Student Reflection: Why I believe it is an Essential Part of the Learning Process

I’m a person that values reflection in every aspect of my life. I reflect on myself in terms of my day to day life.  I reflect on my goals and I reflect on my effectiveness as an educator. It is through the reflective process that I am able to not only make changes and improvements to my teaching methods, but it also helps me evaluate the reasons of why I do things the way I do things. Without reflection, we merely run through the motion without having thought about why we do things. I believe reflection is an essential part of the  learning process which everyone should be involved, including our students.

There are two kinds of reflections that I get my students to do.
1) Reflecting on their performance and their classroom learning process.  

a) At the end of each quarter and semester, I give them a prompt questions in order to help them reflect on how things went for them. I use this opportunity to also get feedback from students about my innovative class structures. (Go to my previous blog posts to see how I structure my flipped classroom and Student Led Project Based Learning class.)

Following questions were given last week to my students.

1. How did you feel about the way the math class was structured for you this year?

2. What were some of the things you enjoyed about your math class this semester?

3. What were some of the challenges you faced in your math class this semester?

4. Share one major growth you went through as a student due to your math class.

5. How do you plan to approach the finals and the second semester for math?

I made the questions very specific because whenever I am not, they tend to just talk about their high school life in general, and I was more interested in getting some feedback on what was going on with them in my classes.

b) Whenever there has been a project or activities that were more “hands on” or “real life application simulation”, reflection of the learning process is always part of the requirement and it is stated clearly in the assessment rubric. (See my blog post about Assessing Student Created iBooks for examples.) When students do hands on activities, they would be making certain choices of how they would go about doing so. Reflection is important to make them think about the choices they made in terms of how things worked out, and how they would go about it in the future when similar choices were given.

2) Reflecting on their philosophies in life and their character as a person.

I’ve started doing this last year, and I have continued it this year. I post up “Discussion of the Week” in our class social network group (last year I used Facebook and this year I am using Schoology) which they have to participate by posting a comment. At first I thought it would just be something fun to do, to get students to think about and comment on non academic things. However, they have exceeded my expectation in what deep thinkers they are, often writing a whole paragraph. So I realised how important it is to get students thinking about themselves and not about their scores or learning. Some examples of questions I’ve posed and student responses in the last semester are:

Discussion of the Week:

"Above all else, never think you're not good enough." - Anthony Trollope

Confidence is often a serious issue for high school students, at this age of self discovery. What are some of the reasons why you would think you're not good enough? Are they external forces, or internal within yourself? What are the standards we are measuring against and why? How can we overcome that feeling not being good enough and build that confidence in ourselves?

"There is a lot of external pressure for high school students, especially in KIS. With hundreds of excellent students, each individual has to fight to make a name for him/herself. The academic level is very competitive, so the pressure is immense. Thus, it is very easy to feel like we are not good enough, that we are not capable of being as good as some of our other fellow students. I think that to overcome this, we need to focus on areas that we are good at. Everyone has their strengths and weaknesses, so focusing on our strengths can help raise our self-esteem."

"I would think I'm not good enough when there are situations where I feel hopeless or unable to move forward. They are both external and internal forces. External are usually grades or physical elements such as height or stamina. Internals are usually lack of motivation, mental elements such as depression or previous failed experiences. We usually measure ourselves with other people or the society. If we feel like we are worth that the person, or if we think we can not approach what the society expects from us, we usually feel that we don't have enough confidence. Basically speaking, we feel unconfident when we move through extrinsic motivations. However, we can overcome this feeling by moving with more intrinsic factors. Working not to fit into society, not to reach the expectations of others, but to work harder for ourself. When someone feels unconfident, he/she should think about what that person can do to fix their mistakes and earn the things they lack in."

Discussion of the Week:

"The past is a source of knowledge, and the future is a source of hope. Love of the past implies faith in the future." - Stephen Ambrose

What does this quote mean to you? How would you foster such love, hope and faith?

