The Usual Suspects

What a Usual Suspects twist to an interesting debate? To discover that Phoenix Park school to move from the reform approach to the tradition approach of Amber Hill. It was disappointed to see them revert, especially since at least for that particular school the open project base approach seem to produce excellent results while fostering critical thinking. But like all publically funded institutions, the funding and values change with the political climate of the time. I always believed we need a hybrid approach, one that encourages mathematical thinking, critical thinking, creativity and flexibility. We needed to avoid falling solely into the trap of teaching to the test, it is important to make connections and prepare our students to such assessments that act as barriers in their educational progression. There are benefits from both the reform approach and traditional approach. As educators it is our duty to reflect on our teaching practices. Palmer challenges us, as teachers, to critically examine our own attitudes and perceptions, to be true to self and admit what is and what is not working in our classrooms. He expects us to re-examine the traditional teaching methods and critique the learning environment we create and its potential impact on the learning process. Through his writing, we realise there is a need for self evaluation and personal reflection, a powerful tool for personal and professional growth and understanding many of the dimensions of curriculum.


Palmer, The Courage to Teach (Excerpt)
http://www.mcli.dist.maricopa.edu/events/afc99/articles/heartof.html

Chapter 9, Girls, Boys and Learning Styles

It is difficult to change stereotypes. It has been a long held belief that boys are better than girls in mathematics and science. Boaler's work indicates that there is no significant difference in abilities between genders. In my own teaching career, I haven’t notice any significant difference between the performances of boys and girls in my own classrooms.

A study of members of the Khasi and Karbi tribes of India suggests that the influence of culture can virtually eliminate at least some of the gender differences. http://healthland.time.com/2011/08/30/the-math-gender-gap-nurture-can-trump-nature/#ixzz1eI4uG5Vl

Studies continuously show that the gender gap in mathematics disappearing and virtually nonexistent in countries with greater gender equality. The gender gap that exist in countries with less gender equality exist due to the mere fact that boys are receiving better and more education in mathematics and the sciences. In our own society cultural views in the past with respect to the role of males and females may have fostered and disempowered females with respect to mathematics. In today’s society’s views on gender equality has fostered the need for all students to pursue mathematics and science. The gap is virtually nonexistence.

Chapter 8: Knowledge, Beliefs, and Mathematical Identities

In chapter 8, Boaler proposes that students developed very different mathematical identities; she proposes that the contrasting learning and teaching experiences of the students led to differences in knowledge and beliefs about mathematics. The students enrolled at Amber Hill developed a static procedural knowledge of mathematics, where they learned the rules and algorithms to successful navigate particular problems and mathematical concepts.  The students at Phoenix Park, however, through a problem oriented approach, viewed math as a tool and were quite capable of connecting it with the real world.   Students at Phoenix Park became efficient problem solvers where as students at Amber Hill had difficulty problem solvers when presented with real life situations.

I believe in fostering automaticity. Automaticity is the ability to effortlessly complete tasks with low interference of other simultaneous activities and without conscious thought throughout the step-by-step process. Mastery of the material reduces the demand on the working memory and allows for higher order thinking. Repetition of math skills leads to the development of automaticity of the particular skills. Automaticity is achieved when a mathematics task can be completed almost effortlessly. The student does not have to think about individual steps and can carry out the task of solving the problem rather than focussing on the details of the basic skills required.

I see no reason that precision and drilled teaching methods need to go together altogether. Students need precision with terms, notation and skills. This does not mean that our students’ education should omit open and creative exploration. Quite the opposite, our students must rely on the accurate use of language, skills, symbols and diagrams that allows them to freely explore their ideas that are fabricated by these essential communicative tools.

In Dan Brown’s novel The DaVinci Code, the author introduces readers to the ‘divine proportion, providing the reader with a romantic vision of the potential of mathematics. The golden ratio is shown to exist throughout nature. When flower seeds grow in spirals, the spirals in seashells, pinecones, etc. I question critics who say that our classrooms should give children a sense of the nature of mathematics and that it is critical in preventing the low achievement. I do agree it is important but is it the gospel for educating our youth. They cite indices that students know what English literature and science are because they engage in bona fide aspects of the subjects in our schools.

