Math Reflections

Reflecting on my learning this last quarter, two themes have continued to come up: students learning through manipulatives and technology and knowing my students.

Using what I know and am learning about my students can help me pick the right kind of technology and manipulatives to optimally engage students in learning.  Students will learn much more when they are able to take their learning into their own hands and it is my job to give the tools to think, not just the tools to complete a task.  We have access to so much technology that can open doors for students and we need to take advantage of it.   The more I know about my students, the more selective I can be about the technology I pick to optimize their learning.

Not so final thoughts about technology in the classroom

One thing that I've taken away from this quarter through my classes and working in classrooms with students is that differentiation isn't just about ability level.  Differentiation can be about individual interests, cultural backgrounds or learning styles too.  Either way, the goal is to help all students learn.  Technology is one way we can do this.  With the use of technology, students have many more avenues through which they can be reached.  While I was not able to take full advantage of having the ipod touch in my classroom,   I am starting to see more and more how it can help differentiate instruction.

The most relevant way that I believe it could help students is to differentiate instruction for students with different learning styles.  Whether they are learning Math, Science, Reading, Writing or Social Studies, there are apps on the ipod that allow students to access those subjects in ways other than those that may have been taught in the classroom.  In Math, students can use the technology to practice facts they've been struggling with or to enrich instruct and go further into concepts they're learning.  They can also use it as a way to see different ways of attacking the same type of problem, differentiating instruction by ability level and learning style.

In reading instruction, students can use ipod touch technology to improve their reading fluency, read a variety of texts and learn about various strategies for decoding.  Using it to enrich a social studies curriculum can allow them to access the internet from right where they are and have access to information on topics that interest them.  These strategies allow for differentiation by ability level, learning style and student interests.  Additionally, there are many apps for translation in a variety of languages, helping some students to overcome a language barrier in their classroom.

Know Your Students

What I Learned
This isn't necessarily new learning.  But it really does affect me differently each time I hear it.   It doesn't matter how much technology I know or can use if I don't know how to adapt it to my students.  It's interesting to think about shifts in technology and how that is going to affect how we look at a school day.  I love the idea of assigning a lecture as homework and collaborating in class the next day to elaborate on concepts from the previous night's learning.  This will give students a more equal playing field (if they choose to take advantage of it) in class the next day.  It would also allow students to take the time to think about what they don't know and give them the chance to come up with relevant questions.  Hopefully, this would better engage students in the learning the day after they do their "homework."  For me, there is a huge different in my level of engagement when I have some sort of background knowledge rather than feeling completely lost.  In terms of knowing our students, it is important to know what kind of access students have to outside technology can help us create assignments that .  We need to teach students to advocate for themselves in order to have access to the resources they need to be successful.  It's true that not all students have the same access to technology at home, but they will need to learn to take advantage of the resources that are potentially available to them outside of their homes.




Implications for Instruction
Knowing our students is the most important thing to remember no matter what subject we teach.  We need to be aware of what kind of background (academically, culturally etc).  In our science class this morning, we talked a lot about knowing our students in terms of how their cultural practices affect how they view themselves as learners.   If we ignore the connections between cultural practices and areas of expertise, we could be ignoring some of the main ways to connect the curriculum to their students’ lives. In terms of what this means for instruction, I want to be able to connect students' lives to all aspects of my curriculum.  Whether this means incorporating their favorite things into their math problems or constructing a curriculum around what you know about their scientific interests, students need to know that we notice things about them and that those things matter to us too.

Geometry Sketchpad

Something I've noticed recently in my own learning is that I've had a hard time paying attention to class lectures (Robin, this isn't specific to your class by any means).  I know that part of it is definitely related to the fact that we only have a few weeks left to go in the quarter, and I'm a little antsy to finish.  However, in reflecting on that, it's becoming increasingly evident that if I want my students to be engaged in their learning, my talking is not what's going to do it.  It was great working in the computer lab with Geometry sketchpad.  Each of us got the chance to complete the task and had to think about why certain shapes worked with other shapes in order to complete the task correctly. It was fun to be able to engage in a thinking task without being lectured about the properties of different quadrilaterals etc.

In terms of bringing these strategies into my classroom.  I'm excited to try different technologies that can help students engage more deeply into task oriented learning.  While it has been difficult to do this within the context of the materials available to me in my main placement, I'm excited to see the difference that task oriented learning and/or group work will have on my students.

This may be some middle of winter quarter "optimism".....

While I love the idea of having so many opportunities to use technology in my classroom, I’m having a hard time reconciling those opportunities to the amount of time I realistically have to use them.  Aside from being able to use my Ipod Touch for Literacy, I have not had many opportunities to use it in the classroom.  Maybe this will change when I take over my 4^th grade classroom in April, but for now, it's difficult to find the time to use it.  I feel like I can see use in the bigger picture, but when I'm co-teaching and/or only teaching a couple of lessons a day, there's not too much time to teach the kids what they need to know about the technology for it to be successful.  