"The past serves as examples of what should be done and what should not be done so that we don't repeat the same mistakes. If you've learned from your past experiences, you're ready to shine in the future. There is a difference between clinging on to the past and embracing it. Those who cling on try to escape the future, but those who embrace are ready to create a better one."

"Personally, I disagree to a portion of the quote. Of course people learn from what happened in the past. Of course there is much to take from one's past for personal development. But, one should not "love" the past, and loving the past definitely does not take one to the next step. Faith in the future only comes with commitment for self-development, brushing off what happened before, and taking a step further. Whether good or bad being swamped by the past drags you down. It becomes a hindrance, through forms of arrogance, over satisfaction, or lack of confidence. 

Love, hope and faith only seems to come from confidence in yourself. You must be able to accept yourself, for all of the emotions above to follow. I would try to figure what I'm good at and who I really am."

Discussion of the Week:

Mark Twain says "Kindness is a language which the deaf can hear, and the blind can read." Share a story of a time when you were moved by seeing someone's kindness, whether it was a kindness shown to you or you saw it shown to someone else.

"This summer, I went to Philippines to meet the child I have been sponsoring for 6 years. When I went her, I saw a skinny child who was still very short even though she was 11. I felt so bad and gave her a trunk full of presents I have prepared for her. I got to spend one day with her and on that one day I was prepared to give her the best day of her life. I took my sponsored child, her teacher, and her mother to this hamburger shop because she said she really wanted to eat hamburger. She looked really hungry and I wanted her to eat a lot. When I ordered hamburgers for the child, her teacher and her mother, the teacher and the mother both did not even touch the hamburger and put them in their bags. I did not understand why. Also, the child did not even finish half of the burger and fries and put them away. I did not understand why she wasn't eating despite her obvious hunger. Later, I discovered that this was because she knew that the rest of her family members would want a bite of the burger as well and she wanted to save some for her family. This act made me truly look back at myself and I still think about her kindness. She could have been selfish and eaten the whole burger for herself but she did not. She was kind even when kindness was not expected of her... At that time, all the times I could have been kind or kinder popped up into my head and I sincerely realised the definition of kindness. I went to give her the best day of my life but instead, she gave me the best day of my life!"

Discussion of the Week:

"The scientist is not a person who gives the right answers, he's one who asks the right questions." - Claude Levi-Strauss. Do you agree with this quote? Why/why not? Relate it to your learning approach to Math and Sciences. Do you think you have the right approach? If not, how should it be different?

"I agree with Claude Levi-Strauss' quote about scientists and asking the right questions. So much focus is on finding the right answer that people overlook the tedious and gruesome process. Great scientists and mathematicians did not all find the right answer. Take for instance Ptolemy. Obviously, he did not find the right answer, claiming that the universe is geocentric. However, he had the right question in mind: how does the universe operate? These acute, precise questions are the first step to find the truth. I think that math is similar in that knowing and understanding the concepts and asking the right questions lead to the right answer."

Discussion of the Week :

"Challenges make you discover things about yourself that you never really knew. They're what make the instrument stretch, what makes you go beyond the norm." - David L. Boren

What does Boren mean by this quote? How does it apply in your life?

"This quote is saying that taking challenges help us reach out to our full potential. We cannot stretch out our abilities without doing something outside the norm. For example, I'm scared of getting injured, however, I took the challenge of risking my physical health in order to achieve athletic success. I pushed myself to the point of even bruises and sores. Trying new things and putting them into the things we know help us challenge ourselves in a way to think "outside the box" Though we struggle through failure, we wouldn't be where we are without taking challenges."

As I have mentioned, students have exceeded my expectation on how deeply they think about the question and commenting from their heart. High school is a time when students seem to be solely focused on academics, but my hope is to give students the time and opportunity to think about some of these important issues that helps shape who they are.

Calculus Activity: Rolling Ball in an Inclined Plane

The second lab activity we did in our AP Calculus AB class was to find the optimal angle for the inclined plane to get the maximum distance on a ball that is rolling from the inclined plane. Below is the activity instructions. 

