistance : - Both students and teachers may resist the change from traditional methods. Solution : Clearly communicate the benefits of the flipped classroom model and gradually implement the approach to allow for adjustment.

16. Example Lesson Plan: Introduction to Functions Pre-Class Preparation : -Students watch a 15-minute video introducing functions, including definitions, notations, and examples of different types of functions (linear, quadratic, exponential). -They complete a short online quiz to check their understanding of the basic concepts. In-Class Activities: 1. Warm-Up (10 minutes): -Quick review of the online quiz results to address any common misconceptions or questions. - Brief discussion to reinforce key points from the video.

17. Example Lesson Plan: Introduction to Functions 2 . Group Activity (30 minutes ): - Students work in small groups to match different functions with their graphs and real-life scenarios. For example, matching a linear function with a scenario of constant speed, and an exponential function with population growth. Each group presents their matches and explains their reasoning. 3. Individual Practice (20 minutes ): - Students individually work on a set of problems involving function evaluation and interpretation, such as finding the value of a function for a given input or describing the behavior of a function based on its graph.

18. Example Lesson Plan: Introduction to Functions 4. Class Discussion (10 minutes ): Students share their solutions and approaches to the individual practice problems. The teacher facilitates a discussion on different methods and common errors. 5. Assessment and Feedback (10 minutes ): Exit ticket: Students write a brief summary of what they learned about functions and any questions they still have. The teacher reviews the exit tickets to plan follow-up activities or provide additional resources.

19. Theoretical Foundations and Practical Implications Active learning strategies and the flipped classroom model are grounded in several educational theories that emphasize student-centered, engaging, and effective learning experiences.

20. Theoretical Foundations 1. Constructivist Learning Theory : Concept: Constructivism, proposed by Jean Piaget and expanded by Lev Vygotsky, posits that learners construct their own understanding and knowledge of the world through experiences and reflecting on those experiences. Application in Math : Active learning and flipped classrooms allow students to build their understanding by engaging with mathematical problems and concepts actively. For example, students might explore geometric properties by manipulating shapes in a software program, thereby constructing their understanding through hands-on experience. In a flipped classroom, students engage with new mathematical concepts at home through videos or readings and then construct their understanding by applying these concepts during in-class activities. For example, after watching a video on solving quadratic equations, students solve various quadratic problems in class, discussing different methods and solutions with peers and the teacher .

21. Theoretical Foundations 2. Bloom’s Taxonomy: Concept: Bloom’s Taxonomy categorizes cognitive skills from lower-order thinking skills (remembering, understanding) to higher-order thinking skills (analyzing, evaluating, creating). Application in Math: Active learning strategies focus on engaging students in higher-order thinking skills during class time. In a flipped classroom, students watch videos to understand basic concepts at home (lower-order skills) and then engage in problem-solving and analysis in class (higher-order skills). For example, students might watch a video on the quadratic formula at home and then solve real-world quadratic problems in class.

22. Theoretical Foundations 3. Social Learning Theory (Vygotsky ): Concept: Vygotsky emphasized the importance of social interaction in learning and introduced the Zone of Proximal Development (ZPD), where learning occurs most effectively with the help of more knowledgeable others. Application in Math: Active learning and flipped classrooms incorporate peer collaboration and teacher guidance. For example, students might work in pairs to solve complex calculus problems, with the teacher providing scaffolding to help them reach the solutions.

23. Theoretical Foundations 4. Experiential Learning Theory (Kolb ): Concept: Kolb’s theory involves a four-stage learning cycle: Concrete Experience, Reflective Observation, Abstract Conceptualization, and Active Experimentation. Application in Math: Flipped classrooms allow students to experience all stages of Kolb’s cycle. For instance, students might watch a video on statistical methods (Concrete Experience), reflect on what they’ve learned (Reflective Observation), discuss the concepts in class (Abstract Conceptualization), and apply the methods to real data sets (Active Experimentation).

24. Practical Implications in a Math Classroom Implementing active learning strategies and the flipped classroom model in a math classroom involves several practical steps and considerations. Active Learning Strategies 1. Think-Pair-Share: Activity: Students think about a problem individually, discuss their thoughts with a partner, and then share their insights with the class. Example: In a lesson on probability, students might first think about the probability of drawing an ace from a deck of cards, then discuss their reasoning with a partner, and finally share their conclusions with the class.

