A fraction of a fraction is....a fraction

So, math class today was very interesting.  I learned two things:
1. We all solve problems differently.
2. If I have an expectation about what the answer should be, then I don't trust my math.

We were presented with a problem about two parks, and had to decide which park would have more blacktop area.  The first park devoted 3/4 of the area to playground space, and 2/5 of that to blacktop.  The second park (having equal dimentions) devoted 2/5 of the area to playground space, and 3/4 of that to blacktop.  I started out with math (multiplying to find the square yardage) and then multiplying by the fractions.  I also started out with the preconceived idea that one would be bigger than the other.  When the math calculations were finished and both had the same blacktop area, I quickly resorted to drawings, figuring that somewhere along the way my math was off.

After some drawings and taking a step back from the problem, I began to see that what was coming into play was the commutative property.  A (the area of the park) x B (3/4) x C (2/5)  was the same as A x C x B.

I liked getting the opportunity to hear how other classmates solved the problem and it was fun to see different lights go on in different people's thinking as some of us shared.  I saw the value in having groups present their ideas for problem solving to the class.  I also saw how this type of problem is a perfect segway into multiplying fractions and I think it would be great for use in the classroom.

I also like how this in-class activity highlighted the teaching model discussed in our reading for the week.  I thought the reading was cumbersome because we had to continually flip back and forth to different figures in the text.  This real-live example was much easier to understand.  The only thing I have questions about or see as a potential problem to using this method is step 1: anticipate possible solutions or methods that the students will use.  I find it difficult to anticipate how others will solve a problem.  I tend to see it from my viewpoint.  Also, students will at times use the wrong operations or math to solve a problem.  I don't know how to anticipate for those "wrong" solutions.

Show me your parallelogram

Today in Math class (college), I learned (or rather, reviewed) the difference between all the members of the quadrilateral family.  It was fun and challenging.  I learned that I have forgotten some of those terms we use to describe the quads.  Things like bisect, perpendicular, congruent...  Oh, would that be more vocabulary? Perhaps that is why I cannot access it in my memory.

I also learned that I can get REALLY excited when I understand a math concept.  I learned I need to check myself so I don't overwhelm my cohort mates (or future students).  I need a little bit of Math filter. :)

From the readings this week, I learned the importance of using manipulatives (especially in the middle level) and some strategies for incorporating literacy in Math class.  I actually think integrating these two is a good strategy because students can use writing to explain the depth of their thinking about math concepts.

My major question at this point is: How do we inspire the kids?  Or how do we motivate them?  My question stems from my experience in the classroom.  The middle school class where I observe has a daily morning work assignment that they work on for 7 minutes and then go over the answers for 7 minutes (so about 15 minutes, or a third of the 45 minute period).  It is my understanding that this work is not correct, graded, collected, reviewed, etc.  I go around the classroom, trying to help students, but some are not working on their morning work.  When we go over the answers, some are following along, and some are not.  And my question is, why should they?  They will not turn in the work or receive a grade for it.  The problems might show up on a future test or even the MSP, but that is not enough of an incentive.  I don't know that grading these, or attaching some kind of reward or punishment to the morning work is the direction I want to go.  So, my question is: how can I motivate the students to do the work?

Giving writing a second chance

I have always enjoyed the reading part of English/Languge Arts, and sort of put my head down and run as quickly as possible through the writing portion.  I'm not gifted with words or story telling.  I don't spell particularly well.  And I have a small vocabulary.  I remember being in 8th grade and trying NOT to learn my vocabulary words.  I did not see the point of learning a big, fancy way of saying something with a word that maybe half of your audience could understand, when you could use one or two smaller words that everyone knows.  I walked away from 8th grade having learned only two vocabulary words: noisome and avaricious.  I'm not sure how these two words managed to stick in my head, but I think it has something to do with the fact that they both sound like they should mean one thing, but they actually mean something entirely different.  Noisome has all the letters of the word "noise" in it, so one might mistakenly believe it has something to do with volume or hearing.  No.  Wrong.  It actually means smelly.  And avaricious sounds so harsh and cutting, but it actually means greedy.  Words are tricky that way.  But as I sit here, some 16 years after 8th grade, I wish I had applied myself more and learned those words.

My feelings about writing are similar to my feelings about vocabulary learning.  I did not ever devote much time or effort towards it.  One part of this school program that has been a constant challenge for me is the reflection papers.  I'm not a very reflective person, and if I do any reflecting, it is in my head or out loud.  I am not one to write things down.  I have nevery kept a diary.  I do have a journal that I write in from time to time.  Mostly I write prayers or things I am thinking, but there have been gaps of 2 years between entries.  So, when I found out we had a Reading/Writing/Literacy class, I was somewhat relieved and sad.  I figured we would learn some great tools for teaching, but at the same time I figured we'd have to do some writing. 

