Thursday, September 27, 2007

Assignment #1: My Response to Conversation with Teacher and Student

How can I keep students motivated in math class? How can I make my math class creative and interesting, while still following the curriculum? What are some of the students’ views about math? These are some of the questions that I have been pondering over for the last few months. Having a conversation with a math teacher and student gave me some answers to these questions. However, even though the conversations Tom and I had with a teacher and student were very informative, I do not think I will ever get complete answers to these questions because the way math is taught and students attitudes towards math are always changing and every teacher and every student has a different view about math and how to teach it. However, I feel that this assignment was useful in letting us get a sense of how some teachers go about teaching math and what feelings students have towards math. Having these ideas will be very beneficial to us when we start our practicum.
We had a conversation with a math teacher who has only been teaching for a few years. However, I found this to be very beneficial because I felt that she could relate to us and the situation we are in now better than a more experienced teacher because she went through the same program not too long ago herself. I really liked the teacher’s idea of only lecturing for about 10-20 minutes at the beginning of class to introduce a new topic and then leaving the rest of the period for the students to practice what they learned by either doing questions or more creative assignments. I really liked this lecturing method and I want to try it myself because I think that students will not get very bored because the lecture time is not very long. I personally think that lecturing is important because, from my experience as a student and a volunteer, I found that students are more capable of understanding a topic/concept and how to work with that topic/concept when a teacher explains it to them, rather than if they have to read the textbook and learn it themselves. My grade 8 math teacher made us learn everything ourselves – he never lectured. The entire class found this very difficult, and the only reason I did good in grade 8 math was because my dad taught me everything. Moreover, I find the activities that she does with her students to be creative and interesting for the students, and I think that when I am doing my practicum I will do some of these activities with my class. Some of her activities include putting students in groups or pairs and having them do questions which they will either present to the class or teach the class. I think by doing these kinds of activities students get a deeper understanding of the topic because they have to teach the question to the class, and I think that a person really has to understand a topic to teach it to the class. I also agree with the teacher that telling students that math is used a lot in the “real world” and without math students limit some of their opportunities in university is a good way to motivate them. Overall, I found the conversation with the math teacher to be very informative.
The student that we had a conversation with is a lot like some of the students in my high school math classes: he is not very interested in math. I found that having a conversation with a student who is not interested in math was very beneficial because it gave us an understanding of what some of these students think of math and what recommendations they have for math class. I was not very surprised by the student’s response to how he would change the way math is taught. He had an answer to this question that I heard a lot during high school and while I was volunteering: remove all the material you do not use after you graduate from the curriculum. I do not think that the answer that he gave to this question is realistic at all because teachers have to teach what is in the curriculum. I know that when I start teaching I am going to have many students in my class who feel this way, but I will just have to motivate them as much as I can. However, I did find it interesting that this student acknowledged the fact that math is a major part of everyone’s life, such as Elaine Simmt’s article mentioned. I think that it is good that even if students do not like math, they still know that it is an important part of life and it increases their opportunities in university. I was most surprised by the student’s response to the use of technology. In an age where many youths cannot live without technology, this student said that math should be taught using the least amount of technology. He believes that students should not rely too much on calculators and computers because this will result in people forgetting how to do simple calculations. I found that students who I graduated with were less able to do simple calculations, such as multiplication, in their heads because they relied too much on calculators. I am glad to hear that there are now “no calculator” sections to tests to make sure that students are still able to do math in their heads.
Prior to my conversation with a math teacher and student I knew that I had to be a creative teacher who could motivate students because not all students are interested in math. The conversation with the math teacher gave me some good ideas of what kind of activities to do with students to keep their interest and to get them to really understand the topic. Whereas, the conversation with the student gave me a chance to come face to face with some of the feelings that students who are not very keen in math have about the subject. I feel that no matter how much I try there will always be students who detest math and complain about it in class; however, I have to help these students be as successful as they can in the subject.