25. Practical Implications in a Math Classroom 2 . Peer Instruction : Activity: Students answer a conceptual question individually, discuss their answers with peers, and then answer the question again. – Example: During a unit on functions, the teacher presents a question like, “Is the function f(x) = x² even or odd?” Students first answer individually, discuss their reasoning with peers, and then answer again, leading to a deeper understanding of even and odd functions.

26. Practical Implications in a Math Classroom 3. Collaborative Problem Solving: Activity: Students work together in small groups to solve complex problems. Example: For a topic on linear equations, students might solve a real-world problem like optimizing a budget using systems of equations. They work in groups to set up and solve the system, then present their solutions to the class.

27. Flipped Classroom Model 1. Pre-Class Preparation : Activity: Students watch instructional videos, read materials, or complete interactive lessons at home. Example: For a lesson on derivatives, students watch a video explaining the concept and basic rules of differentiation and complete a few practice problems. 2 . In-Class Activities : Activity: Class time is dedicated to applying concepts through problem-solving, collaborative projects, and discussions. Example: After watching the video on derivatives at home, students spend class time working on problems involving finding the derivative of various functions, analyzing the meaning of the derivative in different contexts, and solving real-life application problems.

28. Flipped Classroom Model 3 . Assessment and Feedback : Activity: Continuous assessment and immediate feedback are integral to the flipped classroom. Example: The teacher circulates the classroom, providing guidance and feedback as students work through problems on derivatives. Quick formative assessments, such as mini-quizzes or exit tickets, help gauge student understanding.

29. Example Lesson Plan: Introduction to Integrals Pre-Class Preparation : Materials: Students watch videos on the fundamental concepts of integrals, including definite and indefinite integrals, and read a chapter on the applications of integrals. Assessment: An online quiz tests basic understanding, and students submit questions they have about the material. In-Class Activities : 1. Warm-Up (10 minutes ): - Review quiz results and address common questions about integrals. - Brief recap of the basics of integration through a quick class discussion. 2 . *Group Activity (30 minutes):* Activity: Students work in small groups to solve a series of problems involving the calculation of definite and indefinite integrals. – Example: Each group is given a set of functions to integrate, and they must explain their steps and reasoning to the class.

30. Example Lesson Plan: Introduction to Integrals 3 . Hands-On Experimentation (20 minutes ): Activity: Using graphing calculators or software like GeoGebra , students explore the graphical interpretation of integrals. Example: Students plot the graphs of functions and their integrals, analyzing the area under the curve and the accumulation function. 4. Class Discussion (20 minutes ): Activity: Groups present their solutions and findings, followed by a class discussion on the different methods used and any challenges faced. Example: Students discuss the differences between numerical and analytical methods of finding integrals.

31. Example Lesson Plan: Introduction to Integrals 5. Assessment and Feedback (10 minutes ): Exit Ticket : Students write a brief summary of what they learned about integrals and any remaining questions. Teacher Feedback: Review exit tickets to plan future lessons and address any persistent misunderstandings.

32. Benefits and Challenges

33. Benefits Deeper Understanding: Students engage with mathematical concepts more deeply through active problem-solving and discussion. – Personalized Learning : Students learn at their own pace during pre-class preparation, allowing them to review difficult concepts as needed. – Enhanced Engagement : Class time is more interactive and engaging, promoting a more dynamic learning environment.

34. Challenges Student Accountability : Ensuring all students complete the pre-class work can be difficult. Access to Resources : Students need access to reliable technology and internet to view pre-class materials. Teacher Preparation : Developing high-quality instructional videos and materials requires significant time and effort.

35. BEST PRACTICES IN MATH CLASSROOM Implementing best practices in a math classroom involves a combination of effective pedagogy, thoughtful lesson design, and leveraging technology where appropriate.

36. Best practices 1. Clear Learning Objectives Best Practice : Clearly communicate learning objectives to students at the beginning of each lesson. Learning objectives should be specific, measurable, achievable, relevant, and time-bound (SMART). – Example: In a lesson on geometry, the objective could be: "Students will be able to apply the properties of triangles to solve problems involving angle measures and side lengths .“

37. Best practices 2 . Engaging Instructional Strategies Best Practice : Use a variety of instructional strategies to cater to different learning styles and keep students engaged. This includes interactive lectures, collaborative learning, hands-on activities, and problem-solving sessions. Example: Introduce a concept like fractions using visual aids and manipulatives. Students can work in pairs to solve fraction addition problems using fraction bars or circles, fostering both visual and hands-on understanding.

