Hopes, worries and fears for the future

I am hoping that my choice of becoming a teacher was a good one and I will be able to touch my students' lives in some way or other. I would like to be there when my students need any kind of support and let them know that they are important and their opinion counts. Also, I would like to change their misconception that math is hard, and make them believe that everybody can learn it if they put their effort and mind into it. I realize that teachers can have a great influence on how their students view themselves and the world around them, and I would like to help them become critical thinkers. My fear is that being a perfectionist, I will push my students too hard and instead of liking math they might start hating it.

Letters from former math students

Letter #1
Dear Mrs. S,

It' been 10 years since our high shool graduation, when you had your farewell speech in front of our class. At that time I didn't care much about the world around me, but your words touched me so much I can still remember them. I did chose a path in my life I thought would suit me, and you were right, you have to love what you are doing or else you wouldn't be fulfilled in your life. Although I struggled with math you thaught me to think for myself, to see the world with my own eyes and become a critical thinker. I do appreciate that you cared enough for me to not let me quit school when I felt I can't go on anymore.
Thank you for caring,

William

Letter #2
Dear Mrs. S,

Ever since you told me that no matter how gifted I am in math I have to work hard in order to get somewhere I was trying to prove you wrong. Unfortunately this didn't get me far in life and I am blaming you for it. If it wasn't you I would have succeded a long time ago and would have enjojed life like everybody else.
Probably you are an even bigger expert in torturing students, since you have 10 more years in doing it so. I feel sorry for all of your students, because I believe that life should be enjoyed to the fullest when you are a teenager, and your expectations do not allow for that. School should be fun and this would be only possible without homework.
I hope you retire soon or find some other job for yourself!

Mark

Summary of “Battleground Schools: Mathematics Education” by Susan Gerofsky

This paper is discussing the ongoing and never ending battle around North American mathematics education and the reform movements of the 20th century. The three reform movements: the Progressivist (1910-1940), the New Math (1960's), and the NCTM Standards-based Math Wars
can be seen as battles between conservatives and progressivists. Since the existence of public schools in North America, in the late 19th century, there were many public criticism of school mathematics as a process of meaningless memorized procedures without knowing why these particular procedures worked.

The pressure for more meaningful mathematics curriculum increased after the First World War with the increase in international immigration and the rapid changes in society.
John Dewey's work is particularly important because he challenged the Cartesian split between knowing and doing, or abstract and applied knowledge. He believed that students thrive in an environment where they are allowed to experience and interact with the curriculum, and all students should have the opportunity to take part in their own learning. The role of the teacher should be the facilitator where learning situations and materials are carefully structured and prepared in advance. Dewey said that an educator must take into account the unique differences between each student. Thus, teaching and curriculum must be designed in ways that allow for such individual differences. Although Dewey's ideas won a high degree of acceptance in progressive teacher's colleges, most North American classrooms followed a very conservative approach.

After the Second World War both educators and the public recognized the need for more technical and mathematical skills. After the surprise launch of the Soviet Sputnik satellite in 1957, improving mathematics education at the K-12 level became of utmost importance. The resulting movement was called “The New Math”, which gained momentum in 1960 and its influence spread worldwide. The New Math supporters were highly conservative except for a few progressive ideals: they supported understanding over fluency, and to some extent, inquiry and sense-making over absorbing and applying facts.

The NCTM Standards were shaped by both constructivist and progressive approaches emphasizing the development of flexible problem-solving skills, the ability to represent mathematical relationships in multiple forms. The use of calculators and computers was encouraged as an essential part of the problem-solving process. Students should also be encouraged to devise their own plans and explore alternate approaches to problems to gain the ability to communicate mathematically.

The Math Wars today are far from over yet and I think it is very important to separate the education system from political interests. Teaching mathematics should not be dictated by economical or political movements, the goal of teaching and curriculum should be designed to fit the needs of the students regardless of the socio economical circumstances. It would benefit the society as a whole if we could engage students in a reflective inquiry thus increasing their intelligence and knowledge which can be applied to all areas of life.

Microteaching Self-Evaluation

Most of the students in my group were excited about my lesson topic, since they've never tasted a green smoothie before. All three of them agreed that it was very informative and they learnt a lot they hadn't known before. They found that the introduction/bridge was clear, one of them noted that the lesson could have started with listing the health benefits of the smoothie first. They all liked the paricipatory hands-on activity,(they touched and tasted the greens). One of the students noted that there was a bit too much lecturing. All three of them found that my time management needs improvement since the smoothie had to be made in a rush at the end of the lesson. All three students were excited about tasting and drinking the smoothie, one of them noted that she wants to try the recipes at home.

