A Personal Math Poem

So I am going to write a little preamble to this poem. I originally wrote this poem in my senior year of high school. I vividly remember writing this during a study hall block in the empty classroom of my Pre-Calculus teachers room. I think I was trying to find some math tutoring or helping a math teacher during my study block at the time. I did this because I started dreaming of being a math teacher when I was in 8th or 9th grade. I was already planning on going to college to get my degree in math and my masters in teaching at that point. I looked up to my math teachers and noted how they did things. I vividly remember the ways they taught and the activities that made math come alive. So I wrote this when I was in a head space of my senior year of high school when I was going out of my way to find ways to stay involved in math.

So flash forward to now when I have currently started teaching my fifth year. I have taught in Oregon, China, and several schools in Boston. I have worked with a wide array of students including elementary, high school, and college. When I was in 9th grade I didn't have the dream of teaching in China. When I was a senior in high school after coming back from China I was contemplating teaching in China, but never really thought would happen. It made me realize my dream never dies, but can always change. So after having such a great day I wanted to look at it again and update it. I remember having it written in the journal I kept for my college writing class I took my senior year of high school. So I wasn't sure if I still had it. However I typed it up and saved it in my google drive. I used the search feature to locate the poem. I think I typed it up in google drive when I was in China and then had the poem posted near my workspace in China to inspire me. I actually took my journal from high school with me to China which is how I could type it up. This just illustrates how I save everything and like to take everything with me even if that means flying it over an ocean. The main reason I brought that journal was because I took notes and wrote down ideas of how I wanted my class to run, work, and look like. I often wrote down things my various teachers did or used that I really liked and wanted to do when I started teaching. So all of my teachers were my role models and inspiration. So all of my teachers had some sort of impact on how I am teaching now. I think the journal might be in the stuff I took to Boston or maybe not. I could look in my room, but do not feel like. However it is likely that it is in a box in the attic of my old house back in Oregon. Anyways I am glad it is saved in my google drive. I am also glad I have this blog so my ideas are not lost.

Ok last bit of pre-amble. The title is a reference and line from a book called Speak by Laurie Halse Anderson. I read the line and just totally connected with it, but the character said because she hated Algebra and was so confused in Algebra class at that time. So I turned the line into making a student understand algebra and enjoy math. Which is why I became a math teacher to help stop or decrease people's math anxiety or fear of math.

So here it goes. This is the version I wrote in High School:

Algebra divided by Students = Confusion;

(Algebra divided by Students) + Me = Understanding

Tick! Tick! Tick!

Domain, Range, and Functions.

This knowledge is not an onto function.

Tick! Tick! Tick!

Chord, Circumference, and Circles.

This knowledge is not onto, but the output it does include is some of the best.

Tick! Tick! Tick!

Problem solving, Processes, and Puzzles.

This knowledge helps make life a consistent linear system.

Tick! Tick! Tick!

Vacant Desks, Empty Tool Box, and Non Existent Lesson Plans.

A Teacher always dreaming about their future classroom.

So here is the version I wrote now four years and four or more schools into my full time teaching career:

Algebra divided by Students = Confusion;

(Algebra divided by Students) + Me = Understanding

Tick! Tick! Tick!

Domain, Range, and Functions.

This knowledge is not an onto function.

This language must be learned and understood.

Tick! Tick! Tick!

Chord, Circumference, and Circles.

This knowledge is not onto, but the output it does include is some of the best.

This language must be learned, understood, and connected to diagrams.

Tick! Tick! Tick!

Problem solving, Processes, and Puzzles.

This knowledge helps make life a consistent linear system.

All methods and approaches should be valued however different.

Tick! Tick! Tick!

Vacant Desks, Empty Tool Box, and Non Existent Lesson Plans.

A Teacher always dreaming about their future classroom.

Tick! Tick! Tick!

Lots of Occupied Desks, A Partially Filled Tool Box, and Varied Lesson Plans.