I can see using the touches for my own purposes in terms of recording running record assessments or recording student interviews, but in terms of differentiating instruction, I'm not sure how it can work logistically with just one ipod touch. I feel like those that get to use it will be a distraction to the ones that don't and it may hurt more than it helps, having only one.   

Tangrams

This week, continues to reinforce the idea of differentiated instruction for me- not only in terms of struggling students, but also in terms of multiple intelligences.  Working with the tangrams supports the idea that there should be multiple entry points for students to be successful.  One of the main reason people have such a strong opinion about the subject of math is because they’re used to only having one way to correctly solve a problem.  Likely, they are also used to only being presented with one type of problem to solve.  It’s important to emphasize that there is a variety of ways to be smart at math other than just getting the right answer from plugging numbers into an equation.  Allowing students to be successful in multiple areas can give them the encouragement they need to work at math in areas where they aren’t as successful.

Implications for instruction

These principles are important to remember in math and all other subjects as well.  It is important for students to have entry points of success without resorting to remediated instruction.  This kind of work makes me think that I want to focus the differentiation in my classroom as more than just ability level.  Whether the subject is math, reading, writing, science or social studies, at least some of the differentiation should ideally be by interest or learning style.  Differentiation by ability just reinforces ideas that students already have about how smart they are and how successful they can be.  Differentiating in multiple ways allows students to find ways to be successful on their own.

Moving From Assessment to Instruction

This last week, I had an interesting reading conference with R.  He read two separate reading passages, one about Amelia Earhart and one about steam engines.  When we started our reading conference, I gave him a choice of which passage to read.  He chose the steam engine passage.  He had almost not trouble with miscues or comprehension, and he got through it relatively quickly.  Because we had time at the end of the conference, I also assessed him on the Amelia Earhart passage.  His ability to retell and comprehend both pieces was strong.  


Initially, I had predicted that his comprehension level would be higher on the piece he was able to choose, however, his comprehension was strongest on the Amelia Earhart passage.  This is likely because he had more background knowledge going into the reading.  


From these observations it is clear that R has a strong ability to comprehend and infer from grade level text.  He is also interested in realistic fiction as well as literature about sports.  As a result of this, possible learning objectives could be, using a text slightly above grade level for R to make inferences about the author's purpose for writing the text. Analyzing these elements of literature would also be useful in developing R's ideas and content in his writing. 

Geometry!

What I learned:
This week really helped me see the different levels that students can be at in terms of their understanding of Geometry.  In my 4th grade placement, definitely have students who, if they turned a right angle onto a different side, they would no longer see a right angle.  This is most likely because they are used to doing a lot of their geometry on worksheets.  Asking students explicit questions with one answer that only apply to the situation on the paper will not help advance them to the next level of Geometrical thinking.

Even though I wasn't able to recall many of the Geometric properties I'd learned in high school on my own, being able to have a paper in my hand to think about why I knew what I knew was helpful.  I may not have been able to do any two column proofs, but being able to hold the paper in my hand made me think further about what I knew about the shapes and lines and eventually come to conclusions based on prior knowledge.


Questions:
As teachers, is there a way to help students move from one level to the next?


Implications for my teaching practice:
Looking ahead into the spring when I take over my 4th grade classroom, I'm not sure what specific areas of math I'll be responsible for teaching.  I do know that there WILL be ways to incorporate geometry into other types of math (as well as a potential Geometry unit).  Knowing that students learn math best when they get to touch it, my Geometry lessons will not be one-dimensional.

Math Manipulatives

After getting bogged down in teaching standards and worrying about covering tested materials, I sometimes forget that math can be fun....and I like math.  I can imagine that as teachers, the way we feel about math really affects the way our students will feel about math.  If we project the image that teaching math is stressful, we project that stress on to our students.  When we were using the miras in class on Monday, many of us were having so much fun, we forgot we were doing math.  It was interesting to learn that many teachers don't take advantage of the manipulatives available to them at their schools. This seems strange considering how helpful they can be in getting students to move their thinking from concrete to abstract.  Also of interest to me was the fact that today's students don't differentiate greatly between virtual and tangible manipulatives.  This fact increase teacher access to many different ways to help students learn.

In terms of classroom application, I'm encouraged to have the access of so many materials online, even if I end up in a school or district that does not place much emphasis on learning with manipulatives.  It was encouraging as well to see that teachers who had your students in later years, could pick out which students were yours because they had a much deeper grasp of math concepts.  

