problem-based learning in mathematics MATH116.pptx

this presentation is about problem-based learning.

1. PROBLEM-BASED STRATEGY IN MATHEMATICS LEARNING & APPLICATIONS IN CRITICAL THINKING By Alaiza Mae Arique MATH 116

2. LEARNING OBJECTIVES By the end of this presentation, the pre-service teachers will be able to: 1. Define Problem-Based Learning (PBL) in the context of mathematics education. 2. Differentiate between Problem Solving Strategy and Problem-Based Learning. 3. Describe the stages and roles involved in PBL. 4. Identify situations where PBL and problem-solving strategies are most effective. 5. Apply PBL concepts to critical thinking contexts such as argumentation, conjecture, patterning, and conflict resolution.

3. Group Activity: The Locked Box Challenge

4. The class will be divided into two groups. Each group will be given 5 clue sets. Work together to solve each clue set and find the correct 3-digit code. 4. After solving all 5 codes, shout “CODE UNLOCKED!” 5. The first group to shout and have all codes correct wins! Group Activity: The Locked Box Challenge Instructions:

5. Answer: 5-6-7 Group Activity: The Locked Box Challenge Example : The digits form a consecutive sequence . The sum of the digits is 18 . The middle digit is even .

6. Group Activity: The Locked Box Challenge

7. Introduction Mathematics education today focuses on developing higher-order thinking skills. One effective approach is Problem-Based Learning (PBL). This presentation covers PBL, its benefits, comparison with problem-solving strategy, and its applications in fostering critical thinking.

8. Problem-Based Learning

9. WHAT IS PROBLEM-BASED LEARNING IN MATH? Problem based learning (PBL) is a teaching strategy during which students are trying solve a problem or a set problems unfamiliar to them. PBL is underpinned by a constructivist approach, as such it promotes active learning. Activities are carried out with groups of students, typically in a tutorial or seminar setting.

10. WHAT IS PROBLEM-BASED LEARNING IN MATH? Encourages investigation and reasoning. Teacher acts as a facilitator, not just a lecturer. PBL fosters self-directed learning, effective problem solving, communication and collaboration skills.

11. REALISTIC AND OPEN-ENDED PROBLEMS KEY CHARACTERISTICS OF PBL COLLABORATIVE GROUP WORK SELF-DIRECTED LEARNING WITH MINIMAL DIRECT INSTRUCTION INTEGRATION OF MULTIPLE CONCEPTS TO SOLVE A PROBLEM

12. IMPROVES CRITICAL THINKING AND PROBLEM-SOLVING SKILLS WHY USE PBL? PROMOTES ENGAGEMENT AND MOTIVATION ENCOURAGES DEEP CONCEPTUAL UNDERSTANDING CONNECTS MATH TO REAL-LIFE APPLICATIONS

13. THE PBL PROCESS

14. TEACHER AND STUDENT ROLES TEACHERS STUDENTS Facilitate learning Ask guiding questions Provide resources Encourage reflection Explore and investigate Collaborate with peers Formulate and test solutions Present and defend ideas

15. Problem Solving vs. Problem-based learning

16. PROBLEM SOLVING BEST FOR SPECIFIC SKILL PRACTICE AND CLEAR PROCEDURAL TASKS. PROBLEM-BASED LEARNING BEST FOR INTEGRATING CONCEPTS, DEVELOPING REASONING, AND APPLYING MATH TO REAL-LIFE CONTEXTS.

17. Focus Finding the correct answer Understanding the process Problem Type Well-defined Open-ended, real-world Teacher Role Instructor Facilitator Student Role Follows steps Investigates and collaborates Time Frame Short, single task Short cycles (1–4 days) PROBLEM SOLVING PROBLEM-BASED LEARNING FEATURE

18. Problem-based learning as a Critical Thinking Tool

19. PBL AS A CRITICAL THINKING TOOL ARGUMENTATION CONFLICT RESOLUTION CONJECTURE REASONS PATTERNING

20. Argumentation is the thought process used to develop and present arguments. It is closely related to critical thinking and reasoning. ARGUMENTATION In critical thinking, argumentation involves constructing logical connections: premises (supporting statements) leading to a conclusion.