A Teacher achieving their dream and continuing to build their future classroom.

Please find the differences and enjoy! (I highlighted them so the poems would pop out of the post)

A Teachers Dream

So I had an amazing day with my classes. I thought I would share and talk about why it is great.

So I my AP classes were fantastic. My first section surprised me with the different ways they could solve the problem. Then the next section I was shocked that the group with that was working on the same problem came up with another way. Then the third section of AP Calc came up with the same ways of solving it, but within the group of three each person in the group solved it in a different way and shared their methods with each other. That is what I wanted my math class to be about was approaching and explaining the problem in different ways. Then having students to share those methods with each other. I then encouraged them to compare those methods. I felt that in China since they had been taught to memorize formulas and were taught to each solve the problem the same way that they had trouble seeing it in other ways. I did my best to encourage, highlight, and show different ways. Thinking about it now my Chinese students often wanted to see algebraic proof of theorems or problems and did not value the graph or table explanation. Also when we practiced for the AP test they could easily solve the multiple choice problems that required using equations, but often struggled with problems that tested their knowledge of graphs and tables. It might have been because they were used to working with equations. In AP Calculus it is vitally important that you can work with graph, tables, equations, and words because the test will test you in those four ways. I think that is a good skill for a mathematician and what can make the AP test difficult. A mathematician should be able to relate the equation and its graph together. They should be able to use the vocab and explain it in words. They should be able to think critically and think in different ways. So I was so happy that my students were so opening, willing, and able to solve it in different ways. It also means that they will do well being able to think in the four ways on the AP test. I told them and reminded them that you should solve them in multiple ways because the AP test will test you in multiple ways. So the problem that got solved the most ways was a limit problem as x goes to infinity. It was solved using a graph, table, algebra and end behavior model, limit properties and end behavior model, limit properties and algebra, and the l'hopital tule. The l'hopital rule was used by a student who has already studied a little Calculus. So in total for the day that would be six different ways to solve the problem. It was fantastic feeling since I dreamed of being a math teacher since I was in 8th grade. I was planning and dreaming of what type of math teacher I would be from 8th or 9th grade. I started dreaming about how my class would involve students solving the method in different methods, sharing those methods, and then comparing those methods. I wanted their voice or way of mathematical thinking to be valued in my classroom. I think it is now and so I am so happy. My 8th grade self or 9th grade self and espcially the version of me that was working in grad school for a Masters in teaching would be proud of me and the classroom environment I created today.

Also all of my AP classes were good about asking really interesting and good questions. Some of them were specific and good questions about the AP test or what it requires. Then one student in my last section which was the last class of the day made me really think about how or why some people say a limit is equally to infinity or does not exist. He asked good questions and we had a good discussion about a very interesting limit problem. You had to find the limit as x goes to infinity to find the horizontal asymptotes. So I encouraged them to look at the graph. So he said that as x goes towards negative infinity the function goes towards negative infinity. It had no sort of horizontal asymptote in that direction. So the limit was equal to negative infinity, but you can't say that y = -infinity is a horizontal asymptote. That makes no sense, so I wonder if that is why some people often say if a limit is equal to positive or negative infinity that it does not exist since it can mean that the horizontal asymptote does not exist. This function was e to the negative x over x which does happen to have a horizontal asymptote since the limit as x goes to positive infinity is equal to zero. So I was impressed that me and a student could have such a thoughtful discussion of complicated calculus concept.

My Honors Calculus went well as well. At one point we had a little down time and talked about geeky math songs and poems. One of my students told me I should check out a poem by Harry Baker called 59 which focused on prime numbers. I said that I loved number theory and things about properties of numbers so I promised I would check it out. They also each individually presented a problem. All of the students were eager to present and all the presentations were fantastic even some that were given by students who had weaker English.

