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?  

Progressive versus Traditional

Many progressive schools place value in the experience of learning itself much like the teachers at Phoenix Park, believing that learning in groups, creative projects and discussion of concepts are intrinsically good. Traditional schools are the mostly unintended consequence of decades of politically driven school reforms that are often misguided. The debate over progressive versus traditional education pedagogies is not a new one. The principles of progressivism were spelled out in books like John Dewey’s Democracy and Education and Traditional view were spelled out as early as Franklin Bobbitt’s Scientific method in curriculum-making. I believe education should be about achieving a balance or hybrid based on the needs of students in different disciplines. Of course we need to prepare students for adulthood, but focusing only on the future does not make sense either.

With crt scores, public exam results, and mpts leaving our education system in state of unrest. We see high schools accuse intermediate schools who accuse elementary schools for not preparing students, and universities with record high remediation needs (Bridging programs, foundation courses) for entering students in English or Mathematics, and often they need remediation in both English and Math. This is causing stress for teachers, students, and parents. How does this stress affect the love of teaching, the love of learning, and a child centered curriculum? These testing requirements align very well with Bobbitt’s theories.

Bobbitt would appreciate all of the assessment and testing we are going though. Our education system sets us up to fill the students with facts and test them over and over, rather than teaching them where to find the information, or how to love learning, or how to think critically. Historically we have adopted different curriculums at different times depending on the political climate of the time.

References:

Dewey, J. (1916). My Pedagogic Creed in Flinders, D.J., & Thornton, S.J (Eds.). (2009). The Curriclum Studies Reader (pp.34-41). New York:Routledge.

Bobbit, F. (2009). Scientific method in curriculum-making. In Flinders & Thornton (3^rd Ed.), The curriculum studies reader (pp. 15-21). New York: Routledge.

Chapter 1 and 2

Boaler's study in "Experiencing School Mathematics" discuses two approaches to teaching mathematics, traditional and reform. The proponents for either side have gathered strength in research, numbers, followers, believers. It is obvious that students learn differently and teachers teach differently. With either approach some students will connect to the process while others will not. As professionals, we are more likely to use a combination of both to engage students in mathematics during particular lessons, units, and outcomes, keeping with the nature of inclusive schools and classrooms. Which I would call just good teaching! Boaler points out “the effectiveness of any teaching and learning situation will depend on the actual students involved, the actual curriculum materials used, and the myriad of decisions that teachers make as they support student learning."

In chapter 1, the author states “School classrooms should give children a sense of the nature of mathematics, and that such an endeavour is critical in halting the low achievement and participation that extends across America”. It is important that students understand that mathematics is about discovering the patterns that occur all around us, and how those patterns lead to the mathematics we learn and see in our schools. Creating opportunities for students to make connections between mathematics and nature, science, art, and music, will help students identify its importance in their lives. As professionals we implement differentiated instruction and with the implementation of the inclusionary model in our classrooms, we are using a combination of the methods being used in Phoenix Park’s and Amber Hill.

Call me a romantic!

I am one of those romantics, that Lakeoff and Nunez refers to in The Theory of Embodied Mathematics. I do believe that mathematical truth is universal, absolute, and certain; that mathematics would be the same even if there were no human beings; and that mathematicians are the ultimate scientists as described by the author’s description of the Romance of Mathematics. I believe the authors are naive to think that everyone will access mathematical thought in the same way. As a species we are fools to think we will ever truly understand the universe and it inner working. Mankind is young, we have much to understand. Albert Einstein said "If God has created the world, his primary worry was certainly not to make its understanding easy for us." Mathematics is intimidating, but one can still enjoy and respect its existence.

Scientists stride to discover the theory of everything, a theory of theoretical physics that fully explains, predicts and links together all known physical phenomena. Is it so bad to hold such a romantic idea? Creativity is everything, as a species it helps us understand our world and stride to reach greatest.  Lakeoff and Nunez state that the romance of mathematics is the premise of most popular books on mathematics and many a science-fiction movies. When I was a kid, I remember watching Star Trek and Caption Kirk using his communicator to contact the Enterprise from anywhere on the planet below. It was fiction, it was creative, but through our further understanding of mathematics. Many of you are sitting next to your mobile phones as you read this blog. Mine is here next to me as I write it. 

John Brockman’s interview with Reuben Hersh, Hersh states that mathematics is “neither physical nor mental, it’s social. It’s part of culture, it’s part of history. It’s like law, like religion, like money, like all those other things which are real, but only as part of collective human consciousness” (Hersh, 1997). I do agree the importance of mathematics with respect to children’s education is social and cultural, fuelled by the need to have our children to obtain careers such as engineering, medicine, etc. As stated by a popular line from the film Jerry Maguire “show me the money.”

Hersh believes that “math is something human. There’s no math without people” (Hersh, 1997). Maybe Hersh is right. But when I look into the night’s sky, I see a lot of stars. To think we are the only species that have the ability to think and ponder this very issue is naive. But yet, we are a young species. When we are young, we believe everything exist for our own selfish needs. Our understanding of mathematics is human, how we conceptualise it’s exist is based on our limited experience. Albert Einstein once said "Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand." To think mathematics is something human, demonstrates how young we truly are. Call me a romantic!