Subjects Matter Chapters 8 and 9

        My favorite part of Chapter 8 ended up being about how we can use web tools to foster conversations between ourselves and the students, and between the students themselves.  In a classroom where all the students have access to the internet at home, there are many ways I could put this to good use.  The book has mentioned the Edmodo website several times now, and I really like the idea behind it.  Instead of hastily assigning homework at the end of class, the homework is directly sent to the students.  This eliminates the problem of “not knowing there was homework” when the expectation of checking the site every night has been established.  It also gives me a great tool to help students be prepared for the next day and even give helpful reminders or convey something I forgot to mention in class.  I also like the idea of having a blog for the class.  I picture it in my head working somewhat like Ask Dr. Math, only with the option of having many different sources of responses. 

http://mathforum.org/dr.math/

The website that everyone has probably come across at some point or another after getting to the point of typing out the entire math question into the search bar.

Having a designated spot where students can ask questions from home should quell the desire to give up when encountering a problem that they just can't work out.  On our blog a student can ask about any problems they are stuck on.  Other students can go on and they might notice a few of them have the same issue.  From here they can work together and figure it out, or I now have a convenient spot to answer everyone’s question at once.  This is a lot easier for me since the alternative would be replying to several individual emails.  I also think it is beneficial for the students to see one another having trouble so they do not feel like they are the only one having a problem.  Some steps would definitely have to be put in place to avoid this becoming a crutch for students, but I think something along these lines could be a great addition to a math class.

            After reading both chapters I began to think about how I can adapt a book club to a math classroom.  I do not see myself having a true free reading book club as part of my math class since I would like any free time to be focused towards improving math literacy specifically or practicing new and interesting math skills.  One idea I came up with is a take on Dr. Brell’s “Catching the News”.  Once a week, students could bring in stories they find about math, engineering, technology, or anything that involves calculations and computations in some way to share with the rest of the class.  This could be an easy way to help students gain some points or extra credit.  Also, what most likely starts as something the students do to get some points could turn into a student discovering something they are really interested in.  Maybe they read an article about a new software that has been developed and they find it really cool and start reading about how programming works.  I think it would be awesome if I was able to create an opportunity where a student finds a new interest or even a potential career choice. 

A second idea I had would be to have a weekly math club.  Combining a few different ideas from the chapter into one activity, this could be allow for a student assessment of my teaching, a student assessment of themselves, students practicing audience accountability, and a low risk grading opportunity.  Once a week, students could gather in groups of four to talk about the current topics we are discussing.  They would be given organizers where they write down one thing that they feel they learned, one thing they have a question about, and one thing they would like to know about next.  These could be filled out as a group or individually.  If everyone has a different question I would not want to limit the group to only asking one.  In terms of me assessing the students, if every student hands in a paper that is filled out they get full credit. 

One last idea I had that would practice independent content area reading and foster student choice would be to have a long term project relating to the history of math.  Students would choose the time period they are most interested in and work in groups to create a presentation about prominent mathematicians and what types of mathematics were developed during at that time. 

Pythagoras.  This is the guy everyone thinks of when you need to find the sides of a right triangle.  The theorem may be named after him, but did you know that the Babylonians who lived 1000 years before him already knew how the sides of a right triangle were related? How about that Pythagoras was a vegetarian and he required his followers to be vegetarians as well?  Or even that the students of his school also had rules like "Do not look in a mirror beside a light"?  All of this could be genuinely interesting to math students and for some reason is never covered in high school math classes!

Before this project starts, I would give a brief overview on several different periods to help students make a clear and informed choice.  Groups would meet periodically to talk about what they have learned, practice doing math the way the people of their time period did, and decide what they want to research next.  I have a lot of responsibility here to help groups stay on task, guide them in their research, and make sure everyone is working to benefit the group.  I think it would be worth it though, and many of the students might find what they learn interesting and engaging.

            Once again, two chapters about things I never imagined even thinking about while designing my future math classroom have given me plenty of great ideas I can try.

Subjects Matter: Chapters 6 and 7. Math Team

           Chapters 6 and 7 of Subjects Matter reinforced the need for reading and comprehension strategies and then began to establish how having a community of learners can help our classrooms.  Some of the advice that stuck with me regarded how we, as the teachers, need to filter our textbooks.  There is no need for the students to read every word in a textbook and this is even advised against.  Reading every word would not engage any student, never mind help to foster a love for the content.  This is why it is very important that we know our textbooks inside and out.  Knowing exactly what is inside helps us to decide exactly what is most important for our classrooms.  This might not be the same for everyone, but with only 180 days at our disposal, its important to have an opinion on what are the central concepts of the course. 

