"Battleground Schools" Reflection

In this article, the author discusses major reform movements in North America, which include Progressive reform, the New Math, and the NCTM Standard-based Math Wars. The main purpose of these movements is to change the mathematics education system to make an improvement. However, these movements are almost always opposed by people who are on the opposite side of the line. There exist two polarized views of mathematics education, and these are categorized as progressive and conservative or traditionalist views. In addition to this, there are some other complicating factors that has made it difficult for the mathematics education to have much change, such as public stereotypes and unqualified teachers.

As the author suggest, I believe that the most effective form of mathematics education will be formed only if these two opposite views meet in the middle and combine their ideas together. One way is not always better than the other. Both conservative and progressive views contain important aspects of mathematics education. For example, in terms of modes of mathematics teaching, teachers would need to present materials at some times, but also need to elicit ideas from the students on some other times. I think the part of the reason that there are ongoing disputes is that people are afraid to change. Change means that there needs to be a lot of effort put in. However, it is sometimes important to take some risks and make those efforts to bring in the changes. Also, it is important that these efforts need to be made at every level of education. We really need to listen to and respect other people’s opinions and try to come up with the ways to provide the best education for our students. We need to keep in our mind that it would be the students who suffer from these ongoing polarized political debates.

Teacher & Student Interview - Group Report

We interviewed a grade 8 mathematics teacher from a middle school in the Coquitlam school district via e-mail. He had expressed the biggest challenge was trying to teach the basic operations such as addition, subtraction, multiplication, and division to the struggling students such that the students would not give up. Consequently, he would also have to keep the top students from being bored. For the top students, he allows them to be peer tutors and provides math challenges or puzzles for them. The math class schedules goes as: class game of Bus Driver, presentation of the math challenge, lecture (25 minutes) and assigned questions (30 minutes). Bus driver is a game with multiplication flash cards. These cards are never shuffled. The bus driver is the winner from the last game. They start off facing off another student in the class. Whoever is the fastest at answering the next flipped up card is the winner for that round. If it's a tie, the teacher keeps flipping the cards (sometimes many at a time) to see who is the fastest. The winner is the bus driver and goes to the next student. The game ends when everyone has a turn and is proclaimed the bus driver and has their name written on the board as the bus driver. Even the struggling students love participating and sometimes may guess the answer ahead of time to win.

By interviewing two students in different grades, we were able to observe some interesting similarities and differences in their responses. First half of the interview questions dealt with what the students like and not like about mathematics. When we asked them what their favourite parts in mathematics were, the grade 9 student responded that he likes to work with integers because they are straight-forward and it is easy to remember the rules. The grade 11 student responded that he likes algebra for a similar reason, but he also likes riddles and logic puzzles. It is interesting how the grade 9 student likes the straightforward and easy concept, while the grade 11 student likes the challenging puzzles and riddles that allow him to think beyond the simple rules and concept.

We then asked them to share some of the challenges they encounter in mathematic classes. The grade 9 student responded that one thing he finds really difficult is translating the word problems into the equations. Also, he is confused when the same symbols are used to represent different things. Similarly, the grade 11 student had a problem with understanding the idea behind the concepts and rules. For example, he has difficulties with understanding the differences between the inverse function and the reciprocal function. Some of these areas of difficulty in math reminded us of the articles that we have read by Skemp (1976) and Robinson (2006) stressing the idea of relational understanding instead of instrumental understanding. We thought that the students are having difficulties in those areas, because they lack the relational understanding of the concepts.

They also expressed an interest in class when the teacher used different media for explanations (that is, anything but the chalkboard). The use of geometric shape blocks on the projector depicting larger shapes and ideas was found as interesting. Presenting students with “challenge-of-the-week” (COW) puzzles and problems got the students interested in math beyond the daily lessons. With the grade 11 student, humour made the classroom more relaxed and the math lessons more interesting–but we can’t all be comedians! In the students’ opinions, logic puzzles would be an interesting addition to math classes. Real-life applications of math would also make the classes more practical. When asked about group work, the reactions were mixed. The grade 9 student did not prefer group work too much because of the added distractions from getting the work done. The grade 11 student has had math projects, such as designing a water slide using cubic functions, and enjoyed the idea of working with others, finding value in comparing answers and thought-processes with others.

