Classroom Culture: Too Focused on "The Correct Answer."

American Classroom Culture

Today we had an emergency drill and a half day, so each class was only 25 minutes long (compared to the 85 that we are used to on a block schedule). So instead of doing mathematics directly, I decided to play a game: You start out with 21 beans. Each player can take 1, 2 or 3 beans. The person who goes last, wins. It is a very simple game. I wanted the class to know that there is more to this game than just beans, so I told the students that "There is a winning strategy." and "If anyone can beat me, then I will give them a piece of candy."

As students played this game and challenged me, they were looking for the "correct strategy." Only one or two students per class figured it out, mostly by watching me and analyzing my "correct strategy." Now that I reflect on this experience, I shouldn't have said "There is a winning strategy" I should have simply said "If you can beat me, then I will give you a piece of candy." By implying that there is only one correct strategy made students focus on what I was doing instead of exploring other ways to play this game.

In addition to this, my gut instinct as a teacher is to tell everyone the "correct answer" at the end of the class period. I resisted this urge and most students left class without understanding how to win the game every time.

Japanese Classroom Culture

Several months ago I watched two classes solve a simple question. The first class was an 8th grade class and the second was a 7th grade class. The question was if you cut a cube diagonally, what is the shape of the cross section:

image from: The Electronic Journal of Mathematics and Technology, Volume 2, Number 1, issn 1933-2823. 

Retrieved from: http://lib.znate.ru/docs/index-134315.html on Sept 24, 2014

In order to solve this problem, you need to use of the Pythagorean Theorem. The 8th grade students had learned about the Pythagorean Theorem, therefore many of them figured it out. However there were groups who did not figure it out and the teacher did not give the answer at the end of the class period.

The 7th grade students haven't studied about Pythagorean Theorem. Very few students in this class solved the problems, but the teacher did not give any hints or give the answer at the end of the period. But the students still worked until the end trying to solve it.

"Correct Answer" or Process

From watching these Japanese lessons, I realized that I am too "correct answer" focused. I knew going into our bean game that I wasn't going to tell the entire class the strategy. The reason is, if students know that they will get spoon fed the answer at the end, then they loose the incentive to solve it next time. It is the process that we are more concerned about anyway, right?

The Power of Synchronous Flipped Classrooms

Asynchronous
In education social media, it seems that teachers favor asynchronous learning over synchronous learning. citing reasons like:

• Students can go at their own pace.
• When students get stuck, they can slow down and understand that concept before they move on.
• Not all students learn at the same rate.

And all of these points are true, but my experience is that each of those points are heavily outweighed by challenges of asynchronous learning:

• Since students can go at their own pace, they put off their math homework because it isn't necessarily due tomorrow.
• When students get stuck, they lose the pace of the class and then they can't catch back up with the class.
• It is true that not all students learn at the same rate, but everyone is supposed to finish the curriculum by the end of the year. You will be constantly pushing the slower students.

Last year I tried to teach an asynchronous flipped Geometry class. The students were allowed to work at "their own pace" to watch videos and complete textbook problems. I knew that I needed more deadlines than just the end of the year, so every student was required to take the test on the same day. What I found is that the majority of my students didn't finish all the notes and practice before the end of the unit.

What I did find from the data is that there was a stronger correlation with students doing well on assessments and students doing the textbook problems and than students who watched the videos and took notes. So I decided to restructure my class so we focused on completing this practice during class and everyone would work at the same pace.


Synchronous Flipped Learning
What I found was the stronger students were more willing to help weaker students because they were doing the same problem at the same time. When I taught asynchronously, everyone was at a different place so they all wanted my help. I ran around like crazy answering questions and checking off work. The discussions between students are much richer and deeper because they aren't trying to finish their work, they are trying to understand concepts and do problems.

So the entire class follows a pacing calendar. The students are expected to come to class having taken the notes. We also take an open note daily quiz. If students come to class without notes, they don't do well on the daily quiz, but I still allow them to participate in the practice with us. Most synchronous flipped teachers don't allow students who don't have the notes to participate in the practice. They make them watch the video during the practice. I personally have chosen not to do this for two reasons. First I believe that the in-class practice is so much more powerful than doing problems out of a text book, especially for the weaker students who don't come to class prepared. Secondly, these students were in an asynchronous flipped mastery class the previous year, I am afraid that these students will simply get behind and never catch back up. Then I am back to the same problems I had last year, except I would have minimal time to work with these students individually because I am working with the rest of the class. Maybe the social motivation that other teachers state is more powerful in the younger grades. I just didn't think it would be enough of a motivation with my high school students.

I understand that this is not the ideal. In fact, the students who come to class having taken notes generally stated that they have "mastered" or are "getting the hang" of a new idea by the end of the class period. Five of the 13 students who come to class half the time or more without notes stated that they were not getting the hang of the new idea by the end of the class. But this is 5 out of my 85 students, and these are students who would probably struggle anyway.

Another reason that I prefer the synchronous flipped classroom is that parents and students seem to understand it better. Meaning that I have to do far less explaining about what the model is and how it is used.

My Situation
I understand that every teaching situation is different. Maybe my bias is a result of trying to use Flipped Mastery from my first year of flipping. Maybe if a did a traditional flip first and then moved to Flipped Mastery then I would have had the opposite experience. But from talking to other flipped teachers and students at my school, I don't think so. I still think there is more power  the synchronous flipped classroom than in the asynchronous flipped classroom.


Comments?
Are you a flipped class teacher who has had the opposite experience? Do you disagree with my assessment? Please comment below.

Grammar Tools in Communicative Language Teaching

I am taking a class at the University of North Dakota that asked us to do an action research project. Part of that project is to share our research and finding with other teachers. So, being the Flipped Learning teacher that I am, I created a video.

The video overviews the problem, my interventions, and the results that I saw. If you are interested in some tools that will help you teach English Grammar and you use the Communicative Language Teaching approach, you may find this helpful.

 

If you have any comments or questions about this research, please let me know in the comments below. Thanks!

Talent Show 2014

For the past three years I have performed at my school's Talent Show. It all started on March 11, 2011 when there was the 11.0 Earthquake in Japan and Fukushima disaster. About half of the students at my school left. The faculty was desperately looking for more acts to fill out the Talent Show, so I volunteered to sing. I have been involved in Musical Theater since I was in 7th Grade. I have performed in 12 musicals, many of which were lead roles. For example I have been Harold Hill in The Music Man, Warbucks in Annie, and Sky Masterson in  Guys and Dolls.