Determine the ideal angle of an inclined plane in order for a ball to roll the furthest

Material: Inclined plane (using two meter ruler), tennis ball, protractor, measuring tape

Task:

1. Decide on a “starting point” along the inclined plane that you will use.
2. Choose different angles for the inclined plane, drop the ball from the “starting point” and let the it roll down and along the corridor.
3. Record the angle of the inclined plane and the distance the ball rolled. (You might want to take more than one measure for each angle and take the mean). You can choose as many or as few different angles as you think relevant, but don’t forget to choose a range that include “extreme” angles.
4. Using your data, create a scatterplot on your calculator and find a model for the distance the ball rolls in terms of the angle.
5. Algebraically determine the ideal angle in order to have the ball roll as far as possible.
6. Check whether the model works or not.
7. Draw conclusions on what you have seen, calculated and discovered.

In the past, I have asked students to submit a lab report on the activity, but this year, as we are building on the iBook for our learning portfolios, they will be submitting their work as a chapter in their iBook.

Below is a quick video of students performing the activity.

Summative Assessment: Testing for Mastery vs Snapshot of Understanding

As educators, we have varying opinions with regards to student assessments. I myself was a teacher that was very one dimensional when it came to assessments. I felt as a math teacher, there really wasn’t much that could be done for summative assessment except for quizzes and tests. That they had to be a snapshot of understanding in order for the grades to reflect their true ability and if they performed badly, perhaps students would use it as a motivating factor to do better in the next unit. I realised how wrong it was for me to think this way. I am an educator. My goal shouldn’t be to trick students into learning, rather to motivate them to want to improve themselves one day to the next. I used to tell my students “Grades are not important as long as you are improving your understanding and skills and learning from your mistakes.” I say that, but was I really providing the opportunity for that growth? How am I motivating them to learn if they continually feel defeated by their scores? It was time for change.

Our students are not a homogeneous group and have different rates of learning. I wanted to create a system where students take an assessment, be allowed to go back, re-learn/practice concepts they have missed and come back to take the assessment again (of course, a different version of the assessment that tests the same knowledge/skills) to show that they have mastered it. Although it is a summative assessment, it is more formative in nature. This way, we are targeting different skills that students lack and give them multiple opportunities to demonstrate mastery in those skills. But you may ask, to be able to do this, it requires time. Time that we don’t often have to spare in certain classes. I do admit that it is easier to implement such system in a flipped classroom. (Click here for my blog post on developing materials for a Flipped Classroom. Click here for my blog post on how I structure my class time in my Flipped Classroom.)   

When making changes to our teaching practices, it is often unrealistic to apply the changes to all our classes at once. So, I used my experimental Student-Led Project Based Learning class to see how I can promote mastery in their learning. (Click here for the full blog post about my experimental class.) My goal was to allow students multiple attempts at a same skilled assessment until they have mastered it. So I gave them three different opportunities to take the assessment and to improve on it each time. This worked well in theory, but I did run into some obstacles. 1) We have a testing policy in our school, so any summative assessments have to be given at a specific time slot, which means there was limited flexibility in when these assessments could be given, 2) because I work at a school that students are highly stressed, students were not taking the opportunity of the multiple assessment and many of them just took the last one offered, which goes against this whole theory.

Having learned from that, I have now required students to take the assessment a minimum two times and I have included some “Problem Solving Bootcamp” days into the schedule where we all, as a whole class go through a bunch of questions together.

Ideally, I would love to see students be given as many opportunities as they need to demonstrate their mastery. And if it takes many months to master one skill, wouldn’t that be better than moving on without mastering it at all? I know in our current education system this is not easy. However, I do believe it is important for us, as educators, to talk about our assessment practices and to question what purpose our assessments are serving for our students.  

I would love to hear the thoughts of readers out there. Please leave a comment or tweet me if you have thoughts to share.

