Final Project: Unit plan

http://docs.google.com/View?id=dchcpmww_1d8nhrffb

Assignment 3 - Origami Polyhedra

Benefit of the project:

• Hands-on activity
• Help students to visualize the 3 dimensional worlds. For instance, finding information about edges, vertices, faces and etc
• Avoid boredom in the classroom
• Incorporate other subjects such as Arts
• Make students familiar with the background and history of polyhedra

Weaknesses of the project:

• Time-consuming due to making origami: it might be annoying for students, and as a result it might lead to frustrations and confusion.
• Time wise: it might be hard to fit this project into the curriculum.

Uses of the project :
• Make the students to feel for 3-D world
• Make them familiar with what geometry is, in particular polyhedra
• A fun classroom activity to follow

How to modify the project:
• Avoid making the students to do the origami: give them other options for origami. For instance, cut the segments and tape them together. This way, it is less time-consuming, and it gives the students the same result.

Extension of the project:
• We can ask our students to think about volume, surface area, and some other physical properties


Our project (Surface Area):

• Grade level : Grade 9

• Purposes:

- To make a fun activity in the class
- Avoid boredom about the teaching subject
- Make the students to get a notion for a 3-D object/world,
- Practice the concept of “Area” in mathematics.


• Description:

There are two choices for this project:
1. Students must build a “Reasonable” shape object such as a house, car, flower, and etc using at least two 3-D objects.
2. Build a complex structure using only one type of 3-D object of their choice.

Students must choose only one of the above options.
For either one they must follow the below criterions.(2-3 people per group)

- Students must hand in an informal proposal for this project.
- They need to build the structure.
- They need to write a report including the followings:

i) How they got the surface area of the object they made in details. This includes a verbal explanation and diagrams.
ii) Measuring and calculating the surface area of the object in two different units. ( ex. cm and inch)


• Time:

- First session: 20 min for proposal in the class.
- Second session: A full class time for material and making objects.
- Giving them a weekend for the final work.


• Production: Reports and structures.


• Marking Criteria:

- Communication ( how well they explain the work) - 35%
- Calculations(how they got the surface area and units) - 50%
- Structure ( what they made) - 10%
- Creativity - 5%

Two Column Problem Solving

Reflections on my short practicum at Richmond Secondary

I really enjoyed my short practicum at Richmond Secondary school. The whole staffs and the students were extremely friendly and welcoming. My school was one of the project schools, which means my FA was at the school for the whole two weeks to look after us. Having the FA at the school was really great since I was able to discuss about anything at any time and ask questions. In addition, he has been working as a FA at Richmond Secondary for many years so he was really familiar with the school and the staffs.

During my short practicum, I had a chance to observe some different things that happen within the school and participate in some of the events myself. I helped out on the fruits and vegetables program, organizing the trays and delivering the fruits to each class. I also supervised the math help sessions after school. In addition, I chaperoned the Halloween dance on Thursday night. The only thing that I can recall from the dance is that it was extremely loud! Fortunately, one teacher gave us the ear plugs, which saved our ears from going deaf.

I taught four different classes during the second week of my practicum and one of them was observed by my FA. It is really sad that the one class my FA observed was the only class I had a problem with controlling the students. I didn’t get a chance to see the students beforehand and the teacher was away so the TOC was filling in. It was quite difficult to control the grade 10 students who didn’t really know who I was. Fortunately, my FA thought the lesson went pretty well other than some typical mistakes that the teacher candidates make when they first start teaching. I realized that the lesson never goes the way you planned it. Hopefully, I can make the improvements in the areas that did not go so well for the next lesson I teach in February. I can’t wait!

Timed Writing Reflection

This is an interesting activity that I hadn’t expected to encounter in the math class. This activity would be able to provide students with different perspectives of approaching mathematics. It doesn’t always have to be the numbers! I would possibly use this activity as a warm up in the beginning of the class, in order to get students get started. It would also be nice to use this as a conclusion activity when there is some time left at the end of the class. It would help students review the materials that they learned and also provide the teacher some feedbacks.

Some of the weaknesses of the activity may be that writing in a specific amount of time could be a difficult task for the ESL students or students whose English is weak. In addition, it could also be difficult for those who need a longer time to process their thoughts when they are writing. They may have a difficult time with writing in such a short time limit. Also, some students may not find the relationship between this exercise and learning mathematics and lose interests in the activity.

Dividing by Zero

Dividing by zero is impossible as I was told when I was young.

