A Learning Profile

                I interviewed a 14 year old male learner and found him to be working his way through the formal operations stage according to Piaget. He was able to discuss several topics about hypothetical concepts. However, while he is aware of the need to plan for all possibilities when testing some hypothesis, he has difficulty seeing what all the possibilities are.

                Morally, he seems to be in Kohlberg’s conventional morality level. There are two stages of this level, Good Interpersonal Relationships and Maintaining the Social Order (Crain, 2011). He is teetering between the two stages as he recognizes that laws are in place for the good of society and to maintain order, but sometimes fails to view certain laws from society’s perspective. He is sometimes annoyed when laws prohibit him from doing whatever he wants regardless of the possible consequences for others due to his actions.

                According to Erikson, the interviewee is in the puberty stage. His body has been changing rapidly and he is interested in sex. He also takes pains to dress in a certain way that his parents do not necessarily agree with. He does not do it to defy his parents, but to ensure he is accepted by his peers. There are strict, unwritten social rules that he must navigate and follow in order to maintain his social status.

Crain, W. (2011). Theories of development: Concepts and applications (6th ed.). Boston, MA: Prentice Hall.

The Importance of Language Arts

The Common Core standards for language arts, or any curriculum for explicit instruction of language typically goes against Chomsky’s theory of language development. Chomsky finds that the acquisition of language in young children comes from within. As noted by Crain, “Hearing only a fragmentary body of speech, they nevertheless discover its rules, guided by an innate sense of what the rules must be like,” (Crain, 2011, p.362). By age 6, most children have achieved fluency in their language, though they may not be conscious of the rules they are using.

            By the age of 13 children will have mastered most of the rules of spoken language, and Common Core standards are focused on the production and comprehension of written language. The further development of language is rooted in the need to express ideas about specific content rather than inconsequential statements used while learning the rules of the language. For example, a young child who is still learning how the language works may say things like, “The ball is red,” or “I don’t like peas”. Children use simple language while building their knowledge of how the language works. By junior high and high school, having mastered the rules of language, they must develop specific vocabularies and styles in order to communicate content specific ideas. In a history class, in order to discuss the consequences of some historical episode, the older child must be able to take in information, process it, and then devise a way to express a summary or new information in a way others can understand.

            As a math teacher, it is important for students to be able to share their mathematical knowledge in English as well as mathematically. Language arts standards at this level are focused on organization of information and the precise expression of complex ideas. Without the capability to share mathematical ideas, math becomes a purely theoretical activity of manipulating symbols in a dogmatic way. Given the ability to effectively communicate, math can then be applied to the real world and used to solve problems that people naturally encounter. Therefore, it is necessary for junior high and high school math teachers to help students build the bridge between the symbolic language of math and the spoken and written language used to share ideas.

A Cultural Inventory

How many children are in the family in which you were born? What is your birth order?

Both my parents had children before they married each other so I have two brothers and two sisters, though I was only raised with one of my sisters. I am the baby of the family.

What were some of the roles of the sons in our family? The daughters?

My sister and I did typically feminine things like cook and sew, but there was not really a distinction between men’s work and woman’s work. I often helped my father with ‘manly’ jobs like mowing the lawn or maintaining the house. Both my parents worked outside the home so I didn’t see it as a man’s role to be the breadwinner. At the same time, because my mother worked, I saw my father cook dinner or vacuum the floor just as often as my mother because they shared the household responsibilities.

What is the education level of your parents? Your grandparents?

Both of my parents attended college part time while I was growing up and both earned associates degrees. I know that my mother’s mother did not finish high school. My mother’s father may have finished, but he didn’t go to college. I suspect that my father’s parents, being black and from the south during the early 20^th century, did not finish high school.

What language do your parents speak? Your grandparents?

My parents and all my grandparents were native English speakers. The most recent newcomer was my great grandfather from Italy, but he learned and spoke English (as well as other languages) without an accent.

What are the rules of your family regarding courtship and marriage?

The rules are: there are no rules because my parents broke them. My parents married outside of their races and had to deal with the nonsense that goes along with that. Their attitudes about who should marry whom are somewhat relaxed. I presume I could have come home with a person of any color, age, or sex, and my parents would be okay with it as long as the person wasn’t a jerk.

What special occasions do your family celebrate? What special foods are prepared?

Christmas and Thanksgiving were the things we celebrated. Christmas was about Santa Claus and spending time with our immediate family. Thanksgiving was about family and friends and strays with nowhere else to go. We prepared very American food (turkey, mashed potatoes, cranberry sauce), but we did include some southern sweet potato soufflé or maybe pecan pie. Any more ethnic foods we may have had, like tamales at Christmas, were due to where we lived rather than our own family’s heritage.