Reflecting back on the lesson, I think I used too much time at the beginning lecturing, this is why I ran out of time at the end. Also, I was a little anxious troughout the lesson, probably this could have been prevented if I would have practiced it beforehand. I liked how excited my students were learning about the health benefits of green smoothies. I think that showing students the different kinds of greens, then asking them to touch and taste them was a good addition to the lesson. I also think that the handout I prepared with the health benefits was well appreciated.
For the future I really need to pay attention to timing to avoid losing important
parts at the end of the lesson.

Student and Teacher Interview Summary

By: Raman Dhiman, Zsofia Szigeti, Marija O’Neill


We interviewed a teacher with more than twenty years of experience both in public and private schools. She is currently teaching grades nine and ten. Following are some of the highlights of our interview including interesting points from teacher’s answers and our responses.

When we asked the teacher how she manages students with different abilities and work habits she said that she does not like to give her advanced students work which is ahead of the curriculum. Instead, she keeps them busy by giving them work that is broad in the subject and by encouraging them to help others. As a parent, I would like to have this teacher teach my kids, although this may not be a wish shared by some other parents. There are parents and kids who focus on raised goals, raising them as far ahead of curriculum as possible. I like my kids and my students to enjoy more stable growth and not be working ahead for one period then be bored the next, and then possibly even loose the academic momentum, work habits, and the ability to look into the subject deeper.

We were impressed that she was fond of using technology such as Tablet pc, overhead projector, and the Internet. The tablet pc appears quite helpful to give live displays of the graphical presentation, while she is facing the class.

When we asked her what she finds most rewarding about being a teacher she responded by saying that creating a safe environment where students feel understood and that they matter was on top of her list. She added that she enjoys the fact that she can focus and direct their attention to certain things without controlling them. Students on the other hand, are active participants in the learning process because of teacher’s ability to keep them interested in learning.

Showing genuine interest in students and listening helps determine their needs, which allows a teacher to adjust the curriculum accordingly. Offering help after school is very important because there are students who are shy and do not dare to ask questions in class. Being too shy to ask questions in class is not something I had ever previously given much thought about. Given that many students find math difficult she takes extra steps in motivating and even has quotations on her wall such as “It is the attitude not the aptitude that determines the altitude of you success” and “I-m-possible”.

Being a substitute teacher appears to be the most difficult position to be in because there was no relationship between the teacher and the students and she could not bring her own material to make her lesson more appealing. We may be in this position before we get a permanent job and it is good to know that.

Student's interview:

In addition, we interviewed a grade ten student whose strengths she stated are not in math. She shared her thoughts about her learning experiences as well as her emotions towards the subject of mathematics.

In the very beginning of our conversation with the student we gathered that she was one of those typical kids with fear of math. She said that math was the hardest subject and feels very nervous about it. Even if she knew that she is using the right methods to solve problems she was never fully confident about the outcome. The anxiety would usually be over once she had a confirmation that her answer was correct. As a result, she needed more time to complete her work in class.

When we asked what she liked about her teacher she said it was the fact that her teacher listens to her students and adjusts curriculum based on what she feels suits them. For example, the teacher allows them to take extra time to complete their exercises in class if necessary. One of the things she did not like about her teacher is that although she would give enough time to finish work in the classroom, she did not allow enough time to prepare for exams. Also, she would like her teacher to help her build confidence that she needs in order to tackle some of her mathematical challenges. She realizes the importance of math in her daily life. Some of the examples of math applications in her life were: addition and subtraction, percentages in the stores (for discounts), and interestingly she mentioned speed again.

One of the greatest discoveries about her learning was when we asked if she would like to have a career related to math. She answered that she was fascinated with proofs and how and why mathematical theories work. She is one of those kids who takes time to think what the meaning behind a quadratic equation, for example, is and not just trying to solve it quickly. This is why she is slow and needs extra time. From this article, we learnt that we as future educators must be aware of HOW students learn and maybe investigate the reasons why some students take longer to perform math operations.

Thoughts on David Hewitt's Teaching

 
David Hewitt’s teaching style is interesting and impressive at the same time to me.  I’ve never seen anybody teaching this way before. His auditory teaching style without the use of the visual made me realize that there are many possible ways of teaching that can work better than the ones I knew before. I am not sure if someone can learn to teach this way or it’s just a special skill but it is definitely a very effective method of teaching. The loud banging noise he makes with his stick gets all  his student’s attention and it seemed that the students were following along. It was interesting for me to see him do the transition from the number line to equations.
 