Assignment #1: Group Summary of Conversation

Tom and I had a conversation with a math teacher who has been teaching for approximately three years. We felt that it would be beneficial to meet with a teacher who has not been teaching for a very long time because we believed a “younger” teacher would be able to relate to us and the questions we had. Overall, we found the conversation with the teacher to be very educational because we learned a lot about the different kinds of activities we can do to keep students interested and how to make sure our students are successful.
The teacher we met with, who we will call Miss D, mentioned to us that she emphasizes both instrumental and relational understanding. Miss D determines what understanding to use based on the concept that she is teaching. She told us that relational understanding is important because it helps students understand the importance of a concept – and if they do not understand the importance then they will not be interested in the concept. Instrumental understanding is also important because it gives the students the capacity to retain the information that is being taught.
Furthermore, Miss D explained to us that introducing a new concept with a 10 to 20 minute lecture followed by review games and hands-on activities is very effective. Some of the activities that she has her students do are questions from the textbook, working in groups to answer questions which will be presented to the class, and having students teach problems to the class. She finds that these activities keep most of the students interested in math. Moreover, Miss D told us that a good way to convey the relevance of math to students and to further their interest is by relating math to life outside of the classrooms. Furthermore, Miss D indicated that it is very important for the teacher to provide extra help for students whenever they need it. Overall, we really enjoyed the conversation that we had with Miss D.

Manjeet and I talked with a student who had recently completed grade 12 math. The result was interesting – as his general attitude towards math is anything but “keener”, we got a realistic version of how math is seen through a typical math student’s eyes. We asked him a few questions that mainly covered the topics of ‘how it should be taught’ and ‘relevance’.
His ideal change to the math curriculum would be to cut out all the material that you don’t use in the future once you graduate. He added that the best part of Math 12 is the graphing, because it is more common sense than anything; conics, on the other hand, is very useless after high school. This response was surprising, as conics had been mentioned the day before during class as a necessary precursor to calculus. It would seem that it is more of a specialty topic for those who want to pursue university level math, but not suited for the average math student concerned with real-life applications.
Our student goes on to discuss the relevance of math to him, saying that math is used every day in our lives and it’s important to be able to figure out problems using math (i.e. car loan interest, measurements for baking); however, if the math is not applicable to real life, then it becomes boring.
We also asked his views on using technology to teach math – he interpreted it as the use of calculators and computers to solve math equations, while we were also inquiring about illustrating/teaching through technology; nevertheless, his response was heartening: “math should be taught with the least amount of technology as possible, otherwise we wouldn’t know what to do if we didn’t have a calculator or computer. Plus if we relied on computers everyone would someday not know how to do a simple calculation.”
While our student’s responses weren’t all that shocking, it was very interesting to hear his take on what math topics were useful. It is good to hear that even though he is not passionate about math, it still holds some significance for him as preparation for real life.

Assignment #1: Final Four Questions for Teacher and Student

Final Questions for Teacher:

1) How do you make math class creative/interesting?

2) Do you use a lecture approach to teaching math? How often?

3) Do you emphasize instrumental understanding or relational understanding, or both?

4) How do you motivate uninterested students and help students who are struggling?

Final Questions for Student:

1) How would you change the way math is taught so you would benefit more?

2) What part of the curriculum do you like the best? The worst?

3) Do you see the relevance in learning math?

4) Do you think more technology should be incorporated into math (i.e. using computers more often)?

Assignment #1: Original Questions for Teacher and Student

Original Nine Questions for Teacher:

1) How do you make math class creative/interesting?

2) Do you use a lecture approach to teaching math? How often?

3) What is the atmosphere like in your math class? Is it authoritative or open to discussion?

4) Do you emphasize instrumental or relational understanding, or both?

5) How do you use technology in your classroom/assignments (i.e. computers, web assignments)?

6) How do you motivate uninterested students?

7) What opportunities do you give for stronger students to go beyond the requirements?

8) How do you convey the relevance/importance of math to your students?

9) Do you encourage students to find different ways to solve the same problem?

Original Nine Questions for Student:

1) How would you change the way math is taught so you would benefit more?

