Psychology and Mathematics Education by Efraim Fischbein

This week when reading Fischbein's Psychology and Mathematics Education, the main point that came across to me was the fact that for years researchers have classified mathematics education as a part of a larger scientific area in which to apply cognitive psychology theories. This is no longer the case, as mathematics educators have identified unique features found in mathematics education that sets it apart from the other sciences.  Fischbein mentions that Piaget's theories that were applied to mathematics education research for years do not actually fit. This is because "Piaget was not interested in the effects of instruction on the development of mathematical reasoning" and "his belief that intellectual development is essentially a logical one."
In 1976, an "International Group for Psychology of Mathematics Education" was developed to explore "the role of psychology in the teaching process and to do so in a systematic manner." I believe this is extremely important as it is difficult to apply general psychological theories to mathematics education; moreover, as Frischbein states, it is crucial that researchers look for "the interactions between psychology and mathematics education." I experience this daily in my classroom setting. You can try to plan the perfect lesson, taking into account the curriculum and the individual needs of you students, however, in practice, there always students that will need further support or different support that could not have been anticipated. These needs of students vary on a daily basis and general psychological research trends cannot account for daily variances in student's needs.
I think Fischbein explains it well when he states, "the psychological perspective in mathematics education research is genuine psychology, characterized by the style of thinking and its focus on the dialects of the subjective world of the person versus the environmental constraints."

Strong is the Silence: Challenging Interlocking Systems of Privilege and Opression in Mathematics Teacher Education by Herbel-Eisenmann et al.

Upon reading Strong is the Silence by Herbel-Eisenmann et al. I was challenged quite a bit emotionally. I guess I am getting ahead of myself and should first comment on what they have presented. Herbel-Eisenmann et al. presents "the need to break the silence of privilege and oppression in mathematics education. The authors present three distinct reasons for the need to voice these concerns. These reasons are: that the teacher population is not a very good representation of the student population with regards to race, social class, and language spoken, the lack of literature surrounding the diverse nature of the classrooms in the United States and lastly, the lack of literature that confronts the "privilege granted by institutions and society through addressing interlocking systems of privilege and oppression in order for our mathematics education community to thoughtfully avoid replicating imperialism."
I guess this is where the emotional cord comes in. The article addresses the fact that typically "White teachers claim to be 'colour-blind' and treat all students the same." The authors believe this is not possible and covers up the inequities that occur in the classroom with regards to race, class, and power. They go on to say that this "color-blind"ness leads to differing expectations in students from different situations and ultimately may "negatively impact the performance of students of color and undermine multicultural practices and policies." Until this week I would have like to say that I treat all my students the same regardless of their backgrounds and I would never have said I hold different students to different standards. Although it would be impossible to say that you are colour-blind, as having an appreciation for each of your children's life situations is imperative, I truly would like to believe that I treat them equally and have appropriate expectations for each of them.  Although I work in a school that is definitely not a complete representation of society, we do have many students of differing race, social-economic status, and multilingual families, there are students from all walks of life that need extra support or care at different times.
I believe that this question is much more complex than just a simple socio-economic analysis. As we all know as educators, children are extremely multi-dimensional with their needs in school and out of school. However, in conclusion, I do believe it is important to acknowledge the issues of privilege and oppression and I whole-heartedly agree that these two entities do not need to exist in parallel and if they are addressed separately, we as mathematics teachers will be able to help more of our students obtain success.

On the Foundations of Mathematics Education by William Higginson

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.

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