After that first year it has become a tradition that I perform something. However this year I decided to do something special. My talented wife and I decided to perform a duet. We sang "Love is an Open Door" from Frozen. It isn't as good as the movie, but I think we did a pretty good job; especially if you consider that we started rehearsing on Monday and the Talent Show was on Wednesday.

Enjoy!

Stories One Word at a Time

I know that I usually post about Mathematics Education, but I am getting a Masters Degree in Education with an emphasis on English Language Learners. I also teach a free English Conversation Class at my church once a week. This class has a 60 minute lesson and then a 30 minute game. Last week I took a game that I learned from my Drama Students (oh year, my wife and I also run the Drama program at my school).

The students sat in a circle and told a story one word at a time. One of the teachers wrote the story on the board so everyone could see it. The story didn't make much sense. It started off with one of the teachers sleeping and then her bike was flying and then a plane flew between football goal posts, etc. It was all over the place. One aspect of this game that I really enjoyed was that it required students to think about grammar and word choice. We had to corrected the grammar as we went and have short discussions about what is correct and why and it was a great way to emphasis basic grammar including articles, which my students struggle with. My students were initially taught English in a very structured setting with worksheets, this was a very open activity which stretches their abilities.

If you have an ESL class, I would encourage you to try a game like this.

Flipped Geometry Survey Results

When I was a student teacher, my cooperating teacher taught me that I need to embrace my students and allow them to teach me how to be better. Because of that, every year of my teaching I have given my students at least one survey, if not more than one.

At the beginning of the fourth quarter in school year 2013-2014, I gave my Geometry students the following survey using Google Forms. I love Google Forms!! The survey is anonymous, but I told the students that I will be using these results to make decisions about next year so please be honest.

If you are curious here is the Survey:

Many of the results were not surprising, I will show them in the tables below.

I was curious how long it takes students to complete the notes. I commonly assign one or two videos as homework. So students can expect to have an average of 15 to 20 minutes per video. 

The amount of time students spent on one video seemed independent of their overall success in the class. Some students who struggle spend more time on the videos and some students spend more time, which help them do very well. The opposite is also true. Some strong students don't need to take a lot of time on notes and some weak students should spend more time.

From time to time I see students who are watching the video with earbuds in, but I notice that their earbuds are plugged into their music instead of the computer. So I was curious if this makes a difference.

This relationship wasn't very strong, but in general, students who get As and Bs in my class listen to the videos. It was more common among C, D, and F students that they listened to me less often.

Next I will move to one of the most important relationships to overall success in my class.

The relationship between watching videos before class and overall success was much stronger than I expected it to be. Every student who got an A or B in my class either Always watches the video or usually watches the video. Students who got Cs, Ds, or Fs came to class less frequently having watched the video and taken notes.

Students can ask themselves, do I want to act like an A or B student, or a C, D, or F student? Students who act like A or B students usually get As or Bs. And it starts with consistently coming to class prepared.

The next question is about our Daily Quiz. The quizzes I give are only 3 questions and students can use their notes. The questions are written so that if you watched the video and took good notes, all three questions should be easy, but if you haven't watched the video you may only get one correct.

I was very surprised to learn that 77% of my students felt that having a Daily Quiz is a motivation to take better notes. I realized that I spent longer assessing whether or not students watched the videos and took notes than the length of the notes. Meaning I was considering doing away with Daily Quizzes and just showing the video at the beginning of class. This survey taught me that students need more time than the length of the video to process it, and the daily quiz is a motivation to take better notes with more examples.

This is what I hoped would happen when I decided to give daily quizzes and I am very glad that this is what is happening.

We spend about 60 minutes each class period going over problems. I present a problem on the board and the students do the problem on individual white boards or on paper. After doing this for 60 most of the students feel that they have mastered the idea or are getting the hang of it.

There were two students who said "I usually feel just as confused as before we started." I looked very closely at the responses of these two students. These are also students who frequently didn't come to class having taken notes and these are students who "Only listen to Mr. Lewis if I don't understand." This is probably why they are confused.

Now if I separate the above data by whether or not they come to class having taken notes we see some powerful results:

The students who almost always have notes understand the material when they leave, while those who usually don't have notes may be getting the hang of it, but may be confused.

I was surprised that so many students were interested in optional problems. I don't know what I am going to do about this. The idea of it being optional makes me wonder if students would do it. Maybe make it extra credit or something. I need to think about this more.


Finally their third quarter grade separated by how frequently they come to class having taken notes.

If you almost always come to class having taken notes, you will probably get an A or a B. If you usually come to class having taken notes, then you will probably get a B or a C. If you usually don't come to class having taken notes, you will probably get a C or a D. I was shocked at how clear this data was.

One incredible thing about this relationship is whether of not you always come to class having taken notes is something that each student has control over. I think students feel that their grade is determined by how "good they are at math" and although this is true, they have control over how good they get at Geometry, by whether or not they always come to class having taken notes.


Statistics
The AP Statistics teacher in me needs to put a disclaimer. There is a "confounding variable" of each student's dedication to school and ability. Does taking notes make you get better grades? Or do students who get better grades always take notes because that is what they do as a student?

I don't want to imply any cause and effect relationships with this data because it was an observational study. But I think students will understand that if you come to class having watched the video and taken notes, you will be prepare for the practice, you will understand the practice, and then do better on assessments and therefore do better on the class overall.

This data was collected in my class, with my students, within my teaching model. These results can't be used in other Flipped math classes.


Comments or Questions?
If you have any comments about this data or the analysis, please comment below.

Homework in a Flipped Math Class?

I spend more time assessing if my students did notes than the length of the video(s).
This morning I had a realization. I spend more time assessing whether or not my students did notes (via a 3 Question Daily Quiz and me checking notes) than it would take to watch the video in class. For example it may take around 20 or 25 minutes to hand out Daily Quiz Papers, check each student's notes, and correct the Daily Quizzes. The videos are about 10 minutes long and I assign one or more commonly two for homework. This means that I could simply show the video during class and either gain 10 minutes or not lose any time at all.

This is powerful for many reasons:

•  I have seen several students watching the video while listening to music. So they aren't hearing my explanations and listening to my think-alound as I do one or two example problems.
• I have also seen other students who fly through the notes because they move the video scroll bar to where I have writing and pause it, then move the video scroll bar to where I have writing, ... or in other words copy from the video instead of watching and listening.