Another great piece of advice is to know exactly what are on those “big tests”.  For now anyway, it is clear that what is tested by the standardized tests needs to come first.  We still have room to explore and supplement, and we absolutely should, but leaving out something that will be tested on in exchange for a fun activity could be disastrous.  One of our responsibilities in the current educational climate is to become masters of the standardized assessments.  This idea is actually very in line with UbD and backwards design.  If our students are going to be taking these tests, we should start by examining the assessment, and then craft our lessons based on what we know is on the test.  Planning this way allows for teachers to prepare students for the standardized tests while hopefully making an effort to craft interesting and engaging learning experiences.  Last summer I took a course on teaching Calculus with Dr. Humphreys, and she also stressed the importance of becoming an expert on the test we are preparing our students for.  The AP tests are very different from PARCC, but the lesson is still the same.  If I am not absolutely sure of what is going to be on the big test at the end of the year, how can I make sure my students are ready for it?

            I also really appreciated the shoutout to how math textbooks are very different from the rest in Chapter 6.  As I have been doing all the readings this semester, I keep thinking “But my math books are going to be so different, does this really apply? Or how can I change this so it does apply?” Reading this section just makes it even clearer that I need to really focus on these comprehension strategies to make the math textbook digestible for students.  Part of why students have such a hard time with them is definitely because how different they are from the rest of the textbooks!  Reading on their own, if a student does not understand a sentence somewhere along the line in their history book, they will probably still be ok.  They can still take away the main ideas from understanding everything else in the reading.  In math however, not understanding one sentence might handicap a student for that whole section, that whole unit, or depending on the sentence, the whole course.  This is a very serious matter and I need to do something that I did not expect I would be doing as a math teacher before this semester.  I need to arm myself with a full arsenal of reading and comprehension strategies and employ them every day.

            While reading Chapter 7, I was immediately reminded of an article I read last semester while “Catching the News” in Dr. Brell’s class.  “Teaching in the Shadow of the Ferguson Shooting” was written by Inda Schaenen and appeared on edweek.org last September 4^th.  In the article, Mrs. Schaenen explores all the difficulties she will face teaching her 8^th grade language arts class this year.  She knows that the children do not feel safe in their community.  Many of the students deal with the events in seemingly odd ways, even going so far as re-enacting Michael Brown’s shooting in the school.  What I really took away from reading this was that these children are not going to be able to learn until they feel safe again.  They have way too much on their minds and way too much to be worried about to focus on their notebooks, worksheets, and textbooks.  None of that matters to them when they are afraid. 

In Maslow's Hierarchy of Needs, you need each bottom layer to have the layer on top.  Without food and water, a person can not feel security and so on.  Bringing this ideology into the classroom, we see that "achieving one's full potential" is at the very top.  Before students can learn, they need to have the basic needs, feel safe at home and at school, and feel like they belong.  As teachers, we need to try our very best to making sure that all our students feel safe and included.  If a student feels like he or she really belongs in their math class then they will start to succeed.

            I really believe that a classroom community needs to come first and then learning comes second.  And when learning comes second, it is more efficient and more powerful.  Daniels and Zemelman back up this point saying “In schools where teachers explicitly taught the social skills of small-group interaction, the students gained an average of 11 percent on both their course grades and on high-stakes standardized tests given in their state.” (Pg. 203-204)  When students feel safe, then they can focus on all the other things.  When students aren’t worried about being made fun of, aren’t embarrassed to make a mistake, aren’t thinking about whether the bully will stop them in the hall today, that is when they can get excited about learning something new.  Something that I want to do with my classes and something that I think about a lot is turning my classrooms into teams.  I am still not even close to having a fully realized idea, but I know this is something that I will develop and I will put into practice.  I never want to really have a “class”.  “Class” can have a tendency to invoke an image of desks in rows, children working silently, and a teacher in command.  I want to have teams where the players learn together and understand the benefits of helping one another and working for a greater good.  I want to be the coach of this team.  Someone who knows the game of math and can help them execute all the strategies.  I hope that doing this will bring my students and myself closer together and create a space where cooperative learning can take place.