2) When you study for tests/do assignments, do you try to understand or just memorize the methods?

3) Do you learn better through lectures, doing assignments, or textbook learning?

4) Should math be taught more interactively and with more “fun” assignments?

5) What part of the curriculum do you like the best? The worst?

6) Is there too much to learn in one year?

7) What bores you about math, if anything?

8) Do you see the relevance of learning math?

9) Do you think more technology should be incorporated into math (i.e. using computers more often)?

Assignment #1: Conversation with a Math Teacher and Student

My partner for Assignment #1: Conversation with a Math Teacher and Student is Tom Salzmann.

Friday, September 21, 2007

Creative Writing Assignment

Manjeet Mahal
MAED 314A
September 21, 2007

The Best Teacher Ever, the Worst Teacher Ever

The other day I ran into Miss Mahal, my grade 9 math teacher, at the mall. It has been about four years since I have last seen her. She was the best teacher I ever had in high school. She was cool, hip, and fun to talk to. She could always relate to her students and she could always be trusted. Miss Mahal always kept the class under control and many of the students were very successful in her class. Miss Mahal explained everything she did so well and she always made sure that the students understood the topic. If the students needed extra help, Miss Mahal would make sure that they got that help: she would stay in at break, lunch, and even after school to make sure the students got the help that they needed. I can still remember many of the things that I learned in grade 9 math. This is very surprising because I forgot everything else that I learned in high school. Additionally, Miss Mahal made math class fun: we got to work in groups and even teach the class. During review periods we would either work in groups and do posters and present them to the class or we would work on a question and teach it to the class. These review periods helped me and many other students do very well on the tests in Miss Mahal’s class. Moreover, the exams she gave were not always easy – they involved a lot of thinking, but we learned a great deal more through these tests. Miss Mahal not only taught us math, she also taught us to be respectful, hardworking individuals. It was so nice to see Miss Mahal again. I really wish I had her for more than one year.

This morning I was walking down the street and I met my worst teacher ever – Miss Mahal. I wanted to turn around and walk the other way when I saw her, but she saw me first and started talking to me. I could not stand her. She did not know how to teach math at all. Whenever I asked questions she just made the problem more confusing for me. Also, her tests made no sense at all. She tried to make her tests include more higher-level thinking questions, but they were just confusing and they did not relate to what we learned in class or did for homework at all. Furthermore, she was always getting mad at me for talking in class, but what could I do – the class was so boring. As a result of the way Miss Mahal taught, I failed grade 10 math and had to do it in summer school. I am so glad that I only had her for one year.

Response to Elaine Simmt's Article

Manjeet Mahal
MAED 314
September 21, 2007

Response to “Citizenship Education in the Context of School Mathematics

Throughout this article, Elaine Simmt argues that mathematics has an important part in citizenship education because it can help us understand our world and play a role in shaping it. Moreover, she argues that mathematics develops people into informed, active, and critical citizens in a society that is greatly shaped by math.
I agree with Simmt that math is all around us. We cannot go through one day without seeing or doing something that is connected to math. Quantification is an essential part of our society. Having “basic” math knowledge, such as being able to add, subtract, multiply, and divide, makes it much easier to make it through everyday life because we constantly need these skills to do simple tasks such as cooking. I also think it is essential to be able to work with fractions. Furthermore, I agree with Simmt that problem solving is an important part of our world. Problem solving requires people to really use their mind to come to a conclusion. Therefore, I think that problem solving promotes citizenship education because it gets people questioning and analyzing issues and problems. However, unlike Simmt, I do not believe math plays an integral role in citizenship education.
I believe that as math teachers we can encourage students to become better citizens by teaching them respect, open-mindedness, and to view issues/judgments from different perspectives. However, I do not believe that math itself plays a vital role in doing this. According to me, math is a subject that is not open to a great deal of discussion or critique. I believe that there exists many ways to find a solution to a mathematical problem; however, to many of these problems there exists only one right answer. For example, a person can find the third side of a right triangle by using Pythagorean Theorem or trigonometry; however, no matter what method is used the answer will be the same. Hence, I do not view math as a subject, such as social studies, that can be constantly questioned. Furthermore, I like the way that math has a right answer because then you can always know if you are right or wrong and you feel a sense of accomplishment when you get the correct answer.
Overall, I believe that students should be able to ask “why” a certain theorem or problem is the way it is and I believe students have a right to question math techniques; however, I feel that in the end mathematics cannot be questioned too much because math theorems are proven to be true.
Yes, math is an important part of the world and I think that it is essential that math is learned; nevertheless, I do not feel mathematics is a major contributor to citizenship education. According to me, all teachers, regardless of whether he/she teaches math, should help and guide students to become “better” citizens. Therefore, teachers develop students into active, informed, critical citizens – not mathematics.


