California Standards for the Teaching Profession: Standard Four
4.1 Drawing on and valuing students’ backgrounds, interests, and developmental needs
4.2 Establishing and articulating goals for student learning
4.3 Developing and sequencing instructional activities and materials for student learning
4.4 Designing short-term and long-term plans to foster student learning
4.5 Modifying instructional plans to adjust for student needs


 Lynne is a typical fifth-grader in virtually every way. She rarely gets in trouble and completes her assignments as well as anyone else in the class. She was student of the month at the end of the year in fourth grade, and is well like by peers and staff at the school. One thing is different. Since she came to fifth grade, Lynne’s math scores have been moving steadily downwards.

 As I monitor her work on five-a-day problems, I see that she especially has trouble with rounding. One day, she asked me to help with a rounding worksheet assigned several days ago that she has been reluctant to turn in because she had not finished it. As I sat next to her to help, she put her hands to her forehead, shielding herself from the classroom. We discussed the technical aspect of what the worksheet asked her to do, then did a problem together. Suddenly, Lynne dropped her hands from her face, which was now beaming. “Oh, I get it!” she exclaimed. She completed the worksheet successfully and turned it in. The next week there was a five-a-day question dealing with rounding. Again, she was dejected. “How do I do this?” she asked, her face covered by her hands once again.

Lynne’s problem is one that is fairly typical in schools. I often hear teachers in the staff lounge discussing how they will teach concepts repeatedly but there is a lack of comprehension by the students.
 Through the years, many theories and methodologies have been created to remedy the question of how teachers should teach. Using the situation with Lynne, I will explore several of these methods.


 Behaviorists begin by trying to find which stimuli are creating the apparent response or behavior. Pavlov established his ideas about classical conditioning in his experiments with dogs. In classical conditioning, a neutral stimulus is paired with a previously unconditioned stimulus that causes an unconditioned response. With repetition, the neutral stimulus will create the same response as the the unconditioned response. If this happens, the neutral stimulus is termed a conditioned stimulus that leads to a conditioned response.

 J.B. Watson used Pavlov’s research on animals and applied it to human learners. He believed that classical conditioning of emotional reactions was happening constantly in schools. School children are, in essence, trained to have the emotional response triggered by how their teacher teaches. The idea is that if the teacher and school setting are pleasant, then the ideas and subjects being taught will not create negative reactions from the children.

 In the case of Lynne, I would suggest that something in her new fifth-grade classroom is negatively conditioning her responses towards mathematics, particularly with rounding. As the teacher, I need to assess my teaching strategies to be sure I am not creating an uncomfortable or unhappy situation for her. Perhaps I could recondition her with treats each time she gets a problem correct. With repetition, I would expect her to begin remembering how to do the problems and begin succeeding in mathematics.

 A somewhat different branch in the behaviorist tree was introduced by Thorndike. Thorndike established a set of laws having to do with how and when conditioning can occur. These include his law of effect, which states that things that satisfy will lead to learning, whereas things that annoy the learner will lead the learner away from that specific learning experience. He also stated in the law of readiness that level of a learner’s readiness determines whether the experience will annoy or satisfy. So it could be that Lynne is simply not ready for the concept of rounding, therefore, causing all efforts to help her learn to be received as annoying, resulting in her negative reaction. If this is true, then I would need to remove rounding from her set of problems until she is ready for it to avoid punishing her for trying to do the problems and failing.

 Skinner went about the issue of conditioning in a different way than Pavlov. He focused on the actions of his subjects rather than their reactions, using reinforcement for particular actions rather than connecting certain actions with others through conditioning. This is where reward and punishment come into play. Skinner’s theories give plenty of example of how rewards and punishments can elicit unwanted results, as well as only suppressing responses rather than changing them. In Lynne’s case, I could use rewards for correct answers as motivation, and punishments for wrong answers to motivate her to keep trying. In any case, since I know that this methods are powerful in so many ways, I would monitor what works for Lynne, and follow that course of action.


Cognitive research began with the idea that, though many of the behaviorist’s ideas about learning hold true for simple tasks, humans are not that simple. Most of us think about what we do, so there must be more to learning than always being duped into learning what is placed before us. The modal model of memory was created to give distinction between short-term and long-term memory.

 So how does information get encoded into long-term memory? This is something teachers test and evaluate frequently. Some call long-term memory constructive memory to add distinction to the way that remembering involves reconstructing experiences. There are many ways to develop one’s ability to retrieve or reconstruct memories in the long-term memory. As a teacher, I know that it is important to teach learners how to think in order to store and retrieve memories effectively.

 For Lynne, I think I have forgotten to teach this concept. I have helped her on several occasions to round numbers, but she still struggles with it. The next time she has difficulty, we can work through it as before, but as she reaches understanding on the subject, we will stop and talk about how she can help herself remember the concept, rather than moving immediately on to the next question of the five-a-day. With this topic, it would probably work best to use complex organizational strategies, to create an analogy that she can think of when she encounters a similar problem. Perhaps we could write about it in her math journal, or she could create a few problems similar to the first, and work through them using the analogy that she created. By learning how to process the information she receives, Lynne will be more likely to experience success.

