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.

Reflection

Ashley-For me, this was a very challenging topic to research. I chose this subject because I felt learning while researching would be more beneficial than choosing a topic which I already had extensive knowledge about. However once I began to research ethnomathematics, it became a topic, which proved to be both complex and very in depth. For the purpose of this blog, I chose to go the way as a future teacher and create a blog which just had the basic facts and different pieces of ethnomathemtaics which I thought would be most useful for teachers.

Alisha-Writing this blog has definitely been a journey for me from the moment that we picked the topic of ethnomathematics as an inquiry project. The nature of this assignment required us to further investigate a math education related topic that we don’t know anything or knew little about. While looking at the list of topics that our professor suggested I noticed this topic called ethnomathematics. From studying anthropology and sociology before, I recognized ethno as relating to ethnicity as in any group or culture and was curious to see how it would related to mathematics. So I discussed the topic with my partner and here we are now at the end of this project but only the beginning of realizing what kind of implications the study of ethnomathematics can have on our classrooms. My study on this fascinating topic has leaded me through numerous books, websites and journal articles, through different cultures, different languages and different interpretations of ethnomathematics and different implications for teachers. We have only really touched on the surface of what ethnomathematics is and what it can do you for you in your classroom but it is hopefully enough to bud an interest in you into this huge study and field that could have a great effect on how you teach mathematics to your students. So good luck, there is a lot of material for you to discover and take knowledge from, enjoy!