Module 4 application
- 1. Runninghead:MODULE 4 APPLICATION 1 Module 4 Application: Problem-Based Learning Lucas Meister American College of Education
- 2. MODULE 4 APPLICATION 2 Module 4 Application: Problem-Based Learning Introduction Problem-based learning is a learner-centered approaches that increase student engagement and interaction by promoting a learning environment that focuses on active learning and collaboration among students (Davidson & Major, 2014). A lesson was created for a 7th grade math block. This lesson utilized problem-based learning as its main strategy by having the students learn through solving a real-world problem of creating a proposal to reroof their school. The lesson was grounded in the learner-centered principles of the construction of knowledge, the social nature of learning, and student participation. The lesson was also based on the learner- centered classroom characteristics of real-world connections to learning and active learning. Problem-based learning provides teachers with a means to give students an experiential learning environment that focuses on skill acquisition and connecting learning to real-world scenarios and situations. Part 1: Lesson Plan Grade Level: 7th Grade Subject: Math Standards: CCSS.MATH.CONTENT.7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. CCSS.MATH.CONTENT.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Objectives:
- 3. MODULE 4 APPLICATION 3 1. Students will be able to examine scale drawings of the school’s roof and determine the shapes that the roof is composed of. 2. Students will be able to apply their knowledge of area to determine the total area of the school’s roof and create a proposal for reroofing the school. Summary of Problem-Based Experience: The lesson presents a real-world problem in a setting with which the students are familiar. Our school is over 70 years old and there are many leaks whenever it rains. The students will be tasked with determining the area of the school’s roof in order to determine how much material would be needed to reroof the school and create a proposal for the reroofing project. In order to complete this assignment students will have to use scale models of the roof and separate the irregular shape of the roof into composite shapes. Determining the appropriate measurements of the composite shapes will allow them to find the area of each shape and add them to find the total area of the roof. Assessment: Rubrics will be used to assess the final proposal of each student. The students proposal must include a sketch of the roof that shows the composite shapes that make up the roof, correct areas of the composite shapes, the correct total area of the roof, a cost estimate for the reroofing, and a paragraph about why the reroofing would benefit the school. Learning Environment: The students will be in heterogenous groups of 4 for this activity. They will be sitting at tables in their math classroom. This will allow them to discuss their project in their groups and formulate a plan of action to complete the project. The teacher will move around the room to add to each groups discussion and ensure that students are moving in a reasonable direction to complete project. Student Materials: Student Chromebook, irregular shapes video, polygon area formula sheet, scale drawings of the school roof, resource website: https://www.gleassociates.com/commercial-roof- replacement-cost-estimate/, pencil, and paper. Time Frame: This is a 1-day lesson that will occur during a 90-minute math block. Procedure: 1. The teacher will lead the class in a discussion of the problem of the leaky school roof and the importance of determining the cost of a project before proposing it. The students will participate in the discussion. 2. The teacher will pass out the formula sheet and quickly review the concept of area for regular polygons. The students will participate in the review. 3. The students will watch the video on finding the area of irregular shapes.
- 4. MODULE 4 APPLICATION 4 4. The teacher will present the problem task to the students and pass out the rubric and scale model drawings. 5. The students will work in heterogenous groups using their scale drawings, Chromebooks, and rubrics to determine the area of the school roof and create their proposal. Presentation Method: In this lesson, the students are working on the project for the majority of the time using visual aids in the form of the scale drawings of the roof. They also have the irregular shapes video that they may refer back to on their Chromebooks during work time. The teacher will use discussion techniques and probing questions with different groups during work time to assess and extend their understanding and application of the material. Roofing Proposal Rubric 3 2 1 0 Sketch of Roof The sketch of the roof is present, composite shapes are identified by dotted lines, and dimensions are labeled. The sketch of the roof is present and composite shapes are identified by dotted lines, but no dimensions are labeled. The sketch of the roof is present, but no composite shapes are identified, and no dimensions are labeled. The sketch is not present Area of Composite Shapes The area of all composite shapes is correctly identified and labeled. The area of most of the composite shapes is correctly identified and labeled. The area of some of the composite shapes is correctly identified and labeled. The area of none of the composite shapes is correctly identified and labeled. Total Area The total area of the roof is correctly identified, and work is shown. The total area of the roof is correctly identified, but no work is shown. The total area of the roof is not correct, but some work is shown. The total area of the roof is not identified, and no work is shown. Cost of Project A reasonable estimate of the cost of the project is given, based on data from the resource website and work is shown. A reasonable estimate of the cost of the project is given, based on data from the resource website, but no work is shown. An estimate is given, but it does not make sense based on the data from the student’s project. No estimate is given.