Why should mathematics be so different?

Do we expect a student to become a successful writer if he or she does not learn the basics of grammar, aspects of writing? Will a science teacher be successful in completing a simple physics or chemistry lab if the student does not have the basic mathematics skills to interpret the data? Do we sacrifice one for the other? Is there any point in making our students successful at conceptualising how to solve a problem if we do not foster the skills to implement their ideas?

Chapter 7, Exploring the Differences

In Chapter 7, Exploring the Differences the main theme highlights the comparison between traditional and reform approach where reform approach seems better than traditional methods. I think this chapter really showed how math became more meaningful and applicable for the students at Phoenix Park.  The issue here is truly student motivation and how we can motivate them to want to be problem solvers. It may be as simple as finding something that interest the students enough. The hard part is what interest our students and what may work for one group, may not necessary work for another.  The word problems we commonly use in our assessments are curriculum related word problems; they are extensions of rules and procedures that students have to learn in the classroom setting. In Math 3204, we get excited when we model half life problems because it has a real life application of population growth of bacteria or the absorption of medications into the blood stream. But in principle they are just like any other exponential story problem, the procedure is the same. But these types of word problems are not true problem solving scenarios. Do we ever truly give kids opportunities to make real life connections with mathematics?

Chapter 6

Student retention is a major issue presented in this chapter. The facts that the students form both schools were retaining only a small fraction of the material they had learned only six months after writing the GCSE. As teachers we hope our students retain the knowledge we foster as we prepare them for standardised test such as CRTs and pubic examinations. How do we address retention issues? Are teachers at both schools subconsciously teaching to the exam? I have notice my own body language emphasizing the importance of various popular test items. Would such cues impact retention?

When Good Teaching Leads to Bad Results: The Disasters of “Well-Taught” Mathematics Courses

In the article, When Good Teaching Leads to Bad Results: The Disasters of “Well-Taught” Mathematics Courses, Schoenfeld (1988) argues that mathematics curriculum, and pedagogies do not foster students to gain a true understanding of mathematics. The traditional approach to teaching fails to make real world connections. Scoenfeld argument is not new, in my Ed6602 and Ed6300, we studied educational reformist such as Dewey (1933) and Piaget (1970) who made similar arguments.

Scoenfeld also implies that traditional method of instruction is inadequate, focusing on competition of a fixed body of knowledge. The article was written in 1988 and not much has changed. Traditional teaching methods are predominantly the method of choice of teachers, as described by Boaler, teachers of Amber Hill. Scoenfeld further suggest that such traditional methodologies trivialise mathematics and deny students of the opportunities to understand and use what they have explored in their classrooms. Scoenfeld would see Pheonix Park has providing students with these opportunities.

Scoenfeld fails to present all the factors that are impacting student performance, his analysis needs to probe deeper into the true nature of the student as an individual. I believe he has shifted the pendulum too far in the other direction. There has to be a happy medium between the two schools of thought. There is no true model that would work for every classroom, and it would be ridiculous to think it would work for each individual student. Reality is that not every student will be so capable, or feel so compelled to learn. We have adopted a student centered learning model, in the hope that it would provide the best opportunities for our students, in order for them to reach their greatest potential.

Chapter 5 Ensure that all students are working to their potential.

How can teachers ensure that all students are working to their potential in a problem solving environment?

Phoenix Park was successful because not only did it encourage independence and choice but also allowed students to exercise it. From this model the best we can do is hope that students eventually develop an appreciation for the learning process and decide for themselves to spend their in class time engaged. Is this risky business? Are our students mature enough to handle such autonomy? I am inspired by the argument and results presented by Boaler in chapter 5. I love the idea of students exploring problem solving and given control over the depth of exploration and projects they decide to explore. Boaler talks about how it changed the students’ view of mathematics and its influence on real life. The opportunities at Phoenix Park are fostering creativity, independence and respect and enjoyment of the discipline of mathematics. I keep looking at my own students, and I ask are they mature enough to take on such a task. There is no control over the class; the students have autonomy over what and how much they learn. In an educational atmosphere where standardised test are used to measure how much a student has learned. Who would be held accountable if they did not meet such standards?