Calculus Activity: Determining Instantaneous Speed of Usain Bolt as He Crossed the Finish Line

In order to bring Calculus to life for my students, our AP Calculus team are implementing different labs to get students to apply the actual concepts they learned to  real life situations. One such example was to find the instantaneous speed of Usain Bolt as he crossed the finish line when he beat the world record in Berlin (2009). We had provided students with the video of the race and they were allowed to use other online resources. Below is the instruction of the assignment, quick footage of students working on the lab and a sample of one group’s work that was submitted. 

Assignment Instructions

1. Work in pairs. 

2. Download the video file.

3. Goal is to look at the video in iMovie, using frames, to calculate the instantaneous speed of Usain Bolt as he crosses the finish line by using more and more refined, successive values of delta distance and delta time, with minimum 5 iterations. (eg. 100m, 10m, 5m, 2m, smallest possible)

4. Write up like a lab report, answering following questions.
    a) Objective
    b) Plan of action
    c) Process and Calculations
    d) Conclusion and validity of result
Include screenshot of pictures to help explain your process.

Footage of Students Working on the Assignment

Sample of Student Work

Assessment Tools for Student Created iBooks

I believe iBooks are a great way for students to find creative ways to share their learning, as I have talked about in my blog post My Relationship with iBooks Author. Some teachers would find it hard to implement digital tools for learning as it’s hard to find ways to assess them. Here are some rubrics I have used for assessing students’ iBooks for different tasks.

1. Precalculus Conic Sections    This was my first attempt to use iBook as a student project. This was a once off major project. Below is the instruction sheet given to students and the assessment rubric. We have also taken a class time for peer assessment which I modified the below rubric for simple student use.

Conics iBook Project Instructions

Conics iBook Project Rubric

2. AP Calculus AB Limits Activity    In our AP Calculus classes we had decided to utilise the iBook throughout the year to log the learning that happens with the activities we do in class. Following was done for researching different aspects of the use of limits. Instructions sheets and assessment rubric is given below.   

iBook Limit Activity Instructions

AP Calculus iBook Limits Activity Rubric

3. Calculus Year Long Project    In my Calculus class, I use the iBook for the year long project for Student-Led Project Based Learning (details in my Piloting Student-Led Project Based Learning post). Below is the rubric that I use to assess each of the iBook chapters student submit.

Calculus iBook Chapter Rubric

Feel free to download and use any of these documents as you see fit.

Piloting Student-Led Project Based Learning

I had been a flipped classroom teacher for two years when I had the privilege of being accepted as Apple Distinguished Educator, class of 2013. As I talked about in my previous post, this is where I came across iBooks Author and how it became part of my life.  It is also where I felt like what I was doing with my students was not enough. I wanted to make learning a different experience altogether for my students by making them take more control over their learning process to empower them. It was soon after the ADE Institute that I started thinking about how I could implement a Project Based Learning in my classes. By this stage, all my classes have been flipped, so I was done making all the screencasts, meaning, I could shift my focus from having materials ready for my students, to new way of learning, using the resources which I've already created. After brainstorming with a colleague, I decided to approach my principal to ask permission to pilot it in my Calculus class in the new school year. The reason why I chose the Calculus class was because of the following.
1) It is the only class that I am completely autonomous. I am the only teacher who teaches this class and only one section of it exists.
2) Calculus class, unlike the AP Calculus class, isn’t bound by any external exams and students who take Calculus would need to take Calculus in college again anyway.
3) Calculus class is mainly composed of students who don’t really like math and they take Calculus because they don’t want to take Statistics. So, I thought trying new things would actually be more fun for this group of students.
Thankfully, my principal gave me the green lights to go ahead.

The basic idea was to have an iBook as a year long overarching project where their learning will be logged. Each unit of the course will be a chapter of their book. It will contain the concepts of that unit, their learning activity for the unit and a personal reflection of their learning process. The three basic questions they need to address are : What is it that I need to learn? How am I going to learn it? and How will I show that I have learned it? The book will serve as a digital portfolio of their learning in Calculus.