- 5. MODULE 4 APPLICATION 5 Paragraph A paragraph is present that describes how the roofing project would benefit the school. A paragraph is not present. Part 2: Reflection This lesson addressed a number of learner-centered principles, such as the construction if knowledge, the social influences on learning, and a participatory learning environment. Constructing knowledge refers to relating learning to prior learning and making connections to the larger world in order to construct meaning (Saunders, 1992). In this lesson, the students are using their prior knowledge of finding the area of simple polygons to solve the real-world problem of determining the area of the school’s roof. This allows the students to derive a method for determining the area of irregular shapes through their learning experiences. When students work in groups towards a common learning goal, they are able to utilize the strengths of the group to further their own learning (Zakaria & Iksan, 2007). The students are working in collaborative groups for this lesson in order to solve the real-world problem. This allows for student learning to reinforced and extended through frequent student-to-student interaction. Active and frequent student participation in learning activities leads to increased student achievement over more passive learning methods (Bishop, Caston, & King, 2014). For the majority of this lesson, the students are working in their groups on the earning activity. The teacher is acting as a facilitator to clarify and extend each group’s learning as they progress with their projects. The participation of the students reinforces their engagement in the learning process and helps develop their content area knowledge and higher order thinking skills as they work through t he real-world problem.
- 6. MODULE 4 APPLICATION 6 This lesson exhibits the learner-centered classroom characteristic of real world connections to the subject matter. Grounding learning in real-world problems and making explicit connections can lead to increase student engagement, intrinsic motivation, satisfaction with learning, and achievement (Hmelo-Silver, 2004). The students in this lesson are applying mathematical concepts and skills to solve a real-world problem. Math can be a very dry and abstract area of study for many students. By providing them with examples and practice with using applying math content and skills in real-world situations will help them see the value in their learning. This lesson also exhibits the learner-centered classroom characteristic of active learning. Students are better served in active Learning environments, that facilitate their increased engagement and skill-based applications, than more traditional teaching methods (Lord, Travis, Magill, & King, 2005). In this lesson, the students are working towards solving a problem for most of the period. During this time, they are discussing with their group, analyzing the problem and their diagrams, applying their math content knowledge and higher order thinking skills, and creating their final product. This active participation ensures that students stay engaged throughout the learning activity and are able to construct their own knowledge. Problem-based learning is an experiential learning method that engages students in problem solving to learn content knowledge and skills (Dochy, Segers, Van den Bossche, and Gijbels, 2003). In this lesson, are presented with problem of creating a proposal to reroof the school in order to stop issues that arise due to the age of the building. In order to solve this problem and create a proposal, the students will need to use their knowledge of geometry to use the scale drawings of the roof to determine the total area of the roof. This will involve separating the irregularly shaped roof into simple polygons, deriving appropriate dimensions for these polygons, and calculating the area of each. There are a number of potential variations in strategy
- 7. MODULE 4 APPLICATION 7 and configuration that the students could potentially choose at this stage. The students will also use the total area of the roof, choose a roofing material from the resource website, and present an estimated cost for the project. The estimated cost of the project will vary based on the roofing material chosen. The groups will also have to write a paragraph justifying why the expense of the project would benefit the school. The content and skills required by this lesson are derived from the grade level standards and build upon the students prior learning. In sixth grade, the students learned how to find the area of simple polygons and are now extending their learning to finding the area of irregular shapes. Conclusion Learning through inquiry and discovery can lead to increased student engagement, self- efficacy, and achievement (Horak & Galluzzo, 2017). By giving students a problem that allows for student directed learning, students can be engaged to seek their own answers and develop their problem-solving skills. To provide students with a real-world situation in which they can apply and deepen their math content area knowledge and skills, a problem-based lesson was created. The lesson created a learner-centered environment by incorporating learner-centered principles and classroom characteristics.
- 8. MODULE 4 APPLICATION 8 References Davidson, N., & Major, C. H. (2014). Boundary crossings: Cooperative learning, collaborative learning, and problem-based learning. Journal on Excellence in College Teaching, 25. Dochy, F., Segers, M., Van den Bossche, P., & Gijbels, D. (2003). Effects of problem-based learning: A meta-analysis. Learning and instruction, 13(5), 533-568. Hmelo-Silver, C. E. (2004). Problem-based learning: What and how do students learn?. Educational psychology review, 16(3), 235-266. Horak, A. K., & Galluzzo, G. R. (2017). Gifted middle school students’ achievement and perceptions of science classroom quality during problem-based learning. Journal of Advanced Academics, 28(1), 28-50. Laal, M., & Ghodsi, S. M. (2012). Benefits of collaborative learning. Procedia-social and behavioral sciences, 31, 486-490. Lord, T., Travis, H., Magill, B., & King, L. (2005). Comparing student-centered and teacher- centered instruction in college biology labs. Indiana, PA: Indiana University of Pennsylvania. Saunders, W. L. (1992). The constructivist perspective: Implications and teaching strategies for science. School Science and Mathematics, 92(3), 136-141. Zakaria, E., & Iksan, Z. (2007). Promoting Cooperative Learning in Science and Mathematics Education: A Malaysian Perspective. Online Submission, 3(1), 35-39.