Now also mixed in with all this Calculus was my algebra II class. This class is made up with students with lower English. Some of them have strong math skills, but lack the English. At first it was hard to get them to speak English, to participate, and engage them. I was also was reminded that international students don't often take notes or know how to take notes. So after the first few days of teaching I realized that I had to support their English more than I expected and find ways to build some classroom behaviors around notes and homework. It is also a big gear switch from teaching Calculus. I think I have learned to love the gear switch, but sometimes it can be jarring. Today I got a new student which I found out about only a few minutes before the class and the first half of the class I was being observed by the head ESL teacher. I asked for her to observe my class because I wanted her feedback to see what else I could do to support their English in math. They ended up being super talkative and participated a lot. I think I smoothly handled incorporating the new student as best as I could on the fly. We worked on translating from English to math and word problems. We didn't get through as much as I wanted since the kids were talking so much. We goofed around and got sidetracked some, but I was kind of happy about since they were using their English. I think I was able to get them back on track well which made me happy that I could manage the classroom behavior. It was a great lesson on supporting the English in word problems and a great introduction in how to do approach or break down a word problem. I might put up the examples and materials I used later.

I personally think that I enjoy and am teaching so well because I am working with international students. I think that because I work with international students that since my students come from various countries they bring a varying perspective of math and diverse ideas about math. I have learned about how tangent was written differently in Russian (tangent = tg and cotangent = ctg). I also learned different symbols for slope through the years. We use m for slope which refers to the slope of a mountain or in French montagne. However in China I saw my students use k for slope and a Vietnamese student told me that they use a for slope. They said on the placement test we gave that he struggled with some questions because in Vietnam they used different symbols for the terms or concepts. I thought the test we gave got the heart of the understanding of their math and did not test their understanding of English, but when he told me that I reconsidered how I saw the test. I guess it just shows it is hard to write a test that is not culturally biased. I also think that when I teach international students and ESL students specifically it forces me to think about how to support their English and be creative in how I present the material. I have always wanted to make math and my teaching creative, innovative, and interesting. So I think because I have to consider my student's English understanding and their cultural differences it forces me to be creative about my teaching which is what I always dreamed of. I can not express succinctly how much I love and benefit from teaching international students.

I will end this post about how my teaching day ended. My student left saying that I should always be this energetic about class. I hope I can be and I hope I can use this day to keep me energized and fuel me when I am down.

After the AP test

So I have usually not had to plan stuff for the AP test. I am looking forward to it, but also dreading it. I have a feeling some will have fun with it and others will check out.

I have a bunch of funny videos and songs that use Calculus vocab. I think I might just take a class day watching them and talking about them. Then require the students to use vocab from Calculus to write a song, poem, or story. So at minimum they have to hand in some hand written document, but if they would like to make some sort of video or digital project that would go above and beyond. I would tell them to pull from the vocab sheets we have been filling out all year. I would maybe require the use of at least 5 different vocab terms from the vocab sheets. Then maybe give them some time in class to work on it. Then have them present their creative piece of work to the class.

I had my students write a creative essay before the AP test as review. Some of the responses I got were fantastic and so clever. I might have to edit it since we are using a different textbook. Although the students can look up the theorems and definitions easily in their textbook. However I don't know if the textbook will have information about the mathematicians. I have a digital copy of the textbook so maybe I can clip together the information they will need. That will at least get them started and thinking. They are welcome to do more research online. I saved my favorite ones that really blew me away. I think I might save this assignment for after the AP test this year just so I have something for them to work on. I can give them in class time to work on it and ask students to present. Although some of the ones I got last year involved my female students falling in love with the male mathematicians, so I don't know if the student would have been comfortable sharing that with the whole class. I can show the students the examples that I have from the previous year when I introduce the project. The best one uses the theorems in a creative way, but also is applying them to a real world situation. He also used his knowledge of math history to make the story poignant as well. So it points out a lot of aspects and nuances to the assignment. So I can discuss that with the class to hopefully inspire them.