If we watched the video in class then I would know that they were both watching the video and listening to the video.

The downside is that many students watch the video, pause it to write notes, etc. like they are supposed to. I personally love the idea of my students taking notes for homework because they can take notes at their own pace. I would hate to change the nature of the class because a few students think the notes are more important than learning from the video. I know that the videos are available online, therefore they could go back and take better notes if they want, but I don't know if they would.


After this realization ...
If I do decide to simply watch the videos during class, I realized that the video doesn't have to come at the beginning of the class period. It could come somewhere in the learning cycle. Whenever I hear Ramsey Musallam (Twitter: @ramusallam) talk about the importance of exploration, learning cycles, and his explore-flip-apply model I completely agree but I struggle knowing how to do it in Geometry in my classroom. This could be one way that I can do it.

My class could:

1. Spend some time exploring a concept using a paper activity, web activity, NCTM Illuminations activity, etc ...
2. Then watch the video and taking notes
3. Do some practice activities using problems from the textbook, or completing some task to show mastery.
4. Synthesize their learning with a detailed summary.

No homework in a math class?
This will only work if I don't assign any homework at all. No matter what I assign for homework, I will want to go around the room and assess it. This generally takes 20 to 30 minutes of valuable class time. On the other hand if I limit our math learning to 85 minutes every other day, I wonder if this will be a detriment or not. Assigning homework is a great time to have more time on task, especially for my lower students. When I am considering making a change my first thought is "How will it impact my lower students?" My top students will be fine as long as I deliver content, but my low students need support.


Explore-Flip-Apply?
If my students are only working during class, then a struggle is created between exploring and applying. I want to keep my students together. I am afraid that I might spend too much time exploring or applying and not keep up with the pace of the class.

I really struggled last year with asynchronous learning, my top students went really fast and my lowest students went really slow. If I keep them all together then the top students help the lower students. This is especially important my classes because the difference between high students and low students is really wide (at a high school with no honors math classes in a class required for every student).


Well...
This blog post isn't as enlightening as I hoped it would be. But it has helped me think through some different possibilities that I need to keep thinking about.

If you have any suggestions or comments, please leave them below. I would love to read your thoughts.

Teaching in the Information Age

Many people, including Sir Ken Robinson, have talked about the fact that our education system was created for the Industrial Age. Students are required to take similar classes and the hope, originally, was that they all graduate with similar abilities. The education system realized that this is not possible, so it has been adjusting to meet individual needs, a.k.a. "Differentiated Instruction." In other words an Industrial education system is trying to adapt to meet new demands in the Information Age, but I don't know if it will be able to adjust fast enough, especially because the Information Age changes very rapidly.

Information Age Tools
Let me tell you of an experience I had that is not uncommon. Last week, in a Geometry class, there was a day for students to work on their quarter projects and I there was one student who had finished his project. I told him to turn it in and he can do work for a different class. He was working on either Literature or History, I couldn't tell. But this student, who is a very good student, was constantly doing web searches to make sure that he understood the questions on his worksheet and that the answer he wrote down on his worksheet was correct. I have seen this repeated during a study hall period, and watching my students work in my classroom before school, after school, and during lunch. Today's high school students are aware of the Information Age tools that are available to them, and they use them. I think that the days is gone when teachers can close the door and assume that we are teaching in a vacuum. Students carry devices with them that open the door, not only to the entire school, but to a world and history full of information. Maybe it is time for teachers to have their students do more web searches and fewer worksheets.

What does an Information Age Classroom look like?
The next logical question is, what would an Information Age classroom look like? What kind of classroom would prepare our students for the future that they will be working in? My answer is ... I don't know. I imagine that it would have the four c's from the Partnership for 21st Century Skills of communication, collaboration, critical thinking, and creativity. I imagine that it is more project based learning and less content front-loaded instruction. I imagine that it is more open ended solution finding, than finding the "correct" answer. There are complex problems in the world that need to be solved, and students need to be taught how to handle those problems with the tools in their era, not a past one.

My Classroom
I would love to say that my classroom is like this, but it is not. I am still trying to figure out how to adjust my teaching to meet these needs. My last major shift has been to flip my class. I think my next shift will be to more project based learning because I believe that this is what students will need to develop 21st Century Skills. My hesitation has to do with the need to still prepare students for their next math class and future math classes. I will get there, not because I need to, but because my students need me to.


If you have suggestions or examples of what PBL looks like in a Geometry or Statistics class, please comment below.

Japanese Research Lesson

On March 21st I was invited to visit a junior high school in Wakoshi of Saitama-ken. A "research lesson" was being taught by two different teachers. So we saw the same lesson twice. Once with eighth grade students and then with seventh grade students.

Previous Lesson
The lesson prior to this lesson the students were given this picture. It is a cube. Points P and Q are the midpoints of the sides.

The students were asked "What kind of quadrilateral is PQGF?" The students used nets to think it through. I wasn't present for this lesson so I don't know the details of this lesson. It turns out that PQGF is a rectangle.

This Lesson
Then in this class, the students were given this picture. Points P and Q are the midpoints of the sides.

The question that was asked to the students is "What kind of quadrilateral is DQFP?" The students were given time individually to think about it, and then the teacher asked students to raise their hand based on what shape they thought it was. The common answers were square and rhombus, but there were students who thought it was a rectangle, parallelogram. I was impressed that no student was concerned of the social implications of their initial guess. I think that if I asked this question to my students, many students would vote how the few "smart" students vote. I was impressed that students felt safe enough to voice their thoughts, even if they were the only ones.

After students made their initial guess, the students got in groups of 3 in their han. (Their han is a grouping of about 6 students. These groups are set at the beginning of the year and are the same throughout the entire year). Since students had different opinions, they were to discuss their reasoning and as a group decide on what shape they thought it was and why. The students were also given the following net:

As they were reasoning, they were invited to use that net. Some students drew the shape they thought the lid was and then cut it out to see if it matched. For example the groups that thought it was a square constructed a square on the net and then cut it out. Or I saw one group who thought it was a rhombus, construct a rhombus of two equilateral triangles and see if it matched. Neither of these worked. I saw another group cut out the net as shown, then place the lid face down on another piece of paper and trace the top.