I was frustrated by all the blogging assignments at first.  But I am finding that I do like to type out my thoughts.  I don't know that I like sharing them with the whole world, or even all the education faculty, but I'm trying to be a good sport.

I really appreciate that both of our writing texts are engaging and easy to read.  Lots of textbooks are dry and so boring.  I have often wondered if the author ever thought about the poor students who would be assigned to read his or her text, especiall those with 50+ page chapters.  Lamott and Routman both write as if they were talking to me, a real person.  Perhaps that is the key, their writing is personal.  I've learned a lot so far, just from the readings.  I learned how important it is to write (every day) and to model writing for our students.  I am also learning that too much emphasis on form and grammar can kill the writer in all of us.  I don't know if that is what happened to me so many years ago.  I have noticed recently that when I am assigned to write a paper, I am at first disheartened.  Then, as I do the research for the paper, I usually learn something that I enjoy and am excited to share.  When I finish writing my paper (usually the night before because I am such a procrastinator when it comes to writing assignments) I am a little sad that I 1) did not start writing sooner, and 2) wish I could share what I wrote with others.

I am left with one question after doing the readings.  How and when do you correct student writing?  Do you gradually do it?  I don't want to crush the writing spirit, but I also feel like we need to teach the rules of language and proper grammar.   I want to know if spell-check and texting has lead to poor spelling and writing with the general public.

hooked on phonemes

In the first three chapters of her book, Barbara Fox lays out the important role that letter-sounds play in the future reading ability of children.  She argues for the systematic teaching of phonics and phonemes beginning in Kindergarten.  She explains how phonemic awareness is tied to faster reading progress, larger reading vocabulary, and better spelling. 
I am trying to reflect on my own educational experience and I cannot remember the grade I was in, but I do remember learning the sounds that letters make.  I think I was in 1st grade and we had these alphabet workbooks.  I remember that we did not go through the books in alphabetical order, which seems strange  to me at the time because one of the things you are tested on is being able to say the alphabet correctly in order without looking.  I learned from my reading that certain letters are "easier" to learn because their sound is similar to their name (letters like B, P, and T).
Ms. Fox did mention twice that after 1st grade the letter-sounds are not usually taught.  So children who fail to learn them by the time they enter second grade are at a disadvantage.  I am not familiar with the academic standards for second or first grades, but it seems that phonemic awareness should be at the top of the list.  The importance that phonemic awareness plays with regard to reading, spelling, and vocabulary would suggest to me that schools should make it their number one priority to catch those kids who enter 2nd grade without good phonemic awareness.

I am looking forward to tomorrow's lesson and testing our little kindergarten buddies to see where they fall in the stages of word learning.  Based on some of the things people shared in class last time, I think I have a better understanding of what children in the early stages produce.  It is also exciting to be apart of laying the groundwork for language, reading, vocabulary, writing, etc.  It is an awesome responsibility.

i See, i Touch

So, I consider myself one of the tech-challenged kids in my class.  But I impressed myself yesterday by charging my iTouch on my laptop and setting up my email.  This might not seem like much of an accomplishment, but I was glad to have made it that far.
I have not attempted to download any applications or applets yet.  I am not sure how to go about that.  I have iTunes and I think I was able to sync my touch to my computer.  Perhaps we could walk through one in class?
Regarding the apps you have to pay for, is there a 3-day trial where you can return if you don't like the product?  Is there a way to test an app before buying?  I guess I can forsee someone buying lots of apps because they are relatively cheap, but if they are not helpful or if you never use them, then why keep them.  Oh, right, you paid 99 cents for it. 

Thanks to our Professor for bearing with the slow ones in the group.  I think you have convinced us all of the merit of technology, but some of us may still need some hand-holding from time to time.

A lightbulb went on today

So there I sat, in math class (at college), using flat squares, rectangles and small squares as a way to model multiplying algebraic expressions.  I had never done anything like that before, but it made perfect sense and I could see using that in my math class (at middle school).  Then, our professor began answering some of the questions we had posted, and the bomb dropped.  She stood there and told us quite frankly that we would NOT do everything right as teacher and that we were bound to make MISTAKES as we taught.  At first I was horrified, or maybe just surprised.  You know that moment in Oz when Toto pulled back the green curtain to reveal who the Wizard really was?  It was sort of like that.  I had thought that there was some teacher curriculum or education program that would teach you how to do it right EVERY time.  I remember feeling at the end of some of my past classes a sense of disappointment.  I wanted to know when we (my cohort and I) were going to learn all the TRADE SECRETS.  Today, I learned that there is no magic teaching formula that will allow you to always get it right.  There are certain things that will make your teaching better, but every year you have a new batch of kids and every year you will need to tailor your teaching to fit THEM.  You are bound to screw up some of the time.  So, today, after the bomb dropped, I felt this HUGE sense of relief.  I'm a teacher and I am still learning.

