Learning Theories
This section contains artifacts that reflect my interest in learning theories. Even though any one theory does not completely describe people's learning behaviour, I found elements of almost all learning theories that resonated with me. I chose to emphasize many of these elements in both my computerized tutorial and drill and my theory to practice paper. The computerized tutorial and drill uses many concepts from both the behavioral and cognitive psychologies, while the ideas in the theory to practice paper takes more of its elements from constructivist theory.
Computerized tutorial and drill
As the final project for my Athabasca University (AU) course Educational Psychology 479: Introduction to Computer-Based Instruction, I created a tutorial and drill. Both aim to teach approximately high-school aged students about binary numbers and how to convert base 10 numbers to binary. Below is a screenshot from the drill.
Looking back
After the first assignment in this course, I realized that it would be a much different experience from my other UBC Educational Technology (ETEC) courses. I don't know why this surprised me, because I have taken several courses from AU. When a course there is offered on an individualized basis online or through a paper-based format, students can start at the beginning of any month and continue through the course at their own pace with a regular deadline of six months from the time of registration.
The first assignment was to introduce yourself on the course bulletin board. This sounded familiar to me, and very ETEC-like, but as I viewed the postings that other students had made, I realized that the course would not be collaborative at all. After the first posting on the bulletin board to satisfy the course requirements, none of the students had visited it again. I felf my first stab of disappointment in the AU course.
Working further through the course convinced me that my learning experience wasn't the equivalent of previous courses that I had taken in the MET program.The AU course consisted of reading a textbook, interacting with the course tutor by email or telephone, taking online quizzes and completing four web-based projects. While I wasn't enjoying the constant testing, which made me feel like I was back in grade school trying to memorize the book so I could spit it out again, what was interesting to me was that I was getting the same marks in the AU course, if not better, than I had gotten in my previous ETEC courses, with less anxiety.
It has only ocurred to me after looking back on the AU course that this individualized method of learning suits my learning style well. I already know about myself, from several Myers-Briggs Type Indicator tests, that I am slightly introverted. I am also a very visual learner with a preference for text-based rather than pictorial information. After working through so many ETEC courses, I have the feeling that the only way to present a course or any other learning material is in a collaborative and somewhat (or strongly) constructivist manner. However, I need to remember that not everyone learns in the same way, so we, as teachers, should not always be teaching in the same manner. I have decided that it is permissible to include my tutorial and drill from the "dark side" of computer-based instruction to balance the constructivist tendencies of the ETEC courses. Alessi and Trollip (2001, p. 38) note:
Many constructivists believe that instructional methodologies such as tutorial and drill are inappropriate. We disagree. A complete and flexible educational environment includes a combination of media including people, books, computers, and others. The computer software components should include tutorials, drills, hypermedia, Web-based communications and other methods, depending on the subject matter, the learners, the available resources, and the time constraints.
There are many aspects of behavioral and cognitive psychology that are still used in valid ways in teaching, and I will use my tutorial and drill project to highlight some of these.
The principles of behaviorism that I incorporated into my tutorial and drill design include stating objectives, and providing positive reinforcement. Instructional Systems Design (ISD), an approach to designing educational materials primarily for adult learners, has its roots in behavioral psychology, and it was from ISD principles that I chose to break down the material into small portions interspersed with questions that require feedback from the learner in order to continue with the tutorial. However, in contrast to some early ISD materials, which broke down the information into such small bits that the process of learning became repetitive and tedious for some learners, my tutorial presents information in somewhat larger chunks so that it flows better.
Within the realm of cognitive pyschology are many theories and principles that have been used in learning environments. The ones that I emphasized in creating my tutorial and drill are semantic networks, enhancing memory through the principle of organization, and active learning. Some cognitive psychologists view the brain as a vast network of pieces of information called nodes that are interconnected by relationships such as time, cause and effect, similarity, contrast, etc. In this network, learning is represented by changing connections between nodes, or adding or removing nodes. Linking to prior knowledge is critical, because this prior knowledge represents the nodes and connections already in the brain. In my tutorial to teach about the binary number system, I started with our base 10 system, with which everyone who uses the program will already be familiar. Using the principle of organization, which suggests that people will try to impose some type of organization on new material to make it easier to learn, I arranged the tutorial material into tables which can assist the learner in organizing the information (see screenshot below).
Active learning, in which the learner is required to make some responses and/or otherwise interact with the material rather than just passively viewing it, is accomplished in both the tutorial and drill by having the learner answer questions before continuing on in the program (see screenshot below).
