A Teacher's Place in Education

After concluding the final chapter of the text, there were a number of issues circling around the same idea that stood out to me as very important.
A students education is potentially centered on a number of possible methods, however it remains a constant that teachers are the nucleus of a child’s learning.
So, if students fail to produce ideal results, who is to blame? Is it the teachers? Is it the methods they are using? Is it the student at fault? It appears as though through this text, the methods used by each school were scrutinized, regardless of results. Phoenix Park not only created a successful, but open ended, interactive, learning environment for it’s students. And even though these students did better on their exams than those of Amber Hill, the method used to achieve these great results was reprimanded. The teachers of Phoenix Park also took time in collaborating with other teachers and researching interesting projects and examples for their students to complete-what else can teachers do in order to make a successful classroom method, and have it approved by boards. Are teachers today placed in a situation that they simply cannot conquer? I guess it’s an on going quest for perfection. And although yes the classroom is a place that continues to grow and expand, and yes no method is perfect and yes there is ALWAYS room for improvement-where is the recognition for teachers that have begun to expand their own practices?

This book provided me a great deal of insight in terms of the different methods of teaching mathematics, and the impact it has on students. It is truly amazing to consider the impact our way of teaching can shape a young student, not only in one subject area, but how it can shape a students perception of learning. I think this book taught me the importance of striving to keep mathematics interesting for all, and incorporating differentiation of methods so that every child can reach their full level of potential.

ABILITY GROUPING: FRIEND OR FOE

This weeks reading from chapter 10 was really interesting for me and made me reevaluate my own thinking on the topic of ability and mixed grouping.
To think that we the teachers could create such a social barrier between students, and even initiate the social stigma of a lower class within our classroom is quite scary.
Mixed ability, although yes maybe difficult to present material for all students, and at a level all students can benefit from is not the only way students learn. By differentiating work and knowing your students well enough to know who needs more help and who can work just as well independently is part of our jobs and this is how we will succeed in a mixed ability classroom.
Schools are a much more difficult environment then they were 10 years ago, and bullying is now more than ever a huge issue within schools. I do not see any separation for any reason among students having a positive benefit. By separating students we are giving them more reason to be “against” one another, potentially creating more room for bullying to take place.
Although both methods of grouping have both positives and negatives, it is our job as teachers to determine which works best for our students and provide a positive learning experience for all.

Gender and Math

As noted in my previous posting, I have a number of questions and inquires, especially when it comes to gender in mathematics.
After reading a couple of different resources it seems as though the idea of boys being superior to girls in the subject area is an outdated idea, which is coming to a halt. A mere result of “social engineering”, we have actually constructed this false concept ourselves, by giving boys the greater opportunity to succeed in math or abstracting our research under unfair circumstances.
“According to new research published in the journal Science, the "gender gap" in math’s, long perceived to exist between girls and boys, disappears in societies that treat both sexes equally” (Lipsett, 2008). The stereotype exists that males are “better” at math than females, so many do not want to “waste time” on females who are primarily over seen by their male peers. Placing both genders on an equal playing field to start gives each an equal opportunity to succeed.
Another potential cause for a wide range of test scores between males and females is female’s lack of response to competitiveness. It has been recorded that females do not perform as well as males in competitive test taking environments. It only makes sense that males would produce better results, but not from just math intelligence alone, but also being placed in a comfortable environment.
“We find that the response to competition differs for men and women, and in the examined environment, gender difference in competitive performance does not reflect the difference in non competitive performance” (Niederle &Vesterlund, 2009).
I think the most important reminder from this weeks discussion was the importance of placing all students on the same playing field. As educators, we need to ensure equal opportunities are provided to all students-regardless of their race, gender, socioeconomic status, etc. The situation we choose to place our students in always has an effect on their learning.