At the end of the lesson the teacher didn't announce what the shape is. I was really impressed by this. If I was teaching this lesson I would want to wrap it up and say what the answer is. The truth is, if the teacher did give the answer at the end a two things would happen:

• The students would stop thinking about the problem. If the teacher doesn't announce it, there will be students to continue thinking about the problem on their own and may come up with an answer or other connections.
• The next task that the teacher presented, the students would be significantly less motivated to attempt it because they would know that if they wait until the end of the lesson, the teacher will tell them the answer anyway.

My Reflection
I loved this task! It was very simple to understand, but very complex to solve. I loved that it was open on how to answer the question.

I love research lessons! I wish that I could find more lessons like this to use in my class, with my students.

Brainstorming about Next Year

Whenever I hit March, I begin to think about next year. I think there are a few reasons for this. One of them is the weather warms up my students get a little restless; I begin to have more discipline problems, which results in students not doing as well in class and I look for ways to improve them. So this year I have held firm to classroom rules and will not give in to students pushing boundaries in the Spring.

Another, and more important reason why the Spring evokes thoughts of change, is I have been able to see an analyze what a semester in my current model is like, and I want to change a few things. This blog post is for me more than anyone else. I just wanted to get out some of my thoughts about next year.

Definite Changes for Next Year
Assess Less, Learn More. I want to do away with quizzes. Currently we have two quizzes and a test each chapter. I am again embarrassed to say that we spend the same amount of time assessing as we do teaching. I want to do away with quizzes so I spend five or six days teaching and one day assessing.

This would also allow me more time to analyze the test for gaps in understanding and make plans on how to address those misunderstandings in the future (not when I hand back the test. Very few students are motivated to learn a concept that they missed on the test when I hand it back, so I need to come back to it later.)

Deeper than the Textbook. I would like to move past the textbook at some questions that push for deeper understanding. I don't know it will look more like the explore, flip, apply model, or contextualized problems, or integrated pure mathematics questions like Japanese teachers use.

Stricter Homework Policy. I will probably be flipped next year, like this year. I think I was too lenient on what happens if students don't come to class without having watched the video. So I will probably make it a policy that you can't get full credit if it isn't done by the next day.

Require More from the Summary. I have my students write a summary of the video when they are done. I want to do more with this. Maybe I will have them write it at the end of class, after they have had time to apply the ideas.

Possible Changes for Next Year
Throwing away the calendar. This year I have handed out a calendar on the first day of each quarter explaining exactly what will be done on each day of that quarter and we stick to that calendar. I don't know if I will do that next year. I want to be able to adjust to individual needs and spend an extra day on a topic if necessary.

Genius Hour. This year I have freed up about 11 academic days for a Genius Hour project at the end of the year. I have no idea how that is going to turn out. Maybe it will be the most amazing thing I have ever done and I will keep it, but I am almost planning on it failing and so I probably won't do it next year. This is a horrible way to go into something new, it is just that I usually fail the first time I do something. The question is will I come out of it determined to do it differently next year or determined to never do that again. We'll see.

Grades in a Japanese School

On Tuesday, February 25, 2014 Dr. Doug Corey of Brigham Young University (when I was an undergraduate at BYU, I was one of Dr. Corey's research assistants) and Dr. Ninomiya of Saitama University and one graduate student came to my school and observed three lessons. After those lessons we sat down and talked about Japanese Education. I was really inspired by how grades are used in Japanese schools.

Students grades seem to be largely dependent on a few things:

• End of term exam
• Attendance and participation
• And sometimes homework assignments, other tests or quizzes

But students aren't given grades until the end of the semester, which has some very powerful implications, including motivating students, eliminates labeling, shifting the focus to concepts, and it forces students to retain their learning.

Not knowing what your current grade is highly motivating

Students want to know their current grade as an indicator of if they are doing enough, either enough to get an A or enough to pass. Once students grade has received that feedback, they will continue in their current path for the rest of the year. But what if you didn't know if you were doing enough to get an A or if you were doing enough to pass. Would you do more or less? I think most students would do more, to ensure they get the grade they want.

Eliminates student labeling

I think that grades become a label for a student. Many students have been labeled by themselves or by their parents as A students. They, and their parents, expect them to get As in every class. Other students are looking to get a B, or C, or just enough to pass. I believe that this labeling mentality would be eliminated if students didn't carry their grade through the semester, every semester.

Shifts the focus from grades to concepts

Conversations with students aren't about grades, they are about concepts. Students won't come to their teacher and ask the question "How can I get an A?" or "How do I bring up my grade?" Their grade isn't in the forefront of their mind, the content of the class is.

Students are forced to continue working and retain what they learn

Because tests and quizzes aren't given throughout the semester, students understand that a major factor of their grade is a cumulative assessment. This alone has important implications. For example

• Students with strong grades will not "rest on their laurels" and not focus for the exam. These students will work especially hard on these exams. I think we do our students a disservice when they have such a high grade, that their end of semester exam won't change their grade much.
• Students need to remember all of the major ideas and concepts until the end of the term. I have found myself trying to test students right away "before they forget" because I assume that they will. If they know that they won't be assessed for several months, then the expectation is that they will remember.

If you disagree with any of my above implications, please comment below. Or, if you have more implications that you would like to add, please comment below. I would love to have a discussion about these.

How will this affect my teaching?

There is currently a school policy that one grade must be put in the grade book every week. I would not be allowed to have an empty grade book for a quarter, give a quarter test, and then put in two or three grades. If any student failed, then I would face major problems.

On the other hand, this mentality does lend itself nicely to Standards Based Grading. I am not an expert on Standards Based Grading, but I like the idea in theory. My fear is I don't know enough high school math teachers who use Standardized Based Grading, so I am cautious to use it. It is such a mind shift for students and parents. Maybe one day in the future I will look into this.

If you have any other suggestions on how these ideas could be implemented in American schools, please let me know.

Japanese Feedback on My Teaching

On Friday, February 21, 2014 I was invited by Dr. Doug Corey of Brigham Young University (when I was an undergraduate at BYU, I was one of Dr. Corey's research assistants) and Dr. Ninomiya of Saitama University and several other graduate and undergraduate students. Please see my blog post about that "research lesson." (coming soon!)

Then on Tuesday, February 25, 2014 Dr. Corey, Dr. Ninomiya, and a graduate assistant came to my school and observed three lessons. Two that were using the Flipped Mastery model, and a Geometry lesson about Translations and Reflections. After that 85 minute lesson we sat down and talked about the lesson. Since graduating from BYU about five years ago I have never received such though provoking feedback a single lesson.