 Outside of simple analysis of short- versus long-term memory are the theorists, like Piaget, who have varied theories on how to best instruct learners. According to Piaget’s Stages of Cognitive development, Lynne is probably in the midst of the concrete operations stage, but in some ways bordering on the formal operations stage.  Using his theories, I can see that Lynne’s problem is a result of her thought stage. A problem involving rounding requires her to think in terms of abstract ideas. Since her stage of thought, concrete operational, does not allow for abstract concepts, Lynne experiences a swell of cognitive disequilibrium. This is hard for her to handle, as shown by her physical reaction to the situation. According to Piaget, this state of frustration is only temporary. As she matures and sees more problems of this type, Lynne will develop understanding of this kind of abstract thought.

 Vygotsky believed that learning is a social function. As we learn, we are helped along by the development of inner language. According to his theories, a learner is capable of achieving higher when scaffolding is provided. This initially comes in the form of adult help, but people can be taught to use peers or self-talk to encourage their learning. When I have helped Lynne with the rounding problems, I have created a type of scaffolding. She was capable of doing to problem while I guided her through. What I can do now is to model for her how to do this on her own, or by discussing the problem with her peers. As she articulates the process in her own language, she will push her level of understanding up.

 A Constructivist named Bruner established the idea that in order to learn effectively, students must create their own coding system to deal with information. That is, if a student is allowed to explore something entirely on their own, they will remember more because they have organized the information on their own. In discovery learning, the teacher functions as facilitator, mediating the students’ experience rather than presenting complete ideas. For Lynne, I should then create a set of tools and questions so that she could explore the qualities of numbers, and allow her to approach it at her own speed, and draw her own conclusions. Her distress would be lowered, because she would work at her own pace without pressure to finish a certain problem set. Also, her learning would be more permanent because she has concrete memories of discovering and organizing the concepts.

 On the other end of the scale is Ausubel, who sees learners as receivers, waiting to be filled with information. He believes that if learning is presented in a meaningful verbal manner, that it will be incorporated in the long term memory. To teach Lynne in this manner, I would present an advance organizer, a basic explanation of the concept, at the beginning of the lesson. This would create a base of knowledge for her to attach the rest of the concepts to in her mind. For example, I might use a rounding problem using money, or other terms that she is familiar with. I would then expand the lesson and its technicalities, allowing Lynne to connect each new concept to the money problem. At the end of the lesson, she would have created memory from an expository lesson.

 Gardner approaches learners on their own terms. He believes that every learner has seven kinds of intelligences that are at different levels of development. In any learning situation, using combinations of these intelligences will increase comprehension, as well as being able to further develop the different intelligences. So, in order to best help Lynne, I would create a lesson that uses several intelligences together to experience this type of math problem. Since she likes to write stories and tell them to her friends, I might suggest that she create a tale in which a character deals with rounding things, then illustrate it and share it with her classmates. In using her varied strengths, Lynne would have increased her understanding of the problem as well as creating a meaningful long-term meaning.


A few years ago, in the midst of a frustrating discussion in class, I wrote in large letters in my notes, “I only have these eyes to see through!” What I did not know what that I was expressing a very Humanistic viewpoint. Carl Rogers, a psychotherapist who pioneered the idea of humanistic learning, believe that if a person is given a safe, supportive environment, they will develop self-esteem, self-discovery, and self-directed learning. From this came the three main beliefs of Humanist teaching, namely: 1) learning is influenced by self-concept, 2) learning should be self-initiated and involve choice, and, 3) the goal of learning is self-actualization.

 In this approach, if a learner is having trouble, it is likely to be traceable to troubles in their development of their self-image. Lynne appears happy, but in my experience with her in class, I know that she struggles more than the other children with issues of self-esteem. Her struggle with this is consistent with her frustration in math. Her self-concept is consistent with her reaction upon reaching a rounding problem that she cannot remember how to solve. She covers her face, hiding so that others cannot see her crisis. Before we work through the math problem, I would make a point to praise her for the work she has been doing in class, or for her cheerfulness earlier in the day. I would try to help her downplay the feeling failure attached to the five-a-day, or remind her that the master teacher uses it mostly to test progress, not intelligence. I know that it is harder to learn when at a heightened state of anxiety, so I might suggest that she skip it for the moment, and let me know when she was ready to work on it again.

 Ideally, the classroom would be set up so that the students are able to work cooperatively. I believe that most children can learn to work through this process with each other, not just allowing the teacher more time to teach, but also revealing to the kids that they all struggle in some area of school, and can all help each other succeed.


Though many teachers claim to side with one of the above approaches to teaching, I believe that they all have value in appropriate circumstances. I plan on using an eclectic mix of the methods in order to create a classroom that functions well, and allows each student to flourish, especially in the midst of a learning frustration like Lynne’s.

Research in this paper was based on the information packet for ED 600 by M. McMahon, Fall 2000.

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