So, I had to come up with a concrete structure. It all seemed great as an idea, but how would the day to day running of it look like? I was feeling overwhelmed at the thought. It wasn’t until days before school started for the new year, that I sat down to plan out the structure.  I realised the first step was to think about what my gradebook would look like. What did I want to assess? What are the things I valued as a learning process for my students?

Following is an excerpt from my Calculus Syllabus that outlines the structure.

Class Structure and Policy

In this Calculus class, we are implementing Student-Led Project Based Learning. A year long, ongoing project is an iBook of your learning process. Each unit will occupy one chapter of the iBook and that chapter will be assessed at the end of each unit. A clear rubric will be given for the assessment of the iBook. Within each unit, learning teams will form and decide what learning activities they will take on to master the content of each unit. Screencasts of all the lectures will be available for you to view to help with the learning process. You will no longer be given a unit test to demonstrate your understanding of the content, however, quizzes will be given to test your mathematical skills. Following is the breakdown of each assessment component.

Daily work/Activities

• Daily work and activities grade is based on successful completion of the deadlines set by students, individually or in learning teams.
• There will be a pool of points from which one point will be deducted for each missed deadline. A larger deadline for the unit completion will be set by the teacher.
• At the beginning of each unit, learning teams will present a proposal of what learning activities they will take on with mini deadlines they have set to the teacher.
• Same type of learning activities can be used maximum of two times throughout the year.
• For each unit, you must form different learning teams. You may work with the same person maximum two times throughout the year. You may have maximum of three people in each learning team.
• All your daily work and learning activities will be included in your iBook.

Quizzes

• Quizzes will be testing your actual mathematical problem solving skills.
• Quizzes will be given three different times within the unit. You may choose to take it anytime you like and as many of the three times that you like.
• The best scoring quiz will be your final score of the quiz which will be uploaded to Powerschool.

iBook Unit Assessment

• iBook chapter of the unit needs to be completed according to the rubric given.
• Each student will submit their own iBook chapter.
• Each chapter needs to include: introduction of the concepts covered, learning activities you have taken on to learn the concepts, demonstration of understanding that came from the learning activity, and finally a reflection piece of your learning process.
• Due date of the chapter will be given by the teacher and you will be penalized 10% for one calendar day, 20% for two days late, and no credit beyond that.

Class Participation/preparation

• Students are expected to participate in class discussions, oral presentations, group work, and projects.
• The class participation/preparation grade consists of a pool of points from which one point will be deducted from when participation or preparation is not fulfilled.

Final Exam

An exam will be given at the end of the semester which will include the content of all the units covered throughout the semester. It will in a traditional exam format.

Grading: The following components will be used in the evaluation process. Each of these areas is

is compiled to reach a cumulative grade for the semester.

• Class Participation/preparation   : 5%   
• Daily Work/Activities : 15%   
• Quizzes : 25%   
• iBook Assessments : 40%   
• Final Exam : 15%

I stand by the philosophy of each educator needing to find the method and structure that works for them. There is no single recipe that works for everyone. Teacher’s personality, demographic of the student body, dynamics of the classroom all play a part in it. I encourage you to try implementing few different things until you find what works for you.

My Relationship with iBooks Author

I was first exposed to iBooks Author when attended the Apple Distinguished Educator Institute in Bali, March 2013. I spent forever being utterly confused as how the program worked and what was the point of it all. It wasn’t until I started creating my own iBook that I actually saw its full potential as a learning tool. My first class, first day back from the institute, my students were taking a test. Normally I’d be, “woohoo, kids taking tests… quiet time for me to do some work” but not this time. I sat there feeling angry and was thinking what was the point of all this. Yes, my students were taking a test but it hit me that a test was a terrible way of showing their learning. Things needed to change. After spending the day in anger and frustration, I decided to approach my team. You see, because there are multiple teachers teaching the same course, we need to have common assessments. So unless we come to an agreement on our assessment, there was nothing I could do.