Teaching Perspective Inventory Response

Manjeet Mahal
MAED 314A
September 19, 2007

Teaching Perspective Inventory Response

I found the Teaching Perspective Inventory self-test to be very interesting. I did the test according to views that I have now – before actually teaching. Perhaps after I start teaching, my views on some of the questions that were asked will be different; therefore, resulting in a different result in the end. My most dominant perspective from the test is nurturing, which is followed closely by transmission. Apprenticeship and developmental perspectives are in between dominant and recessive. On the other hand, social reform was a recessive perspective for me. From the point of view that I have towards teaching at this point, I agree with the results that I received from my TPI self-test.
Nurturing is my most dominant perspective. This perspective implies that the teacher is caring, understanding, and willing to help the students in any way to succeed. A nurturing teacher gives students the feeling that they can succeed if they just try. In general, students who have teachers who are characterized by a nurturing teaching perspective do not have a fear of failing. Although nurturing teachers support and encourage their students, they do not just “hand out” marks. These types of teachers continue to challenge students to reach their goals and potentials. Moreover, to ensure achievement, nurturing students do not sacrifice students’ self-confidence. Overall, I think this perspective fits very well with the type of person that I am. Throughout the volunteering that I did in the past, I have realized that I care about the students and I want them to be very successful. I do not want my students to fear being in my classroom because they have failed the course before or they are not doing well in the course. I will do everything that I can to help these students; however, these students must also be willing to help themselves.
Transmission was also a fairly dominant trait for me. Having this perspective implies that the teacher comprehends the subject matter very well. The teacher’s responsibility is to convey what he/she knows effectively and accurately to his/her students. Teachers who teach with a transmission perspective clearly state the objectives of the course, use class time efficiently, direct students, and answers questions effectively. I think these characteristics are important for a teacher to possess because they guide learning – and to learn is why people go to school. Moreover, having these characteristics are important to me because I think they keep the class focused and organized – while still fun.
The apprenticeship and developmental perspectives where not dominant or recessive – they were in the middle of the ranking. I think this is fairly accurate because, when relating to the apprenticeship perspective, I think it is important for teachers to be skilled in what they teach; however, I do not think they have to be “highly skilled.” Therefore, teachers should know how to teach the subject that they are teaching, but they do not have to be geniuses in the subject area. On the other hand, after getting my results I wish the developmental perspective was more dominant. I think teachers should understand how students reason and think about the content. Moreover, teachers should have students think in more complex ways.
Social reform is the only recessive perspective I have. I think this is very accurate because, while teaching, I am not trying to change society – especially when teaching math. I want students to understand that there are different points of views about everything and they should understand and respect these different views. Only if students object to something a great deal should they go and change it.
Overall, the results I got from the TPI self-test were accurate. However, according to me, to be a good teacher it is essential that teachers possess qualities from each of the five perspectives.