I am also thinking about having them install LaTeX on their personal computers and teaching them how to use it. I always dreamed of exposing them to the program, so they can be more professional mathematicians and get them ready for college level math classes. I was thinking I could assign them the project I designed for my Calculus class before and have them do a rough draft on paper, then a rough draft on LaTeX, then a final draft on LaTeX. I would critique each draft for content and justification, but I would also critique formatting/use of LaTeX. I have plenty of rubrics for the assignment that include organization and clarity, so I wonder if I can tweak that so it sort of fits with LaTeX format or use of LaTeX.

I already have the project broken up into pieces. So I think I could make it take up May and June that will be leftover after the AP test. Then have the other two assignments be mostly outside homework. So in-class they would write or LaTeX up the project and outside of class write their poem, song, or story. I mean I would have to give up a couple of days to go over the assignments and to go over examples, but then the bulk of the creative work and creative assignment could be down outside the class. I mean they don't need as much help on the song and creative essay since it is so open ended and creative. However they will need help writing the project and they will need a lot of help trouble shooting LaTeX, so that would be best done in class where I can answer questions. I really like this plan and set up.

I would make my AP Calculus class focus on the FTC project since it ties together a lot of ideas from Calculus. I can stretch the project out by making them do several drafts and then making them present it to the class. I would give them plenty of time to develop the presentation visual and what they are going to say. Then it will take up a lot of time having everyone present. If I did both projects it would easily take up all of May and June, but since both projects are very similar I don't think I would want them doing both. So just the FTC and the creative ones. If I find I have more time at the end of the year I can always see if I could figure something else out.

If for someone reason in my Honors Calculus I finish the content that I have planned out for them early. I will do the same thing with them, but have them do the project connecting a function and its derivative. However we will see how the pacing of that class goes and what content I end up getting through.

Honors Calculus

I don't think I am going to go slower necessarily, but I know I won't cover as much content. I think I might throw in more review days. I can have them fill out the vocab cards, work on the review in the textbook, and have them work on another review sheet of problems.

I can have them work on a review sheet of problems and then present. That means that will be two days of reviewing. Then have them work on the review problems in the textbook in class the third day and whatever they don't finish is homework. The fourth day could be finishing the vocab cards and having me check them. That is way more review time then I plan on giving my AP class.

Content:
Functions and their properties (chapter 1)
Limits and Continuity (all of chapter 2)
Derivatives: basic definitions and uses, basic rules, trig, chain rule, exponential and logarithmic (3.1-3.6, 3.9)
Applications: Extreme values, optimization, and curve sketching (4.1/4.4, 4.3)
Integrals: Approximation, FTC (evaluation), and u-substitution (5.1/5.5, 5.4, 6.2)
Application of Integrals: Net Change, Area, and Volume (disc and washer, but no shell or cross sections?) (7.1 - 7.3)

I was talking to the other honors calculus teacher and he pointed out reviewing functions would be good. I used to do a review period at the start of the year that covered chapter 1, but eventually stopped to give myself more time to focus on the Calculus content before the AP test. So I won't cover chapter 1 with my AP class, but I will cover it with my Honors Calculus class.

Calculus update

So I still plan on flipping the classroom for my calculus class and using the model and structure I talked about in my previous post. I however just found out I will normally have 50 minute classes then every other Wednesday I will see the class for 90 minutes. So I am thinking that the 50 minute classes I will have students get in groups to solve a problem then present. I won't get through all the presentations in one 50 minute class usually so Monday and Tuesday I should be able to get through a section of content. Then Thursday and Friday get through another section. I was wondering what to do with the long Wednesdays though.

I am teaching two sections of AP Calculus and one section of Honors Calculus. I was thinking the long Wednesdays could give the AP class time to practice AP questions. We can practice Multiple choice questions and once we get far enough we can practice Free response questions. I can still have them get in groups and present free response questions. The free response question presentations can still go in the presentation part of the grade.