38. Best practices 3. Active Learning Best Practice : Incorporate active learning techniques where students are actively involved in the learning process, rather than passive recipients of information. This can include think-pair-share, group discussions, and peer teaching. Example: After teaching a concept like quadratic equations, divide students into small groups. Each group is assigned a different type of quadratic equation problem (factoring, completing the square, quadratic formula). They work together to solve the problems and then present their solutions to the class .

39. Best practices 4. Formative Assessment Best Practice: Use formative assessment throughout the lesson to monitor student understanding and adjust instruction as needed. This can include quizzes, exit tickets, classroom polls, and teacher observation. Example: During a lesson on probability, use clicker questions to assess student understanding of basic probability concepts like outcomes, events, and probabilities of simple events. Use the results to identify common misconceptions and provide immediate feedback.

40. Best practices 5. Differentiated Instruction Best Practice : Differentiate instruction to meet the diverse needs of students. Provide opportunities for students to work at their own pace, offer alternative methods of content delivery, and scaffold learning for struggling students while challenging advanced learners. Example: In a unit on linear equations, provide extension activities for advanced students, such as exploring systems of equations with three variables or applying linear equations to real-world scenarios. For struggling students, offer additional practice problems and one-on-one support during class.

41. Best practices 6. Technology Integration Best Practice : Integrate technology tools that enhance learning experiences and facilitate understanding of abstract mathematical concepts. This includes graphing calculators, interactive simulations, educational apps, and online learning platforms. Example: Use a graphing calculator app or software like Desmos to explore the behavior of quadratic functions. Students can manipulate coefficients and see how changes affect the graph, deepening their understanding of quadratic transformations.

42. Best practices 7. Real-World Connections Best Practice: Relate mathematical concepts to real-world applications to make learning meaningful and relevant to students. Show how math is used in everyday life, careers, and other subjects. Example: Teach exponential growth and decay by examining population growth, financial investments, or radioactive decay. Discuss how these concepts apply to environmental science, economics, or health sciences, making connections between abstract math and real-world scenarios.

43. Best practices 8. Reflection and Metacognition Best Practice : Encourage students to reflect on their learning process and develop metacognitive skills. This involves thinking about how they learn best, setting goals, monitoring progress, and adjusting strategies accordingly. Example: At the end of a unit on geometry, ask students to write a reflection on their understanding of geometric concepts, identifying areas of strength and areas for improvement. Have them set goals for future learning and suggest strategies they can use to achieve those goals.

44. Best practices 9. Collaborative Learning Best Practice : Foster a collaborative learning environment where students work together to solve problems, discuss ideas, and learn from each other. Collaboration promotes communication skills, teamwork, and deeper understanding of mathematical concepts. Example: Organize a group project where students research and present different applications of trigonometry in architecture, engineering, or art. Each group member contributes their understanding of trigonometric ratios, angles of elevation, and applications in real-world structures.

45. Best practices 10. Teacher Reflection and Professional Development Best Practice : Continuously reflect on teaching practices, seek feedback from colleagues and students, and participate in ongoing professional development to improve instructional strategies and student outcomes. Example: Attend workshops or webinars on innovative teaching methods in mathematics, such as flipped classrooms, inquiry-based learning, or integrating STEM disciplines. Apply new strategies in the classroom and reflect on their effectiveness in enhancing student engagement and understanding.

46. Collaborative learning in mathematics Collaborative learning is a type of active learning that takes place in student teams. The students participating in a collaborative learning are actively exchangeing , debating, and negotiating ideas within their group, which increases their interest in learning. Collaborative learning in mathematics involves students working together in small groups to solve problems, discuss concepts, and deepen their understanding through peer interaction. This approach not only enhances mathematical reasoning and problem-solving skills but also fosters communication, teamwork, and critical thinking.

47. Collaborative learning in mathematics According to Gerlach , collaborative learning is based on the idea that learning is a natural social act in which participant talk among themselves. It is through the talk that learning occurs.

48. Theoretical Foundation Collaborative learning is supported by several educational theories: 1. Social Constructivism (Vygotsky ): Emphasizes that learning is enhanced when students interact and collaborate with peers, as they can scaffold each other’s learning and collectively construct knowledge. 2 . Zone of Proximal Development (ZPD ): According to Vygotsky, the ZPD is the gap between what students can do independently and what they can achieve with assistance. Collaborative learning allows students to work within their ZPD, challenging each other and receiving support from peers and the teacher. 3 . Piaget’s Theory of Cognitive Development : States that learners actively construct their own understanding through interactions with the environment and others. Collaboration provides opportunities for students to discuss, debate, and refine their ideas, promoting cognitive growth.