Literacy Project 1

Analysis

This analysis is based off of the writing sample of one short story written by “R,” my fourth grade buddy.  The sample is taken from the rough draft of a creative writing assignment called “The Bottle.”  I believe this story was written in response to a prompt that asked students to write a story about what happens when their character finds a mysterious bottle.  I have analyzed the spelling in both the writing sample and the spelling inventory.

Meaning

In the piece of writing we chose, “The Bottle,” R has responded to a creative writing prompt regarding the events that take place after the character finds a strange bottle.  Because we spent most of our time talking to our buddy about the outline for his next writing piece, we weren't able to discuss the meaning of this piece other than in relation to the prompt.    

Six Traits

Ideas

In terms of assessing his rough draft on the ideas and content, R chose a narrow and manageable topic.  He generally stays on topic but hasn’t developed a clear theme or sense of purpose. Additionally he tends to be drawing on his own knowledge and experience, using a video game sale as the main purpose for the message in the bottle.  While his ideas are reasonably clear with attempted support, the ideas aren’t expanded upon in a way that relates to the prompt at all.  As a reader, it was hard for me to pick out which events were the most important.  Many of them did not seem related to the prompt.

Organization

From this writing smaple, R shows a strong sense of organizational abilty.  His introduction introduced the topic clearly, creating anticipation for the rest of the story.  His transistions, such as “seconds later…” and “thirty long minutes later…” and even “then…” clearly showed how his ideas connected to one another.   In this piece, the sequencing occurs in logical order.  While the writer  controls his pace fairly well, he often does not slow down and elaborate on potentially important parts of the story.  While the title is present, it mainly just restates the prompt. 

Voice 

When reading this writing sample, it was hard to pick up on a distinct voice.  His writing is sincere, but doesn’t reflect his individual perspective on the topic. From this piece, it does not appear that R took many risks in the development.  Although the piece was intended to be a creative writing assignment, he mostly wrote about what he was comfortable with and did not risk revealing much about himself. 

Word Choice
Overall, this piece displays word choice that serves to get the point across, but does not enhance the interest of the reader.  R uses words that are specific and accurate.  At times he attempts to use more colorful language but can go beyond what would be appropriate for the described situation.  He mainly uses familiar words and phrases, but once or twice shows evidence of revision to phrases that are more eye catching such as “so hungry I could eat a…”

Sentence Fluency
R’s sentence fluency, much like his word choice, is generally functional.  With a few changes, he could make this story much more expressive.  His sentences vary in length and structure, however, the included dialogue sounds slightly unnatural.  While he does attempt to vary his sentence beginnings, there are multiple sentences that start with “then…” “it…” and “I…”  He uses appropriate and sometimes creative connectives between sentences and thoughts to show their connectedness such as “Thirty long minutes later…”  These thoughtful transitions allow for some expressive oral reading, but other sentences are still stiff and choppy.

Conventions

Overall, R’s conventions are strong.  His grammar is always correct and his capitalization skills are consistent.  His end punctuation is almost always accurate, however, his internal punctuation is sometimes missing.  For example, a few of his compound sentence did not include a comma prior to the conjunction, and many of his transitions lacked punctuation.  Moderate editing, some of which is included in the sample, would be necessary before taking the draft to publication.  The spelling in this sample is generally correct.  There are a few misspelled words (their instead of both they’re and there, lightning and trafic).

Ownership

While we did not formally engage our buddy in discussion in terms of his ownership of writing, we were able to collect a few pieces of information on the topic. When we discussed the subject of writing with our buddy, he was eager to tell us about how much he enjoyed it.  He sees himself as a capable writer and speller.  He enjoys writing mostly about topics that he has some experience with such as sports and school and likes writing less in the genres of fantasy or adventure.

Spelling
I believe that R’s spelling is advanced for his age.  He missed only 2 words in his spelling inventory (pleasher and oposition).  When looking at his writing, he appeared to be using but confusing double consonants to change the sound of the vowel in the word (shinny, trafic).  He seemed to know that the double consonant changed the sound, but was confused as to whether it made the vowel long or short.  It might be useful for him to pay attention to consonant doubling (Bear, Invernizzi, Templeton, Johnston, 2004).  He also confused their, there and they're, catching himself once as he was writing.  

Lesson Plan

Objectives:

The student will understand the way that a double consonant affects the vowel sound in word.