Response to Heather Robinson's Article

Manjeet Mahal
MAED 314
September 17, 2007

Response to “Using Research to Analyze, Inform, and Assess Changes in Instruction”

Heather Robinson’s article is about why and how she changed her teaching methods during her fifth year of teaching. During her fifth year Robinson experienced many professional changes: she transferred to a new school and she entered graduate school to get her masters. During her first four years of teaching Robinson was good at her job: her students were able to do their homework and assignments with some ease, and they were achieving fairly good grades on her quizzes and exams. However, her students were not very successful on the final exam. Students who had excellent marks going into the final exam sometimes failed the exam. Moreover, after videotaping herself teaching, Robinson realized that she spent most of her time lecturing. Her lectures involved regurgitating the textbook and they were not engaging or intriguing for students. Sometimes at the end of a unit Robinson would include an activity, but, overall, her lessons involved lectures and were very teacher-centered. After watching this video and examining her students’ final exam marks, Robinson realized that she had to change her teaching methods. If she did not then her students’ understanding would not improve.
Robinson’s first step towards changing was decreasing the amount of lecturing that she did. By examining her previous years of teaching, Robinson realized that lecturing resulted in her students contributing less to the lesson. Moreover, she did not want her students to get the idea that math just involved learning skills so they could do well on exams – she wanted her students to understand and appreciate math. So to reduce lecturing time, Robinson limited herself to lecturing for only 60 minutes/week. Furthermore, Robinson used two strategies during every class to motivate her students. The first strategy was starting the class off with a question that provided a focus for that day’s lesson. The second strategy involved using strategies to get students’ interested and prepared for answering the question. Furthermore, she used the lesson activities and group activities throughout her lesson to keep the students interested. Hence, by getting the students more involved in the lesson by asking them questions and getting them to do activities, Robinson made her lessons more student-centered.
Robinson also implemented change by having her students think at a higher level. This involved her having to change her quizzes and tests. Robinson changed her quizzes from just containing lower-order questions to containing a mixture of lower-order and higher-order questions. After giving her “new” quiz to her students for the first time, Robinson realized that her students were not equipped to answer these higher-level questions. However, her students’ marks on these quizzes started improving after they became familiar with these higher-level questions from doing their “deeper” thinking class activities, and homework and in-class assignments.
Moreover, Robinson promoted change by supporting student-student discussion. This was very difficult for Robinson to do because she never liked having a noisy classroom because she felt students would never be able to learn in such an environment. Nevertheless, Robinson went forward with supporting student-student discussion by including group activities into the lesson. She also used the “Think-Pair-Share” strategy to get students involved in understanding the topic. The jigsaw was also a very useful strategy to get students involved in mathematical discussion. Hence, Robinson acted more as a facilitator in her classroom and the students were responsible for their own learning.
Overall, Robinson found the changes she made to be worth it. As a result of these changes, students who never used to speak in class started contributing to mathematical discussions. Moreover, students starting losing their fear of being wrong or asking for help from a class member. Robinson found that with the changes that she implemented, students were not just practicing a skill – they were also thinking logically about the concepts and coming to rational conclusions. The students were also more interested in math and were excited to come to math class since she made the changes to her teaching. Additionally, after making the changes, fewer students failed the final exam. Therefore, the changes that Robinson made to her lesson proved to be very beneficial for her students.
I found this article very interesting because it shows that lecturing does not result in students really understanding the concepts that they are taught. I agree with Robinson that having lessons student-centered is more beneficial for the students. When I start teaching I want to incorporate the students into my lesson and I think this article gives some good ideas on how to do this. When I teach, I also want to include higher-level thinking questions on my quizzes and exams to make sure the students understand what is going on. However, I think it is important for the teacher to also lecture a little bit because I think that lecturing gives an overview of a topic. I would want to use a lecture to introduce a new topic and some new ideas, but then I would use class discussions and activities to get the students to further comprehend the topic. Overall, I liked this article because it reveals that you can be creative when teaching math.

