Battleground Schools Review

The article categorized math education methods into 2 polarities: progressive and conservative. It then shows the different views each category has in many different areas. It also discussed many different factors that complicated the math education in North America. The article went on to explain three twentieth-century reform movements in math education. First, it introduced “Progressivist Reform” from 1910-1940. It explained John Dewey’s teaching techniques along with progressivist’s views of math teaching to give students “the challenge of doing and experimentation in mathematics, accompanied by the sense-making activities of reflective practice.” Second, it introduced the “New Math” during 1960s. The Cold War between the United States and Soviet Union pushed the reformation for more abstract and highly complicated math at high school. Led by the School mathematics Study Group (SMSG), they created mainly conservative and even “teacher-proof” curricular materials, aiming to educate “future elite scientists and mathematicians.” Third, it discussed the “Math Wars over the NCTM Standards” beginning from 1990s. NCTM standard was under the influence of progressive and constructivist approaches and focused on the back-to-basics curricula. However, the low ranking of American eighth-grade students in the world caused the traditionalists to fights back for more rigorous math in high school. Based on the views of the different groups, I stand on the progressive side. However, on many areas, it sounds to me both conservative and progressive have valid points of view. For example, on “Goal of math learning”, I would think fluency is as important as understanding. I remember I once did a complicated computation during a math exam at G12. When I reached a step which needs the square root of 49, I simply stopped there and thought I must have done something wrong. I simply forgot square root of 49 equals 7. Less of fluency stopped me from doing the calculation further. Looking back from this experience, without fluency, the result would still be frustrating even if you think you understand the materials perfectly well. Furthermore, math abilities are usually evaluated by exams in high school. How can a person say he’s good at math if he cannot finish the math exam in time and constantly make basic mistakes because of fluency problems? On the other hand, if a person reaches a certain level of fluency at math, it also helps him to understand the materials better. Therefore, I feel fluency and understanding are two inseparable sides of math education.

Interview Review

Based on our interviews, I have found that a student teacher needs to have extended knowledge not only on math but also on other science courses. That’s the reality of a substitute teacher. We need to prepare for the unexpected classes to teach. For math teaching, I not only need to know how to solve the problem, but also need to know other different ways to solve it and understand it. As a teacher, we also need to deal with other issues such as grading on students, which sometimes is the greatest challenge even for seasoned teachers. Also, classroom management skill is the key to student's success. Especially for lower grades, effective teaching also means to manage the students effectively. For students’ interviews, I notice that the likes and dislikes of math are closely related to how well the students feel they can do on math subject. It’s more likely that the students will study hard on math and do well if the teachers encourage them and help them do well at the beginning. Most students agree that math is useful, but only on the basic calculation level. If we can provide more useful (not make up unrealistic ones) real life and work examples, students will gain further understanding of math’s role in our society and have better motives (other than go to the University) to study well in math. For example, how do experienced carpenters find a perpendicular line to the existing line?

Interview with Stduents and Teachers

Interview with Mr. Lucas:
1. What’s the greatest challenge you or new student teacher will face?
• For student teachers, you can’t get all classes in math. Sometimes you need to teach other courses you are not well prepared for.
• Even for seasoned teachers, the greatest challenge would be the constant arguments among students, parents and teachers whether the students should get the mark they desired.

2. How well prepared were you for your teaching?
• I am very well prepared
• This includes mastery of the curriculum, background concepts, and extended fields

3. How about the use of lesson plan? Do you think it would be useful?
• I have taught the course for many years. I don’t need a complete lesson plan.
• I use assignments and tests to evaluate the students, and I know very well how the class will go on.
• A checklist of what to do in class is good enough.

4. Do you approve variable standards in your math class?
• No. Students should meet certain standards in order to continue studying in math.
• It doesn’t have to be the common standard set by the school, but when the standard is set, students should work to meet the standard.

5. How different is it to teach different grades and which grade do you prefer?
• For different grades, different standards are required and different focus is concerned, for example, calculation skill based or concept based
• Higher level of math teaching(such as calculus) is preferred for me because students will focus more on the problems and then develop on the problem solving and critical thinking skills
• Teaching students at lower grades often need to deal with behaviour issues.


