Summary: Battleground Schools: Mathematics Education

The article has discussed the base of the standards of Mathematics education in North America since the beginning of the 20th century til present, which is actually, based on the two  view points: the progressive views, and the conservative views.There has been a kind of war between these two opinions to decide the standards, and implement the same. The progressives view understanding, eliciting, inquiry and sense making vital for Mathematics teaching and learning process, while the conservatives consider  fluency, authoritative, presentations and deductive explanations to be more important.The conservative views are influenced by a set of assumptions that are based on several attitudinal factors, that are responsible for creating fears in the minds of parents and educators that has resulted in a Math phobic society comprising of fearful parents and educators, untrained teachers, and bewildered students.

The three reform movements emerged during different time intervals in North America who battled against the preexisting system of Math education, and opened new gates for hope. The first was the progressive reform movement, which dated back to early 20th century, and opposed to the system of meaningless memorizing of the rules and algorithms. This movement was influenced by the changing patterns of the society as a result of rapid urbanization and industrialization. It urged for inquiry approach, active participation of the students that needed teacher as a facilitator who has to carefully structure the learning situations, in order to make their children think independently and democratically. The second movement was the "New Math" around 1960, emerged out of the post war situations as a result of increase in competition in science and technology at international levels, and aimed at producing future scientists.Their reformers advocated for unified logical, and highly abstract algebraic structure, but it soon came to an end because of the problems in implementing the curriculum as it needed fully qualified Math teachers, and also, the parents found it hard to help their kids in their homework.     

A new shift in setting the standards of Math education took place around late 1970s, and further NCTM developed its own standards and principles around 1980. They emphasized developing of the  problem solving skills, ability to represent mathematical relationships in different ways, use of technology,and ability to communicate mathematically. It urged for developing curricular material, professional development workshops for the teachers, new modes of assessments, involvement of the parents, and the use of the new technology. However it was not so easy to implement these curricular reforms as it had to bear the criticism from various organizations advocating traditionalists and new Math reform supporters, in many parts of North America.Thus mathematics education has been a puppet in the hands of concerned authorities on  various political grounds.

My Response

The article has been successful in presenting the history and the present of the Math education in North America. At first I was shocked to know about the political motives behind the educational policies, and the reasons why these motives were given more preferences, rather than actual reforms. I, personally, would like to go with NCTM reformed standards, which aim at developing the ability to think in the  students, so that they don't consider Mathematics as a hard, cool and dry subject, and use it as a way of life to become more capable citizens.

First Micro-Teaching : Feedback and Reflection

Micro-teaching lessons have set a small stage just to asses our performance as new teachers, and getting a feedback from our peers. Lesson planning and demonstration are the two main components of micro-teaching. According to my peers' views my lesson was well-planned, and and there was proper time management. Every one was involved in the lesson. However, my demonstration part needed some improvement. One of my peers said that she could not see properly while I was presenting the stress relieving tip, and I should have asked them to practice on their legs before they do it on someone Else's back. Being a teacher candidate, I found it very much useful and beneficial to know my weakness. All enjoyed the lesson, and found it very useful in their daily life.

I find micro-teaching to be an amazing activity, truly informative, creative and entertaining in such a short duration of time,as there is so much fun in learning small lessons. Micro-teaching provides an opportunity to explore the hidden talent of a person. We are able to show our abilities, and also get a chance to share our learning experiences with others. In a multi-cultural country like Canada, we got a chance to know some particular cultural activities of different cultures. I learned how to create the "best out of the waste." Learning how to  make use of chopstick wrappers was really informative. I also learned how to design a bobby pin with beads. The 10 - minute stress releaving exercises can do wonder. Another important outcome of micro-teaching is the opportunity for more interaction within in the classroom.

Lesson Plan - Releaving Stress in 10 minutes.

Bridge (1 minute)
All of us bear some kind of stress now a days, and look for some stress releaving techniques which take short time. I am going to teach one of the Chinese stress releaving exercises, that takes a few minutes, and can be done any time, any where. You will also enjoy and be amazed how effective are they. No materials required.