My Most Memorable Math Teacher

Manjeet Mahal
MAED 314A
September 14, 2007

My Most Memorable Math Teacher

My most memorable math teacher was one of my university teachers. This teacher, who I will refer to as Mr. Brady, was not my most memorable teacher because he was the best math teacher I ever had, but because he was the worst math teacher I ever had.
Many things resulted in Mr. Brady being my worst teacher. First of all, he could not explain what we were being taught very well. During the lecture he would spend a lot of time trying to figure out how to solve the problem. Moreover, his lectures were never very organized – he would always jump from one part to the next and back again. Additionally, Mr. Brady was never clear on his instructions. Many times I would go and ask him how he wanted something done and he would tell me one way, but when I got my assignment or paper back it was quite evident that what I gave him was not what he wanted. Hence, I was always frustrated in his class because I, along with many other students, felt that he did not communicate with us very well. As a result of all of this, I was always stressed out in his classes.
One positive aspect of having Mr. Brady as a teacher is that I now know what kind of things not to do and what kind of teacher not to become. When I teach I want to be very organized and understand what I am teaching. Furthermore, I want to make sure that whenever I give instructions all the students understand them and know what I expect. Moreover, I think it is very important to listen to the students’ concerns and help them along whenever they need it – something that Mr. Brady did not do.
Although I stressed out a lot in Mr. Brady’s classes, it was a beneficial experience because I learned that it is important for teacher’s to listen to students and make sure they always understand what you want. Overall, I learned not to teach like Mr. Brady did.

Micro-teaching: Self- and Peer-assessments

Manjeet Mahal
MAED 314A
September 12, 2007

Peer Feedback Form for 10 Minute Microteaching

Topic: Doing a manicure

Focus on use of BOOPPPS planning format and initial strengths and areas for development

Learning (& possibly teaching) objectives, clear?

Debby: No comment
Ed: Good! Method and tools laid out for objectives
Tam Tran: How to do proper manicure – clear
Yuri: Yes clear. I was excited to learn about the topic
Jason: How to do your own nails. Good and clear
Afsoon: Students will learn how to polish nails

Bridge/Intro?

Debby: Questions were good
Ed: Nice intro, lively and energetic
Tam Tran: Have anyone have a manicure done?
Yuri: Made good opening point
Jason: Good
Afsoon: She explained how to polish your nails

Pre-test of prior knowledge?

Debby: Gave me some ideas on equipment and their use
Ed: Check mark
Tam Tran: Named all the equipment
Yuri: She answered my questions. Provided extra information
Jason: Asked “have anyone done their nails before?”
Afsoon: She asked if we ever have done our nails before

Participatory activity?

Debby: Very clear explanation
Ed: Good use of materials and passing them around
Tam Tran: Try the equipment out
Yuri: Yes, very
Jason: I got my middle finger nail polished
Afsoon: Each student had a chance to try the manicure on their own nails

Post-test/check-in on learning?

Debby: Review of the manicure equipment. I was able to remember what they were and how to use them
Ed: I liked the little quiz at the end on the tools
Tam Tran: Rename all the equipment
Yuri: Asked us the name of the equipment – which was good
Jason: Answer questions responsively
Afsoon: Watching students while they were polishing their nails

Summary/conclusion?

Debby: “Ask and answer” time was helpful
Ed: Check mark
Tam Tran: Handful to get manicure done
Yuri: O.K., good way to finish up. Everybody was happy
Jason: Repeated all the items needed to get your nails done
Afsoon: It is cheaper to do it yourself – save money

What were the strengths of the lesson?

Debby: Clear voice, step by step procedure was good
Ed: Very receptive to questions, kept lesson fun and engaging
Tam Tran: Clear, good eye contact, and good interaction
Yuri: Really interesting, positive energy, good voice, and kept us entertained. Coolest presentation I heard today. Made good use of equipment names during presentation
Jason: Clear, enthusiastic about the lesson, friendly, timing was awesome
Afsoon: Clearly explained

What areas need further work and development?

Debby: It was excellent overall
Ed: A summary of the different steps to reinforce the ideas
Tam Tran: Good job
Yuri: Not really, but you shouldn’t steal your sister’s equipment
Jason: Can’t think of any yet
Afsoon: No need for further improvement

Self Assessment: Microteaching

I thought these things went well in my lesson:

Everyone seemed to be very entertained by the lesson, and everyone followed along very well. I think that I talked clearly and I think everyone in my group understood what I was doing. I planned my lesson well because I did not run out of time and I was a able to answer the questions that my group members asked. I also think that the members of my group learned a lot about giving yourself or someone else a manicure from my lesson.