I think for the Honors Calculus I can use the long Wednesday for Free Response questions that review what we learned so far as well. I just won't use AP ones. I will use practice ones from a couple different textbooks I have. Those should be easier for them, but still somewhat challenging. I might have to edit them since I plan on not teaching all of the same content in the Honors Calculus class. I might just find difficult or challenging problems over stuff they have covered for them to work on and present.

This will set aside time to go back and review previous content. It will also help to connect several concepts together since free response questions cover several content areas. It will also give them plenty of practice on free response questions through out the year. I usually only did it at the end of the a unit and I think this might give them more chances to practice. I also waited until I finished all the content to really focus on free response questions when students gave individual presentations on free response questions.

I think I will also use it as time for them to review and update their vocab sheets. I was planning on giving time for this at the end of the unit, but if I do this through out the unit then I won't need to save as much time. It will also be a way for students to review and solidify concepts that they have previously learned. I plan on checking and grading the vocab sheets at the end of the unit before the unit test as well so this will give them more time to work on it and get feedback from me. It will also chunk out the assignment more I think.

So I found out the students have the textbook I had been using to make all my tests. So I can't really use my previous tests since most of the questions the students already have access to. I can pull off the questions that got from other textbooks. I think for quizzes I will use multiple choice questions and short answer question that are similar to AP questions from other textbooks. Then for the end of the unit exam I think I will use free response questions from different textbooks. I will have one free response question with calculator and one without.

However for the Honors Calculus I think the end of unit exam may be a lot of short answer questions from various textbooks that will be similar to free response questions, but not as hard. I want to change the level some since they are taking a lower level.

Calculus and Pre-calculus classes Next Year (2015-2016)

So next year I am going to flip both my Pre-calculus and Calculus class. For those of you that don't know that means for homework students watch videos and take notes as they are watching. Then in class they work in small groups on problems similar to those in the video. I then have the students present the problem that they solve. I will be using a similar structure or plan as I did when I flipped Pre-calculus in China.

Final: 20%
Presentations: 20%
Tests: 20%
Quizzes: 15%
Journal Entries/Notebooks: 15%
Homework: 10%

The presentations category will include their graded presentations using the rubrics I have used in the past. However before each presentation I will have students fill out a presentation outline. I will collect and grade the outlines as well. I came up with this outline last year in China. I was doing presentations with my grade 10 students in Pre-calculus and their English teacher was working on presentations. So I talked to my colleague which happened to my principal. He was having students fill out an outline before each presentation. It seemed very helpful for ESL/ELL learners about how to structure their presentation. It was also the structure I wanted my math presentations to follow. So I took the outline and I adjusted to fit my math presentations. It gave them something to work on once they were done solving their problem. It seemed to make students put more thought into their introduction and conclusion. It would have helped to have at the beginning of the year because I think it outlined and explained the structure I was looking for. Those first few presentations of my grade 10 students were not very good. I mean they were learning and it was the first time being in an English class, so it was not surprising. I just think it would have helped model and explain what I was looking for better. However I can start this year off using them and making students fill them out before the presentation. I also encourage students to bring them when they present, so they can refer to the outline as they are presenting.

The Journal Entry and Notebooks will include a few things. There will be content related journal entries that will be completed at the end of each unit. I have entries for each unit of Calculus and used them in China. They were fantastic and this is the rubric I used. When I taught 9th grade Honors math I had students answer a few journal entries. I covered some Pre-Calculus content so I think I can pull some prompts from the textbook they used which was Algebra & Trig: Graphs and Models, 5th edition, Bittinger, Beecher, Ellenbogen, and Penna. They had discussion or collaboration questions in the mid-chapter review and in the chapter review. They made good writing prompts. I also went to a talk at the NCTM conference that looked at supporting ESL/ELL students. After the talk I asked about writing prompts and if the speaker knew of resources that had good writing prompts. The speaker suggested Algebra Out Loud and Pre-Algebra Out Loud by Pat Mower. I have not checked these out yet, but I might.

