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Design Project Home Page: Problem-Based Learning in a Mathematics Classroom
Intent of Project
The intent of this project is to educate mathematics teachers on the concepts of Problem-Based Learning and how to incorporate Problem-Based Learning into their mathematics classrooms.
The topics that will be covered are:
♦ Problem-Based Learning
- Define PBL
- Define importance of PBL
♦ Roles of the teacher and students
♦ Examples of mathematics through PBL
Needs Analysis
Instructional Problem
Learners in today's world need to build 21st Century Skills so they can lead successful lives when they enter the work force. Education today promotes more rote memorization and step following than developing deep understanding, especially in a mathematics setting. Important 21st Century skills that need to be further met within the classroom are critical thinking and problem solving. The instructional problem that will be the focus of this course is how to incorporate Problem-Based Learning into a mathematics classroom to foster critical thinking and problem solving skills.
Key Thoughts:
♦ How do you teach your mathematics students so they reach higher-level thinking and develop deep understandings of various concepts?
♦ What is Problem-Based Learning?
♦ How do you incorporate Problem-Based Learning into a mathematics classroom?
Nature of What is to be Learned
♦ You will learn the characteristics of Problem-Based Learning.
♦ You will learn why Problem-Based Learning should be incorporated into a mathematics classroom.
♦ You will work through mathematics Problem-Based Learning exercises.
Who Will Benefit From This Course?
♦ This course will benefit any educator who is interested in the concepts behind Problem-Based Learning.
♦ Anyone interested in becoming knowledgeable of the steps in creating a PBL exercise will benefit.
♦ Mathematics educators, particularly, will benefit from the Problem-Based Learning examples used within this course.
Instructional Context
This course will be fully online, using key resources from other websites to provide various information on Problem-Based Learning.
Exploring the Problem and the Solution
There is a need within the educational system to incorporate more Problem-Based Learning and authentic learning exercises into the curriculum. This course will allow the educator to gather information about problem-based learning and experience exercises using problem-based learning for a mathematics setting.
Goals
The goals of this course are to provide basic information about problem-based learning and deeper understanding of how and why educators should incorporate this type of learning activity into their daily lesson plans.
Performance Objectives
1. The learner will identify by naming the characteristics of Problem-Based Learning.
2. The learner will state orally the need for Problem-Based Learning within the classroom.
3. The learner will classify by writing the roles of the teacher and student in a Problem-Based Learning environment.
4. Given a variety of mathematical tasks, the learner will discriminate between problematic tasks and non-problematic tasks by listing the characteristics of the given task, and determining which tasks fit into each category.
5. Using the provided resources, the learner will generate in writing a problematic mathematics task or change an existing traditional task to a problematic task.
6. The learner will choose to adopt Problem-Based Learning by incorporating problematic tasks into their classrooms.
Task Analysis
Purpose
The purpose of this course is to provide educators with the basic key ideas behind problem-based learning to allow for the incorporation of problematic tasks into more classrooms.
Prerequisites
The following are the essential and supporting prerequisites for the above performance objectives (1, 2, 3, and 6). The types learning outcomes represented within these prerequisites are verbal information, cognitive strategies, and attitudes.
Essential Prerequisites:
♦ Familiar with the term "problem-based learning"
♦ Realizes the connection between problem-based learning and the mathematics classroom
♦ Familiar with and realizes traditional mathematics methods
♦ Discriminates between a problematic tasks and a traditional task
♦ Realizes and understands when tasks are problematic in nature
Supporting Prerequisites:
♦ Recognizes and understands disadvantages of traditional mathematics methods
♦ Recognizes roles of teacher and students in traditional mathematics class
♦ Values need for change in tasks in a mathematics class
♦ Desires to seek improvement in understanding of mathematical concepts in students
The following are learning hierarchies for the intellectual skills from the above performance objectives.
Performance Objective #4: Given a variety of mathematical tasks, the learner will discriminate between problematic tasks and non-problematic tasks by listing the characteristics of the given task, and determining which tasks fit into each category. Learning Hierarchy
Performance Objective #5: Using the provided resources, the learner will generate in writing a problematic mathematics task or change an existing traditional task to a problematic
task. Learning Hierarchy
Learning Outcomes
♦ The learner will identify components of Problem-Based Learning.
♦ The learner will be able to explain the roles of both the teacher and the students in Problem-Based Learning.
♦ The learner will have knowledge of Problem-Based Learning within the mathematics classroom by experiencing examples of authentic mathematics problems.
♦ The learner will identify the steps to planning Problem-Based Learning activities.
Instructional Curriculum Map
Course Outline
Unit 1
Objectives:
1. The learner will describe Problem-Based Learning in his/her own words.
2. The learner will identify by naming the characteristics of Problem-Based Learning.
3. The learner will state orally the need for Problem-Based Learning in the classroom.
4. The learner will classify by writing the roles of the teacher and student in a Problem-Based Learning environment.
5. The learner will identify differences between a Problem-Based Learning environment and a traditional classroom environment.
Instructional Methods
As a brief introduction to the course, the learner will watch a YouTube video that discusses the importance of mathematics in the real world. The learner will then read two articles that discuss the importance of Problem-Based Learning and how collaboration within the classroom will foster the development of 21st Century skills. Lastly, the learner will reflect upon what s/he has learned in their reflective journal.
Unit 2
Objectives
1. The learner will list in writing the key factors to consider when creating problematic mathematics contexts.
2. Given a variety of mathematical tasks, the learner will discriminate between problematic tasks and non-problematic tasks by listing the characteristics of the given task, and determining which tasks fit into each category.
Instructional Methods
The learner will work through various mathematical problems, analyzing the qualities and discriminating between problematic tasks and traditional mathematics tasks. After being able to list the differing qualities of traditional tasks and problematic tasks, the learner will watch problem-based learning in action within a 7th grade mathematics classroom and reflect on and analyze various aspects of the lesson.
Unit 3
Objectives
1. The learner will analyze two problematic tasks writing their thoughts in a reflective journal.
2. Using the provided resources, the learner will generate in writing a problematic mathematics task or change an existing traditional tasks to a problematic task.
3. The learner will choose to adopt Problem-Based Learning by incorporating problematic tasks into their classrooms.
Instructional Methods
The learner will read an article about important concepts to consider when creating authentic mathematical contexts. Then, the learner will watch two lessons that are problematic in nature. From their knowledge gained through the previous resources and units and their thoughts and findings on the lessons presented in the videos, the learner will generate their own problematic mathematics tasks.