What is the birthplace of your parents? Your grandparents? To what culture do your parents belong? Your grandparents?

My parents and grandparents were all born in the United States. My great grandfather was Italian but did not bring any foods or traditions with him when he came to the United States. He was assimilated, and his children were raised as Americans. My father is from the south and his ancestors have been American for many generations (although some were not considered citizens, or even human). Overall, we are very American.

A Few Learning Theories

Piaget’s Cognitive-Developmental Theory is based on an invariant sequence of stages of development; every being passes through each stage, in order, at their own pace. The general periods of development are Sensorimotor Intelligence, Preoperational Thought, Concrete Operations, and Formal Operations (Crain, 2011). The underlying idea to Piaget’s theory is that the act of learning comes from within the learner. I agree with the majority of his theory and can make use of it in my own teaching by being aware of the level of development of my students, and using methods that are at or slightly above their developmental capabilities.

Closely related is Kamii’s Constructivism, which could be considered the application of Piaget’s theory. Kamii’s theory is based on Piaget’s idea that children construct their own knowledge. In practice, children should be allowed to work on problems that are of interest to them, and given the opportunity to solve them on their own (Crain, 2011). I wholeheartedly agree that a learner is more successful when problems are solved independently, rather than being told the correct answer and moving on. My own son can attest to my (inadvertent) use of this method: when he asks me a question about something, my answer is another question. It is my hope that in giving him something else to think about, he can glean the information necessary to solve the problem on his own.

Skinner’s Operant Conditioning is based on the idea that behavior is guided by its consequences. A behavior that elicits a positive consequence will be more likely to occur than one that has negative consequences (Crain, 2011). In my class, I plan to use this type of conditioning to guide the behavior of students in order to maintain an environment conducive to learning. I will try to reward students who exhibit good behavior (turning in homework, being respectful, helping other students), and discourage poor behavior (acting up, showing off) by withdrawing attention.

Crain, W. (2011). Theories of development: Concepts and applications. Boston: Prentice Hall.

Learning Styles Tests

        I took the Learning Styles and Strategies test that gives a score based on four sets of “opposites”. For example, an Active learner learns best by doing something active (discussing, collaborating), and Reflective learners prefer to think about the material and work alone. My own test results showed that I am a much more Reflective than Active learner. Between Sensing (facts, details) and Intuitive (the big picture) I lean slightly more toward Sensing. I am slightly more Visual than Verbal. Lastly, I am almost balanced between Sequential (step by step) and Global (gathering all information, then making connections).

The second test I took was the Grasha-Riechmann Student Learning Style Scales. This scale gives a low, moderate, or high score for six different learning styles. My scores were: Independent - moderate (3.8), Avoidant - moderate (2.5), Collaborative - low (1.5), Dependent - moderate (3.3), Competitive - moderate (1.9), and Participant - low (2.3). The only one of these that surprised me was the moderate score in the Avoidant category. Avoidant students do not typically enjoy going to class and are uninterested in the content. On the contrary, I love going to class and learning new things, I would just prefer to do it with as little interaction with other people as possible.

Both tests show that I prefer to do my learning quietly and privately. I tend to avoid collaboration if possible. It makes me wonder a little why I chose such an interactive career. However, teaching and learning, while similar in some ways, are not mutually exclusive. Even though I don’t learn by interacting with others, I can still present material in various ways depending on the needs of my students.

A Personality Test

I took a personality test at http://www.teamtechnology.co.uk/mmdi/questionnaire/. The results are based on a scale developed by Isabel Briggs Myers.  I scored as an ISTP. According to the website:

If your closest personality type is ISTP then you have both a logical and a practical mind and therefore enjoy solving tangible problems. You are very interested in how things work, and may have a tendency to take things apart if you don't know how they work. You may also enjoy using your craftmanslike skills to fix things that are broken, or doing investigative work, collecting facts and clues to find out the truth of what has happened.

I think this is a pretty good estimation of my personality and shows why I have chosen to teach math in particular. When solving a math problem, you have to gather information and put it together in logical ways.

This could also help me in teaching. I can attack the problem (getting all that math into students’ heads) by gathering information (students’ learning styles, standards to be met, students’ previous experiences) and finding a logical way to put it all together.

Hello There!

 Hello there! My name is Andrea and I’m working on my single subject teaching credential in math. I would like to be a junior high algebra teacher, but I am open to teaching high school as well. I decided to teach because I of my tumultuous relationship with math: I love math when I understand it, I hate math when I don’t. I thought if I could help kids understand math, they wouldn’t hate it so much.

I have about a year left before I’m finished with my education and can start working on the education of our youth, so check back here often to see what’s happening on my journey.