Learning Objective
Students will be able to perform this tip of stress releaving technique without spending a penny, and also enjoy while performing the same.

Teaching Objectives
Teacher will be able to teach using participatory activities, the tip of Chinese stress releaving exercise.

Pretest (2 minutes)
Teacher will ask some questions:
1. How many of you are going through stress these days?
2. Can you suggest some ways to releave it?


I have a way for you, which is easy to learn, at home/school, without spending any money.

Participatory Activities  (3 minutes)
We need two person for this activity. One who will be performing the stress releaving tip on the other. Learning steps:
1. Put your hands together in prayer position.
2. Open your figures wide, so that they do not touch each other.
3. With the hand in this position, bang the same on back of the stressed person, just 5 inches below the neck
    i.e. on and around the shoulder blades. While doing so, make sure the particular sound made by the   
    banging of the fingers. 
4. This should be done for 15 times in one set.

Post test (3 minutes)
Now I am going to call two my friends and one person will do this exercise on other person, so that I can check whether you are able to perform it easily. 

Summary and Conclusion (1 minute)
Everyone is now able to do this exercise that is easy to learn as you have seen, and  must remember the sound of the figures is important. Do not forget to perform this exercise 14-15 in one set.

Students 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.

Sounds for mathematical problem solving

Sounds for Mathematical problem solving

Sounds always call attention. Dave Hewitt has given a new approach to Mathematical problem solving by introducing the use of sounds, which is a new step in progressive Math education. He has made use of sounds to make the students attentive in the classroom as well as increase their participation. I think this approach is really helpful while introducing concepts of number line and integers. It was amazing how he has used sounds to teach lenear equations with one variable.As all the students can be made to involve in the process of learning, thus students have to make their own mind to answer the questions in response of the sounds, and the outcome will be their whole-hearted participation with attention. I would like to try to it on my students. The teacher must be  well planned and well prepaired in order to apply this approach.

Questions for a High School Mathematics Teacher and Student.

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?

My memories of favorite Mathematics Teacher

All through my education I had so many Mathematics teachers, as I have done my Masters in Mathematics, but my favorite Mathematics teachers are two of them. The first one is my Grade 10 Mathematics teacher Mrs.Khullar. I liked her teaching style as she never let us sit free for a moment in the class, always ready with a new set of mathematics problems for us to solve. She mastered the technique of questioning. On the same topic, she could frame so many questions to engage her students. Our class always wondered how she can manage to research. Her other best qualities were cheerful and open mind while teaching. We never felt Mathematics as a difficult subject. I never felt Mathematics as a burden after I was under her guidance to solve typical problems.
 
Second was Mr.Daljit Singh, who was lecturer in Mathematics while I was doing my B.Ed. He had a strong personality with a positive attitude in life. Every time he used to start his lecture with a small magical trick to engage the attention of students. I remember the first question he asked from the students of B. Ed., "Can you teach Mathematics?" He always insisted to provide various methods to solve a mathematical problem. He also stressed upon motivational techniques that are necessary for a Mathematics teacher.

Relational Understanding and Instrumental Understanding.

Richard R. Skemp's, "Relational Understanding and Instrumental Understanding" has touched the core of my heart as I am a Mathematics student as well as teacher. The issue of understanding Mathematics is discussed in the article; in a way that now I have got to know that why in my High school days I had so much trouble understanding the same. From those days I decided to become a Mathematics Teacher, so that I can make use of relational understanding to make my students comfortable with this subject. In my opinion the topics in Mathematics must be introduced through relational understanding. The story of seven years old boy with an I.Q. of 140 clearly tells the importance of relational understanding. My nephew having a high I.Q. level, felt shocked in his first week of attending Mathematics classes in Grade 8 being sick of instrumental understanding. In my opinion even the students with lower I.Q. should be taught through relational understanding. The article has successfully attained its aim to highlight the issues related with this subject.

Reference:

First Published in Mathematics Teaching, 77, 20-26, 1976.

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