Looking forward
My vision for learning will continue to include individualized learning for students as well as collaborative and constructivist activities. Individualized learning can help address the gaps that students often bring to their learning experiences, and certain aspects of the behavioral and cognitive psychologies, when applied to learning situations, may assist students to organize, remember and recall their learning.
Reflections on a math class: theory to practice
The ETEC 512 theory to practice paper presents my personal definition of learning and details six learning principles that I will try to incorporate in my teaching. My personal definition of learning includes the following elements: learning is a life-long process that can take place anywhere and at any time; it can be intended or unintended, such as when a child learns through cause and effect; and learning is better retained when words (written or oral) are paired with action.
The six learning principles that I distilled from the learning theories are as follows:
- Provide an emotionally and physically safe space for students to learn.
- Have students work in groups as much as possible.
- Provide multimodal experiences for the students.
- Use scaffolding to allow students to work at a higher level than they would be capable of without assistance.
- Find out and build on what students already know.
- Use a variety of learning contexts to promote the students’ transfer of information from one situation to another.
Looking back
A criticism of this paper was that I did not give an exact definition of learning; I described learning, but did not define it. With this reflection, I can now take this opportunity to correct that omission. I believe that learning occurs when learners take in new information, whether visually, aurally or kinaesthetically, and connect it to something they already know. This new information might be additional details about something that they already know, or the new information might be about something that they have never heard of before. In this case, the learners may try to fit it into a category of things they already know by examining similarities and differences between the new information and the old.
It has been interesting to look back to my ETEC 512 Learning Theories to Learning Practice paper almost one year after starting to teach the Mathematics for Elementary School Teachers course. I re-read the paper with questions in my mind about how well I had actually translated the learning theory to practice in that particular classroom. What follows is my analysis of and reflection on my success at applying my six learning principles and how they relate to my vision for learning.
- Provide an emotionally and physically safe space for students to learn.
- Have students work in groups as much as possible.
- Provide multimodal experiences for the students.
- Use scaffolding to allow students to work at a higher level than they would be capable of without assistance.
- Find out and build on what students already know.
- Use a variety of learning contexts to promote the students’ transfer of information from one situation to another.
This is always uppermost in my mind when teaching a class. The primary guideline is to be respectful to oneself and others, and one of the keys for me as an instructor is to have infinite patience. Math can be a terrifying subject for many students, so it was very important for the students to feel emotionally safe in this classroom. I tried to support, encourage and scaffold the students as much as possible. Any questions, answers, ideas or methods were encouraged and discussed with the class or in small groups.
Within the small groups, I encouraged the students to support each other as well. This was an ideal class in which to encourage this, because the graduates of this certificate program would become classroom assistants. Students were expected to practice their "people helping skills" both during and outside their own learning area.
I noted in my paper that "[n]urturing instructors often find their roles changing from instructor to counsellor, and must be prepared for this." Even though I usually encounter this in my Adult Basic Education classes, in this math class I found myself not so much being a counsellor for basic life issues as I did a supporter for the academic content. It was a real change for me and probably reflected the difference between the ABE class to a class where many of the the students were working at a first-year university level. Even though the students are generally the same, the ones in this class had matured or worked through their issues to the point where they were ready to move on in life.
Even though it is important to be positive and supportive with the students all the time, there are occasions where an instructor must be honest with students who are severely affected with undiagnosed disabilities. It is extremely difficult for a student to be told that he or she will never be able to achieve a certain educational standard, especially when many of their peers are meeting with success. That can be emotionally devastating for an adult student, and we (at our department at the college where I work) have still not found a good way to deal with this.
Throughout the course the students were placed in five groups of four students each. Twice during the course, students changed groups in order to have them interact with as many different people as possible. At the beginning of the course, I placed students in groups according to their self-identified skills and comfort level with math. The other two moves were made in a random fashion because the students didn't want to be identified in any way (even by themselves!) according to their level of skill.
The groups worked in some ways and did not work in others. Because students are still marked on an individual basis, group work or sharing of information seemed to some like cheating. Students with higher skills sometimes felt dragged down by having to help group mates who had a lower skill level or who took longer to understand some of the concepts. Some students felt that I was not doing my job as a teacher when I required students to check with their group mates first instead of going directly to me for help. Many students were not used to learning in a classroom without having the teacher explain everything, and being asked to think, remember, discuss and work through the math with their groupmates made some of them grumpy. Some of the students in this class knew each other previously, and it became apparent that a few did not get along well with each other. One pair in particular almost couldn't be in the same classroom together, let alone the same group, so even though the groups were set up randomly, keeping those two students separate became a classroom management issue.
On the other hand, being in groups honed the students' abilities to explain math concepts to others. For students who were used to sitting in desks in rows, this experience enabled them to see that there are other ways of learning in a classroom.
