EDUC 450: Reading #4 - The Kind of Schools We Need

While I can appreciate the ideas, suggestions, and values Eisner presents in his article, I also feel that the presentation of the type of school he describes is quite idealistic. I agree that teacher inquiry, encouraging diverse students and their strengths, conversations, student inquiry, and community interactions are all essential aspects that schools need to address within curriculum delivery and student teacher relationships. However, the extent to which each idea Eisner believes should be accommodated would not serve the best interest for students as society is structured presently.

For example, if students are given the option to specialize themselves and pursue mastery of specific subjects, thus ignoring others, then it is assuming that the student knows how to best prepare themselves for a future that they have decided upon. In reality most students, even adults, require exposure to many interests and experiences before even considering areas that they wish to further study or develop skills. Encouraging students to foster their talents and passions is essential, yet as teachers, it is also our responsibility to ensure they are equipped with a diverse set of skills for any situation they may encounter.

Later on, Eisner states, “The point of learning something in school is to enrich life outside school and to acquire the kills and ideas that will enable one o produce the questions and perform the activities that one’s life will require.” (p. 581) In my opinion, this cannot be supported if we solely encourage an education system that excludes content from all subjects. It is important to note that confidence, self-esteem and a higher level of mastery is acquired through specialization. Having students work through subjects that are more difficult to grasp, challenge their intuition, and require effort is in itself a valuable learning opportunity. If students are continuously allowed to only pursue areas that they have talent or are driven by passion and interests, they will not ever learn how to deal with difficult situations and learn to overcome adversity of all types.

Currently, our society continues to move towards a more complex grouping of specialized fields. Before we are able to become experts in one field, it is crucial to be aware and appreciate the challenges of all fields.

EDCP 342: Reading #5 – Arbitrary and Necessary

Hewitt’s differentiation between arbitrary and necessary aspects of math education emphasizes the reliance on memory by some students that in fact hinders their understanding. Teachers that solely impart information cause students to perceive math as one massive set of rules and situations they need to commit to memory and are then unable to discern the concepts themselves.

The arbitrary outlines the tools that teachers need to explain so that students become equipped with otherwise unknown knowledge. Without being told standard conventions, and using ways such as math history to establish these practices, students are unable to explore mathematics in a way that can be understood by the general community. They will also encounter difficulty in understanding higher level concepts as they will not be able to interpret other information and explanations that heavily employ standard expressions. By strengthening memory capacity surrounding arbitrary knowledge, teachers move to building awareness and comprehension when necessary knowledge is later introduced.

As the author states “… a teacher’s role is to work within the realm of awareness rather than memory.” (p. 5) By first establishing a firm foundation of arbitrary knowledge, students can move to uncovering knowledge that they have acquired the ability to discover on their own.

Arbitrary and necessary knowledge divide methods of gaining mathematic knowledge. It serves as a specific model of scaffolding to assist students in having a firmer grasp of how to approach the subject of math and develop the required skills at all academic levels.

You can’t build a house without knowing how to use a hammer…

EDCP 342: Reflection – The Locker Problem

A school has 1000 lockers and 1000 students. On the first morning:

*The first student walks along and opens every locker.

*The second student walks along and closes every second locker.

*The third student walks along and changes the position of every third locker door.

And so on. Once all 1000 students have completed this process, which lockers are open?

Briefly describe how you solved it?

To solve this problem, I first tried reduced the number of lockers to ten to see if there was a pattern that could be found with a smaller set. I manually wrote out how the locker positions would change given ten students walked along and changed the positions for the first ten lockers. After ten students had walked along, the firs ten lockers would o longer be changed. I circled all the locker numbers that were left open and tried to see any pattern of this smaller set. The open lockers were 1, 4, and 9 and these are all the perfect squares found between 1 and 10. I assumed then that all of the perfect squares less than 1000 would be left open once all the students had walked through. From this point, I “guess and checked” the largest number whose square was less than 1000 - this is 31. Thus there are 31 lockers left open after all of the students pass through all 1000 lockers.