The same thing I tell the students when they ask

As hard as it may be to explain why,

They need to know the reason behind it

Explain the non-reversibility

Or even better,

Argue by the limit

So that they can understand

Microteaching reflection

Our group taught variables and equations from the grade 8 curriculum. I realized how short 15 minutes can be as we were trying to be responsive to all of the students’ comments and questions. Overall, I thought that our group’s microteaching had both strengths and weaknesses that I can learn from.

Things that went well:
We were told that we had a good opening question, which grabbed the students’ attentions. We had a good intro to variables and solving equations, using the problem solving approach. Our peers thought that we taught at the appropriate level of the class and provided good examples to work with. We used the board space efficiently and had good visuals. Some of the peers also commented that we reacted well to the changes (ie. Students’ questions and comments). Also, many people liked the idea of the last exercise but we didn’t have enough time to work on it.

Areas that need work:
The major mistake we made was leaving out one of the tables during our discussion. I was occupied by the other two tables and I didn’t make any eye contact with the people on the other side. Another major problem was the time management. I spent too much time on going over the example on the board and we were running short on time. This left too little time for one of my group members to do her part, which was leading the class activity. We also need to work on coming up with better context for the word problems and make connection to other areas of life.

Lesson Plan-Microteaching

MAED 314 Assignment #2

Microteaching Lesson PlanGroup: Elaine, Alice, Prem

Topic: Math 8 Variables & Equations
model and solve problems using linear equations of the form

Bridge:
Simple Word Problem:
Say on Sunday you went shopping, you bought 5 video games and in total you have spent $100.
How much is it per game?

Take a minute to think........how did you come up with your answer?

Pre-Test: A rectangle with an unknown side length

Teaching Objective:

-To effectively teach the concept of solving linear equations -To develop student's problem-solving/thinking ability -To relate the Mathematics of the lesson to real-life applications -To allow students working in groups and to encourage group learning -To help students take responsibility of their learning by asking them to design a word problem using the concept learned

Learning Objective: -Students will be able to solve for the unknowns of the linear equations by the end of the lesson -Students will be able to design a real-life problem using the concepts they have learned -Students will have the opportunity to present their learning and also to learn from each other

Participatory:
We will teach the PLO's on solving.5 word problems to teach the equations

Eqn 1: ax=b (introduced in Bridge)

Eqn 2: x/a=b, a is not zero
Agnes has a bag of candies. She distributed the candies equally to her five friends. It turned out that each of her friends received 3 candies. How many candies were in Agnes' bag in the beginning?
Eqn 3: ax+b=c
Find three consecutive integers whose sum is 258

Eqn 4: x/a+b=c

Peter's teacher gave him a container full of 140 bricks.One-sixth of the bricks were red and there were 20 blue bricks. How many red bricks were there?

Eqn 5: a(x+b)=c
Ask how they got their answers and do people have different methods of solving the problem

Post-Test: Make your own word problem (group) and present it with solutions to everyone.

Summary: -We will adjust the amount of teaching accordingly under the time constrain (we might not be able to teach all 5 main types of solving for linear equations) -We want our students to understand the importance of the lesson and how applicable it is to our daily life -We want to encourage students to have different methods of solving a problem -We want our students to participate in their own learning

Citizenship Education in the Context of School Mathematics

In the paper, “Citizenship Education in the Context of School Mathematics,” Simmit write about the critical role mathematics education plays in the development of democratic citizens. For many people, it is not easy to make the connection between the mathematics education and the citizenship education, because they do not realize that our society fundamentally operates on mathematical ideas. As Simmit says in his paper, nearly everything we encounter in the world is linked with some numbers. Then, why do many people not able to see mathematics as the fundamental basis of our everyday lives? Simmit blames this partly on the teachers and the current mathematics education system, in which students are led to view mathematics as a set of facts that they need to get right answers to. In order to overcome these challenges, Simmit suggests three ways of teaching, which are posing problems, the demand for explanation, and mathematical conversations.

In order to educate the students to become active and democratic citizens, they would need to build on their problem solving skills that they can apply in their lives. Thus, rather than teaching the students with facts and concepts only, I would try to help them have a relational understanding of mathematics. Using the “What-If-Not” strategies that I read from the book, “Art of Problem Posing”, I will help the students to look at the mathematical concepts from different perspectives and get them used to posing problems of their own. Also, I will engage the students in my classroom through various methods so that they can participate in the class discussion actively. Through the interactions between the students and the teacher, as well as the interactions within the students, they will be able to learn how to communicate their ideas effectively with each other. Through these ways, I hope to encourage my students to learn useful skills that they can use in their lives and become active and well-informed citizens.

