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.