Kadai (underlying deeper mathematical idea)

The first comment that Dr. Ninomiya made to me was describing mondai (pronounced moan-die) and kadai (pronounced ka-die). The mondai are the kind of problems or questions that are asked to the students. The kadai are the underlying deeper mathematical ideas. The goal of the lesson is not for students to solve the mondai, but to think and learn about the kadai. The kadai is sometimes a phased as "Let's think about ________". The kadai isn't specifically shared with students, but teachers will talk about the kadai as the goal of the lesson with the students. This is especially true at the end of the lesson, with a summary of what students have done by solving these problems.

Dr. Ninomiya didn't understand the kadai of my lesson... because there wasn't one. American curriculum is a collection of separate topics and problem sets, it doesn't lend itself easily to underlying big mathematical ideas. On the other hand, Japanese curriculum is more focused and builds upon a single mathematical idea over several lessons. As I progress as teacher through my career, I have been thinking of pulling away from the textbook (not from the Standards). I don't know how valuable remember types of problems are in the long term. This seems like a topic for another blog post. At the very least, I can work on framing the lesson within a kadai.

Notes and Summaries

Another topic that we discussed was students effectively using their notebook. In my class, the students watch a 10 minute video, take notes, and then write a summary. Dr. Ninomiya liked the idea that I had my students write a summary. He said that many teachers want their students to do lots of problems, but it is better that students are asked to summarize what they learned. It becomes a synthases exercise.

In my class, for about an hour, we do problems from the textbook. The students write down the answer on individual white boards. I do this because:

1. Students enjoy it. At the beginning, the students loved the idea of using white boards. Even after using them everyday for months, they still enjoy it. Maybe after using paper and pencil so much, they like the change.
2. Because students are writing with a large white board marker, it is very easy for me to scan the room and see what all of their answers are. I then know what mistakes have been made and the kind of thinking my students do.

Dr. Ninomiya commented about the fact that students don't have a record of what they did in class. Once they erase their white board, then it is gone. They can never go back to that problem and look at it. Notes have several purposes:

• Record of what they, the student, did: The textbook isn't always what they did, but their notebook is a record of what they did. (By the way, because textbooks are so small and thin, students are encouraged to bring, not only their textbook to class, but all of their math textbooks from junior high school or high school to class.)
• Notes remind students of what they did last class: Teachers ask students to review their notes from last class, so they can continue the ideas from last class and build onto the previous class period's discussion.
• Notes are used to study: Studying for semester exams are very important, and a student's notes are very useful when preparing for these exams. These notes are for their future self.

I don't think I am ready to give up white boards, because of the above reasons, but I think students could add things to their notes as we are doing problems on white boards.

Whys that I might implement these ideas in the future:

• Require more from the summary: Right now my student's summaries are very simple and are only two or three sentences long. I want to look into Cornell Notes and other AVID materials and see what they say about summaries.
• Use their summaries at the beginning of the lesson: Occasionally have them switch notebooks with someone around them and have them read each other summaries. Are there any important ideas that this person left out?
• Add to their notes during the lesson: My students usually don't write down the example problems that are in the videos in their notes. They just don't see value in them. (This is one reason why I been shortening the videos by removing about half of the example.) I want to change this perspective. I want my students to work out a problem or two, in their notes, show their work and write down explanations.
• Add and clarify their summaries at the end of the lesson: At the end of the lesson, the students need the teacher to remind them what they did that day. This also gives a teacher a chance to summarize the lesson and, by example, the importance of summarizing the lesson. By the way this is called the matome (pronounced mah-toe-mei) in Japanese education. The students will then add or clarify what they have written from the summary.

The Dropout Rate No One is Talking About

There is frequent talk about the national drop out rate. From a quick google search, it seems that the national dropout rate is around 7% or 8% (https://nces.ed.gov/fastfacts/display.asp?id=16 and http://www.statisticbrain.com/high-school-dropout-statistics/) I should probably do more research on this, but I was looking for a quick estimate. This is an important number, and something that does merit the concern and effort of our education system. But there is another dropout rate that concerns me, and that is the rate at which teachers leave the teaching field.

According to The Atlantic between 40% and 50% of teachers leave the field within their first 5 years of teaching. By the way, I am about to hit my four year anniversary of teaching. Maybe some of them enter education planning on it being a temporary career, but I don't think that this is the case for the majority of teachers. I think that this is another matter that is something that should be investigated and worked to correct. When a teacher leaves, they take their experiences and expertise with them. We have no way of capturing that and sharing it with future teachers. We also have a huge demographic of teachers who will be retiring in the next 10 years and we need experienced teachers to fill these positions. I believe that teachers need more administrator support, quality professional development, time to prepare, and then be left alone.

The motivation behind this post is I recently heard that we will have to begin documenting why individual students get Ds and Fs and what I have done individually to help these students. I am not disagreeing with the need to help these students individually, but I am concerned about the documentation and it being something that takes away from my time to prepare for doing what I love, teaching!

If you have any comments about this topic or further research, please share in the comments below. I am not an expert in this field, but every time I see a fellow teacher leave the teaching field I feel a sense of loss.

Another visit to a Japanese High School

Today I returned to Kanagawa Sohgoh High School with two math teachers from my school.

We observed three math classes and a technology class. During first period we watched two different teachers teach the same lesson. They were sophomore level math classes. We were in the first class for 45 minutes and then switched classes to the other teacher for the remaining 45 minutes. The most amazing thing is that they were teaching the same lesson on the same day at the same pace. We walked into the second class almost exactly where the first teacher left off. I don't think that this is common, but it was amazing!

Curriculum

I am continually amazed that on the surface, Japanese schools and American schools don't look much different. The teaching styles are similar enough that most people wouldn't notice huge differences between Japanese teaching and American teaching. American teachers would categorize Japanese teaching as very traditional. What is drastically different is the curriculum.

Again, we watched a sophomore level math class (Math I) and they were studying Number Theory. Specifically they talked about:

• Categorizing according to divisors and reminders. For example categorizing numbers according to 3k, 3k+1, and 3k+2, where k is an integer.
• Proved theorems that involved categorizing numbers. For example proving that the square of any odd number minus 1 is a multiple of 8. Or proving that multiplying n consecutive numbers makes a number that is a multiple of n!.
• Finally they proved and then used the Euclidean Algorithm to find the Greatest Common Divisor.