Art of Problem Posing- Reflection 2

This section of the book dealt with the problem posing technique, using the “What-if Not” question. Asking “What-If-Not” questions are technique that can help us to look at the concepts and theorems in different perspectives and give us chance to obtain the broader sense of the phenomenon. By cycling through the five levels of the “What-If-Not” strategy, one can get in to the habit of posing creative problems and strive to learn more than just the given theorem. However, “What-If-not” technique may not always be beneficial. For some people, asking too many ambiguous questions may make them extremely confusing. It is important that the person understands the given theorem to certain extend, before posing so many different questions. Also, following each of the steps may be difficult and time-consuming. Even if we pose problems after “What-If-Not-ing”, it could be difficult to analyze the problem well enough to come to a useful conclusion. Thus, it may take some practice of using this strategy, in order to use it in the most effective way.

I think that the “What-If-Not” strategy can be very useful for the next week’s microteaching in helping students develop a problem solving technique. For my microteaching, I will first introduce my topic to the class and give brief explanations of the theorems. Then, I will have the class to look at the concepts from different perspectives and come up with some interesting questions. Following the steps of the “WIN” strategy, we will carefully analyze the problem to lead the class to understand the theorems better. (Our group didn’t pick a topic yet, so it’s hard to answer this question in detail..)

"The Art of Problem Posing" -Reflection

In the book, “The Art of Problem Posing”, Brown and Walter stress the importance of posing the problems. In many articles that we have read for this class, we were told how important it is to use the quality problems to create effective learning environments for the students. As a result, I have been thinking only about how to select good problem sets and how to use those problems successfully. Thus, this new emphasis on creating the question came to me as a new area of mathematics. By following the authors’ examples, I realized that the questions that we usually ask our students are limited to the instrumental understanding. By giving the students the chance to freely come up with their own ideas, we help them to extend the idea of mathematics into their real life. Students can start to think from different perspectives and approach the topic in various ways, gaining a deeper understanding of the concept. One thing that I thought was very interesting was the question that can provoke the historical background of the mathematical concepts. I have never thought that the historical portion is important in Mathematics. However, by asking “what might have encouraged people to come up with some concepts?”, students seek to have a relational understanding of the concept. I think that the idea of posing abstract and challenging questions can be a very helpful tool in teaching mathematics and I hope to gain better insights into it through this book.

Letters from the future students

Dear friend

I have just finished my grade 12 and I am going to start studying in the university next year. My favourite class during my high school years was the Calculus class. I particularly liked this class because I had a great teacher who has been teaching the course for 10 years. Her name is Ms. Kim and she is just an expert in mathematics. She was a very energetic and compassionate teacher who always tried to make the class more interesting for the students. I had always thought that the math is a boring subject. But, after taking her course, I realized how I fun mathematics can be! She was always open for questions and helped us after classes if we didn't understand some concepts. I really recommend that you take her class!

Dear Ms. Kim

I'm sending this e-mail because I want to let you know that I have not enjoyed my time in your class. In all my previous math classes, the teachers presented imporartant concepts and gave me some time to apply what we learned by working on the problems. Howevaer, what you taught us was all problem solving skill, which I don't think is useful at all. I need to learn the rules and concepts so that I can do well on my exams. Working on the problem solving questions just confused me and I didn't learn anything from your class.

Writing these two letters gave me a chance to think about what kind of teacher I want to be. I want to become an enthusiastic teacher who cares about each and every student in my classes. I want to create a fun and engaging learning environment for all. At the same time, I am afraid that there will be students who do not like my teaching style and do not gain much knowledge from my lessons. I hope that I can keep all of these in my mind even after 10 years of teaching. I will always try to remind myself of my goals as a teacher and become conscious of my concerns.

DVD reflection

In the video, Dave Hewitt illustrates a very creative way of teaching mathematics. Oftentimes, mathematics teachers tend to tell the students the new topic in the beginning of the class and present the materials. However, Dave Hewitt attempts to approach mathematics in different ways. He first starts out his class by helping students to visualize the new topic. For example, he uses a stick to point sequence of spots around the wall to visualize the number sequence. By counting back and forth, he allows the students to build up the pattern and helps them understand the relationships between subtraction and addition. He started out with the simple counting and then built up to the more complex system. What I really liked about his lesson was that he had the full attention from his students through the whole class. By not giving away the topic too easily and allowing them to work toward the topic, he made the lesson interesting and made the students eager to find out what he would do next. Also, the second part of the video showed how he approached algebra as if he was playing a guessing game with the students. This is much more interesting than just having the students work on a bunch of problems on paper. Again, he grabbed the students’ attention right from the beginning and kept them engaged in developing their problem skills.

"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.