As I wrote in my last post I will have students write about math in more general terms. They can relate math to different parts of their life and hopefully see math in a different way. I will grade these more simply and quickly. The key is just get the students thinking in a new way, writing, and using their English. Hopefully the way I have it set up will ensure that everyone gets a high score on these types of entries to improve the grade in this category. 

I will also be checking their notebooks at the end of each unit. I will check that they have the syllabus, vocab sheets, all of their notes, worksheets, previous journal entries, some presentation outlines and rubrics, previous quizzes, and previous tests. 

I am thinking about scoring it in this way:

5 points: missing one or two items
4 points: missing three or four items
3 points: missing five or six items
1 point: missing seven or more items

subtract a half point if not easy to find things. I will require the sections and will emphasize keeping things organized in the sections. Therefore I expect the notes and worksheets to be in the right order. They are numbered so they just need to stay in the right ordering. 

I am not grading the items just checking that they have all of them in their notebooks. I am planning on using 3 ring binders. They would have the syllabus and vocab sheets in beginning. Then it would be divided into the following categories: Notes, Worksheets, Journal Entries, Presentations, Quizzes/Tests.

I am planning on keeping a notebook for each class that would be the model and would have all the solutions in it. So completed vocab sheets, completed notes, completed worksheets, and answer keys to tests and quizzes. 

Homework category will include graded notes, worksheets, and vocab sheets. 

I will collect the notes handout once students are done presenting. I will grade them. I got pretty good and fast grading them when I taught in China. I looked that they filled in each part and each example then it was 5 out of 5. If they didn't fill out one or two things it was a 4 out of 5. If they left a lot of it blank then it was a 3 out of 5. That was pretty much it. However if students who went above in beyond like added things to the notes that were not required or showed that they highlighted key terms or content. So of my students turned in extremely neat, organized, and colorful notes that showed they put a lot of thought into the content. I gave them extra credit which means they got 6 out of 5. 

The worksheets are the problems students work on in class and the problems they present. I will tell students they have to finish the problems that were not presented as homework. I am thinking the first day of a section will be students solving the assigned problem, preparing the presentation and filling out the presentation outline, and then getting through some of the presentations. I don't think I can get through all of them in one day. So the next day will be the remaining presentations and then with whatever time is left they can finish the worksheet. I am thinking to minimize my grading I will pick 5 problems to grade that cover most of the worksheet and most of the objectives. I won't grade the problems that were presented. Then award points as following:

5 points: 1 problem wrong
4 points : 2 or 3 problems wrong
3 points: 4 problems wrong
1 point: 5 problems wrong

subtract half a point if they did not fill in the problems that were not presented on or did not complete entire worksheet. 

I think I will try having students keep vocab sheets. I have some great vocab sheets from an AP workshop that includes all the major theorems and concepts that come up the most often on the AP test. I think I will give time to review before each test to fill these out. I think I will encourage students to check these each night and fill them out as we go through the unit, but I don't want to require it and give them too much homework. So I usually give time in class to review before the exam and then I will have students fill those out. I will tell them which words they need to have done before the exam. Then I will check them in class while students are working in small groups working on review problems. I am thinking about how to grade them and want to do it fast. However I know the AP test looks for key things on the test and I want the vocab sheets to include everything that the AP test requires, but I don't want to spend forever grading them. I could make each one worth two points and if a word is missing something key in the definition or something is incorrect in the definition then subtract one point. 

I don't have vocab cards for Pre-calculus. However when I taught it in China I made digital ones use the grading software we had. I also gave online vocab quizzes to test them over the vocab. I also had fill in the blank questions that tested students over the definitions of the vocab words that I put on every test. So I have some of the vocab picked out and defined. So I will have to generate the vocab and definitions for some of the units as I go along.  