Lipsett, A. (2008) Boys not better than girls at maths, study finds. Education Guardian. Retrieved Nov 12, 2011 from http://www.guardian.co.uk/education/2008/may/30/schools.uk1

Niederle, Muriel & Vesterlund, Lise (2009) Explaining the Gender Gap in Math Test Scores: The Role of Competition. Retrieved November 21, 2011 from http://www.stanford.edu/~niederle/NV.JEP.pdf

Gender and Math... Initial thoughts

This week’s chapter 9 in the text really sparked my interest on the subject of gender differences in mathematics learning.

I can’t help but wonder, with all the circulating research on gender inequality in mathematics education- boys being the gender of dominance- is this an example where our expectations are creating a reality? Are the affects of society determining our students’ performance in the class? Are we creating the pressures students are feeling to succeed on a level according to their gender and the expectations society is placing on them? Do students feel the pressure to conform to a certain identity that compromise their ability and willingness to learn math?

These are just a few initial questions and thoughts I have on the subject. I will follow up with a post on an article on the subject.

Jack of All Trades, Master of None?

I found the article posted by my classmate Too Many Teachers Can't Do Math, Let Alone Teach It to be very interesting and so I decided to express my concerns and opinions on the subject here. In brief, the article expresses growing concerns with the lack of educating educators in math and how unprepared teachers are in the classroom to teach young students the subject.

I think this article pertains a great deal to the idea of teachers being “jack of all trades, master of none”. And although I did enjoy my undergrad program, I do not feel it fully prepared me for a number of different aspects of the teaching profession. There are such a number of subjects, and a specific number of outcomes per grade per subject. Besides the facts/information presented in each subject, teachers also must juggle many day to day routines- organization, preparation for lessons, along with maintaining an environment which promotes fair and equal opportunities for all, social justice and much more. I am just wondering how and where teachers are expected to get the detailed training for all aspects of this career within their university education?

This being said, one of the biggest points we are taught in our teaching education is to “be prepared for the unexpected”. How can one prepare for the unknown?
Also, quite often, teachers are offered positions in an unfamiliar territory- weather it be in an unexpected grade level, a specialized subject area, or in a multigrade/age classroom. Teachers are expected to adapt to their environment and prevail while

Yes I do agree that in order for teachers to successfully teach students, an established level of familiarization with the information at hand must be established. But are teachers expected to know everything about everything at all times? I think the most we can do is prepare for the unexpected and really make the extra effort in learning it ourselves before we teach.

Math from the Past

When asked to describe a memorable math experience from my grade school past, I was unable to recall just one that stood out to me. I can say that I do remember activities where we used manipulatives such as those wooden pattern blocks, connecting blocks, place value charts, fake money, etc. For me, like many others, it was using these types of resources that would make math concepts much more tangible.
One thing I do not recall ever having to do much of, especially compared to know, is explaining and giving reasons to support your answers. I was teaching in a class last week where one of the questions was ended with “explain how you know”. Almost every student in the class had to correct answer, knew how they did (in terms of correctly carrying out the right formula) but they could not put into words how they did it. I think this is a great addition to the curriculum, as students will not just have to plug in formulas and move on. Instead, students will be forced to think about and reason why they did what they did, making more sense out of the problem. I think this is something students at Amber Hill did not have to do much of. If they did maybe they would have been able to understand what they were doing, and would not have developed such a resentment towards math. Just a thought ☺

The Contents of Today's Curriculum

While trying to research articles to correspond with the text, “teach for the test” is one common phrase that continues to make an appearance. It appears as though it is a vicious cycle- teachers strive for their students to be the best (or have the top grades), but being the best is only recognized if certain material is taught and not necessarily easily transfered education into real life for students, but aren’t we supposed to have our students best interest at heart, etc etc.

