My initial reactions to the title and first few paragraphs:
Higginson introduces his article, On the Foundations of Mathematics Education, by raising the idea of Gulliver's Travels relevance across many generations. He raises the idea of the author's ability to make light of actual government issues of the time while also foreshadowing future topics of interest, like the computer. My initial thinking is that Higginson will relate early mathematics education thinking to the ability of Gulliver's author to predict future topics of relevance.
Upon reading the whole article:
Higginson goes on to explain how mathematics educators fail to make mathematics education relevant for their students and much like a section of Gulliver's Travels just feed them knowledge they are expected to digest and make sense of. Higginson believes we need a better understanding of the mathematical foundations in order to make it relevant for our students. The dimensions of mathematics education is much more complex than initially acknowledged by research mathematicians at elite universities. Higginson acknowledges the psychological dimension as an area of utmost importance. I agree completely and have experienced both the positive and negative sides of this in my teaching experiences. This is where I see the connection now more clearly with Higginson's Gulliver's Travels references. Higginson remarks on Gulliver visiting the '"Academy of Projectors at Lagado" where in their projects, "the professors contrive new rules and methods" with the intention of improving the lot of the citizens of Lagado' but the projects never make it to the streets to improve the citizens lives. I believe this is true with professors who only ever see mathematics being taught to willing participants at high levels. It is easy to see mathematics in isolation in these scenarios, however, when you experience teaching mathematics to all children in your classes each day, you realize that mathematics education does not happen in isolation and without other factors.
Higginson introduces the concept of a MAPS-tetrahedral model of mathematics education. This model includes four disciplines: mathematics, psychology, sociology, and philosphy. "The fact that the tetrahedron is closed may be one way of quickly perceiving the claim that the four foundational areas are not only necessary, but also sufficient, to determine the nature of mathematics education." I agree with this completely! We need to acknowledge that mathematics is not learned in isolation and there are many factors that are different for each child, and each scenario in which mathematics is taught. All the four dimensions influence each other and are varying.
The model does an excellent job in my opinion of demonstrating the complexities that accompany mathematics education. When looked at in isolation we can break down where difficulties may arise; however, without looking at all other experiences our students bring into our classrooms, you cannot begin to break down their deficiencies.
I appreciate Higginson's application of this model to past trends in education and also more relevant shifts that may need to occur in the future. I thought it very interesting how he mentioned the industrial society's focus on quantity of production and how we may need to look into a more practical and appealing notion of "optimal as beautiful" rather than "bigger is better."
Finally, I agree with Higginson's notion that the model is not perfect. It is a hard model to apply to all situations; however, it does create a common ground for educators to be united and have discussions around how we can best support our students when learning a historically difficult and sometimes daunting subject matter. The model allows for the whole student to be taken into account not the just the subject matter in isolation. I believe we are educators of the whole child and without understanding the student's life context, we cannot begin to be able to help support them in their mathematical journey.
Higginson's notion of understanding what our students bring to the class and making relevance to our students' life experience remind me of John Dewey's philosophy of education. It is optimal and nearly utopian to consider each and every student individually yet educators recognize that it is the key to elicit student interest and release their imagination and wonder. This is not a new concept or idea. In fact, we all have experienced this ourselves. A student can understand better learning one-on-one with a teacher than in a large group. The teacher can better tailor his or her explanation to one child than to a whole class. At the same time, it is much more feasible to incorporate a student as a whole into the mathematical content when the student population is unitary. However, this kind of individualized education is both costly and time-consuming. In a class setting, teachers can only seek ways to best employ this pedagogical philosophy. It is impossible to know every aspect of every child in one's math class. However, it is possible to be interested in the students beyond the math classroom. This is why building a strong student-teacher report affects the quality of student learning. Making connection and draw meaning to students' daily life is another excellent way to provoke student interest in the subject matter. These are the century old vision Dewey left us with to implement and continue to discover.
ReplyDeleteI definitely agree that mathematics is not learned simply because it has been taught. There are so many factors that affect a child's learning, in all subject areas (not just math). In an elementary school setting I believe that this tetrahedral model may be more easily implemented. A teacher is more likely to have a fuller understanding of where their students are coming from (socially & psychologically) when there are only 30 of them. In a secondary setting, where a teacher can have over 200 students I would think that it would be much more difficult to meet those individual needs of every student. That said, there are certain things that can be done in any classroom to create a positive learning environment. First and foremost, a student needs to feel safe in their classroom, and be comfortable to inquire and ask questions of the teacher, their peers, and them self. Once this is established, I believe that a more effective learning experience will present itself.
ReplyDeleteDavid, I don't think that the tetrahedral model is one that Higginson meant to be implemented in the classroom. I think it is a model for understanding how one could do research in mathematics education -- by considering math teaching and learning in relationship to mathematics, and to sociology, philosophy and psychology.
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