The school is a boarding school. So I will have to check how much access to the internet the students have. If it is a problem I have an easy solution. I had to find a way around using the internet when teaching in China since it was a boarding school with little access to internet, but also because general internet problems of China. I have digital copies of all the videos that I can download and copy over to a student's USB stick. In China I would download and copy the video onto the computer that was in the classroom. The students were then responsible to get a copy for themselves and to watch them. I wonder though if students will have enough access to a laptop or computer to watch the videos. I will have to ask my supervisors and the students.

Journal Entries that Challenge Students to See Math in a New Light

So I haven't posted in a while, but it was mainly because I had not been inspired at my previous jobs. However next year I will be teaching Pre-Calculus and AP Calculus AB at  an International school. I taught internationally for three years and learned to embed English into my curriculum to develop my ESL learners. I loved teaching in that environment and I found that I excelled at finding ways to embed English into my curriculum. I almost do it out of habit and it is hard to pick out all the ways I embed English. This idea of working on not only the content, but the language of mathematics has continually inspired me and pushed me to be more creative. The school seems to support innovative teaching and looks for teachers who find ways to embed English into their classroom. So I believe I will find my inspiration and get back to working on my passion.

Anyways last night I could not sleep and kept thinking about what I wanted to do for next year. I came up with some great ideas. I would to record them and share them so I don't forget. With my calculus class almost two years ago I had students write journal entries after each unit which related to the content. This past year I had my 9th grade honor students also write journal entries. I saw some amazing results. Many students demonstrated a very deep understanding of concepts through writing. One of my 9th graders wrote a beautiful piece that read just like any English assignment, was structured like an essay, and included three different mathematical perspectives or justifications. I know it challenged students that were not used to being challenged or challenged in this way.   I have often debated or thought of how to include writing pieces that were not about content. I thought about having students write about their feelings or attitudes towards math, so that I can understand students struggles in general. I would also hope that through these writings I could change students attitudes about math since many arrive to my classroom hating math or thinking they are bad at math. Although I didn't know how well students would receive such prompts. I personally have contemplated why math is so amazing, beautiful, and interesting to me. I want to open my students to that kind of thinking. So I want to try having students write about how math relates to some other concept that students may not have thought about in hopes to change their attitude or view of math. This is my idea for how to start the year.

I want to do a think, pair, share where students think about what is math. Many of my teachers in grad school had us do this. I think to the point that we got sick of it, but hey it is still cool to see the results. I did this with my Chinese students and I found it fun. I would generate a list for each class then combine the lists and enter the words in on wordle. This will show the words that came up more often as bigger. I am thinking that the next day I would show them and give them a copy of what was generated. I would then have students write what they think makes a good mathematician? I would encourage them to look back to what defines math, so they think about what skills you would need. I think this will get them in a mindset of what they need to do in my class (and beyond my class) to succeed.

However after the what is math discussion I want to lead it to another discussion. I want students to think about if math is a language. I have taken several Education classes that focused on teaching ESL students. I often was one of the few math teachers in the course. I believe you have to be creative in finding ways to embed English into math because you have to make sure students get practice on language of math as well as the English of math. Some of my classmates did not think you needed English to succeed in math. So not everyone can see the English involved in math or see that math is a language. My high school math teacher once said that math is a universal language that we can use to barter or haggle when we travel to other countries. After teaching international students for three years I gained a very deep understanding of how it is a language. For example many of my students had to learn how to say natural log of x (ln x). In China they say the function as "loin". I taught them and corrected them when they said that. I did this so that if they were discussing or talking about a problem with someone in America they would be understood. Students also asked me how to read x^2 or x^3. I told them to say x squared or x cubed. These are common examples I came across and there are more. So I want my students to understand or see how it is a language. I went to a talk at the National Teachers Council of Mathematics (NCTM) conference that introduced activities or strategies to support ESL students in mathematics. One activity was sort of like mathematical telephone. One person had to read an equation while two people listened. The people listening had to write down the equation. You switched roles until everyone had a turn reading an equation. I found it difficult to do as a reader because I had a very complex equation the had a bunch of fractions and parentheses in it. So I had to make sure I was very clear about what went where. I want to try this with my students on the first day. I was thinking I could use equations or expressions that they already know. For example equations that will help them review or prepare for the new content. I thought this would be a nice ice breaker and help get their brains thinking of the math they already studied. I think it would also demonstrate how math is a language. I would have students discuss what they learned or how they felt after the activity. Through this discussion I would guide students to think about how math is a language. Then I would have students write whether math is a language and why they believe that.