Standards

3.3.2   Spells words appropriate for the grade level accurately.  

Materials

·         List of words with single consonants that cause a long vowel sound

·         List of words with double consonants that cause a short vowel sound

·         White Board

·         Dry Erase Marker

·         Eraser

Instruction

• The teacher will begin the lesson by giving the student a list of 15-20 words, of varied lengths, that either follow the rule of double consonants creating a short vowel sound or words that have a single consonant and a long vowel sound.  Some of these words will be ones misspelled in the students writing.  Using words from the student's own writing and incorporating this into the patterns in other words will make the spelling more relevant to the student (Templeton and Morris, 1999). 
• The student(s) will use a white board to put the words into categories however (s)he choses.  (Words are written out to reinforce correct spelling as well as to make the student aware of the patterns as he is writing them).  As this is happening, the teacher will be doing a formative assessment to see how the student choses to sort the words.
• After the words are sorted, the teacher will discuss with the student(s) how the sorting decisions were made.  Based on this, the teacher may ask to see if there is a different way to sort the words, or, if more support is needed, may sort them and ask the student what (s)he notices about the patterns (both in spelling and sound).
• The teacher will then explain how words with a double consonant before the vowel sound different than some words with a single consonant before the vowel.  She will then model (using words from the sort as well as new words) how she thinks aloud when spelling about the way the word sounds and how that relates to how they are spelled.
• The teacher will repeat the process, asking the student to spell the words aloud with her.
• After guided practice, the student will independently practice correctly using these types of words in his writing over the course of the week.

Assessment
Teacher will assess student ability to spell words correctly by assessing their knowledge while the student sorts the words and through a spelling test using some of the words from the word sort as well as new words that follow the same spelling patterns.  The teacher will look for correct spelling of the words both on the spelling tests and in the student's writing.  

Technology in the Classroom

After spending the last couple of weeks getting acquainted with my Ipod Touch (and reacquainted with the students in my main placement), I'm noticing more and more ways in which the Ipod Touch can help differentiate instruction. There are quite a few "endearing quirks" that would benefit from different resources that some of these apps have to offer.

While I'm not a huge fan of learning math through repetitious drill exercises, there are 1 or 2 students for whom their lack of speed with basic multiplication, division, addition and subtraction facts is significantly holding them back in learning new math concepts. The "Basic Math" app drills students on all basic math operations and could help these students improve on their accuracy and speed so that the rest of their work was hindered. This would be something they could work on while the class is finishing up on morning routines. The extra 10 or so minutes per day would help keep these facts fresh in their head.

I also have a student who is working on, in reading, reading fluently to help the text make more sense. When she reads aloud, she tends to plow through text with little attention to punctuation. The ability to read aloud, record herself and listen to those recordings could help her notice points in the text where she needs to speed up or slow down, hopefully improving her comprehension.

One student in my main placement struggles a lot with learning disabilities that affect her writing and especially her reading. She is constantly frustrated because her reading level is not near that of the rest of her classmates. She does, however, love writing and she and I have talked quite a bit about how she would much rather read books she writes herself. Her learning disability causes some difficulties with writing as well, but she loves to write and tell stories. Lately, I've been trying to think of a way to use her love of writing to help her reading as well. Using the Writer's Studio App, she would be able to create her own stories with pictures and then read them aloud as well.

Concrete to Abstract

It's interesting to me how at first it seemed so counterintuitive to go from concrete to abstract in math. It's a method we use to learn and teach most everything else, and it seems strange that we would choose to learn or teach math differently. We're often looking for someone to tell us a formula and give us the quickest way to find an answer. While there's nothing wrong with efficiency, we lose a lot of understanding by not thinking about why the algorithm we use works. Our brains are constantly looking to make connections from the patterns we see, and we can make generalizations about those patterns when we connect our concrete learning to our abstract thinking.

In terms of classroom practice, I'm seeing manipulatives in use much more often than I experienced in my own education. In my dyad 7th grade math placement, we used chip boards to teach the students the difference between the adding and subtracting of negative and positive numbers. I did notice that the teacher's comfort with a particular manipulative had a big effect on the students choice to use that particular strategy. For me there's still a question of how to know when to use them, and how long should we allow students to rely on them before we encourage them to use a more efficient algorithm?

First of all, algebra tiles are probably one of the coolest math manipulatives I've seen so far. It

I'll be the first to admit, I've always liked math. Growing up, I was what you would call a "math person.' I was very good at plugging numbers into an equation to get a right answer. Throughout this program I am continuing to learn that this is not necessarily what that is about. I'm learning about the excitement that comes with working collaboratively on a problem and then coming up with an answer in a way that means something to me. Not only do I have a better understanding of why I'm doing what I'm doing on certain problems, but I also get to share this with others and see the many different and very cool ways that others go about solving the same problem.

In terms of translating this into classroom practice, the idea of group work and collaborative problem solving seems great--in theory. It's not that I don't see the value in these types of problems or their ability to cover multiple standards at a time. In fact, it's clear that the type of learning that occurs through this type of work goes much deeper than plugging numbers into formulas and memorizing how to solve specific types of problems. It was clear both in class and from the videos that this type of teaching engages students much more than other methods I've seen. I guess what I'm wondering is how to incorporate this when working in one of many districts that adheres very strictly to a scripted math curriculum.