Teacher & Student Interview - Individual Reflection

Through this assignment, I was able to obtain the perspectives on mathematics education from both the students and the teachers. Not only was it interesting to refresh my memories of high school years, but it also allowed me to listen to some of the teachers’ opinions and learn from them. In addition, it was very interesting to listen to other groups’ presentations and see how each student and teacher has different views and opinions.

One particular response from the students that caught my attention was that they are just worried about getting good grades on the provincial exams and want to learn formulas and rules, rather than having group activities and having fun in mathematics. By reading Skemp’s article, we now understand how important it is to reinforce the students to have relational understandings and develop problem solving skills. However, when students are not motivated to learn, it would be extremely difficult to try teaching them something beyond the formula. Thus, it becomes apparent that the efforts to motivate students to learn problem solving skills have to come in from all levels of education, including the education system.

In addition, I was glad to acquire some teaching tips through the teachers’ interviews. One point that was mentioned the most was the importance of having the patience with the students. Each student has different needs and different pace of learning. Thus, having the patience with the students is the one of the most important aspects that the teachers should have. Another thing that I thought very useful was how one teacher came up with a way to assign homework for her students. She assigned homework to everyone but only the students who did not pass the quiz needed to hand in their homework. I think this is a very effective way to reinforce hard working habits in students, while making them to take responsibilities for their own actions.

My most memorable teachers

One of my most memorable math teachers is Mrs. Shim from my middle school in Korea. She used to have a very unique dialect and students always made fun of her accents. I also remember her being very strict and always pushing us to try the challenging questions. However, the reason I still remember her is the kindness she had shown toward the students who were falling behind the class. At first, I had thought that she was a very scary person who doesn’t allow any failures. However, I later realized how she was the type of person who set appropriate levels of expectations according to student’s compatibility with the subject. She encouraged the excelling kids to learn more but tried to help the kids who were slow in learning by giving them extra time to finish their work and tutoring them after class.

Another memorable teacher is my Gr.11 and 12 math teacher. She respected our opinions and always tried to make the class more interesting for students. At the end of each class, she wrote a puzzle on the board for everyone to think about and she gave out prizes to encourage students to actually work on them. She also invented the math jeopardy games, in which we could choose a category of a various mathematical concepts. These games and puzzles helped us to build confidence in mathematics, while having fun.

I was fortunate to have encountered great teachers throughout my life and was provided the opportunity to work with many of them. Just as each student is unique, each teacher is similarly unique. I have observed unique teaching styles and tried to establish my own teaching style, building on my strengths. Oftentimes, it is challenging for a teacher to maintain an appropriate level of learning for all of the students at the same time. In order to overcome these challenges, I will try to search for the most effective and interesting method of teaching, with the goal to meet the needs of each unique individual in my class. I will also provide my service and care to each student I work with throughout their learning processes. I also aim to form healthy bonds with my students and become a teacher whom they can rely on when they run into hardships and require guidance.

Robinson article - Reflection

In the article, Robinson emphasizes the importance of using research to assess one’s own teaching styles and bringing changes to his/her instructional methods. There are many teachers who just follow the curriculum guidelines for years and are afraid to make changes. However, when Robinson realized that something was not going the right way, she took a brave step to assess her own teaching style and strived to improve it. I admire how she tried to bring changes to her classroom in a very strategic way. Rather than just making changes right away, she first observed herself to analyze what needs to be improved. Then, she set a specific goal for her class and designed her classes in such way that she restricted her lecture time and gave the students time to actively participate in their learning processes. One thing that resonated with me was Robinson’s vision for her classroom. I also believe that it is very important that students take parts in their own learning processes, in order for them to view mathematics in relevant and related ways. Reading Robinson’s article gave me an insight into what teachers can do to try improving their instructional methods. I would like to always keep Robinson’s student-centred classes in mind and not be afraid to bring changes in my classroom.