Where do you think a student might get stuck?

 A student can be overwhelmed when initially reading the problem. The shear number of lockers and students to account for may present itself as an overly large counting task. If a student does not know how to initially break down the problem into steps that are more approachable then he/she will not feel as if they can find a solution. Even if a student is able to simplify the problem, he/she may not make establish a pattern between the open lockers and perfect squares. Perfect squares are often a concept that takes time to become familiar with recognizing its presence.

How might you assist that stuck student?

To assist students having trouble, especially those intimidated by the problem parameters, can suggest breaking it down into a smaller number of lockers – counting open lockers from 1-20 is more approachable than 1000. When acknowledging patterns, can encourage students to think about how mathematicians describe and classify numbers – whether they are even, odd, prime, and their possible factors.

What extensions could you offer students ready for a challenge?

Those students who are looking to be challenged can be asked to:

·      Find any pattern that exists between the occurrence of perfect squares.

·       Determine how many lockers were open after 100 students pass through? 200 students? 35o students? Is there another pattern found to how may lockers would be left open for any number of students passing through that is less than the number of lockers?

EDUC 450: Exit Slip - Mission Statement

My mission as an educator is to:

1. Empower students with knowledge and understanding of subject matter.
2. Engage students to be active in their own learning.
3. Coach students as they develop the skills and habits needed to pursue their aspirations.
4. Become a support system and confidant that students can comfortably seek help and advice.
5. Challenge students to a higher standard to help them meet their full potential.
6. Inspire confidence in students’ own abilities.
7. Take time to be familiar with students on a personal level.
8. Act as a role model through my conduct to support kind, moral, and ethical behavior.
9. Be an active member in many facets of the school community and its programs.
10. Ensure each student is treated equally with respect and dignity. 

EDUC 450: Reading #3

Reflective Teaching and Educational Inquiry    

Last week’s article by Zeichner and Grant focused on reflection and highlighted not only the benefits of incorporating this practice, but emphasized its necessity in the field. Henderson’s article added to this idea through the examination of inquiry and its role in the classroom. Developing the habit of asking questions, altering habits, and questioning the purpose and authenticity of our actions is not enough. I agree with the article and its push to have teachers take the next step and put into action their reflections – that is to inquire and construct an external dialogue besides having an individual internal dialogue. As teachers, we should be always searching for methods that have the most impact on our students for both content delivery as well as societal and contextual circumstances. We are not able to design all of the methods that can be most effective on our own so the idea of a team approach seems intuitive. By inquiring with our colleagues and with our students, the diverse amounts of knowledge and ways in which it is explored can be expanded and enriched for both the student and teacher experience.

What’s Old is New Again!

                         

Clarke and Erikson’s historical account of the evolution of classroom and teacher inquiry supports the idea of inquiry needing to be at the forefront of education. After first attempting to examine the process of understanding through a research and scientific approach, all involved acknowledged the need for a more experiential concept. The history of education research itself indicates the need for teacher inquiry. Interactions with students and witnessing the change in understanding and behavior as a direct result of teacher inquiry produces ensure success for both the student and the teacher.

An element that especially caught my attention was the difference between “teacher knowing” and “teacher knowledge” as compared in the closing statements of the article. Once again, the concept of relational and instrumental understanding came to mind. If a teacher does not reflect and inquire into their practices, then they are acting as a conduit of information thus promoting instrumental understanding. While those teachers who actively seek information, are curious about their own actions and how to best interact and challenge their students, they begin to engage and promote rational understanding. Teachers themselves must model the type of understanding that they wish to encourage in their students.

Overall, the two articles created a link between reflection and inquiry. As beneficial as reflection can be to improving a teacher’s self awareness and habits, inquiry is the process that allows us to put into action what has been thought and challenge the reflexive practices.