21. In a PBL task about designing the safest ramp for wheelchair access, students calculate slopes using different formulas. One group claims slope m = is safest, citing the ADA recommendation. Another group challenges this, saying is okay because it saves space.   ARGUMENTATION EXAMPLE: Argumentation: Students present calculations, standards, and real-life measurements to justify their chosen slope, and critique the other group’s reasoning.

22. Conflict resolution is the process by which two or more parties reach a peaceful solution to a disagreement, often through negotiation and reasoning, not force. CONFLICT RESOLUTION Solving disagreements respectfully and fairly.

23. CONFLICT RESOLUTION EXAMPLE: During a group activity to solve a system of equations representing ticket sales, one student prefers substitution, another prefers elimination. Conflict Resolution: They decide to solve it both ways, compare results, and agree to present the method they find clearer for the audience.

24. A conjecture is an unproven claim or hypothesis based on patterns or observations. It is common in mathematics and science. CONJECTURE REASONS Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds true for many cases does not mean that the pattern will hold true for all cases. Conjectures must be proved for the mathematical observation to be fully accepted.

25. EXAMPLE: While exploring the sum of the first n odd numbers, students notice: Conjecture & Reasoning: “The sum of the first n odd numbers is ”. They try n=4,5,6 to test the pattern, then attempt a proof using algebra or visual representation.   CONJECTURE REASONS 1= ,   1+3= ,   1+3+5=  

26. Patterning involves recognizing repeated sequences or structures in data, like shapes, numbers, words, or behaviors. PATTERNING In Mathematics, patterns are sequences that repeat according to a rule or rules. A rule is a set way to calculate or solve a problem.

27. In a PBL challenge about predicting phone plan costs, students record: 1 GB → ₱150 2 GB → ₱300 3 GB → ₱450 EXAMPLE: Patterning: Recognizing the linear pattern helps them write the function C=150g and predict future costs. PATTERNING

28. CONCLUSION Problem-Based Learning (PBL) is more than just a teaching strategy as it is a mindset that places students at the center of the learning process. By engaging learners in real-world, open-ended problems, PBL develops essential skills such as reasoning, collaboration, and adaptability. Its application to argumentation, conflict resolution, conjecture, and pattern recognition demonstrates its power in fostering critical thinking within mathematics. As future educators, embracing PBL means preparing students not only to solve problems but to approach challenges with curiosity, creativity, and confidence, bridging the gap between classroom learning and life beyond school.

29. Thank You for listening!

30. REFERENCES Barrows, H. S. (1996). Problem-based learning in medicine and beyond: A brief overview. New Directions for Teaching and Learning, 1996(68), 3–12. Hmelo -Silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. Jonassen , D. H. (2011). Learning to solve problems: A handbook for designing problem-solving learning environments (2nd ed.). Prince, M. J., & Felder, R. M. (2006). Inductive teaching and learning methods: Definitions, comparisons, and research bases. Journal of Engineering Education, 95(2), 123–138. Tan, O. S. (2003). Problem-based learning innovation: Using problems to power learning in the 21st century. Thomson Learning.

31. ASSESSMENT

32. A. MULTIPLE CHOICE Problem-Based Learning (PBL) is primarily based on which teaching philosophy ? A. Constructivism B. Behaviorism C. Essentialism D. Perennialism Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

33. A. MULTIPLE CHOICE 2. In PBL, the teacher’s main role is to: A . Facilitate learning B. Provide daily quizzes for recall C. Model every solution before practice D. Present a detailed lecture on each topic Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

34. A. MULTIPLE CHOICE Which of the following is a key characteristic of Problem-Based Learning ? A. Practice activities that focus on a single skill B. Guided demonstrations of a fixed solution process C. Step-by-step instruction for mastering a specific formula D. Realistic, open-ended problems that integrate multiple concepts Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