I didn't learn the content that they were learning until I was half way through my undergraduate mathematics program. Not that American students couldn't learn this material, it just isn't found anywhere in our curriculum.

The third class we attended was a senior level class. There were a total of five students in this class and they were preparing for College Entrance Exams. They played math games for the first half of the class and then reviewed one very challenging math problem during the second half of the class. This problem involved triangles, circles, inscribed angles, area formulas, trigonometric identities, and vectors. Even if the problem was written in English, I don't know if I could solve this problem. This again shows how integrated their curriculum is, and I admire them for it!

I found out today that there are many different levels of textbooks. The mathematics textbooks that are used by Kanagawa Sohgoh High School are some of the hardest textbooks offered. This may explain why the content was so challenging. There is a lot of talk in American schools about Standards and about the Common Core. The Japanese school system does have content standards, but they value the textbook over the standards. This works very well because their textbooks have a very demanding curriculum.

 

Games

This third class played a number of games during the first part of the class. They were very interesting. I will share them with you.

Game 1: Police and Thief

One player starts as the Police and the other player as the Thief. The Police get to go first and they can move one space. The Thief can then move one space. Through playing the game the players learn that the triangle at the top is a very important part of this game. If the thief goes in there, then they will be caught. Otherwise they won't be caught.

Game 2: Two Groups of Stones

The game is played by drawing two groups of stones one with 25 stones and the other with 18 stones. The first player can remove as many stones of the same color as they want, the second player can remove as many stones of the same color as they want, and it returns to the first player. The goal is to be the last person to take a stone.

I won't tell you the strategies of how to win this game. The trick is to play it several times and begin to notice patterns. What I will tell you is that one of the players (player 1 or player 2) has the advantage. But I won't tell you which. If you have any guesses, please leave them in the comments below.

Game 3: Three Groups of Stones

A third game is a similar game about removing stones. The rules are the same, two players alternate turns by removing stones of the same color and the player to remove the last stone wins. But now there are three groups. The first version has 3 stones, 2 stones, and 1 stone. Like this:

Another is with 7 stones, 5 stones, and 3 stones. Just like the other stone game one of the players has an advantage and will win, unless they make a mistake. I won't tell you which player has the advantage. But if you think you know, please leave your thoughts in the comments below.

Games

I was so glad that I watched this class play games. These games are very different than the games I have ever played in American schools. These games still required critical thinking and problem solving, and it took some mathematics understanding to understand the strategy.

Student Presentations

I wanted to mention some of the things that I saw in the technology class. The students were giving presentations from PowerPoint that they prepared on technology in the future. For example they talked about designing Smart Phones so they can be used by blind individuals, 4D televisions (including things like smells), food that can be stored in data and then reproduced at will, and a way of finding lost items using a Smart Phone. The students had three minutes to present their ideas and they were graded by their peers by answering 13 yes or no questions, and overall score, and comments. These kinds of things are not uncommon in America, but I was very impressed by these presentations.

Teachers

A learned a few more things about Japanese teachers. First of all many high school teachers don't have degrees in education, they have degrees in their content area and then get a teaching certificate later. They also teach about two out of the four 90 minute periods each day (not three like is common in America). So the teachers have much more time to plan and collaborate.

Finally their school is divided up into committees. We have this at my school as well, and I am guessing this is not uncommon. But in case you are interested here are the committees at this school:

• Research (look at how they can prepare their students for entrance exams, decides how many home room classes to have, and fills out reports).
• School Management
• Career Advisory
• School Activities
• School Behavior (discipline)
• International (this school has several sister schools around the world and their students travel all over the world)

I just thought it would be interesting to compare the kinds of committees at this school and your school. Also there are between 5 and 10 teachers on each committee. Committees between 8 and 10 are the most common.

What I Learned my First Year of Flipping

I had said many times before that my first year of "Flipping" my class was the hardest year of my teaching career, but the second year of flipping was the best! I learned so much during that first year of Flipping about things that worked and things that didn't. I changed things every quarter to make improvements, but by the end of the year, I figured out I should flip my class.

Flipping is different for everyone

There is no one way of flipping a class, just like there is no one way of teaching a traditional class or a PBL class. Each teacher needs to find the way of flipping that works well for them and their students. This isn't helpful for first year teachers or teachers preparing for their first year of teaching. But I would encourage a teacher planning on flipping to stay as close to what they have found successful in the past. For example, one of my biggest failures during my first year of flipping was trying to implement a Flipped Mastery approach, because that seemed like was the direction that everyone who was flipping was heading. But a Flipped Mastery model does not work for me. I like giving students second chances and meeting my students where they are, and I found that about half of my students were constantly falling behind. I was afraid of them falling too far behind, so I required students to test on the same day. So more than half of my class hadn't watched all the videos or done the required textbook problems by the day of the test.

Be Flexible

As I mentioned before I changed things about my class every quarter. Here are the things that I tried:

• I collected data and talked to my students, using their data, to convince them that the students who did more of their notes and textbook problems, did better on assessments.
• I changed the grading policies to place more emphasis on textbook problems, because that showed the highest correlation with assessment grades.
• I changed how frequently I put grades in the grading system and how frequently I contacted parents about grades.
• I tried giving note packets for students to use to take notes
• I tried giving a few problems after the notes for students to try before doing the textbook problems.
• I tried making short videos to help students through the few problems after the notes.
• I tried created guided notes for students to use when they were taking notes

The point is that I was willing to adjust things during the entire first year. If things aren't working, change them. Also, don't be afraid of failure. Many of the things that I tried were a total failure (ex: videos explaining example problems and guided notes were both huge failures) and that is okay. I continued changing things and eventually found a system that worked for me.

Keep it Simple

The model that I am using during my second year of flipping is very simple and it works very well. I would recommend teachers that are considering flipping, keep it very simple. Specifically what I mean is:

• Make your own videos (there is a lot of power in doing this, if you are willing to do it. Use the materials that you used in class for the videos, but keep them short. Don't give a lot of examples.)
• Give the homework that you used to give at home, in class.
• Give the same tests and quizzes that you used before. (This is good to compare data between before and after.)

I know that this recommendation goes along with some of the "less than admirable" forms of flipping, but it is the simplest way of flipping. Your focus will be on making videos, so keep everything else the same. Then the second year you can adjust what you do in class to be something more meaningful than old homework problems.

