Inquiry Project: Discovery Learning
| "Learning
is not a spectator sport." ~D. Blocher |
Context of Study
My inquiry project will be based on students in one of two Geometry Level 3
courses that I will be teaching this semester.
There are students in grades 10, 11, and 12 in both
of these classes.
Courses at
Over one third of the students in my geometry courses have Individualized Education Plans and 504 Plans, which requires me to focus on differentiated instruction and modifications of daily lessons. In addition, a team teacher plays an active role in the classroom to meet the needs of special education students. While there are some students who truly need very individualized assistance, there are other students who are extremely self-sufficient. All of the students have the potential and ability to learn and understand the concepts being taught, but it seems that some of them lack the motivation and/or fail to make the effort to learn the material. Based on the context of my study, I believe that this project will be a challenge, both for me and for my students. Ultimately, however, I truly hope that they will each benefit from the implementation of this project.
Description of Study
Throughout the years, the way in which mathematics is taught, particularly at the secondary level, has changed considerably. The traditional teaching method typically involves providing students with notes: algorithms, definitions, theorems, postulates, etc. The teacher then instructs the students how to solve some example problems. The students are then expected to accurately solve a multitude of similar problems. Although some students may benefit from this method of teaching, many students can simply memorize the way in which certain problems are solved and then “regurgitate” this method on assessments. As a result, there has been a shift in mathematics teaching to helping students develop a more conceptual understanding of the topic, which in turn will allow them to accurately solve problems without completing a multitude of example problems.
To assist students in achieving a more conceptual understanding of topics in mathematics, many educators are now incorporating the idea of “Discovery Learning” in their lessons. According to the National Board for Professional Teaching Standards, “Discovery Learning provides students with opportunities to develop hypotheses to answer questions…Students propose issues or problems, gather data and observations to develop hypotheses, confirm or refine their hypotheses, and explain or prove their problems”(1). In my opinion, Discovery Learning is a positive, (typically) hands-on experience in which students truly must critically think and apply previous knowledge to gain understanding of new concepts. Because there is a shift from a teacher-centered to a student-centered learning environment, students become more responsible and adept learners of mathematics. Furthermore, this is one of the New Jersey Core Curriculum Content Standards which teachers of mathematics are supposed to meet in their classrooms. Standard 4.5A (Mathematical Processes) states that students will “Learn mathematics through problem solving, inquiry, and discovery” (2).
I studied the effects of Discovery Learning during a six-week period in my Geometry Level 3 course. Although I knew I wanted to implement some Discovery Learning activities in the course, I began teaching using the traditional method, as modeled above. I provided the students with notes, and they solved problems using the information and examples they were given. As I continued to teach, I guided the students in performing kinesthetic activities, in which they had to “discover” certain properties of triangles. Between each assessment, I changed the strategy in which I questioned the students, as well as the way in which the students completed the Discovery Learning activities. While the Baseline Assessment focuses on strictly traditional teaching methods, the First Assessment is a measure of both traditional teaching methods and Discovery Learning, and the Second Assessment is a measure of solely the results of Discovery Learning. My goal in this inquiry project was to determine if Discovery Learning seemed to truly assist the students in understanding the material, both conceptually and through application of mathematical procedures. Due to the recent emphasis on Discovery Learning in the mathematics classroom, I wanted to determine if this method was effective in my own classroom in order to provide me with ways in which I can improve my own teaching style in the future.
After becoming somewhat familiar with the students, I chose to study the effects of Discovery Learning on “Becky” and “Sam”. Unfortunately, the most of the students in Level 3 courses have little motivation to participate and generally not concerned with the grade they receive in the class. “Becky” is a student who has an Individualized Education Plan. Although she has the ability to understand the material, she repeatedly asks for clarification, and also is quick to respond with the comments “I don’t get it” or “I don’t understand” when presented with new material. She is an intelligent student, but immediately shuts down if she feels that she cannot understand a new concept. “Sam” is an “average” student in the class. She is conscientious and completes all assignments, but does not always complete them accurately. She is rather quiet and does not participate willingly, although she will respond if called upon. I felt that these students represented two different types of students in my Geometry Level 3 courses, and I wanted to measures the effects of Discovery Learning on different types of learners.
Sources:
Baseline Assessment | Student Work
First Assessment | Student Work
Second Assessment | Student Work