Self/Peer Evaluation

In general, my peers liked how I prepared the flashcards with the English pronunciation. The cards made it easier for them to learn how to speak the Korean words. In addition, they found my competency in my topic as one of my strengths. They wrote that I was able to answer all of the questions during the lecture quickly and clearly. I was glad to see that my peers found my lesson informative and interesting. One of the main weaknesses that my peers pointed out was the time management. During my lesson, I gave short background information of the Korean language, and I taught them three Korean words that they can use. However, I ran out of time at the end of lecture and didn’t have enough time to do any summary/conclusion of the lesson. Some of my peers suggested that it would have been better to prepare handouts, in order to increase understanding of the topic. Lastly, they pointed out that it was hard to hear my voice in a loud classroom.

Overall, I was pleased to find that my students (peers) had a great attitude in learning. They were eager to learn more about Korean and were actively participating during my lesson. As my peers pointed out, one thing that I would have to work on is time management. Though I knew that it would be difficult to teach a language in 10 minutes, I should have planned the lesson more carefully. Another thing that I need to work on is getting more relaxed when speaking in front of other people. I got really nervous when it was my turn to teach and wasn’t confident enough. Overall, this was a very fun experience for me. By teaching something other than mathematics, I was able to gain a new experience of teaching.

Lesson Plan: Korean

Bridge:
-Does anyone know how to speak a language other than English?

Teaching Objectives:
-Introduce students with the basic Korean alphabets
-Teach the students how the consonants and the vowels are combined to form words
-Compare and contrast Korean with English to help understanding

Learning Objectives:
-Get an idea of how Korean alphabets are combined to form meaningful words
-Learn to say several basic phrases in Korean: Hello, Thank you, Sorry, etc.

Pretest:
-Ask students about their knowledge of English alphabets
-Ask students of basic knowledge of Korean language/Korea

Participatory Activity:
-Materials: word cards with pronunciations in English.
-Prepare different sets of words, so that the students can choose the words that they want to learn.
-If the students find the phrases too difficult to learn, teach them the easier words
-Have the students say the phrases one by one and correct their pronunciation

Post-test:
-Test them on the phrases that they learned today.

Summary:
-Give them an idea of how useful it can be to learn Korean language
-Review the phrases that were taught today

Skemp's Article

In the article, Relational Understanding and Instrumental Understanding, Skemp writes about the differences between Relational Understanding and Instrumental Understanding and how they affect the student learning processes in current education system. I read this article with a great interest because I remember feeling lost back in my high school mathematic classes, even though I was getting all the answers right. Reading this article made me realize that the reason for my confusions was due to the fact that I only had instrumental understanding of the concepts, not the relational understanding, which is what I searched for.

“A person who is unaware that the word he is using is a faux ami can make inconvenient mistakes.” -Starting the article with defining a new term, faux ami, seems like a very nice way of introducing the topic, since it helps the readers to think of the importance of understanding the true meaning of the word.
“This anticipates one of the arguments which I shall use against instrumental understanding, that it usually involves a multiplicity of rules rather than fewer principles of more general application.” -People often think that instrumental understanding can be achieved with less effort than relational understanding. However, this quote points out that in long term, instrumental understanding involves memorizing more rules and requires more efforts.
“The other mis-match, in which pupils are trying to understand relationally but the teaching makes this impossible, can be a more damaging one.” -I agree with this statement. When I was in my high school years, I always wanted to understand more about mathematical background than just using given formulas to solve problems. However, most high school teachers tended to enforce instrumental understanding only, which created a lot of confusions in my part.
“There is more to learn-the connections as well as the separate rules-but the result, once learnt, is more lasting. So there is less re-learning to do, and long-term the time taken may well be less together.” -This quote illustrates one of the practical advantages of the relational understanding very well; relational understanding is a more effective form of learning in a long term.
“But the most important thing about an activity is its goal.” -I think it is really important that the students and the teachers have the same goal, in order for the learning/teaching processes to become more effective.