My precalculus team were receptive in trying out the iBook as a project for our students. Soon after that, I was able to set up a department iBooks Author training from one of our Ed Tech members (Tim Bray). Students were also very receptive to the project. The product of their efforts were astonishing. Their books could easily be used as a textbook. They demonstrated their understanding of the topic clearly and were able to use a lot of creativity to make the book interesting. After the iBooks were completed, we had a peer assessment class where they viewed and critiqued each other’s books. During that time, I would frequently hear “whoa, that’s so cool!” They blew each other away in the way they presented the topic. The iBooks Author project was a success! Here are few of the statements made by students when I asked them to reflect on the project.

"I personally enjoyed doing the iBooks author because I can create a book of my own using the knowledge I know. Compared to other projects, I was interested in my own project for the first time."

"Wow, what a fun project! The project was fun; I learned to use iBooks author, a new program! I think that my book was very creative, and that a lot of my classmates had very creative and sophisticated projects. The peer assessment was also very beneficial because I got fresh eyes to look at my project. This type of project is beneficial to our learning, and I hope that we do more of these in the future"

"I really enjoyed the ibooks project. It was my first time to write a book and I was surprised how easy it is to write a book because I am not that good with computers."

It was from this that I thought about a year long iBook project as their digital portfolio. My next post will be about how I used this idea to pilot my Student Lead Project Based Learning class.

Below are some screenshots I have taken from various student created iBooks from my classes.

How I Structure the Class Time in My Flipped Classrooms

The whole purpose of flipping my classes was to have more time to assist students in the learning process. To make the learning process more meaningful and engaging for them, rather than having to listen to me speak. I strongly believe that, a well structured class can take the learning to a whole another level for your students.  

Most common question I get asked is, “How do you know if your students watch the screencasts? How can you make sure that they come to class prepared?” This is one of the main reasons why teachers can be hesitant about trying this method. So, what did I do to make this method work for me? The most important thing I have learned is to have students’ “buy in” with the method. If students believe that this is something that is worth investing their time and energy into, they will do it. And once they start seeing the benefits, they are willing to try out new techniques and go with you on this ride.

So here is my typical structure, in a nutshell. I have adopted some of the Kagan Cooperative Learning Strategies in my day-to-day running of the class.

1) I group the students in mixed ability groups, 3-5 students per group. 4 is ideal but sometimes the numbers in class does not allow the perfect grouping.

2) I set a task for them to complete while watching the screencast at home. Previously, I have asked them to come up with concept questions, but this year I am asking them to take notes on the lecture.

3) They come to class with their notes, which I check for completion, and we spend the first 6-8 minutes at the beginning of the class for them to go through their notes in their groups. At the end of their sharing session, I throw a few concept questions to different groups to check for understanding.

4) I give each student a handheld whiteboard and I ask them to solve a question I have selected from the textbook. After a minute of solving on their own quietly, one member in each group is selected to explain step by step to the rest of the group how they went about solving the given question. This process happens for 5-6 questions, while each member in the group is taking turns in explaining the steps to others. I will step in and explain concepts and/or methods of problem solving to the whole class when needed.

5) For the remaining of the class, they are given time to work on individual practice problems, ask questions and just solidifying their understanding of what they just learned.

The above structure is for the day-to-day lecture learning classes. The verbalisation and repetition of explaining helps with the retention of the information and it also creates an engaging,  comfortable and cooperative learning environment. Students, in their reflection and feedback, have all said that they enjoy the group discussion, as it keeps the class interesting and really helps them to understand the concepts better.

Having said that, each teacher needs to find a structure that works to their teaching style, their personality and the dynamics of the classroom. I have tried number of different things and I’m still tweaking as I go along. Through reflection and student feedback, I am confident that we all can find a structure that each of us are happy with that engages our students in a dynamic way.

Below are some images of students working in groups explaining their solving process to each other.