Questions and Conclusion

If the first year of flipping is hard, then why do it? Because the second year is so worth it! Everything that frustrated me about how I taught before flipping has been corrected by my second year. It is a better way of teaching.

If students get a similar lecture at home and similar homework in class, then what is the point of flipping at all? This year my students walk into my classroom in the morning with a similar understanding as when my students left my classroom before I flipped. And I believe that I can move my students future forward while they are in the same room as me, than when they are at home. Plus, as a math teacher, I know that every student can complete my homework if they are only asked to watch a video and take notes. No student "gets stuck" anymore.

If you have any questions about my first year of flipping or what I learned, please contact me at Twitter at @mathlewis.

Differences between Japanese Education and American Education

I am continually fascinated by Japanese education. It is just interesting to see another education system, especially a successful one, and look at the similarities and differences. The more I talk about my experiences and things that I am learning, people want to know "Why is Japanese Education better?" and my answer is "I don't know." Anyone who is involved in education understand that it is very complex and connected to the students that we serve, so it would be impossible to research and find the that make Japanese education work that American education is missing. That is the wrong question to ask. But I do want to point out some differences:

1. Children are left behind

The responsibility of learning information is set squarely on the student's shoulders. Teachers come to class, they lecture, the students take notes, and speak only when invited to by their teacher. In fact, Japanese high school is more like American college than American high School. The students know that if they don't study well, they won't pass their next entrance exam and therefore won't be on a track to get into a good university. But it is their choice to learn or not. I have seen multiple students with their head on their desks sleeping during class. The teacher doesn't make any comments about it, as long as they aren't disturbing the class, it is fine.

2. No Differentiating

Differentiated Instruction is a hot topic and a discussion among American teachers, but not Japanese teachers. American teachers strive to adapt their teaching to meet their kinesthetic, auditory, and visual learners as well as meeting Garners Intelligences. Japanese teachers stand at the front of the room and lecture and draw diagrams on the chalk board. From what I can tell, they may not even know their student's names, let alone their learning styles. When they call on a student they are usually looking at a class list.

3. Not Standards, Curriculum

I have limited working knowledge of Japanese curriculum, but it is an area of interest. There are national education standards approved by the Ministry of Education. But in talking with Japanese teachers, I have never heard them say anything about standards, but they do talk a lot about textbooks. There are only a few textbooks that are used in Japan and they are all approved by the Ministry of Education and therefore you don't deviate from them. The examples that the teacher gives are the examples that are printed in the textbooks. Very little is done that isn't directly from the textbook.

4. Teacher Observations

American teachers are not used to being observed. In my entire teaching career of about four years, I have only been observed about three or four times. I have only had two individuals come into my class and watch me teach. This is very different from Japanese teachers. During a few months of the year, there are open lessons where anyone can come and observe a teacher. So each teacher may have one open lesson a year where the principal, other teachers, or parents are welcome to come and watch them teach. I have also heard that the first full year of teaching is done with an experienced teacher assisting them. Usually in the back, but providing feedback.

Conclusion

I don't know what will fix the problems that we are seeing in American Education. It is my opinion that the American Education system is too complex for simple solutions. Slow and gradual progress is the only way that we will improve our schools. I have highlighted some areas that are very different between Japanese Education and American Education. I find them interesting, I hope you do too.

How my iPhone changed my career

About a year ago, I purchased an iPhone and it has been the greatest professional development tool I have ever used. When I started using my iPhone, I wasn't sure how it could be used. But I noticed that it had a podcast app, and I found a few educational podcasts, like the Flipped Learning Network Podcast, and began listening to it.

The next step happened a few weeks later. The guests who appeared on this Podcast said that they can be reached on Twitter. So eventually I realized that I could use Twitter to connect with amazing educators and learn from them. I don't think I am very good at using twitter, but I love the ideas that I get by reading other teacher's tweets and blog posts.

Since then I have expanded to listen to a variety of podcasts, many of which are from EdReach and my iPhone has become a constant source of professional development that inspires me to try new things.

In case you are curious, here are some of my favorite educational podcasts:

• The Google Educast
• The Flipped Learning Network Podcast
• The EdGamer Podcast
• Chalkstar to Rockstar
• The Flip Side with Jon Bergmann

If you have others that you would recommend, please leave a comment below!

Using Requirements on Teachers to Inspire Creativity

One of the most liberating and powerful attributes in education is freedom. Sometimes as teachers we don't feel that we have a lot of freedom. We are required to teach Common Core, State or other Standards. At the same time we are required to meet other school or district improvement plans. This is on top of lesson planning, grading, and differentiating for a wide variety of learners. But the truth is, in all of this, there is still room for freedom. In fact, the demands on you as a teacher can inspire creativity.

One TED talk that I think about frequently is Phil Hansen's TED talk entitled Embrace the shake.

He is an artist who developed a tremor in his hand which kept him from drawing pointillist drawings. So instead of giving up, he decided to embrace the shake. I love the moment when he goes to the art store and can buy anything, he doesn't know what to do. He then sets limitations that inspire the creativity.

My goal as a teacher is to use standards, improvement programs, and other demands on me and my time to inspire creativity. I am always willing to try new things in my classroom. Some of them fail, but most of them work and can then be improved upon.

This same idea is passed to my students. I love to assign open ended projects. For example

• Create a game that reviews the ideas from this chapter, the game must include content questions from the chapter that you wrote. This can be:
• A board game
• A card game
• A video game
• Present a summary of all the important ideas from this chapter. Be creative, for example:
• Make a video: a movie trailer, news broadcast, or video of toys discussing the ideas.
• Write a story: a children's story that incorporates the ideas from this chapter.
• Create a PowerPoint, Prezi, etc.
• For more ideas go to:
• http://khsgeometry.weebly.com/quarter-1-projects.html
• http://khsgeometry.weebly.com/quarter-2-projects.html

I have been amazed at the quality of work that I get when I allow the students freedom with specific parameters. Last year when I detailed exactly what I wanted, I received exactly what my rubric stated, but it lacked passion and enjoyment.

I hope that educators will embrace the demands on us, and use it to inspire creative solutions to the daily struggles of being a great teacher.

How do you get your students to watch the videos?