So where does this problem stem from? Do school boards understand the pressure teachers and students are faced with when it comes to testing and curriculum contents in education today? Do they realize the difficulties students are having in translating this information into the real world? Do we need to revise our curriculum into one which could be more useful for students? What is the purpose of an "education" if it cannot be used in the outside world? To me, this seems like an issue of what is the educational value of material being taught? And what is more important, the quantity of material vs the quality. Students are beginning to recognize the lack of relevance information, they are learning, has in their everyday lives, soon they will probably loose interest altogether, forcing even more lack of interest in the classrooms. I think we need to reevaluate what and why we are teaching and keep students our top priority, and not the test.

The Best Teaching Approach Is ???

For me, I think the most interesting part of the text Experiencing School Mathematics is the comparing of the different approaches used by each school. I think by reading the approaches used, side by side, creates an easy way to compare and contrast the two. Having the students input and commentary added a great deal to the comparison.

Center based approach is a great way to teach certain students. Yes, this method provides a very open concept, allowing students to create their own learning. Yes, by creating their own learning students will have a more memorable and beneficial experience, which will potentially result in great academic achievement. HOWEVER, before any of this amazing and great learning experience can take place, the students have to be capable of learning in this capacity. Students at Phoenix Park demonstrated that any such class using this method can and probably will have students that will not benefit from this style of learning. I am a firm believer in giving students the opportunity to explore all aspects of a student’s capability.

A combination of the two approaches used by the schools would be an ideal effective teaching environment. Placing emphasis on students creating their own learning, and providing the opportunity for them to challenge themselves by going above the outcomes provided. Also, using given resources and texts to solidify what is being learned.

I’m interested to continue reading this text to see how the teachers at both schools continue teaching the students using their approaches, and how the students academic state of mind ends up.

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), we are looking at how students are lacking true knowledge and comprehension of math.

Using word based problems; we see how students are unable to make real world connections, therefore demonstrating not a lack of comprehension, but rather memorization of a formula, and not necessarily the correct way of doing something. If we look at the example of how many buses are needed, students plugged in a formula they believed to be correct, and that was it resulting with a response as "31 with 12 left over" instead of responding with a number of busses. I wonder if this problem was given to students outside of math if students wouldn’t feel the necessity to just look at this as numbers. Could students answer this problem correctly if we change the context of their learning?


A "good teacher" is identified as one who teaches a number of different ways to look at the same thing so all students "get it". But is this enough? Just because there is more than one way to explain something doesn't make it any easier for students to truly understand. The practice of math and students understanding will be different for every child with every topic, and that's where problems occur. I think it's easy for teachers to say; well their workings are right so that's enough. We need to reinforce the importance of proof of knowledge in students. This can only accomplished by students making connections for themselves.

post 2.... what exactly IS math?

I really enjoyed this weeks articles and video, I thought there was such a diverse collection of ideas and concepts. However after reading and watching, I’m not sure if my idea and perception of mathematics has shifted, if they have cleared, or if I am more confused. One thing is certain, is the need for math teachers to really develop and form their own beliefs and understandings as to what math really is to them.

All articles produce a great deal of knowledge and comparisons for math in our culture today.

I think an important concept that doesn’t seem to have an answer, might reflect a too complex idea for young students to grasp. Therefore I think its important in teaching mathematics we try and instill an idea or basic concept as to what math is, why it is important and relating it in terms of their everyday lives. I think in order to give our students a chance at learning and actually understanding this subject, we as teachers have to decide which ideas and concepts apply to our own personal beliefs of mathematics and it’s place in our society. By at least providing students with a number of ideas or assumptions, they can then decide what they choose to believe in terms of mathematics. This might eliminate the on going complaint of “why do we have to learn this?”

I never before looked at philosophy and mathematics. However I now think it is important to look at philosophy as PART of mathematics, and a means to understanding it.

For me, an important concept I took away from Hersh’s interview was looking at math in terms of being external or internal. Personally I believe math is external, in that it is all around us. But in order for math to work, in other words in order for us to understand it, we must internally make connections for ourselves. By making connections across other beliefs- political, social, humanistic, etc- we can then formulate our own thoughts, and understandings.