Although I was not able to provide as many hands-on experiences as I would have liked, the students really enjoyed using manipulatives. One of the more successful use of a hands-on approach came when we studied set theory. The students used an 11" x 17" piece of paper on which they drew two large interlocking circles representing two intersecting sets. Students were asked to specify the characteristics of items in the two sets (eg., blue or triangles, etc.), and then had to place small markers in the correct positions on the paper according to the characteristics of the two sets. This was a great lesson for teaching set membership, union, intersection and the universal set. We also used fraction strips to develop the idea of common denominators in fractions, but that lesson met with less success, partly because most students already knew and remembered how to add fractions, and partly because I was not clear with the instructions for the activity. Rather than it being a "discovery" type lesson, it became an exercise in frustration for some students who couldn't understand the point of it.
To help connect math with language and the process of explaining or modelling solutions to others, I asked the students to keep a math journal and gave them assignments to describe or explain math concepts. This was a very foreign and difficult type of assignment for many students who were not used to having to explain their answers or describe math concepts in words. Students who "get" math often make leaps in their thinking of which they are unaware. Because these students would become classroom aides or perhaps even teachers, I wanted to make them aware of these leaps and how important it is to show and describe all of the steps when teaching someone else.
Two areas that I felt I did not spend enough time on were showing videos and practicing math concepts through interactive manipulatives on the computer. Although I did show a video early in the course, I began to feel time-crunched as the course went on and felt that I could not show any others. With respect to using the computer, I had registered the class to go online with a website provided by the textbook publisher whereby almost the whole course can be taught and managed online. At the beginning of the course I was excited to try the system, but early on realized that given the wide range of abilities in the class, I would lose a lot of students who probably would understand the math content but would almost certainly flounder given the added complexity of trying to learn it through a computerized system. However, the students did enjoy working on the computer with math concepts found at the National Library of Virtual Manipulatives. I was introduced to this site earlier in ETEC 533: Technology in the Mathematics and Science Classroom, and I wrote a short review in the category of Dynamic Visualization Software.
Scaffolding was accomplished in two ways: first, by having the students work in groups and supporting each other in their daily work; and second, by having the instructor and tutorial assistant provide hints and model solutions to various problems. Scaffolding was very helpful to the students because some of the assignment questions in the textbook were at a level that required thinking beyond the basic concepts, or required the student to make connections between two or more concepts.
During the course, my plan was to always have the students discuss prerequisite skills before moving on to the topic(s) for the day. Nothing is more frustrating for students than to have the teacher assume they have the prior skills that are needed to understand a more advanced topic. However, I only followed my plan sporadically, perhaps due to the nature of the material that we covered and the wide range of ability levels of the students in the course.
At its most basic level, much of the material was math that the students had already covered in their courses up to about a grade 10 level. About one-half of the students had completed grade 12 and had no problems understanding the math concepts. Within the other one-half of the students was a wide range of ability levels from very capable to those who struggled from the very start due to learning disabilities. A discussion of prerequisite skills might be met with blank stares or a look of fear from some students, while others would be nodding enthusiasitcally or smiling confidently. At that level and within the time frame for the course, however, I had to assume that the students had the prerequisite skills and move on to the course material. In the end, we were able to work out a plan for the few students who could not cope with the academic level of the course while still keeping them involved in the class and groupwork.
This is one area that I find it hard to do well given the content-driven nature of most courses. Becuase of the sheer volume of concepts that we had to cover as well as the somewhat awkward scheduling of the course, I felt that we did not have as much time as I would have liked to delve into some of more intriguing or fun aspects of the concepts, or even go through as many different types of problems as we should have.
As much as possible, I tried to weave reality into the theoretical aspects of the math concepts that we were studying. One time, in particular, I noted the students' inability to translate geometric figures on a page to real structures outside the classroom window. I was shocked to discover that while some students could draw an obtuse angle, they were totally stumped when I asked them to locate one through the window: they could not distinguish one in the angle of a roof on a building outside.
Looking forward
Each one of the six points discussed above reflects my vision for teaching, which hopefully translates to a positive and well-supported learning experience for the students. My vision for the future is to continue to push myself beyond my teaching "comfort zone" to include more group work, discussion and multi-modal experiences. I would also like to pursue the concepts of authentic learning and project-based learning, both of which can be a challenge in an area like mathematics which is very theoretical, especially at the higher levels.
References
Alessi, S, and Trollip, S. (2001). Multimedia for learning: Methods and development. Needham Heights, MA: Allyn & Bacon.
Driscoll, M.P. (2005). Psychology of learning for instruction. USA: Pearson Education Inc.