I want to try to incorporate writing assignments and writing prompts like this one during the year. I am hoping I could alternate between content specific journal entries and more general entries about the field of math.  Below are a few ideas for writing prompts that I have. If you can think of more or have some resources I would greatly appreciate it. I am hoping I will get inspired by my colleagues, students, and friends as the year goes on though.

There was an article I read a while back of a study that proved that when people look at a beautiful math equation the same part of the brain lights up if that person was looking at a beautiful piece of art. I think I could give the students the article and then ask them to respond in their own words whether they think math is beautiful. They would have to support their answer with examples and could refer back to the article if they wished.

Then related to the concept of beauty and art that was mentioned in the last one. Have students explore and write about how math is related to art. There is a big push and some resources out there to change the field of  Science Technology Engineering and Math (STEM) to include Art. So instead of thinking about STEM you would think of STEAM. This is because with those fields you need to experiment, fail, and explore. That requires some creativity and ingenuity that often is learned through art. I am working for the Calculus Project right now which strives to help students of color succeed in math and to reach Calculus. Numbers show that students of color are under represented in Calculus and other upper level math courses. In Oregon where I student taught most of the students in my lower level course that went twice as slow as the standard course were on free and reduced lunch. So there are factors outside of academics that could impact a students success in math as well as in other subjects. So the program gives students a preview and head start of the next years material. The program also brings in speakers and takes students on field trips. Recently a company called DEILAB came and ran a team building activity. They talked about the students to motivate them to succeed. They explained how art, creativity, and innovation were related to STEM. I like how they pointed out the Da Vinci painted art and was also an inventor to show art and STEM go hand in hand. Afterwards students got to design a robot that would win. They did this with lego pieces and a motor. The robot had to be a certain height. Then they would turn on the motor and the robot would spin to hit the other robot with arms and other weapons. Students would design and use their creativity to build a robot. Then they test their design and if it failed they were taught to learn from their failure. They were encouraged to fail so they could improve their design. It was amazing seeing students creativity and determination to perfect their designs and ideas. So I would like to have students write about how math and art are related. They could discuss how math is used in music or art. However I think they could also write about how you need the creativity from art to succeed in math. There was a book I read for an Education class that showed how math was used in art and in nature for kids. I think I could let students use that as a resource for the writing. As well as find a good article that explains how math is used in music.

I thought about how I would grade these. I would put these in the journal entry category of the grade. I would hope that these pieces would raise their grade in the journal entry category. I have a high expectation for the content entries and make getting a high grade on the assignment hard. So I would hope these more open and creative entries would be easier and raise grades. I was thinking of a rubric that would be fast and easy to use on these. So I am not spending forever grading these. I think these are the elements I would look for:

1. Answers question fully/Answers all parts of question
2. Includes math examples
3. Includes other non-math examples (art, music, or other topic that is discussed in prompt)
4. Connects/compares math examples and non-math examples
5. Organized/clear and neat

I think I would give them a check or a check minus in each category. A check would be two points and a check minus would be one point. So it would be a ten point assignment that they could get at least 5 points on. As long as they include all the pieces then they would get full points. However if they use unclear examples or their connections are unclear then they would lose points in the last category. So I see students losing points in the last category or the first.