If I were to teach this lesson again, I would work to improve it in these ways:

I would want to have more materials so that more students could do the manicure at the same time. I would summarize the steps to do a manicure at the end of the lesson to make sure that everyone understood the lesson, and the ideas I put out to the students were reinforced. However, overall I think this lesson went well and the students found it educational.

Here are some things I reflected on based on my peers’ feedback:

Overall, I got very good feedback from the members of my group on my lesson on doing a manicure. The members of my group found the topic interesting and they enjoyed the participatory activity of doing a manicure. My group members said that I talked clearly and was very energetic. I think that these are very good qualities for a teacher to possess because it keeps the students engaged in the lesson. I have to keep my enthusiasm up when I am doing my practicum and when I become a teacher. The only negative comment I received was that I forgot to summarize the method of doing a manicure. I have to keep in mind not to forget this when I am teaching. I also enjoyed the questions my group members asked me.



Lesson Plan: The Art of Doing Your Nails

Manjeet Mahal
MAED 314A
September 12, 2007

Lesson Plan: The Art of Doing Your Nails

Teaching Objectives:

  • Allow students to participate in the activity while the teacher is doing the demonstration. By having the students participate in the activity while the teacher is demonstrating, the students are using auditory, visual, and kinetic learning methods.
  • To introduce students to the different tools needed to do a manicure.
  • To teach students the method for doing a manicure.

Learning Objectives:

  • Students will be able to state what tools are needed when doing a manicure and what the uses for each of these tools are.
  • Students will know the procedure needed to do a manicure on either themselves or someone else.

Materials Needed:

  • Nail-cutter: to cut nails and cuticles
  • Cuticle pusher: pushes cuticles back and clean up nails
  • File: To file nails
  • Buffer: To smooth out the nails and shine them up
  • Base coat: Acts as primer
  • Nail Polish: To give the nails a nice color
  • Top coat: To protect the nail polish from chipping and it finishes off the look

Bridge: (1 Minute)

  • Ask students “Who has ever had a manicure?”

Pre-test: (1-2 Minutes)

  • Ask students “What tools do you think you need to do a proper manicure?”
  • Ask students “What do you think is the procedure to do a manicure?”

Participatory Activities: (4 Minutes)

  • The teacher will demonstrate to the students step by step how to do a manicure and the students will follow the teacher along through the procedure.
  • First the teacher will introduce the tools. Then tell students that the first step would be to soak their hands in warm water so that the cuticles and nails become soft. Students should then push back their cuticles and cut them. The students will then file their nails to make them either square or round. Students then buff their nails so that they become smooth. Next students will put on a base coat, followed by two coats of the nail polish. Once the nail polish is close to dried a top coat is put on the nails to protect the manicure and finish off the look.

Post-test: (2 Minutes)

  • Ask students to verbally go through the procedure for doing a manicure. Do this by getting each student to say a step in the procedure and the tool needed to do that step.

Summary/Conclusion: (1 Minute)

  • Tell students that it is useful to know how to do a manicure because it is a lot cheaper to do it yourself than to get a professional manicure all the time.
  • Doing a manicure is basically an art; therefore, it is very satisfying when you are all done and you have beautiful nails that people can not stop staring at.

Thursday, September 20, 2007

Response and Quotes for “Relational Understanding and Instrumental Understanding”

Manjeet Mahal
MAED 314A
September 10, 2007

Response for “Relational Understanding and Instrumental Understanding”