35. A. MULTIPLE CHOICE Which statement best explains the difference between PBL and traditional problem solving ? A. PBL and problem solving require the same approach for every task B. PBL avoids real-life applications, while problem solving promotes them C. Problem solving focuses on collaboration, while PBL focuses on independent work D. PBL emphasizes real-world processes, while problem solving often targets one correct answer Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

36. A. MULTIPLE CHOICE In the context of critical thinking, “argumentation” refers to : A. Listing facts without explanation B. Sharing opinions without evidence C. Presenting unrelated statements for discussion D. Building logical connections between supporting statements and a conclusion Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

37. A. MULTIPLE CHOICE Which scenario best demonstrates “patterning” in mathematics ? A. Writing down a list of random numbers B. Using a calculator for each separate computation C. Identifying a repeated relationship in a number sequence D. Completing exercises that practice a single arithmetic operation Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

38. A. MULTIPLE CHOICE During a PBL activity, a group is designing a budget plan for a school event. Which action shows self-directed learning ? A. Copying another group’s completed budget B. Using sample prices from an unrelated example C. Waiting for the teacher to give all the required amounts D. Researching actual catering prices and integrating them into the plan Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

39. A. MULTIPLE CHOICE In a PBL ramp design task, a group uses the ADA slope guideline (1/12) to justify their answer. This demonstrates: A. Patterning B. Argumentation C. Procedural recall D. Conflict resolution Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

40. A. MULTIPLE CHOICE While exploring the sequence 1, 3, 5, 7..., students claim that the sum of the first n odd numbers equals n². This is an example of : A. Making a conjecture B. Recording unrelated data C. Applying a fixed formula D. Resolving a disagreement Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

41. A. MULTIPLE CHOICE 10. In a ticket sales PBL activity, one student prefers substitution while another prefers elimination. They compare results and decide which to present. This process is an example of : A. Conflict resolution B. Pattern recognition C. Argumentation D. Data gathering Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

42. A. MULTIPLE CHOICE 11. Which situation best shows integration of multiple concepts in PBL ? A. Practicing multiplication tables repeatedly B. Calculating the area of a rectangle using a single formula C. Measuring a single object without making further calculations D. Designing a school garden layout using measurement, budgeting, and geometry Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

43. A. MULTIPLE CHOICE 12. In a PBL investigation about rainfall and crop growth, students find that higher rainfall in certain months corresponds with taller plants. Recognizing this relationship is an example of : A. Patterning B. Argumentation C. Conflict resolution D. Self-directed learning Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

44. A. MULTIPLE CHOICE 13. A class is tasked with creating a water filtration system. One design is quick to assemble, while another filters water more effectively but takes longer to build. Which decision-making process aligns with PBL principles ? A. Comparing the benefits and limitations of each design, then selecting the most suitable B. Choosing the design with the least assembly steps C. Following the design from the teacher’s example D. Voting on the design most students like Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

45. A. MULTIPLE CHOICE 14. During a PBL science-math integration activity, two different formulas are proposed to calculate wind energy output. What is the most effective way to decide which formula to use ? A. Apply both formulas to sample data and evaluate accuracy and usefulness B. Choose the formula suggested by the loudest group member C. Use the formula from last year’s project without testing D. Select the formula that seems easier to compute Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

46. A. MULTIPLE CHOICE 15. A teacher wants to introduce PBL in geometry. Which activity would best promote creative application of PBL concepts ? A. Copying a floor plan from a textbook B . Calculating the area of a given triangle C . Listing all formulas for the area of polygons D . Designing a floor plan for a small shop that meets specific size and cost requirements Direction: Choose the letter of the correct answer. Write your answer in a ½ crosswise.

47. B. ESSAY (5 POINTS) How can Problem-Based Learning (PBL) help students learn mathematics and apply it in real life? Answer in more or less 5 sentences. You will be graded according to the content of your answer, the completeness of your explanation, and the clarity of your ideas.