Interview with students:
1. What is Math to you? Why are you taking math? Do you like it?
2. What is the greatest difficulty or barrier you face in learning math?
3. Has it ever come across your mind you feel that math is not important?
Why or why not?
4. Do you think that your math teacher actually care about your grades? Or
do you think he only pays attention to those who are good at math?
5. Math is only for smart people. True or False? Why or why not?

Berta
1. Math is I don't know what math is to me but I think it is important and that’s why I’m taking it. I like math when I understand it but it can be really difficult if I don’t.
2. Most of the difficulties I have in learning math is when I don’t understand the question like if it is a long question with hard words I have to read it at least 5 times to understand it.
3. Somehow. Because there are something that we learn in math class that I think we won’t use in the future but math is important.
4. NO I don't think my teacher cares. But he is funny in class
5. False. Math is for everyone.

Winie
1. Math is a course that is required for me to graduate high school. I do like math as it teaches me how to apply different formulas to different equations.
2. Trigonometry was the biggest barrier I had encountered when learning math in school as I had a difficult time trying to understand it.
3. To be honest, unless one wishes to pursue a career that involves serious math skills, I don't find that learning more complicated math is very useful in everyday life.
4. My math teacher does care about my grades and everyone else's in class. He tries different methods to help everyone with different learning paces to understand the material.
5. False, as everyone can do it, but only if they are motivated and willing to do so.


Summary:
1. For new teachers, the challenge is not only from math teaching, but also from administration and management jobs.
2. We need to have extended knowledge on math, not just knowing how to solve a question.
3. A student teacher need to have a good and detailed lesson plan to guide us. As we become more experienced, we can just use checklists.
4. Variable standard might be Ok for some other courses. But it is not a good idea for math because new math skills are built on previously learnt skills.
5. Classroom management is very important in lower grades.
6. Most students think math is useful, but only at basic calculation level.
7. Most Students like math only when they can do well on math. The reason they want to learn math is because they need math to go to university.

Article Review: Changes in Instruction

Mr. Robinson’s article illustrated a period of time that he changed his teaching method from a “controller” of the classroom to a “facilitator” of the classroom. Instead of making the class his one man show, he changed his teaching style by letting students actively participate in the math topics. The classroom has shifted to become student-centered environment. As a math tutor for many years, I know the importance to get students involved. Active participation means better understanding of the materials and better results. Furthermore, by letting students discuss with each other. Students will begin to help each other. I remember one seasoned teacher told me: “Students usually have the same age and similar living experience, one students’ explanation to another student is usually better than teacher’s. An example obvious to the teacher is not necessarily being so obvious to the student. “ Another important change Mr. Robinson mentioned was his questioning method. He changed his assignments from procedural questions to the ones that need deeper thoughts. I totally applaud his changes. Procedural will not help students understand the materials better. That’s why some of the students did very good at every assignment for each chapter, yet they failed the final exam which needs the students to combine the knowledge from different chapters to solve the problems. For many students I tutored, if I just review the contents of the textbook, the students will get bored. They have already spent so much time in class to understand the materials. Therefore, questioning skill is the one I use most often. Through insightful questions and listening to student’s answers, I will get an idea of how the student understands the materials. Then I will either use examples or exercises to help them correct the misunderstandings. That way, my students were doing very well in the school.

Two of my most memorable teachers

One of my most memorable teachers is my math teacher from G4 to G6. Although she was very strict with students, she encouraged discussion during the class. Everyone was involved in her classroom. Even those girls who hated math got involved and raised their hands to answer the questions. She aroused me of great interest in math. When I told her my thoughts about a problem, even if it was not perfect, she would encourage me to continue and help me grasp the ideas through her guidance. The other one was the math teacher from G7 to G9. She was memorable to me because she brought me great pain in learning math. I was so into the teaching methods of my previous teacher that it was a torture for me to listen to her classes. During all her classes, she was copying things from the books and explained it very very slowly. She hoped that by going slow, everyone would understand it. Her classes were all about writing nicely and drawing the perfect circles. Every time she drew a perfect circle, students cheered. She was enjoying that. She also gave out tons of assignments which were just a repetition of basic questions. By comparing different teachers' teaching methods, I realized the teacher who encourages discussion will encourage students to learn more actively. The teacher who can arouse greatest interest of math from the students will make students learn better. As a teacher, one not only need to teach the materials, but also need to motivate the students to study and make the most out of the learning.