I got an email from another teacher who is flipping and they asked the question "How do you get your students to watch the videos?" How you answer this question as a flipped learning teacher is very important. In my opinion, here are a few options:

1. Make them by not allowing them to move on until they do it.

This is taking the approach of a Flipped Mastery model where students can't move on until they have watched the video. The teacher in us assumes that students can learn unless they are first exposed to content. So this is the approach that I used during my first year of flipping. I have since found that students learn more from doing problems than from watching a video. I don't think that students have to watch a video before being ready to do problems on a new topic, but this is a better sequence for most students.

The main problem with this problem is that students will struggle on harder sections, especially weaker students. The first year that I flipped I found that my lower achieving students were the ones who were always falling behind. These were also the same students who were not motivated to do more work to catch up. There are lots of teachers who have found ways to make Flipped Mastery work, but it doesn't work with my teaching style because I couldn't give my lower achieving students the support that they needed.

2. Don't require them to watch the video

Simply giving them points or not giving them points won't be enough motivation for most students to watch the video. If you offer points for doing it late, then students will put it off until just before the test or quiz and then the opportunity for depth of understanding is lost. Or if you don't accept it late, then students who didn't do it have no reason to go back. This is a recipe for failure.

3. Find a "happy medium"

I think this is where most flipped teachers settle, is some combination of the first two elements. These aren't discrete suggestions, it is a continuum and different teachers and groups of students will need to find a different "happy medium."

The "happy medium" that I use is: all of my students watch the same video on the same night and come to class ready to do textbook problems as a class, usually on individual whiteboards. If a student shows up to class without having watched the video, I don't send them to the back of the class to watch the video, even though many Flipped teachers do this. They have the choice of going to a computer, taking notes and then completing some textbook problems later or they can participate with the class in doing problems together and watch the video later on their own time. Most students choose to participate with the class because they learn more with the class than they do from doing textbook problems alone. There is a penalty though, the students do take a 3 question, open notes, quiz about the assigned video. Students may not retake these daily quizzes and they are worth, in total, about 10% of their overall grade. Not a lot, but enough to show them that I am serious about them coming to class prepared.

I am sure that there are other "happy mediums" that you can find, but this is the one that has been working very well for me. As I have said before: the first year of flipping is very hard, but the second year of flipping is worth it. It will take you about one year to work out the system, but after that it is awesome! I will never go back.

Disclaimer

I would like to point out that am assuming that the videos are accessible to students. With my current students I have never had a problem with students getting access to the videos. I teach at a one-to-one laptop school and all of my students have internet at home and most of them have personal internet devices. I also post my videos in multiple locations just in case one source has problems. So my main focus has been on motivation.

Japanese perspective of American Teaching

On December 18, 2013 I invited two Japanese teachers to my school. One was a math teacher and one was a "society" teacher. The math teacher and I watched three math classes and talked about American teaching styles. I was very intrigued by what he found interesting. These things highlight differences between Japanese and American education.

1. Similarities

The thing that this math teacher found the most interesting was how similar American school and Japanese schools were. He had the perception that in every American classroom, everyday, students sat in groups and had discussions. I believe that there are classes like this in America, but it isn't the common method of instruction. He was surprised that he saw many teachers in the front of the class delivering content and the students were listening to (or in Japanese receiving the) lesson just like as is common in Japanese classes.

2. Technology

The math teacher that I talked to also taught a few technology classes, so he was very interested in the technology that was used. My school, like many American schools, has worked very hard at increasing the amount of technology in the classroom. My school is a one-to-one laptop school and every classroom has a SmartBoard. In every class that we visited there were students using the laptops appropriately and 2 of the 3 classes had teachers using a SmartBoard for instruction. I think it would surprise most American educators to learn that the most high tech device in a Japanese classroom is a chalk eraser vacuum.

This teacher was surprised that all of the students that he observed were using their laptop appropriately. He said that in Japanese schools they would be afraid that students would be looking at other things during class. I didn't want to tell him that this is a constant struggle. He attributed this to the high expectations of American students. We had this discussion in a Flipped Mastery classroom, where students were expected to watch videos, complete notes and practice problems, and then take quizzes. I feel that these expectations are high for typical America classes, but especially when compared to Japanese classes. In many Japanese classes there is no homework, no quizzes, and a few tests. In the American paradigm this would be seen as having low expectations. But to balance this, Japanese schools have very rigorous entrance exams. Students study hard to pass entrance exams so they can go to a good junior high school, then to a good high school, then to a good college, and then have a good career. I think there are pros and cons to both systems.

Previously we had talked about the fact that I use video to deliver my instruction. During our lunch break, we went to my classroom and I showed him how I use my SmartBoard and a laptop to record lessons of me teaching and then upload it to the internet. This seemed hard for him to grasp. I am sure it is a stretch for a teacher who usually uses colored chalk, erasers, and a cardboard roll as a pointer.

3. American Classrooms - Desk Configurations

In Japanese schools the students stay in the same room and the teachers move. Teacher's prepare their lessons in shared work spaces, so I was interested in what he would say about American classrooms. The thing that surprised him the most about American classrooms is desk configurations. Since Japanese teachers share teaching space, the desks in every class are the same. Columns of individual desks. He was very surprised that in all three of the classes that he visited the students were in clusters of four. I explained that this was to encourage students to help each other and work together. He said that he was interested in trying different desk configurations.

He also commented about the walls of classrooms. Again, since teachers share teaching space, the walls in Japanese classrooms are bare. He liked that there were posters and student work posted on all the walls. I was surprised that he didn't say more about the differences between American classrooms and Japanese classrooms.

4. American Math Textbooks

The last topic that we discussed in detail was American Textbooks. Japanese mathematics instruction is very textbook driven. The textbook is approved by the Ministry of Education and you don't deviate from the textbook. At first this teacher was trying to follow along with the teacher in the textbook, but I had to explain that the examples that the teacher was using are different from the printed textbook. This is never done in Japan.

He was surprised that he didn't see American students reading and studying the textbook and asked if students did this at home. I had to explain that most American students don't read the textbook unless they can't do a homework problem. He commented on the colored pictures and the detailed step by step examples with explanations. He kept saying that it was a waste that American students don't use their textbooks more because they are so good.

Another thing he commented about American math textbooks is that there are problems that are based outside of mathematics. I never realized that every problem in a math textbook in Japan was pure math, there were never word problems about two students, or problems related to science. He thought that this was very good.

Conclusion

I really enjoyed talking with this teacher and American education and noticing what he found to be interesting. Many things that were surprising to him were things that are emphasized in American teacher training and professional development like technology use and student desk configurations. Even though we complain about professional development, it does shape our education system for the better.