In this article Richard R. Skemp examines relational mathematics/understanding and instrumental mathematics/understanding. He defines relational and instrumental understanding and discusses the advantages and disadvantages of both, while drawing on many examples. Overall, I agree with what Skemp argues about these two types of understanding.
Before reading this article, my definition of understanding was knowing how to perform a certain task and why that method worked for performing that task. Therefore, I considered understanding to be relational understanding. I never considered instrumental understanding – just knowing how to do something – as a definition of understanding.
From my experiences as a student and volunteering in high school math classrooms, I have come to the conclusion that instrumental mathematics is the form of understanding mathematics that many high school students use. This form of understanding allows students to answer questions quickly and in many cases perform well on exams – which is the goal of many high school students. Furthermore, many of the questions on exams are very similar to the lecture notes or homework questions the students have worked on; therefore, they just follow the same method from notes and homework assignments to answer test questions. I think Skemp is accurate in saying that students who do not have a relational understanding of certain mathematical concepts have a difficult time answering questions that vary from the questions that follow the “rule” for that particular concept. I found this to be especially true in junior level math classes. Moreover, I think it is accurate to say that relational understanding is a difficult form of understanding to always use because it does take longer to tell students why a certain method works than just telling them how it works. Also, with the amount of topics to cover in a year it is difficult to spend a great deal of time on each one.
Skemp’s article is informative about relational and instrumental understanding and it gives excellent examples about each form of understanding.

Quotes from the Article

Quote #1:

In the past the author used to describe instrumental understanding as “rules without reasons” (Skemp, 2).

I liked this quote because in very few words it summarizes basically what instrumental understanding means. This definition also makes it easy to distinguish between relational and instrumental understanding.

Quote #2:

“If the teacher asks a question that does not quite fit the rule, of course they will get it wrong” (Skemp, 4).

I thought this is a very good quote about how, unlike relational understanding, instrumental understanding makes it difficult for students to work on and solve questions that vary from the questions that follow the “rule” that they were taught. I think this quote is very true because while volunteering in high schools I experienced many incidents when students had no idea how to do certain questions because they were slightly different from the examples they got during the lecture.

Quote #3:

“If pupils can get the right answers by the kind of thinking they are used to, they will not take kindly to suggestions that they should try for something beyond this” (Skemp, 5).

I found this quote to be very accurate because many high school students are mostly concerned about getting answers on assignments and exams correct. They feel that since they are getting answers correct by using the method that they are using then there is no need for them to do extra work and find why the method works or to find another way to solve the problems. Therefore, like this quote indicates relational understanding is not extremely important to all students because in some cases they can get answers correct without it.

Quote #4:

“Relational understanding would take too long to achieve, and to be able to use a particular technique is all these pupils are likely to need” (Skemp, 11).

I found this quote to also be very accurate. There are a great deal of topics to cover in a mathematics curriculum; therefore, it is difficult to spend a lot of time on one particular topic – and in many cases it takes a lot of time to explain why a certain method works for a particular problem. Additionally, on in-class and provincial exams students just need to know how to use a certain technique to solve a problem. Therefore, teachers have to teach the techniques and sometimes they run out of time to get the students to understand why the techniques work.

Quote #5:

“In view of the importance of examinations for future employment, one can hardly blame pupils if success in these is one of their major aims” (Skemp, 11).

Doing well on exams is very important to students because report cards and entrance into university are based on marks; therefore, getting questions correct is all that matters. In many cases students “cram” for exams and, thus, they only have time to learn the techniques needed to solve the problems – they do not have the time to learn the reason why the technique works for the certain problems. Hence, I think this is a good quote in explaining why it is sometimes difficult to use relational mathematics.


Time Write-up Regarding Relational and Instrumental Mathematics/Understanding

Manjeet Mahal
MAED 314A
September 7, 2007

Relational mathematics/understanding and instrumental mathematics/understanding are two forms of understanding that I have never heard of before this class. Instrumental understanding involves knowing the “rules” or methods to perform the task without really understanding why that certain rule allows you to get the answer to a certain question correct. On the other hand, relational understanding involves knowing the “rule” for doing something, and also knowing why that “rule” works. Therefore, relational understanding involves a deeper understanding of the topic. Before this class, I just considered understanding to be relational understanding – not instrumental understanding. During my high school years I found that, especially in the junior levels of math, my teachers used instrumental understanding to teach topics. However, in senior level math classes teachers started incorporating relational understanding into the lectures a little more. I used relational understanding more in university than high school.