 

How to make a smoothie

Name: Zsofia Szigeti	Lesson Plan	Date:22 Sept 2010
What	How Long	Materials
Bridge: Introduce the concept of green smoothie to the students. Ask students to list some of the green leafy vegetables they know.	1 min
Learning Objectives: Students will be able to identify green leafy vegetables and make their own smoothie.
Teaching Objectives: Students learn about the nutritional value and health benefits of dark green leafy vegetables.
Pretest: Ask students to identify the different types of green leafy vegetables.	1 min	Kale, Russian Kale, Swiss Chard, Red Chard.
Participatory Learning: Students will explore different smoothie recipes and develop their own.	4 min	Print-out with smoothie recipes and health benefits.
Post -Test: Students choose a recipe and make their own smoothie.	3 min	Blender, Fruits, Greens, Water.
Summary and Closing: Ask the students about the health benefits of greens in our diet.	1min

My Memorable Math Teacher

   The amount of math we did in high school was so huge that it didn't leave time for social interaction between us, students, and our math teacher. We hated the extra amount of work he gave us because even without that extra work we spent 2-3 hours studying math.
Sometimes, instead of coming to school at 8'clock he asked us to come an hour before, at 7'clock, so we can better prepare for our university admission exams. During winter it was almost dark at that hour and we hated getting up at 6 for an extra hour of math and did not appreciate his efforts. He wasn't paid for that extra hour but cared enough for us to sacrifice one hour of his sleep to make sure that we know everything we need to make it to university. At the end of grade 12 we had our exams for admission to different universities in the country and 30 out of 33 made it that year, the rest of 3 the following year.
  The most memorable thing about my teacher though has not much to do with math. It was our one and only two day class bus trip, going halfway across the country to visit the hometown of the famous Hungarian mathematician, Janos Bolyai. It was late November, dark and raining and our bus broke down. All of us had to get off the bus so the driver could be able to fix the problem. We were told that it will take at least an hour to fix the bus so our teacher decided that in order to keep ourselves warm we have to start walking until the bus will catch us up. We were cold and wet and our teacher's gesture to offer us his scarf, his hat and his umbrella made us realize that he was more than a teacher to us. He taught us because he cared for us and I carry his memory in my heart forever.

Questions for a High School Mathematics Teacher and a Student

(Raman, Maria and Zsofia)
Questions for a teacher:

1. What do yo do when advanced students have finished their work in class well ahead of the rest of the class, do you give them extra work?
2. What kind of technology do you use?
3. What do you find most rewarding being a teacher?
4. What challenges did you face as a new teacher?
5. What teaching strategies work best with your students?

Questions for a student:

1. How do you feel about solving Math problems?
2. What do you like about your Math teacher?
3. What do you not like about your teacher?
4. Do you find it useful in your daily life?
5. Would you like to have a career related to Mathematics?

Response to the Richard Skemp article

Instrumental Understanding vs. Relational Understanding

It is my experience as a tutor, that most students prefer instrumental understanding versus relational understanding and most math teachers are in favor of the former. Instead of trying to solve a given problem, students with instrumental understanding are focused on getting the solution right, rather than using logical reasoning. I have seen students do the calculations of the values of a function perfectly but getting stuck at graphing the function because they don't see the biger picture. Many of these students have an amazing speed and accuracy at computation but are lacking in understanding even the basic principles of Mathematics. This ability at computation gives them an advantage over students who use relational understanding, students who have a deeper understanding of principles but are lacking in computational skills. These students know how to figure out the solution to difficult “mindbenders”, but, often make errors and are a lot slower in performing computations.

I find it unfortunate that most students in our school systems are taught instrumentally. This might be due to the structuring of a one year curriculum into one semester, this way teachers have to rush trough material making sure they finish it by the end of the semester. It is hard to accommodate students whose goal is to understand relationally since the majority of each classroom are students who understand instrumentally. Most teachers also prefer students with computational abilities and are not willing to change their teaching style in order to accomodate relational understanding. Even most regional and provincial level individual Mathematics competitions are designed to fit the learning style of those who understand instrumentally. In team competitions though, where higher level critical thinking is required, students with relational understanding thrive, they have a great advantage over the former group of students.