The implications of this realization will of course filter down to my teaching.  I think it will take some of the pressure off and allow me to be excited about learning from my mistakes instead of dreading that I will make any.  I also think it allows me to see my master teachers in a new light.  I can watch what they do and learn from them.  I can record what I like, the things that they model well.  And I can give them a break because of course they won't be perfect all the time, they are still learning too!

My only question for the day is where can one purchase cool manipulatives like the multi-colored shapes we used for solving the algebra expressions today?

explaining equivalent fractions failure

As I observed and participated in the middle school math class today, I worked with students to add, subtract, and multiply fractions.  I learned a new method for adding fractions that have different denominators from a required course reading.  I had never heard of this method before.  I will try to explain it here:
Say you want to add 5/6 and 2/7.  Instead of finding the common denominator between 6 and 7, cross multiply and add the products: (5*7) + (6*2) = 35+12 = 47 (this is the numerator).  Multiply the denominators and their product is the denominator (6*7) = 42.  So, the sum of 5/6 + 2/7 is 47/42.
Check this by doing it the other way:
5/6 = 35/42
2/7 = 12/42
35/42 + 12/42 = 47/42

You learn something new every day!

My question is how do you handle a situation where you explain to a student how to do a problem, you do multiple problems with them, explaining each step, and they still do not get it.  I worked with a student for 20 minutes one-on-one explaining again and again how to find equivalent fractions, and the student did not understand.  I kept waiting for the lightbulb to come on, but it never did.  How do you proceed?
What do you do when you are the sole teacher and you cannot spend 20 minutes in a one-on-one reteaching?

first math class

On September 29th, I attended the first session of my math class.  I learned about my instructor and about myself.  I could tell from the way the instructor called our class to order that she was a real teacher - that she had been in a classroom of students and knew what she was doing.  I learned that I have a similar feeling towards writing papers as my instructor has to reading them.  I appreciated how she encourages us to get to the point.  Our whole class worked together in small groups to come up with an algorithm that would be true for any number in a series.  I learned to be patient and take time to work out the problem in my head or on my paper, allowing all the group members ample time to try to find their own solution.  I also learned that even though we all had the same problem, there were MULTIPLE ways to solve it.  If I had jumped in and told my group how I figured it out without waiting for them to come up with their own solutions, then I would have missed learning about the multiple ways to solve the problem.

Even though this was a great learning opportunity, I am still wondering how you would proceed in a classroom where a majority of the students understood or saw the pattern quickly, and only a few did not.  Or, is it important for the students to know and understand each of the different methods for finding a pattern?  Is it okay if they only know one?

The implications from this lesson for my classroom - well, I would love to use this same activity as an introduction to see where my kids are at.  I would be sure to encourage each group to think through the problem on their own before sharing with the group.  I might even tip them off that there is more than one solution and see if they can find out multiple ways for solving the problem.

I am so excited for this course.  I love math!

Literacy Post for Oct. 7th

I am currently enrolled in two college courses that deal with child literacy.  I did five separate readings for the upcoming classes this week.  I learned quite a bit about early literacy.  First, I was surprised that most of the readings included descriptions of children interacting with books or text or print or signs before the child could actually read.  This kind of interaction (babies or toddlers and books) is very important.  Even small children can pick up on the fact that there is a certain method for book reading and a way that books are handled.  Eventually, the children can understand that the words on the page convey meaning.  Children will engage in play reading, where they open the book and turn the pages, they may even be able to retell the events of the story that take place on a particular page before they can actually read.  Some children will even point to the words with their fingers, moving from left to right, giving the illusion that they are reading.  I find all this pre-reading activity to be fascinating.

In class last week, we got the opportunity to go around and share a book that we remember reading.  Lots of my classmates also shared about how their families demonstrated reading.  I noticed a tread that some of my classmates, when small children, were not read to and they did not grow up reading or enjoying reading.  The opposite also seemed to be true.  Families that promoted or demonstrated reading to their children, had children who grew up reading and enjoying it.  Another thing I noticed was that 4 or 5 of my classmates listed "Where the Red Fern Grows" as being an influential book in their young lives.

I first became interested in education when I heard some statistics about reading.  I concluded that literacy is an important skill to have, and I wanted to become a teacher and help children learn to read.  I am excited to learn more about teaching children how to read and working with students who struggle with reading.