Hersh also gives us three philosophical attitudes towards mathematics: Platonism, formalism, and humanism. After reading these, I was able to identify which attitude I possess towards mathematics and clarify why I feel this way. This was important for me because it allowed me to explore other aspects of math. I believe math is always there, we clarify and study it to comprehend it.

I think we take for granted the existence of mathematics, and so maybe more effort should go into studying what it is. Providing students with reason and support of the art of math, teaching them reason for practicing it, and demonstrating in such a way that they can relate to and see how it is used in their everyday lives.

After watching Ken Robinsons video on killing creativity, he made some great points on how we allow students to “out grow” creativity as opposed to growing into- are we stifling a child’s right to an education by limiting their choice of curriculum due to what we consider to be valid education?

One thing is certain: interaction and communication are key in the teaching of math. Math to me is a subject across all subjects- numbers, coordinates, ratios, and lengths are everywhere. So in order for students to recognize the importance, we need to show them math in a variety of creative, inspiring ways.

Math Autobiography

For the majority of my life, I referred to myself as a “lucky one” because throughout my grade school years I always enjoyed math and considered myself pretty good at it. I enjoyed working with numbers, multiplication was easy, I liked making patterns, and working with angles was enjoyable. I would much rather have an upcoming math test rather than a science or social studies test. I believed this was because once you got the jist and understood a sequence or pattern in math, most problems were doable. Other subjects involved much more memorization, which I have always struggled with. I do not recall any teacher in particular who obviously disliked math, however even now I have come across many people who have shuttered in response to finding out my focus area is that of mathematics.

Math in high school proved to be more difficult than that of prim/elem, however it was still do able. But math in high school appeared to loose its color, its excitement, it’s dimension of objects. Instead everything “fun” about math was replaced with a scientific calculator that we were allowed to use some of the time. High school was not my most memorable math experience.

Although I took the following math courses in university:

Finite mathematics I, finite mathematics ii,linear algebra i, linera algebra ii, discrete mathematics, Euclidian geometry, set theory and mathematics in PE grades. I can honestly say I do not use ANY of these course-based materials in my day to day life. For me, I feel the basic mathematics I learned in my prim/elem days are the most useful- quick multiplication, figuring out which is the better buy and comparing prices at the grocery store, small tasks like that which I take for granted, others struggle with, and so I am thankful for that

Even though I completed these courses, I was TERRIFIED at the hard reality I was faced with upon entering university. There were many different “math” courses, and being good at one type, does not mean success will prevail in the other. My worst memory of math was not too long ago… throughout my university career I stumbled upon a math course that was nearly the death of me.. Euclidian geometry was unlike any course I’d seen before and so I was sadden and upset at the fact that I struggled with this course- but my math courses were supposed to be the easiest of my load. I felt the frustration and anger others felt throughout their whole lives in not being able to comprehend this subject. I felt defeated and disappointed in myself and never wanted to feel that feeling again. ( This is not to say I never had any difficulty with math ever in grade schoo, however this was definitely the hardest course and I could barely tell if instructions were English)

Now it is evident that manipulatives and tactiles are obvious useful strategies and objects when doing math. Working in prim/elem grades I see much more math even in the classrooms- birthday graphs, favorite leisure activity tally’s as well as estimating included in morning routines. I do not remember seeing any of this when I was younger- I honestly don’t remember seeing much math evident in the classroom- the walls were covered with calendars, and other writing projects, very little having to do with mathematics.

When I teach today, I still hear students say “ohh no… not math miss!!!!!” I try and make the extra effort to try and make a lesson more appealing- whether using examples students can relate to, or getting them to use manipulatives in a beneficial way ( not just for the sake of having blocks to play with during math). I think it’s so important to try and show students practical uses for math and ways that we use math everyday in our lives. Far too often teachers (past and present) use math as a threat (“if you don’t like this art project we could always do some more math??”) I think everyone needs to realize the importance of math, and how we as teachers can have such an impact on our students idea and attitude towards the subject.