Subjects Matter: Chapters 4 and 5

           While reading Chapter 4 of Subjects Matter I knew from when I first read about easycalculation.com that it was going to be one of my favorite takeaways from this chapter.  In the part of the website the book recommends there are shortcuts, tricks, ancient numerals, and genuinely interesting things you can do with math.  This site is definitely a resource I would use in my classroom.  I have always been a fan of number theory and the history of math and I think that the topics are extremely engaging because of how surprising, useful, (and even cool!) they are.  This is one of a few times while doing this reading that I was reminded of Dr. Kraus’ lessons on games in the classroom in SED406.  We learned that while it is nice to take a break sometimes and do something fun, our activity should still have a purpose and foster learning.  For example, I could hold a class centered on the trick for figuring out what day of the week a given date from the past was.  I could preface the lesson by showing a clip out of one of my favorite Ted Talks: Arthur Benjamin: A performance of "Mathemagic".  There is a piece in the segment where he very quickly figures out that June 6, 1824 was a Sunday. After watching that, we could go over and practice the trick as a class by picking dates randomly and figuring out what day of the week they were.  The purpose here, besides getting to show a class that math can be fun and giving them something to impress their friends and family with, is to have an engaging lesson where students are actually excited to practice arithmetic.  This kind of practice will certainly help out students all the time in math, since arithmetical processes are constantly worked with.

http://www.ted.com/talks/arthur_benjamin_does_mathemagic?language=en

Here is the Ted Talk if anyone wants to watch it.  The whole thing is 15 minutes, but it is definitely entertaining and impressive.

            Another point from Chapter 4 that got me thinking was how teachers of every subject should build a classroom library.  Having varied and interesting books for students to read is great even in a math classroom.  After getting suggestions for fun books from students I could even start to sneak in some math books that fall outside the traditional high school subjects for the particularly daring math lovers.

            After reading Chapter 5, I definitely agree that it will be a useful resource in the future.  There are tons of suggestions for strategies all revolving around the “gradual release of responsibility”.  This is certainly a chapter that I will be able to return to over and over again in the future to get more ideas, or even take ideas I might have and turn them into a structured classroom event.  While all of the suggestions are good reading strategies, I thought of ways that you could tweak a few of them to turn them into computational strategies as well.

            The first strategy I really liked was Vocabulary Predictions.  This is very in line with an idea that I wrote about in Dr. Brell’s class that would be used while teaching geometry.  To engage history lovers or students who might not warm up to math very quickly, I could run a geometry class in the style of how geometry was studied in Ancient Greece.  In our class we would not work from the definition to the term, but create our own definitions from the term, concept, or idea just like the Greeks did.  As a class we discuss all the aspects of a line for example and try to create a really polished definition.  We stick with our definition and continue crafting more geometrical results from it.  As we continue the unit, we can go back and revise definitions if we run into contradictions.  I think this would be a great way to have the concepts stick in the students’ heads.  The students will have created their own definition, worked with their creation, and then realized what about it did and did not work.  The last part is what I believe is most important and is what will help them remember the details of geometry. 

 All the students know what a line is, but instead of just telling them that in geometry a line is straight, has no thickness, and extends infinitely in both directions, why not challenge the students to figure that out?  This could be a scaffolding exercise where they use all their background knowledge about lines and points and make a prediction about which of the characteristics of a line will be most important and truly shape what a line is.

            Another great strategy for a math class is multi-column notes.  This is also one that can be adapted to work for more than reading a text.  I have already used this method for demonstrating mathematical processes and I think that it works really well for students.  It also makes it very easy to look back at notes from a while ago and be able to immediately recognize everything that is going on.  Here you would put all the steps of an algebra problem on the left hand side of the page and then write out in words what happened at each step and why that action was taken on the right hand side.  One of the most frequent questions in a math class is “How did you go from A to B?”  Using these kinds of notes should cut down on that kind of confusion immensely.

            The last strategy I will discuss is the use of exit slips.  I think this is a fantastic feedback system for shy students or students who feel they would be embarrassed to have the rest of the class know they did not understand something.  After a geometry class where we read about different definitions and their interactions, or even get into some proofs, students could take the last three minutes of the class to say what they learned, where they didn’t understand the connections, or what they thought our lesson today was leading up to.  All of this feedback is useful for the students and for myself.  The students take accountability for what they did and did not understand and now that they have this self-realization they can take actions to improve their learning.  I can also take accountability for what might have been unclear to the students.  This feedback can alter my next lesson and help me to realize what I need to focus on to get everyone on board with the material.  It also helps me to see the connections students are or are not making and I can choose to emphasize these when appropriate.

            This has been another reading that further convinces me of the importance of reading strategies and comprehension in a math classroom.  Being able to demonstrate to the students how to read the text and then work them up to being able to read properly all on their own is crucial.  There are so many strategies I did not discuss that I could use to improve the students’ confidence when reading a math text like Coding Text, List Group Label, Partner Reading, Turn and Talk, a Word Wall, and RAFT essays that I feel like I will have plenty of different lessons to try and refine when I begin teaching.  I am pretty excited to be able to try some of these and start to bridge the gap between reading and math in my classroom.