Self Assessment on Microteaching

1. I thought these things went well in my lesson: * For introduction, I have made a good introduction so that everyone knows that fast and neat is the characteristic of this new folding method. * For pretest, I have asked some girls and guys to show their ways of folding before I showed mine. Through comparison, people can really see the difference in speed and quality. * For activity, everyone participated and enjoyed the learning. I have received seven feedback sheets in total. Thank you guys!

2. If I were to teach this lesson again, I would work to improve it in these ways: * I wish I had brought more T-shirt so that everyone can practice on their own pace instead of being watched by everyone. * I wish I had brought long sleeved shirts so that people can see this method also works on long sleeved ones.

3. Here are some things I reflected on based on my peer's * People will get interested if the topic you do is useful and your teaching method is easy to follow. * People all want to participate in a fun activity. * I should have made a folding competition to get everybody activated.

[PLAN] Fast and Easy way to fold a T-shirt

1. Bridge: As Education students, we are all have a busy schedule and little time. Can we finish our household chore fast and easy? Today, I am going to introduce a fast and easy way to fold a T-shirt. 2. Teaching Objectives: Learn a good life skill in 10 minutes. Save your time for the rest of your life. 3. Learning Objectives: Everyone in the group will have a firm grasp of how to fold a T-shirt fast and easy. 4. Pretest: Let a guy try to fold a T-shirt. Keep a timing of how long does he take to fold the T-shirt. Do he do a good job? 5. Activities: A: Show how to fold a T-shirt step by step, with detailed explanation. Hold Q&A sessions. B: Let everyone try to fold the T-shirt. We will all comment on the speed and looking of the folded T-shirt. 6. Posttest: See who fold the best looking T-shirt and who fold the fastest! 7. Summary: If everyone of us can pay attention to little things in our life, we can save a lot of valuable time to enjoy the best of life.

Relational Understanding vs. Instrumental Understanding

After reading Mr. Skemp’s article, I have got mixed feelings towards both approaches. Through many years’ of study, I have got math teachers try to explain things in a marvellous (relational) way. But after the whole class, we are still at a loss regarding steps to solve the questions. By saying “Relational knowledge can be effective as a goal in itself”, Mr. Skemp have admitted that teaching in the relational way is a daunting task to accomplish by itself. Especially for students at young ages, their understandings and experiences are very limited. One relational explanation, which the teacher feels to be excellent, might be harder to understand than the original question for students. Thus, we need an explanation for the explanation. For example, on page 6, Mr. Skemp used the music teaching as an analogy to prove his point. For those readers who are familiar with music, they might feel the analogy is excellent. But for those readers who aren’t music fans, the words such as “stave, minim, crotchets, and quaver” took a whole course to explain well. Not to say let the readers understand what the author is trying to prove. Nor do I agree that math be taught purely instrumentally. For this part, I feel Mr. Skemp has done a good job to prove the point. See quote 4 and 5. In summary, the approach I suggest is: First, teach the students instrumentally. Give them a crutch to help them walk on their own. Second, when the students get an idea of what’s going on but still confused why they do this, give them relational explanation to clarify. The students will suddenly realize what they have done make sense and they will have a firm understanding of how to do it. [ Quotes ] 1: knowledge can be effective as a goal in itself 2: Imagine that two groups of children are taught music as a pencil-and paper subject. 3: Within its own context, instrumental mathematics is usually easier to understand; sometimes much easier. 4: It (Relational understanding) is more adaptable to new tasks. 5: It (Relational understanding) is easier to remember.