49. Characteristics: 1. Interdependence : Students rely on each other to achieve common goals, sharing resources and responsibilities. 2 . Interaction : Frequent communication among group members, where they discuss ideas, clarify doubts, and explain concepts to one another. 3 . Individual Accountability : Each student is responsible for their part of the work, ensuring that everyone contributes to the group's success. 4 . Group Processing : Groups reflect on their performance and discuss ways to improve their collaboration and effectiveness. 5 . Social Skills : Development of skills such as leadership, decision-making, trust-building, communication, and conflict management.

50. Characteristics: 6 . Problem-Solving : Emphasis on solving real-world problems, which enhances understanding and application of mathematical concepts. 7 . Constructive Feedback : Students provide and receive feedback, helping to improve their learning process and outcomes.

51. Benefits of Collaborative Learning in Mathematics 1. Enhanced Understanding : Students articulate their thinking processes and learn alternative methods from peers, leading to deeper understanding of mathematical concepts. 2 . Improved Problem-Solving Skills : Working together encourages students to analyze problems from multiple perspectives and apply various strategies, fostering critical thinking and creativity. 3 . Development of Communication Skills : Students articulate their thoughts, justify their reasoning, and clarify their understanding through discussions with peers, enhancing communication skills. 4 . Promotion of Equity : Collaborative learning provides opportunities for all students to contribute and learn from each other, regardless of their academic abilities or background knowledge.

52. Practical Implementation Group Formation Heterogeneous Groups : Mix students of different abilities and backgrounds to promote peer tutoring and mutual support. – Roles: Assign roles within groups (e.g., facilitator, recorder, presenter) to ensure equal participation and accountability.

53. Activities and Strategies 1. Problem-Solving Tasks : Example: Give groups a complex problem related to algebra or geometry that requires multiple steps to solve. For instance, calculating the volume of a composite shape involving cylinders and cones. 2 . Exploration of Concepts : Example: Provide groups with a set of trigonometric functions and angles, asking them to discover and discuss patterns in their values. For instance, examining how the sine function behaves in relation to angle measurements.

54. Activities and Strategies 3 . Real-World Applications : Example: Assign groups a project to research and present on the application of mathematical concepts in fields such as engineering, economics, or physics. For instance, exploring the use of calculus in designing roller coaster tracks . 4. Peer Teaching : Example: Have each group become experts on a specific topic within a unit (e.g., quadratic equations, statistics), then teach the rest of the class through presentations or mini-lessons.

55. Facilitation and Assessment Teacher’s Role : Act as a facilitator, circulating among groups to monitor progress, clarify concepts, and guide discussions. – Assessment: Evaluate group dynamics, individual contributions, and the quality of mathematical reasoning demonstrated in group work. Use rubrics to assess collaborative skills, mathematical accuracy, and depth of understanding.

56. Example Collaborative Learning Activity: Solving Systems of Equations Objective: Students will solve systems of linear equations using different methods (substitution, elimination, graphing) in collaborative groups. Activity Steps : 1. Preparation: - Students review methods for solving systems of equations (e.g., watching instructional videos or reading a textbook section) as homework. 2 . Group Work in Class : - Divide students into small groups (3-4 members per group) and assign each group a set of systems of equations problems to solve. - Encourage groups to discuss and decide on the most effective method for solving each problem (e.g., substitution or elimination).

57. Example Collaborative Learning Activity: Solving Systems of Equations 3 . Problem-Solving Process : - Groups work together to solve assigned problems, discussing strategies, checking each other’s work, and explaining their reasoning . 4. Class Discussion : - Each group presents their solutions and explains their thought process to the class. - Facilitate a whole-class discussion on the advantages and disadvantages of different solution methods, encouraging students to compare and contrast their approaches. 5 . Reflection: - Conclude with a reflection activity where students write about what they learned from the collaborative experience, including any challenges faced and strategies for improvement.

58. END Resources: https:// teaching.cornell.edu/teaching-resources/active-collaborative-learning/collaborative-learning https://teaching.cornell.edu/teaching-resources/active-collaborative-learning/active-learning